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Name_________________________________________ 3.7 Learning Target: Solve two-step Practice Addition problems Example You have 5 stamps and collect 12 more. Your friend has 21 stamps. How many stamps do you and your friend have in all? Plan Circle what you know. Underline what you need to find. Solve Step 1: Find how many Step 2: Find the sum of your Stamps you have. stamps and your 5 +12 = 17 friend’s stamps. 17 + 21 = 38 38 Stamps 1. You see 14 zebras and 4 elephants at the zoo. Then you see 20 snakes. How many animals do you see in all? _____ animals ____________________________________________________________ 2. You have 15 pieces of blue beach glass and 9 pieces of white beach glass. Then you find 11 pieces of green beach glass. How many pieces of beach glass do you have in all? _______ beach glass
3. You win 14 tokens at one game and 15 at another at an amusement park. You and your cousin win 40 tokens in all. How many tokens does your cousin win? ________ tokens ____________________________________________________________ 4. Your class sells 40 raffle tickets. Your friend’s class sells 15 more than your class. How many raffle tickets do your class and your friend’s class sell in all? ______ raffle tickets 5. Model Real Life Your aunt picks 33 apples. You pick 11 more than your aunt. How many apples do you and aunt pick in all? _____ apples 6. DIG DEEPER You read 10 haiku poems and 5 rhyming poems. Your friend reads 28 more poems than you. How many poems do you and your friend read in all? Review & Refresh 7. A classroom has 3 rows of chairs. There are 5 chairs in each row. How many chairs are in the classroom? ____+____+_____= _____ chairs
Question 1. You see 14 zebras and 4 elephants at the zoo. Then you see 20 snakes. How many animals do you see in all? Answer : Number of zebras = 14 Number of elephants = 4 Number of snakes = 20 Total Number of animals = Number of zebras + Number of elephants + Number of snakes = 14 + 4 + 20 = 38 Question 2. You win 14 tokens at one game and 15 at another. You and your friend have 40 tokens in all. How many tokens does your friend have? Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 134 Answer : Number of tokens won in one game = 14 Number of tokens won in another game = 15 Total Number of tokens with me = 14 + 15 = 29 Number of tokens with me and my friend = 40 Number of tokens with my friend = total tokens – number of tokens with me = 40 – 29 = 11 Question 3. Your class sells 40 raffle tickets. Your friend’s class sells 15 more than your class. How many raffle tickets do your class and your friend’s class sell in all? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 135 Answer : Number of raffle tickets sold by my class = 40 Number of tickets sold my friends class = 15 more than my class = 15 + 40 = 55 Total Number of tickets sold by my class and friends class = 40 + 55 = 95 Question 4. Modeling Real Life Your friend picks 33 apples. You pick 11 more than your friend. How many apples do you and your friend pick in all? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 136 Answer : Number of apples picked my friend = 33 Number of apples picked by me = 11 more than my friend = 11 + 33 = 44
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Total Number of apples with me and my friend = 33 + 44 = 77 apples. Model the story. Newton has 15 books. Descartes has 22 more. How many books does Descartes have? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 125 Answer : Number of books with Newton =15 Number of books with Descartes = 22 more = 22 + 15 = 37 How many books do Newton and Descartes have in all? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 125.1 Answer : Total Number of books with Newton and Descartes = 15 + 37 = 52 Show and Grow Question 1. You have 7 cherries. You pick 6 more. Your friend has 45 cherries. How many cherries do you and your friend have in all? Answer : Number of cherries with me = 7 Number pf cherries picked by me = 6 Total Number of cherries with me = 7 + 6 = 13 Number of cherries with my friend = 45 Total Number of cherries with me and my friend = 13 + 45 = 58 Apply and Grow: Practice Question 2. You have 15 blueberries. You pick 12 more. Your friend picks 32 blueberries. How many blue berries do you and your friend pick in all? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 127
Answer : Number of blueberries with me = 15 Number of blueberries picked by me = 12 more Total Number of blueberries with me = 15 + 12 = 27 Number of blueberries with my friend = 32 Total Number of blueberries with me and my friend = 27 + 32 = 59 Question 3. You have 26 green crayons. You find 10 more. You have 16 red crayons. How many crayons do you have in all? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 128 Answer : Number of Green crayons with me = 26 Number of green crayons found = 10 Total Number of green crayons = 26 + 10 = 36 Number of red crayons = 16 Total Number of crayons = 36 + 16 = 52 Question 4. You take 24 pictures on Friday. You take 20 more on Saturday. You and your friend take 50 pictures in all. How many pictures does your friend take? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 129 Answer : Number of pictures taken on Friday by me= 24 Number of pictures taken on Saturday by me = 20 + 24 = 44 Number of pictures taken by me and my friend = 50 Number of pictures taken by friend = 50 – 44 = 6 Think and Grow: Modeling Real Life There are 31 children at a craft fair. There are 20 more adults than children at the craft fair. How many people are at the craft fair in all? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 130
Circle what you know. Underline what you need to find. Solve: Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 131 Answer : Number of children at craft fair= 31 Number of adults at craft fair = 20 more than children’s = 20 + 31 = 51 Total Number of people at craft fair = 31 + 51 = 82. Question 5. Your friend has 40 pens. You have 16 more than your friend. How many pens do you and your friend have in all? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 132 Answer : Number of pens with my friend = 40 Number of pens with me = 16 more than my friend. = 16 + 40 = 56 . Total Number of pens with me and my friend = 40 + 56 = 96 Question 6. You plant 28 seeds. Your friend plants 13 more than you. How many seeds do you and your friend plant in all? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 133 Answer : Number of seeds planted by me = 28 Number of seeds planted by my friend = 13 more than me = 13 + 28 = 41 Total Number of seeds planted by me and my friend = 28 + 41 = 69 Your friend picks 33 apples. You pick 11 more than your friend. How many apples do you and your friend pick in all? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 136 Answer : Number of apples picked my friend = 33 Number of apples picked by me = 11 more than my friend = 11 + 33 = 44 Total Number of apples with me and my friend = 33 + 44 = 77 apples. Review & Refresh
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Get to 10 to subtract Question 5. Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 137 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Problem-Solving- Addition-Homework-Practice-3.7-Question-5 Question 6. Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 138 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Problem-Solving- Addition-Homework-Practice-3.7-Question-6 Question 1. You go to an amusement park. The wait times and ride times for the rides are shown below. a. Find the total number of minutes it takes to wait and ride each ride. Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 139 Answer : Total Time = Wait time + Ride Time Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Addition-to-100- Strategies-Performance-Task 3-Question-1 b. How many more minutes do you spend at the log ride than at the bumper cars? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 140 Answer : Number of minutes at log ride = 68 minutes. Number of minutes at Bumper cars = 44 minutes . Number of more minutes spend at the log ride than at the bumper cars = 68 – 44 = 24 minutes. c. You want to ride 2 different rides in less than 90 minutes. Which rides can you ride? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 141 Answer :
The two rides which i can ride less than 90 minutes are Ferris wheel and Bumper cars. Explanation : Number of minutes at Ferris wheel = 42 Number of minutes at Bumper cars = 44 Total Time = 42 + 44 = 86 86 > 90 minutes. Question 2. At 12:30, you spend 25 minutes eating lunch and 30 minutes playing games. How many more minutes are there until the show starts? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 142 Answer : Time spent in eating lunch = 25 minutes Time spent in playing games = 30 minutes Total Time = 25 + 30 = 55 minutes From 12 : 30 total time spent is 55 minutes so the time is 1:25 The show starts at 1 : 30. The time left to start the show is 5 minutes. Lesson 3.4 Decompose to Add Tens and Ones Explore and Grow Use a model to solve. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 74 Which addend did you break apart to add ? Explain. ________________________________ ________________________________ ________________________________ Answer : 50 + 18 = 68 Explanation :
The addend which we break apart to add is 18 . Break 18 into tens and ones that is 10 + 8. Add the tens to the first addend that is 50 + 10 = 60. Then add the ones that is 60 + 8 = 68. So, the sum is 68 . Show and Grow Use place value to break apart an addend. Then find the sum. Question 1. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 75 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Show-Grow-Question-1 Explanation : The addend which we break apart to add is 12 . Break 12 into tens and ones that is 10 + 2. Add the tens to the first addend that is 61 + 10 = 71. Then add the ones that is 71 + 2 = 73. So, the sum is 73 . Question 2. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 76 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Show-Grow-Question-2 Explanation : The addend which we break apart to add is 24 . Break 24 into tens and ones that is 20 + 4. Add the tens to the first addend that is 74 + 20 = 94. Then add the ones that is 94 + 4 = 98. So, the sum is 98. Question 3. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 77 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Show-Grow-Question-3
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Explanation : The addend which we break apart to add is 44 . Break 44 into tens and ones that is 40 + 4. Add the tens to the first addend that is 23 + 40 = 63. Then add the ones that is 63 + 4 = 67. So, the sum is 67 . Question 4. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 78 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Show-Grow-Question-4 Explanation : The addend which we break apart to add is 53 . Break 53 into tens and ones that is 50 + 3. Add the tens to the first addend that is 31 + 50 = 81. Then add the ones that is 81 + 3 = 84. So, the sum is 84 . Apply and Grow: Practice Use place value to break apart an addend. Then find the sum. Question 5. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 79 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Apply-Grow-Practice-Question-5 Explanation : The addend which we break apart to add is 11 . Break 11 into tens and ones that is 10 + 1. Add the tens to the first addend that is 71 + 10 = 81. Then add the ones that is 81 + 1 = 82. So, the sum is 82 . Question 6. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 80 Answer :
Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Apply-Grow-Practice-Question-6 Explanation : The addend which we break apart to add is 23 . Break 23 into tens and ones that is 20 + 3. Add the tens to the first addend that is 65 + 20 = 85. Then add the ones that is 85 + 3 = 88. So, the sum is 88 . Question 7. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 81 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Apply-Grow-Practice-Question-7 Explanation : The addend which we break apart to add is 47 . Break 47 into tens and ones that is 40 + 7. Add the tens to the first addend that is 32 + 40 = 72. Then add the ones that is 72 + 7 = 79. So, the sum is 79 . Question 8. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 82 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Apply-Grow-Practice-Question-8 Explanation : The addend which we break apart to add is 43 . Break 43 into tens and ones that is 40 + 3. Add the tens to the first addend that is 25 + 40 = 65. Then add the ones that is 65 + 3 = 68. So, the sum is 68 . Question 9. 54 + 36 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Apply-Grow-Practice-Question-9
Explanation : The addend which we break apart to add is 36 . Break 36 into tens and ones that is 30 + 6. Add the tens to the first addend that is 54 + 30 = 84. Then add the ones that is 84 + 6 = 90. So, the sum is 90 . Question 10. 21 + 61 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.4-Decompose- Add-Tens-Ones-Apply-Grow-Practice-Question-10 Explanation : The addend which we break apart to add is 61 . Break 61 into tens and ones that is 60 + 1. Add the tens to the first addend that is 21 + 60 = 81. Then add the ones that is 81 + 1 = 82. So, the sum is 82 . Question 11. Precision Which expressions have a sum of 72. Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 83 Answer : Two Equations 41 + 31 and 11 + 61 have sum of 72 . Explanation : 52 + 22 = 74 51 + 11 = 62 41 + 31 = 72 47 + 30 = 77 11 + 61 = 72 Think and Grow: Modeling Real Life You have 32 coins in a piggy bank. You put in 45 more. How many coins are in the bank now? Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 84
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Addition equation: Big Ideas Math Answers 2nd Grade Chapter 3 Addition to 100 Strategies 85 Answer : Number of Coins = 32 Number of coins added in piggy bank = You put in 45 more = 32 + 45 = 77 Therefore, Number of coins in bank = 77 Show and Grow Question 12. There are 81 fans at a game. 18 more arrive. How many fans are at the game now? Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 86 Answer : Number of fans = 81 Number of fans arrived = 18 more Number of fans at the game = 81 + 18 = 99 fans . Question 13. You have 54 songs on a music player. Your friend has 31 more than you. How many songs does your friend have ? Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 86.1 Answer : Number of songs in my music player = 54 Number of songs my friend have = 31 more than me = 31 + 54 = 85 Decompose to Add Tens and Ones Homework & Practice 3.4 Use place value to break appart an addend. Then find the sum. Question 1. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 87 Answer :
Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-1 Explanation : The addend which we break apart to add is 34 . Break 34 into tens and ones that is 30 + 4. Add the tens to the first addend that is 53 + 30 = 83. Then add the ones that is 83 + 4 = 87. So, the sum is 87 . Question 2. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 88 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-2 Explanation : The addend which we break apart to add is 13 . Break 13 into tens and ones that is 10 + 3. Add the tens to the first addend that is 46 + 10 = 56. Then add the ones that is 56 + 3 = 59. So, the sum is 59 . Question 3. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 89 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-3 Explanation : The addend which we break apart to add is 73 . Break 73 into tens and ones that is 70 + 3. Add the tens to the first addend that is 14 + 70 = 84. Then add the ones that is 84 + 3 = 87. So, the sum is 87 . Question 4. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 90 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-4 Explanation :
The addend which we break apart to add is 67 . Break 67 into tens and ones that is 60 + 7. Add the tens to the first addend that is 31 + 60 = 91. Then add the ones that is 91 + 7 = 98. So, the sum is 98 . Question 5. 28 + 61 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-5 Explanation : The addend which we break apart to add is 28 . Break 28 into tens and ones that is 60 + 1. Add the tens to the first addend that is 28 + 60 = 88. Then add the ones that is 88 + 1 = 89. So, the sum is 89 . Question 6. 51 + 41 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-6 Explanation : The addend which we break apart to add is 41 . Break 41 into tens and ones that is 40 + 1. Add the tens to the first addend that is 51 + 40 = 91. Then add the ones that is 91 + 1 = 92. So, the sum is 92 . Question 7. DIG DEEPER! Use the numbers to complete the equation. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 91 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-7 Question 8.
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Modeling Real Life You see 38 ladybugs. Then you see 21 more. How many ladybugs do you see? Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 92 Answer : Number of lady bugs seen = 38 Number of Lady bugs seen later = 21 more = 38 + 21 = 59 Therefore, Total Number of lady bugs seen = 59 Question 9. Modeling Real Life You read for 18 minutes and play outside for 35 minutes. How many minutes do you read and play in all? Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 93 Answer : Minutes used for reading = 18 Minutes used to played = 35 Number of Minutes used to read and play = 18 + 35 = 53 Review & Refresh Question 10. Draw a line through the shorter object. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 94 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Decompose-Add-Tens- Ones-Homework-Practice-3.4-Question-10 Lesson 3.5 Use Compensation to Add Explore and Grow Match the numbers that make a ten. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 95
How can making a ten help you add greater numbers? _________________________________ _________________________________ _________________________________ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Explore-Grow Explanation : Making a ten help you us in adding numbers easily . It helps to divide the addend into tens part and ones part. tens parts can be easily added to any numbers then later the ones part is added . Show and Grow Use compensation to add. Question 1. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 96 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Show-Grow-Question-1 Explanation : Takes ones from one addend to make other addend number a decade number . Here 1 is taken from addend 5 and added to 59 addend to make 59 a decade number that is 59 + 1 = 60 Then add the changed addends we get, 4 + 60 = 64 . Question 2. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 97 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Show-Grow-Question-2 Explanation : Takes ones from one addend to make other addend number a decade number . Here 4 is taken from addend 37 and added to 16 addend to make 16 a decade number that is 16 + 4 = 20
Then add the changed addends we get, 33 + 20 = 53 . Apply and Grow: Practice Use compensation to add. Question 3. 52 + 19 = ? Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 98 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Apply-Grow-Practice-Question-3 Explanation : Takes ones from one addend to make other addend number a decade number . Here 1 is taken from addend 52 and added to 19 addend to make 19 a decade number that is 19 + 1 = 20 Then add the changed addends we get, 51 + 20 = 71 . Question 4. 43 + 8 = ? Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 99 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Apply-Grow-Practice-Question-4 Explanation : Takes ones from one addend to make other addend number a decade number . Here 2 is taken from addend 43 and added to 8 addend to make 8 a decade number that is 8 + 2 = 10 Then add the changed addends we get, 41+ 10 = 51 . Question 5. 26 + 35 = ? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 100 Answer :
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Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Apply-Grow-Practice-Question-5 Explanation : Takes ones from one addend to make other addend number a decade number . Here 5 is taken from addend 26 and added to 35 addend to make 35 a decade number that is 35 + 5 = 40 Then add the changed addends we get, 21 + 40 = 61 . Question 6. 68 + 15 = ? Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 101 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Apply-Grow-Practice-Question-6 Explanation : Takes ones from one addend to make other addend number a decade number . Here 5 is taken from addend 68 and added to 15 addend to make 15 a decade number that is 15 + 5 = 20 Then add the changed addends we get, 63+ 20 = 83 . Question 7. Structure Show two different ways to use compensation to find 25 + 17. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 102 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.5-Use- Compensation-Add-Apply-Grow-Practice-Question-7 Explanation : Takes ones from one addend to make other addend number a decade number . Here 3 is taken from addend 25 and added to 17 addend to make 17 a decade number that is 17 + 3= 20 Then add the changed addends we get, 22+ 20 = 42 . Takes ones from one addend to make other addend number a decade number . Here 5 is taken from addend 17 and added to 25 addend to make 25 a decade number that is 25 + 5= 30 Then add the changed addends we get, 30+ 12= 42 . Think and Grow: Modeling Real Life
You need 100 tickets for a prize. You have 79 and win 17 more. Do you have enough tickets for a prize? Addition equation: Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 103 Answer : Number of Tickets for a prize = 100 Number of tickets with me = 79 Number of tickets won = 17 Total Number of tickets with me = 79 + 17 = 96 100 > 96 . No, I don’t have enough tickets for a prize . Show and Grow Question 8. You need to set up 80 chairs. You set up 32. Your friend sets up 49. Do you and your friend set up enough chairs? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 104 Answer : Numbers chairs required to setup = 80 Number of chairs set up by me = 32 Number of chairs set up by my friend = 49 Total chairs set up by me and my friend = 32 + 49 = 81 80 < 81 Yes, me and my friend set up enough chairs . Question 9. DIG DEEPER! You need 50 containers of slime for a party. You have 28. You buy 17 more. How many more containers do you need? Big Ideas Math Answer Key Grade 2 Chapter 3 Addition to 100 Strategies 105 Answer :
Number of containers required for slime a party = 50 Number of containers with me = 28 Number of containers bought = 17 Total Number of containers with me = 28 + 17 =45 Number of containers required more = 50 – 45 = 5 Use Compensation to Add Homework & Practice 3.5 Use compensation to add. Question 1. Big Ideas Math Answers Grade 2 Chapter 3 Addition to 100 Strategies 106 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-1 Explanation : Takes ones from one addend to make other addend number a decade number . Here 1 is taken from addend 31 and added to 46 addend to make 31 a decade number that is 31 – 1 = 30 Then add the changed addends we get, 47+ 30 = 77 . Question 2. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 107 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-2 Explanation : Takes ones from one addend to make other addend number a decade number . Here 5 is taken from addend 27 and added to 15 addend to make 15 a decade number that is 15 + 5 = 20 Then add the changed addends we get, 22+ 20 = 42 . Question 3. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 108 Answer :
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Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-3 Explanation : Takes ones from one addend to make other addend number a decade number . Here 4 is taken from addend 34 and added to 66 addend to make 66 a decade number that is 34 – 4 = 30 Then add the changed addends we get, 70+ 30 = 100 . Question 4. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 109 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-4 Explanation : Takes ones from one addend to make other addend number a decade number . Here 1 is taken from addend 56 and added to 29 addend to make 29 a decade number that is 29 + 1 = 30 Then add the changed addends we get, 55+ 30 = 85 . Use compensation to add. Question 5. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 110 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-5 Explanation : Takes ones from one addend to make other addend number a decade number . Here 4 is taken from addend 75 and added to 6 addend to make 6 a decade number that is 6 + 4 = 10 Then add the changed addends we get, 71+ 10 = 81 . Question 6. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 111 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-6
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Explanation : Takes ones from one addend to make other addend number a decade number . Here 2 is taken from addend 44 and added to 38 addend to make 38 a decade number that is 38 + 2 = 40 Then add the changed addends we get, 42+ 40 = 84 . Question 7. Writing Explain why you make one addend a decade number when using compensation to add. ________________________________ ________________________________ ________________________________ Answer : Addends are numbers used in addition problems, they refers to the numbers that are added together. … When solving addition problems, it is advisable to make one of the addends a tens number because, it makes the addition operation easier to manipulate. Compensation is a mental math strategy for multi-digit addition that involves adjusting one of the addends to make the equation easier to solve. Some students may prefer this strategy as an alternative to left-to-right addition or the breaking up the second number strategy. Question 8. Modeling Real Life You want to read 50 pages. You read 18 on Monday and 27 on Tuesday. Do you reach your goal? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 112 Answer : Number of pages i want to read = 50 Number of pages read on Monday = 18 Number of pages read on Tuesday = 27 Number of pages read by me on Monday and Tuesday = 18 + 27 = 45 50 > 45 . No, I didn’t reach the goal. More 5 pages required to read . Review & Refresh
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Draw one line to show the parts Question 9. 2 squares Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 113 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-9 Explanation : The above rectangle is divided into 2 squares by drawing a line in the middle of the rectangle. it is drawn on half of the length of the rectangle . Question 10. 2 triangles Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 114 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Use Compensation-Add- Homework-Practice-3.5-Question-10 Explanation : Draw any line from any of the vertexes of the triangle . It divided the given triangle into two equal triangles as shown in the above diagram . Lesson 3.6 Practice Addition Strategies Explore and Grow Use any strategy to find the sum. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 115 Compare your strategy to your partner’s strategy. How are your strategies alike? How are they different? ________________________________ ________________________________ ________________________________ Answer :
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Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Explore-Grow Explanation : In the first method We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 76 In the Second Method The addend which we break apart to add is 41 . Break 41 into tens and ones that is 40 + 1. Add the tens to the first addend that is 35 + 40 = 75. Then add the ones that is 75 + 1 = 76. So, the sum is 76 . Show and Grow Question 1. 50 + 35 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Show-Grow-Question-1 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 85 Question 2. 64 + 32 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Show-Grow-Question-2 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 96 Question 3. 19 + 26 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Show-Grow-Question-3
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Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 45 Question 4. 78 + 13 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Show-Grow-Question-4 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 91 Apply and Grow: Practice Question 5. 32 + 41 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Apply-Grow-Practice-Question-5 Explanation : The addend which we break apart to add is 41 . Break 41 into tens and ones that is 40 + 1. Add the tens to the first addend that is 32 + 40 = 72. Then add the ones that is 72 + 1 = 73. So, the sum is 73 . Question 6. 56 + 18 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Apply-Grow-Practice-Question-6 Explanation : The addend which we break apart to add is 18 . Break 18 into tens and ones that is 10 + 8. Add the tens to the first addend that is 56 + 10 = 66. Then add the ones that is 66 + 8 = 74. So, the sum is 74 .
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Question 7. 47 + 36 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Apply-Grow-Practice-Question-7 Explanation : The addend which we break apart to add is 36 . Break 36 into tens and ones that is 30 + 6. Add the tens to the first addend that is 47 + 30 =77 . Then add the ones that is 77 + 6 = 83. So, the sum is 83 . Question 8. 91 + 9 = ___ Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Apply-Grow-Practice-Question-8 Explanation : The addend which we break apart to add is 9 . Break 9 into tens and ones that is 10 – 1. Add the tens to the first addend that is 91 + 10 = 101. Then add the ones that is 101 – 1 = 100. So, the sum is 100 . Question 9. ___ = 67 + 22 Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Apply-Grow-Practice-Question-9 Explanation : The addend which we break apart to add is 22 . Break 22 into tens and ones that is 20 + 2. Add the tens to the first addend that is 67 + 20 =87 . Then add the ones that is 87 + 2 = 89. So, the sum is 89 . Question 10. __ = 51 + 39
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Answer : Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Lesson-3.6-Practice- Addition-Strategies-Apply-Grow-Practice-Question-10 Explanation : The addend which we break apart to add is 39 . Break 39 into tens and ones that is 30 + 9. Add the tens to the first addend that is 51 + 30 = 81 . Then add the ones that is 51 + 39 = 90. So, the sum is 90 . Question 11. YOU BE THE TEACHER Your friend breaks apart an addend to solve 24 + 56. Is your friend correct? Explain. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 115.1 Answer : Yes , he is correct. Explanation : The addend which we break apart to add is 56 . Break 56 into tens and ones that is 50 + 6. Add the tens to the first addend that is 24 + 50 = 74 . Then add the ones that is 74 + 6 = 80. So, the sum is 80 . Think and Grow: Modeling Real Life You collect 23 cans of a food drive. Your friend collects 35 more than you. How many cans does your friend collect? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 116 Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 117 Answer : Number of cans collected by me = 23 Number of cans collected by my friend = 35 more than me Number of cans collected by my friend = 35+ 23 = 58 Show and Grow
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Question 12. You jump rope 67 times today. Tomorrow you want to jump rope 15 more times than you did today. How many times should you jump rope tomorrow? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 118 Answer : Number of rope jumps today by me = 67 Number of rope jumps by me for tomorrow = 15 more times than you did today Number of rope jumps by me for tomorrow = 15 + 67 = 82 Question 13. Your friend uses 19 fewer nails than you to build a birdhouse. Your friend uses 13 nails. How many nails do you use? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 119 Answer : Number of nails used by my friend = 13 Number of nails used by me = x Your friend uses 19 fewer nails than me x – 19 = 13 x = 13 + 19 x = 32 Therefore , Number of nails used by me = 32 Question 14. The book club has 27 fewer students than the art club. The book club has 24 students. How many students are in the art club? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 120 Answer : Number of students in book club = Numbers of students in art club – 27 Number of students in book club = 24 Numbers of students in art club = 24 + 27 (From given condition ) = 51
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Practice Addition Strategies Homework & Practice 3.6 Question 1. 20 + 40 = __ Answer : 20 + 40 = 60 Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Practice-Addition- Strategies-Homework-Practice-3.6-Question-1 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 60 Question 2. 60 + 26 = ___ Answer : 60 + 26 = 86 Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Practice-Addition- Strategies-Homework-Practice-3.6-Question-2 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 86 Question 3. 19 + 61 = ___ Answer : 19 + 61 = 80 Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Practice-Addition- Strategies-Homework-Practice-3.6-Question-3 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 80
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Question 4. 43 + 28 = ___ Answer : 43 + 28 = 71 Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Practice-Addition- Strategies-Homework-Practice-3.6-Question-4 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 71 Question 5. __ = 45 + 46 Answer : 45 + 45 = 91 Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Practice-Addition- Strategies-Homework-Practice-3.6-Question-5 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 91 Question 6. __ = 33 + 59 Answer : 33 + 59 = 92 Big-Ideas-Math-Book-2nd-Grade-Answer-Key-Chapter-3-Addition-to-100-Strategies-Practice-Addition- Strategies-Homework-Practice-3.6-Question-6 Explanation : We use place value and break the addends into tens and ones. Then add the tens values and ones values .Write the number formed . So, the number is 92 Question 7. YOU BE THE TEACHER
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Your friend uses compensation to solve 28 + 33. Is your friend correct? Explain. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 121 Answer : No , he is wrong . Explanation : After adding 2 to 28 then we should subtract 2 from 33 .then we get 28 + 2 = 30 and 33 – 2 = 31 . now add the changed addends we get 30 + 31 = 61 . So, the sum is 61 . Question 8. Modeling Real Life You have 15 blue crayons and 26 red crayons. How many crayons do you have in all? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 122 Answer : Number of blue crayons = 15 Number of red crayons = 26 Total number of crayons = 15 + 26 = 41 Question 9. Modeling Real Life The home team scores 46 points. The visiting team scores 13 more than the home team. How many points does the visiting team score? Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 123 Answer : Score of home team = 46 Score of visiting team = 13 more than the home team = 13 + 46 = 59 Therefore, visiting team score = 59 points . Review & Refresh Question 10. Big Ideas Math Solutions Grade 2 Chapter 3 Addition to 100 Strategies 124
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Answer : Number of Drums = 5 Number of Guitars = 5 + 4 = 9 5< 9 It means the number of Guitars are greater than the number of drums. ine It Use your vocabulary cards to match. 1 ine It Use your vocabulary cards to match. Question 1. Answer: Lesson 2.1 Add in Any Order Explore and Grow
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Use the table to find the sum. Change the order of the addends. Write the new equation. Show and Grow Question 1. Answer: Explanation: Changing the order of the addends does not change the sum.
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The expressions 6 + 3 and 3 + 6 are both equal to 9. The addend 6 is represented by orange color and addend 3 by blue. Question 2. Answer: Explanation: Changing the order of the addends does not change the sum. The expressions 5 + 1 and 1 + 5 are both equal to 6. The addend 5 is represented by yellow color and addend 1 by green. Find the sum. Then change the order of the addends. Write the new equation. Question 3. Answer: Explanation: Changing the order of the addends does not change the sum. The expressions 8 +2 and 2 + 8 are both equal to the sum 10. Question 4. Answer: Explanation: Changing the order of the addends does not change the sum. The expressions 4 + 3 and 3 + 4 are both equal to the sum 7. Apply and Grow: Practice Find the sum. Then change the order of the addends. Write the new equation.
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Question 5. Answer: Explanation: Changing the order of the addends does not change the sum. The expressions 4 + 3 and 3 + 4 are both equal to the sum 7. Question 6. Answer: 7 + 3 = 10 3 + 7 = 10 Explanation: Changing the order of the addends does not change the sum. The expressions 7 + 3 and 3 + 7 are both equal to the sum 10. Question 7. Answer: 6 + 5 = 11 5 + 6 = 11 Explanation: Changing the order of the addends does not change the sum. The expressions 6 + 5 and 5 + 6 are both equal to the sum 11. Question 8. Answer: 17 = 9 + 8 17 = 8 + 9 Explanation: Changing the order of the addends does not change the sum. The expressions 9 + 8 and 8 +9 are both equal to the sum 17. Question 9. Answer: 2 = 0 + 2 2 = 2 +0 Explanation: Changing the order of the addends does not change the sum.
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The expressions 0 + 2 and 2 + 0 are both equal to the sum 2. Adding 0 to any number gives the sum the number itself. Think and Grow: Modeling Real Life You paint 12 shapes. 8 are rectangles. The rest are circles. How many circles do you paint? Write two equations that describe your shapes: Answer: Given: Total number of shapes painted = 12 Number of rectangles painted = 8 Number of circles painted = total shapes painted – number of rectangles painted 12 – 8 = 4 8 + 4 = 12 4 + 8 = 12 Total circles painted = 4. Show and Grow Question 11. There are 13 race cars. 6 of them have numbers. The rest do not. How many race cars do not have numbers? Write two equations that describe your shapes: Explain how you know your answer is correct.
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_______________________________ _______________________________ _______________________________ Answer: Total number of race cars = 13 Number of race cars with numbers = 6. Number of race cars without number = total number of race cars – Number of race cars with numbers 13 – 6 = 7. number of race cars with number + number of race cars without number = total number of race cars 6 + 7 = 13 when we reverse the order 7 + 6 = 13 Explanation: Changing the order of the addends does not change the sum. Given total race cars = 13 Race cars with number = 6 To find the race cars without number we need to minus race cars with number from the total 13 – 6 = 7 Add in Any Order Homework & Practice 2.1 Question 1. Answer: Explanation: Changing the order of the addends does not change the sum. Given 6 blue linking cubes and 4 red linking cubes Adding blue and red gives the sum. 6 + 4 = 10. when we reverse the colors order adding red and blue gives the sum . 4 + 6 = 10.
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Question 2. Answer: Explanation: Changing the order of the addends does not change the sum. Given 1 yellow linking cubes and 8 orange linking cubes Adding yellow and orange cube gives the sum 1 + 8 = 9. when we reverse the colors order adding orange and yellow cubes gives the sum 8 + 1 = 9. Question 3. Answer: 7 + 0 = 7 0 + 7 = 7 Explanation: Changing the order of the addends does not change the sum. Adding any number to 0 gives the sum the number itself. Question 4. Answer: 2 + 4 = 6 4 + 2 = 6 Explanation: Changing the order of the addends does not change the sum. The expressions 2 + 4 and 4 + 2 gives the same sum 6. Question 5. Answer: 15 = 8 + 7 7 + 8 = 15 Explanation: Changing the order of the addends does not change the sum. The expressions 8 + 7 and 7 +8 gives the same sum 15.
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Question 6. Answer: 11 = 3 + 8 8 +3 = 11 Explanation: Changing the order of the addends does not change the sum. The expressions 3 + 8 and 8 + 3 gives the same sum 11. Question 7. Number Sense Complete each equation. Answer: Explanation: Changing the order of the addends in the expressions. Question 8. Modeling Real Life You have 14 blocks. 8 are cubes. The rest are cylinders. How many cylinders do you have? Write two equations that describe your blocks: Answer: Total number of Blocks = 14 Number of cubes = 8. Number of Cylinders = total number Blocks – Number of Cubes 14 – 8 = 6.
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Number of cylinders = 6 number of Cubes + number of Cylinders = total number Blocks 8 + 6 = 14 when we reverse the order the expression 6 + 8 = 14 Explanation: Given total Blocks = 14 Number of cubes = 8 From the above calculation Number of Cylinder = 6 Blocks = number of cubes + number of cylinders 8 + 6 = 14 Changing the order of the addends does not change the sum. 6 + 8 = 14. Question 9. Modeling Real Life There are 16 kids in a class. 7 have gone camping. The rest have not. How many kids have not gone camping? Write two equations that describe the kids: Answer: Total number Kids in the class= 16 Number of kids gone camping = 7. Number of kids who have not gone camping = Total number of kids in the class – Number of kids gone camping 16 – 7 = 9. Number of kids who have not gone camping = 9 number of kids who have gone camping + number of kids who have not gone camping = total number kids in the class 7 + 9 = 16. when we reverse the order the expression 9 + 7 = 16. Explanation: Given total number kids in the class = 16 Number of kids who have gone camping = 7 From the above calculation Number of kids who have not gone camping = 9 Total number kids in the class = number of kids who have gone camping + number of kids who have not gone camping 7 + 9 = 16
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Changing the order of the addends does not change the sum. 9 + 7 = 16. Review & Refresh Question 10. Which time does not belong with the other three? Answer: Explanation: Half past 5 means 5:30. In the fig first three images indicate 5:30 where as half past 6 means 6:30. Lesson 2.2 Use Doubles Explore and Grow
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Find each sum. How are the equations alike? How are they different?
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Answer: Explanation: First two expressions are double. 6 + 6, 7 + 7 In the next two expression one is doubles plus 1 expression 6 + 7. second is doubles minus 1 expression 7 + 6. Show and Grow Find the sum. Write the double you used.
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Question 1. Answer: 4 + 5 = 9 4 + 4 = 8 Explanation: Doubles plus 1 4 + 5 is equal to 4 + 4 and 1 more. Question 2. Answer: 7 + 6 = 13 7 + 7 = 14 Explanation: Doubles minus 1 7 + 6 is equal to 1 less than 7 + 7. Question 3. Answer:
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Explanation: Doubles minus 1 6 + 5 is equal to 1 less than 6 + 6. Question 4. Answer: Explanation: Doubles plus 1 8 + 9 is equal to 8 + 8 and 1 more. Apply and Grow: Practice Question 5. Answer:
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Explanation: Doubles plus 1 3 + 4 is equal to 3 + 3 and 1 more Question 6. Answer: Explanation: Doubles minus 1 8 + 7 is equal to 1 less than 8 + 8 Question 7.
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Answer: Explanation: Doubles plus 1 5 + 6 is equal to 1 less than 5 + 5. Question 8. Answer: Explanation: Doubles minus 1 10 +9 is equal to 1 less than 10 + 10. Question 9. Answer: 2 + 3 = 5 2 + 2 = 4 Explanation:
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Doubles plus 1 2 + 3 is equal to 2+2 and 1 more. Question 10. Answer: 5 + 4 = 9 5 + 5 = 10 Explanation: 5 + 4 is equal 1 less than 5 + 5. Doubles minus 1. Question 11. Answer: 6 + 7 = 13 6 + 6 = 12 Explanation: 6 + 7 is equal to 6 + 6 and 1 more. Doubles plus 1. Question 12. Answer: 9 + 8 = 17 9 + 9 = 18 Explanation: 9 + 8 is equal 1 less than 9 + 9. Doubles minus 1. Question 13. DIG DEEPER! What double might Newton be thinking?
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Answer: Given Sum greater than 4 Addends less than 5 As per the above information the doubles can be 3 + 3, 4 + 4. Think and Grow: Modeling Real Life You make 9 mud pies. Your friend makes 1 fewer than you. How many mud pies do you and your friend make in all? Addition equation: What double can you use? Answer: Number of mud pies i make = 9 My friend makes 1 fewer mud pies then me = 9- 1 = 8 Total number of Mud pies we both make = 9 + 8 = 17. Double 9 + 9 = 18. 9 + 8 is 1 less than 9 + 9 Doubles minus 1. Show and Grow Question 14. You score 6 goals. Your friend scores 1 more than you. How many goals do you and your friend score in all?
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Answer: Number of goals i scored = 6 Number of goals my friend scored = 6 + 1 = 7 Total number of goals we both scored = 6 + 7 = 13. Question 15. DIG DEEPER! You and your friend jump in 13 puddles in all. You jump in 7. How many puddles does your friend jump in? Answer: Total number of puddles me and my friend jumped = 13 Total number of puddles i jumped = 7 Number of puddles my friend jumped = 13 – 7 = 6. 7 + 6 = 13. Use Doubles Homework & Practice 2.2 Find the sum. Write the double you used. Question 1. Answer: 4 + 3 = 7 4 + 4 = 8
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Explanation: Doubles minus 1 4 + 3 is equal to 1 less than 4 + 4. Question 2. Answer: 5 + 6 = 11 Doubles 5 + 5 = 10 Explanation: Doubles plus 1 5 + 6 is equal to 5 + 5 and 1 more Question 3. Answer: Explanation: Doubles minus 1 9 + 8 is equal to 1 less than 9 + 9
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Question 4. Answer: Explanation: 6 + 7 is equal to 6 + 6 and 1 more. Doubles plus 1. Question 5. Answer: 8 + 7 = 15 8 + 8 = 16 Explanation: 8 + 7 is equal to 1 less than 8 + 8. Doubles minus 1. Question 6. Answer: 9 + 10 = 19 9 + 9 = 18
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Explanation: Doubles plus 1 9 + 10 is equal to 9 + 9 and 1 more. Question 7. Number Sense Which doubles can you use to find 8 + 9? Answer: To find the expression 8 + 9 8 + 9 is equal to 8 + 8 and 1 more 8 +9 is equal to 1 less than 9 + 9. Question 8. Modeling Real Life You tell 5 jokes. Your friend tells 1 fewer than you. How many jokes do you and your friend tell in all? Answer: Number of jokes i told = 5 Number of jokes my friend told = 5 – 1 = 4 Total number of jokes me and my friend told in together = 5 + 4 = 9 9 jokes together. Question 9. Modeling Real Life Newton paints 3 paw prints. Descartes paints 1 more than Newton. How many paw prints do they paint in all?
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Answer: Number of paw prints by Newton paints = 3 Number of paw prints by Descartes paints is 1 more than newton = 3 + 1 = 4 Total number of paw prints both Newton and Descartes paint =3 + 4 = 7 Total 7 paw prints. Review & Refresh Is the equation true or false? Question 10. Answer: Question 11.
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Answer: Lesson 2.3 Add Three Numbers Explore and Grow Find the sums. What is the same? What is different? _________________________ _________________________ _________________________ Answer:
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The sum remains same. The difference is the order of the addends added. Explanation: Changing the order of addends does not change the sum. In all the three expressions the sum is same :14 Show and Grow Circle two addends to add first. Write their sum. Then find the sum of all three addends. Question 1. 7 + 3 + 4 = ___ Answer: Explanation: Addends are represented in circle and Sum is represented in square.
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First adding two addends 7, 4 give the sum 11 and then adding the another addend 3 to the sum 11. Gives the sum 14. Question 2. 1 + 5 + 3 = ___ Answer: Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 1 , 5 give the sum 6. and then adding the another addend 3 to the sum 6. Gives the sum 9. Question 3. 9 + 4 + 4 = ___ Answer: Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 4, 4 give the sum 8.
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and then adding the another addend 9 to the sum 8. Gives the sum 17. Question 4. 5 + 2 + 5 = ___ Answer: Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 5, 2 give the sum 7. and then adding the another addend 5 to the sum 7. Gives the sum 12. Apply and Grow: Practice Question 5. 3 + 5 + 5 = ___ Answer: Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 5, 2 give the sum 7. and then adding the another addend 5 to the sum 7. Gives the sum 12.
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Question 6. 9 + 0 + 7 = ___ Answer: Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 9, 0 give the sum 9. and then adding the another addend 7 to the sum 9. Gives the sum 16. Question 7. 4 + 2 + 3 = ___ Answer: Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 2, 3 give the sum 5. and then adding the another addend 4 to the sum 5. Gives the sum 9.
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Question 8. Answer : Question 9. Answer :
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Question 10. Answer : Question 11. Answer : 9 + 5 + 6 = 20 Question 12. Answer :
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Question 13. Answer : 3 + 7 + 7 = 17 Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 5, 2 give the sum 7. and then adding the another addend 5 to the sum 7. Gives the sum 12. Question 14. Structure Write the missing addends. Answer : Think and Grow: Modeling Real Life You have 6 presents. Newton and Descartes each have 4 presents. How many presents are there in all? Addition equation:
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Answer : Number of presents with me = 6 Number of presents with Newton = 4 Number of Presents with Descartes = 4 Total Number of presents in all = 6 + 4 + 4 = 14 Show and Grow Question 15. You have 8 crayons. Newton and Descartes each have 5 crayons. How many crayons are there in all? Answer : Number of Crayons with me = 8 Number of Crayons with Newton = 5 Number of Crayons with Descartes = 5 Total Number of Crayons in all = 8 + 5 + 5 = 18 Question 16. You, Newton, and Descartes eat 18 apple slices in all. Newton and Descartes each eat 6 slices. How many apple slices do you eat? Answer : Number of apples slices eaten by Me , Newton and Descartes = 18 Number of apples eaten by Newton =6 Number of apples eaten by Descartes = 6 Total Number of apples eaten by Newton and Descartes = 6 + 6 = 12 Number of apple slices eaten by me = 18 – 12 = 6 Question 17. A treasure chest has 20 jewels in all. 7 are blue. 6 are green. The rest are red. How many jewels are red?
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Answer : Number of jewels in Treasure chest = 20 Number of blue jewels = 7 Number of green jewels = 6 Number of blue and green jewels = 7 + 6 = 13 Number of red jewels = 20 – 13 = 7 Add Three Numbers Homework & Practice 2.3 Circle two addends to add first. Write their sum. Then find the sum of all three addends. Question 1. Answer : 2 + 5 + 1 = 8 Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 5, 1 give the sum 6. and then adding the another addend 2 to the sum 6. Gives the sum 8.
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Question 2. Answer 6 + 4 + 4 = 14 Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 4, 4 give the sum 8. and then adding the another addend 6 to the sum 8. Gives the sum 14. Question 3. Answer : 0 + 8 + 7 = 15
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Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 8, 7 give the sum 15. and then adding the another addend 0 to the sum 15. Gives the sum 15. Question 4. Answer : Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 6, 5 give the sum 11. and then adding the another addend 5 to the sum 11. Gives the sum 11. Question 5. Answer :
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Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 4, 9 give the sum 13. and then adding the another addend 0 to the sum 13. Gives the sum 13. Question 6. Answer : Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 3, 3 give the sum 6. and then adding the another addend 3 to the sum 6. Gives the sum 9. Question 7. 2 + 8 + 7 = ___ Answer :
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Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 8, 7 give the sum 15. and then adding the another addend 2 to the sum 15. Gives the sum 17. Question 8. 9 + 8 + 1 = ___ Answer : Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 8, 1 give the sum 9. and then adding the another addend 9 to the sum 9. Gives the sum 18. Question 9. 8 + 7 + 5 = ___ Answer :
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Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 7, 5 give the sum 12. and then adding the another addend 8 to the sum 12. Gives the sum 20. Question 10. DIG DEEPER! Complete the number puzzle so that each branch has a sum of 20. Answer : Explanation :
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Sum should be 20 8 + ____ + 7 = 20 so , _____= 20 – 15 = 5 10 + ____ + 10 = 20 so , _______ = 20 – 20 = 0 _____ + 3 + 9 = 20 so , _____ = 20 – 12 = 8 4 + 7 + _____ = 20 so, _____ = 20 – 11 = 9 Question 11. Modeling Real Life You, Newton, and Descartes have 17 stampers in all. Newton and Descartes each have 6. How many stampers do you have? Answer : Number of stampers with me , Newton and Descartes = 17 Number of Stampers with Newton = 6 Number of stampers with Descartes = 6 Total Number of stampers with Newton and Descartes = 6 + 6 = 12 Number of Stampers with me = 17 – 12 = 5 Stampers Question 12. Make a quick sketch. Complete the sentences. Answer :
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Lesson 2.4 Make a 10 to Add Explore and Grow Use counters and the ten frames to find the sum. How can you make a 10 to solve? Answer :
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Explanation : We have 7counters in first table and 6 counters in second table. To make ten counters in first table we should move 3 counters from second table to first table. then,we will have ten counters in first table and 3 in second table. add both 10 + 3 = 13 So, 7 + 6 = 13 . Show and Grow Make a 10 to add.
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Question 1. Answer : Explanation : To make addend 9 as 10 we should add 1 to the 9 then write addend 7 as 6 + 1 . then add 9 + 1 we get , 10 and then later add 6 to 10 we get sum , 16 . Question 2. Answer :
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Explanation : To make addend 9 as 10 we should add 1 to the 9 then write addend 5 as 4 + 1 . then add 9 + 1 we get , 10 and then later add 4 to 10 we get sum , 14 . Question 3. 6 + 8 = ? 10 + __ = ___ So, 6 + 8 = ___ Answer : 6 + 8 = 4 + 2 + 8 = 10 + 4 = 14 So, 6 + 8 = 14 Explanation : To make addend 8 as 10 we should add 2 to the 8 then write addend 6 as 4 + 2 . then add 8 + 2 we get , 10 and then later add 4 to 10 we get sum , 14 . Question 4. 7 + 4 = ? 10 + __ = ___ So, 7 + 4 = ___ Answer : 7 + 4 = 7 + 3 + 1 = 10 + 1 = 11 So, 7 + 4 = 11 Explanation : To make addend 7 as 10 we should add 3 to the 7 then write addend 4 as 3 + 1 . then add 7 + 3 we get , 10 and then later add 1 to 10 we get sum , 11 . Apply and Grow: Practice Make a 10 to add. Question 5. 2 + 9 = ?
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10 + __ = ___ So, 2 + 9 = ___ Answer : 2 + 9 = 1 + 1 + 9 = 1 + 10 = 11 So, 2 + 9 = 11 Explanation : To make addend 9 as 10 we should add 1 to the 9 then write addend 2 as 1 + 1 . then add 9 + 1 we get , 10 and then later add 1 to 10 we get sum , 11 . Question 6. 8 + 4 = ? 10 + ___ = __ So, 8 + 4 = ___ Answer : 8 + 4 = 2 + 2 + 8 = 2 + 10 = 12 So, 8 + 4 = 12 Explanation : To make addend 8 as 10 we should add 2 to the 8 then write addend 4 as 2 + 2 . then add 2 + 8 we get , 10 and then later add 2 to 10 we get sum , 12 . Question 7. 9 +6 = ? 10+ ___ = ___ So, 9 + 6 = ___ Answer : 9 + 6 = 9 + 1 + 5 = 10 + 5 = 15 So, 9 + 6 = 15 Explanation : To make addend 9 as 10 we should add 1 to the 9 then write addend 6 as 5 + 1 . then add 9 + 1 we get , 10 and then later add 5 to 10 we get sum , 15 . Question 8. 7 + 7 = ? 10 + __ = ___ So, 7 + 7 = ___ Answer : 7 + 7 = 7 + 3 + 4 = 10 + 4 = 14 So, 7 + 7 = 14
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Explanation : To make addend 7 as 10 we should add 3 to the 7 then write addend 7 as 3 + 4 . then add 7 + 3 we get , 10 and then later add 4 to 10 we get sum , 14 . Question 9. 6 + 5 = ___ Answer : 6 + 5 = 6 + 4 + 1 = 10 + 1 = 11 So, 6 + 5 = 11 Explanation : To make addend 6 as 10 we should add 4 to the 6 then write addend 5 as 4 + 1 . then add 6 + 4 we get , 10 and then later add 1 to 10 we get sum , 11 . Question 10. 8 + 9 = ___ Answer : 8 + 9 = 7 + 1 + 9 = 7 + 10 = 17 So, 8 + 9 = 17 Explanation : To make addend 9 as 10 we should add 1 to the 9 then write addend 8 as 7 + 1 . then add 9 + 1 we get , 10 and then later add 7 to 10 we get sum , 17 . Question 11. 7 + 5 = ___ Answer : 7 + 5 = 7 + 3 + 2= 10 + 2 = 12 So, 7 + 5 = 12 Explanation : To make addend 7 as 10 we should add 3 to the 7 then write addend 5 as 3 + 2 . then add 7 + 3 we get , 10 and then later add 2 to 10 we get sum , 12 . Question 12. 6 + 6 = ___ Answer : 6 + 6 = 6 + 4 + 2 = 10 + 2 = 12 So, 6 + 6 = 12 Explanation :
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To make addend 6 as 10 we should add 4 to the 6 then write addend 6 as 4 + 2 . then add 6 + 4 we get , 10 and then later add 2 to 10 we get sum , 12 . Question 13. 9 + 9 = ___ Answer : 9 + 9 = 9 + 1 + 8 = 10 + 8 = 18 So, 9 + 9 = 18 Explanation : To make addend 9 as 10 we should add 1 to the 9 then write addend 9 as 1 + 8 . then add 9 + 1 we get , 10 and then later add 8 to 10 we get sum , 18 . Question 14. 8 + 7 = __ Answer : 8 + 7 = 5 + 2 + 8 = 10 + 5 = 15 So, 8 + 7 = 15 Explanation : To make addend 8 as 10 we should add 2 to the 8 then write addend 7 as 5 + 2 . then add 8 + 2 we get , 10 and then later add 5 to 10 we get sum , 15 . Question 15. __ = 4 + 7 Answer : 4 + 7 = 1 + 3 + 7 = 1 + 10 = 11 So, 4 + 7 = 11 Explanation : To make addend 7 as 10 we should add 3 to the 7 then write addend 4 as 1 + 3 . then add 3 + 7 we get , 10 and then later add 1 to 10 we get sum , 11 . Question 16. __ = 9 + 4 Answer : 9 + 4 = 9 + 1 + 3 = 10 + 3 = 13 So, 9 + 4 = 13 Explanation : To make addend 9 as 10 we should add 1 to the 9 then write addend 4 as 1 + 3 . then add 9 + 1 we get , 10 and then later add 3 to 10 we get sum , 13 .
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Question 17. __ = 8 + 8 Answer : 8 + 8 = 6 + 2 + 8 = 6 + 10 = 16 So, 8 + 8 = 16 Explanation : To make addend 8 as 10 we should add 2 to the 8 then write addend 8 as 6 + 2 . then add 2 + 8 we get , 10 and then later add 6 to 10 we get sum , 16 . Question 18. __ = 6 + 8 Answer : 6 + 8 = 4 + 2 + 8 = 4 + 10 = 14 So, 6 + 8 = 14 Explanation : To make addend 8 as 10 we should add 2 to the 8 then write addend 6 as 4 + 2 . then add 2 + 8 we get , 10 and then later add 4 to 10 we get sum , 14 . Question 19. Number Sense How can you make a 10 to find 7 + 6? Answer : 7 + 6 = 7 + 3 + 3 = 10 + 3 = 13 So, 7 + 6 = 13 7 + 6 = 3 + 4 + 6 = 3 + 10 = 13 So, 7 + 6 = 13 Explanation : To make addend 7 as 10 we should add 3 to the 7 then write addend 6 as 3 + 3 . then add 3 + 7 we get , 10 and then later add 3 to 10 we get sum , 13 . To make addend 6 as 10 we should add 4 to the 6 then write addend 7 as 3 + 4 . then add 4 + 6 we get , 10 and then later add 3 to 10 we get sum , 13 . Think and Grow: Modeling Real Life There are 13 boys and 4 girls in a line. How many girls must join the line so that the numbers of boys and girls are equal? Addition equation:
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Answer : Number of boys = 13 Number of girls = 4 Number of girls required to add more to become 13 = 4 + _____ = 13 = 13 – 4 = 9 Therefore, Number of girls must join the line so that the numbers of boys and girls are equal = 9 girls . Show and Grow Question 20. There are 16 seals and 7 whales. How many whales must join them so that the numbers of seals and whales are equal? Answer : Number of Seals = 16 Number of Whales = 7 Number of whales must join them so that the numbers of seals and whales are equal = 7 + ____ = 16 = 16 – 7 = 9 Therefore, Number of whales must join them so that the numbers of seals and whales are equal = 9 Question 21. You and your friend count 15 stars in all. You count 8. How many stars does your friend count?
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Answer : Number of stars Counted by me and my friend = 15 Number of stars counted by me = 8 Number of stars Counted by my friend = 15 – 8 = 7 Question 22. There are 17 fish in a tank. 9 are green. The rest are blue. How many fish are blue? Answer : Number of Fishes = 17 Number of green Fishes = 9 Number of blue Fishes = 17 – 9 = 8 Make a 10 to Add Homework & Practice 2.4 Make a ten to add. Question 1.
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Answer : Question 2. Answer : Question 3. 7 + 6 = ? 10 + __ = ___ So, 7 + 6 = ___ Answer :
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7 + 6 = 7 + 3 + 3 = 3 + 10 = 13 So, 7 + 6 = 13 Explanation : To make addend 7 as 10 we should add 3 to the 7 then write addend 6 as 3 + 3 . then add 3 + 7 we get , 10 and then later add 3 to 10 we get sum , 13 . Question 4. 8 + 3 = ___ 10 + __ = ___ So, 8 + 3 = __ Answer : 8 + 3= 8 + 2 + 1 = 1 + 10 = 11 So, 8 + 3 = 11 Explanation : To make addend 8 as 10 we should add 2 to the 8 then write addend 3 as 2 + 1 . then add 2 + 8 we get , 10 and then later add 1 to 10 we get sum , 11 . Make a 10 to add. Question 5. 3 + 9 = ___ Answer : 3 + 9 = 2 + 1 + 9 = 2 + 10 = 12 So, 3 + 9 = 12 Explanation : To make addend 9 as 10 we should add 1 to the 9 so write addend 3 as 2 + 1 . then add 1 + 9 we get , 10 and then later add 2 to 10 we get sum , 12 . Question 6. 8 + 8 = ___ Answer : 8 + 8 = 8 + 2 + 6 = 10 + 6 = 16 So, 8 + 8 = 16 Explanation : To make addend 8 as 10 we should add 2 to the 8 so write addend 8 as 2 + 6 . then add 8 + 2 we get , 10 and then later add 6 to 10 we get sum , 16 .
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Question 7. 7 +4 = ___ Answer : 7 + 4 = 7 + 3 + 1 = 10 + 1 = 11 So, 7 + 4 = 11 Explanation : To make addend 7 as 10 we should add 3 to the 7 so write addend 4 as 3 + 1 . then add 7 + 3 we get , 10 and then later add 1 to 10 we get sum , 11 . Question 8. 4 + 9 = ___ Answer : 4 + 9 = 3 + 1 + 9 = 10 + 3 = 13 So, 4 + 9 = 13 Explanation : To make addend 9 as 10 we should add 1 to the 9 so write addend 4 as 3 + 1 . then add 1 + 9 we get , 10 and then later add 3 to 10 we get sum , 13 . Question 9. ___ = 6 + 9 Answer : 6 + 9 = 5 + 1 + 9 = 10 + 5 = 15 So, 10 + 5 = 15 Explanation : To make addend 9 as 10 we should add 1 to the 9 so write addend 6 as 5 + 1 . then add 1 + 9 we get , 10 and then later add 5 to 10 we get sum , 15 . Question 10. ___ = 4 + 8 Answer : 4 + 8 = 2 + 2 + 8 = 10 + 2 = 12 So, 4 + 8 = 12 Explanation : To make addend 8 as 10 we should add 2 to the 8 so write addend 4 as 2 + 2 . then add 8 + 2 we get , 10 and then later add 2 to 10 we get sum , 12 . Question 11. __ = 7 + 8
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Answer : 7 + 8 = 5 + 2 + 8 = 10 + 5 = 15 So, 7 + 8 = 15 Explanation : To make addend 8 as 10 we should add 2 to the 8 so write addend 7 as 5 + 2 . then add 8 + 2 we get , 10 and then later add 5 to 10 we get sum , 15 . Question 12. ___ = 9 + 2 9 + 2 = 9 + 1 + 1 = 10 + 1 = 11 So, 9 + 2 = 11 Explanation : To make addend 9 as 10 we should add 1 to the 9 so write addend 2 as 1 + 1 . then add 9 + 1 we get , 10 and then later add 1 to 10 we get sum , 11 . Question 13. Number Sense Complete each equation. Answer : Question 14. Modeling Real Life There are 12 giraffes and 5 elephants. How many elephants must join them so that the numbers of giraffes and elephants are equal? Answer : Number of Giraffes = 12 Number of Elephants = 5 Number of more elephants must join them so that the numbers of giraffes and
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elephants are equal = 12 – 5 = 7 Therefore 7 more elephants must join them so that the numbers of giraffes and elephants will be equal . Question 15. Modeling Real Life There are 14 horses on a farm. 7 are brown. The rest are white. How many are white? Answer : Number of Horses = 14 Number of Brown Horses = 7 Number of White Horses = 14 – 7 = 7 Review & Refresh Compare. Question 16. Answer : 21 < 22 Explanation : 21 is lesser than 22 Question 17. Answer : 43 > 34 Explanation : 43 is greater than 34 Lesson 2.5 Count On and Count Back to Subtract Explore and Grow
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Show two ways to find the difference on the number lines. Answer :
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Explanation : Count back to find the difference – start at 13 and count back 9.the arrow ending at 4 shows the difference. Count on to find the difference – Start at 9 and count on to 13. Show and Grow Question 1. Answer : Explanation :
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Count back to find the difference – start at 11 and count back 5.the arrow ending at 6 shows the difference. Question 2. Answer : Explanation : Count back to find the difference – start at 15 and count back 8.the arrow ending at 7 shows the difference. Question 3. Answer : Explanation : Count back to find the difference – start at 9 and count back 6.the arrow ending at 3 shows the difference. Question 4. 16 – 8 = ___ Answer :
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Explanation : Count back to find the difference – start at 16 and count back 8.the arrow ending at 8 shows the difference. Apply and Grow: Practice Question 5. 11 – 8 = ___ Answer : Explanation : Count back to find the difference – start at 11 and count back 8.the arrow ending at 3 shows the difference. Question 6. 10 – 6 = ___ Answer : Explanation : Count back to find the difference – start at 10 and count back 6. The arrow ending at 4 shows the difference. Question 7. 14 – 6 = ___ Answer :
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Explanation : Count back to find the difference – start at 14 and count back 6. The arrow ending at 8 shows the difference. Question 8. 11 – 4 = ___ Answer : Explanation : Count back to find the difference – start at 11 and count back 4. The arrow ending at 7 shows the difference. Question 9. 15 – 9 = ___ Answer : Explanation : Count back to find the difference – start at 15 and count back 9. The arrow ending at 6 shows the difference. Question 10. 16 – 7 = ___ Answer :
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Explanation : Count back to find the difference – start at 16 and count back 7. The arrow ending at 9 shows the difference. Question 11. 14 – 9 = ___ Answer : Explanation : Count back to find the difference – start at 14 and count back 9. The arrow ending at 5 shows the difference. Question 12. 12 – 4 = ___ Answer : Explanation : Count back to find the difference – start at 12 and count back 4. The arrow ending at 8 shows the difference. Question 13. 10 – 7 = ___ Answer :
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Explanation : Count back to find the difference – start at 10 and count back 7. The arrow ending at 3 shows the difference. Question 14. Answer : 8 – 4 = 4 Explanation : Count back to find the difference – start at 8 and count back 4. The arrow ending at 4 shows the difference. Question 15. Answer : 11 – 6 = 5
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Explanation : Count back to find the difference – start at 11 and count back 6. The arrow ending at 5 shows the difference. Question 16. Answer : 18 – 9 = 9 Explanation : Count back to find the difference – start at 18 and count back 9. The arrow ending at 9 shows the difference. Question 17. __ = 9 – 2 Answer : Explanation : Count back to find the difference – start at 9 and count back 2. The arrow ending at 7 shows the difference. Question 18. ___ = 13 – 5 Answer : Explanation :
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Count back to find the difference – start at 13 and count back 5. The arrow ending at 8 shows the difference. Question 19. __ = 14 – 7 Answer : Explanation : Count back to find the difference – start at 14 and count back 7. The arrow ending at 7 shows the difference. Question 20. Structure What strategy did Newton use to solve? How do you know? Answer : 13 – 8 = 5 The Method Used here is Count On to find the difference Explanation : It started at 8 and count on to 13 . Think and Grow: Modeling Real Life There are 13 backpacks in your classroom. 9 are taken. How many backpacks are left?
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Answer : Number of backpacks = 13 Number of backpacks taken = 9 Number of backpacks left = 13 – 9 = 4 Explanation : Count back to find the difference – start at 10 and count back 6. The arrow ending at 4 shows the difference. Show and Grow Question 21. There are 17 trays in a stack. 7 are used. How many trays are left?
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Answer : Number of trays = 17 Number of used trays = 7 Number of trays left =17 – 7 = 10 Therefore 10 trays are not used . Question 22. DIG DEEPER! Newton wants to download some songs. 8 songs are downloaded. There are 6 songs left. How many songs did Newton want to download? Answer : Number of songs downloaded = 8 Number of songs left for downloading = 7 Total Number of songs = 8 + 7 = 15 . Therefore , newton want to download 15 songs . Count On and Count Back to Subtract Homework & Practice 2.5 Question 1. 7 – 5 = __ Answer : Explanation :
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Count back to find the difference – start at 7 and count back 5. The arrow ending at 2 shows the difference. Question 2. 11 – 7 = __ Answer : Explanation : Count back to find the difference – start at 11 and count back 7. The arrow ending at 4 shows the difference. Question 3. 12 – 5 = __ Answer : Explanation : Count back to find the difference – start at 12 and count back 5. The arrow ending at 7 shows the difference. Question 4. 17 – 8 = ___ Answer : Explanation : Count back to find the difference – start at 17 and count back 8. The arrow ending at 9 shows the difference. Question 5. 7 – 2 = ___
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Answer : Explanation : Count back to find the difference – start at 7 and count back 2. The arrow ending at 5 shows the difference. Question 6. 16 – 9 = ___ Answer : Explanation : Count back to find the difference – start at 16 and count back 9. The arrow ending at 5 shows the difference. Question 7. Answer : 9 – 3 = 3 Explanation : Count back to find the difference – start at 9 and count back 3. The arrow ending at 6 shows the difference.
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Question 8. Answer : Explanation : Count back to find the difference – start at 13 and count back 4. The arrow ending at 9 shows the difference. Question 9. Answer : 12 – 6 = 6 Explanation : Count back to find the difference – start at 12 and count back 6. The arrow ending at 6 shows the difference. Question 10. ___ = 10 – 8 Answer : 10 – 8 = 2
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Explanation : Count back to find the difference – start at 10 and count back 8. The arrow ending at 2 shows the difference. Question 11. __ = 8 – 5 Answer : Explanation : Count back to find the difference – start at 11 and count back 5. The arrow ending at 3 shows the difference. Question 12. __ = 12 – 3 Answer : Explanation : Count back to find the difference – start at 12 and count back 3. The arrow ending at 9 shows the difference. Question 13. DIG DEEPER! Complete the squares so the differences on the outside are correct. Answer :
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Explanation : 9 – 4 = 5 7 – 4 = 3 9 – 7 = 2 4 – 4 = 0 All above equations are correct Question 14. Modeling Real Life 15 kids are in line to play four square. 7 of them leave. How many kids are left? Answer : Number of kids = 15 Number of kids left the play = 7 Number of kids left to play = 15 – 7 = 8 Question 15. Modeling Real Life Newton has 6 pieces of macaroni. Descartes has 15. How many fewer pieces does Newton have than Descartes? Answer : Number of pieces of macaroni with Newton = 6
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Number of pieces of macaroni with Descartes = 15 Number of fewer pieces does Newton have than Descartes = 15 – 6 = 9 Therefore , Newton 9 fewer pieces than Descartes . Question 16. Precision Draw more lines to show fourths. Lesson 2.6 Relate Addition and Subtraction Explore and Grow Write an addition equation. Complete the part-part-whole model to match. Write a related subtraction equation. Answer :
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Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 9 and 6 to get 15 is the opposite of 15 minus 9, leaving 6 or the opposite of 15 minus 6, leaving 9 Show and Grow Question 1. 5 + 3 = ___ 8 – 5 = ___ Answer : 5 + 3 = 8 8 – 5 = 3
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Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 5 and 3 to get 8 is the opposite of 8 minus 5, leaving 3 or the opposite of 8 minus 3, leaving 5 Question 2. 4 + 7 = __ 11 – 4 = ___ Answer : 4 + 7 = 11 11 – 4 = 7 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 4 and 7 to get 11 is the opposite of 11 minus 4, leaving 7 or the opposite of 11 minus 7, leaving 4 Question 3. 3 + 9 = ___ 12 – 3 = ___
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Answer : 3 + 9 = 12 12 – 3 = 9 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 3 and 9 to get 12 is the opposite of 12 minus 9, leaving 3 or the opposite of 12 minus 3, leaving 9 Question 4. 8 + 6 = ___ 14 – 8 = ___ Answer : 8 + 6 = 14 14 – 8 = 6 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 8 and 6 to get 14 is the opposite of 14 minus 8, leaving 6 or the opposite of 14 minus 6, leaving 8 Question 5. 7 + 8 = ___ 15 – 7 = ___ Answer : 7 + 8 = 15 15 – 7 = 8 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 7 and 8 to get 15 is the opposite of 15 minus 7, leaving 8 or the opposite of 15 minus 8, leaving 7 Question 6. 9 + 9 = ___ 18 – 9 = ___ Answer : 9 + 9 = 18 18 – 9 = 9 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 9 and 9 to get 18 is the opposite of 18 minus 9, leaving 9 Question 7. 4 + 5 = ___
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9 – 4 = ___ Answer : 4 + 5 = 9 9 – 4 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 4 and 5 to get 9 is the opposite of 9 minus 4, leaving 5 or the opposite of 9 minus 5, leaving 4 Question 8. 5 + 7 = __ 12 – 7 = ___ Answer : 5 + 7 = 12 12 – 7 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 5 and 7 to get 12 is the opposite of 12 minus 7, leaving 5 or the opposite of 12 minus 5, leaving 7 Question 9. 8 + 8 = ___ 16 – 8 = ___ Answer : 8 + 8 = 16 16 – 8 = 8 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 8 and 8 to get 16 is the opposite of 16 minus 8, leaving 8 Question 10. 5 + 2 = ___ 7 – 2 = ___ Answer : 5 + 2 = 7 7 – 2 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 5 and 2 to get 7 is the opposite of 7 minus 2, leaving 5 or the opposite of 7 minus 5, leaving 2
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Question 11. 4 + 6 = ___ 10 – 4 = ___ Answer : 4 + 6 = 10 10 – 4 = 6 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 4 and 6 to get 10 is the opposite of 10 minus 4, leaving 6 or the opposite of 10 minus 6, leaving 4 Question 12. 2 + 6 = ___ 8 – 2 = ___ Answer : 2 + 6 = 8 8 – 2 = 6 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 2 and 6 to get 8 is the opposite of 8 minus 2, leaving 6 or the opposite of 8 minus 6, leaving 2 Question 13. 7 + 7 = ___ 14 – 7 = ___ Answer : 7 + 7 = 14 14 – 7 = 7 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 7 and 7 to get 14 is the opposite of 14 minus 7, leaving 7 Question 14. 6 + 5 = ___ 11 – 6 = ___ Answer : 6 + 5 = 11 11 – 6 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 6 and 5 to get 11 is the opposite of 11 minus 5, leaving 6 or the opposite of 11 minus 6, leaving 5
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Question 15. 9 + 6 = ___ 15 – 6 = __ Answer : 9 + 6 = 15 15 – 6 = 9 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 9 and 6 to get 15 is the opposite of 15 minus 9, leaving 6 or the opposite of 15 minus 6, leaving 9 Question 16. 3 + 8 = ___ 11 – 8 = ___ 11 – 3 = __ Answer : 3 + 8 = 11 11 – 8 = 3 11 – 3 = 8 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 3 and 8 to get 11 is the opposite of 11 minus 8, leaving 3 or the opposite of 11 minus 3, leaving 8 Question 17. 9 + 7 = ___ 16 – 9 = ___ 16 – 7 = ___ Answer : 9 + 7 = 16 16 – 9 = 7 16 – 7 = 9 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 9 and 7 to get 16 is the opposite of 16 minus 9, leaving 7 or the opposite of 16 minus 7, leaving 9 Question 18. 8 + 5 = ___ 13 – 5 = ___ 13 – 8 = ___ Answer : 8 + 5 = 13
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13 – 5 = 8 13 – 8 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 8 and 5 to get 13 is the opposite of 13 minus 5, leaving 8 or the opposite of 13 minus 8, leaving 5 Question 19. Structure Complete the number bond. Write related addition and subtraction equations. Answer : Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 7 and 8 to get 15 is the opposite of 15 minus 7, leaving 8 or the opposite of 15 minus 8, leaving 7 Think and Grow: Modeling Real Life You have 17 glow sticks. You give away 9 of them. How many glow sticks do you have left? Which addition fact can help you subtract?
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Answer : Number of Glow sticks = 17 Number of glow sticks given away = 9 Number of glow sticks left = 17 – 9 = 8 Show and Grow Question 20. A box of sidewalk chalk has 20 pieces. You use 10 of them. How many pieces are not used? Answer : Number of chalks = 20 Number of chalks used = 10 Number of chalks not used = 20 – 10 = 10 Question 21. There are 7 more butterflies than birds. There are 8 birds. How many butterflies are there? Answer : Number of birds = 8 Number of butterflies = 7 more butterflies than birds = 7 + 8 = 15 Question 22. A kitchen drawer has 9 fewer forks than spoons. There are 15 spoons. How many forks are there?
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Answer : Number of spoons = 15 Number of forks = 9 fewer forks than spoons = 15 – 9 = 6 Relate Addition and Subtraction Homework & Practice 2.6 Question 1. 5 + 5 = ___ 10 – 5 = ___ Answer : 5 + 5 = 10 10 – 5 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 5 and 5 to get 10 is the opposite of 10 minus 5, leaving 5 Question 2. 5 + 8 = ___ 13 – 8 = ___
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Answer : 5 + 8 = 13 13 – 8 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 5 and 8 to get 13 is the opposite of 13 minus 5, leaving 8 or the opposite of 13 minus 8, leaving 4 Question 3. 3 + 4 = ___ 7 – 3 = ___ Answer : 3 + 4 = 7 7 – 3 = 4 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 3 and 4 to get 7 is the opposite of 7 minus 3, leaving 4 or the opposite of 7 minus 4, leaving 3 Question 4. 8 + 6 = __ 14 – 6 = ___ Answer : 8 + 6 = 14 14 – 6 = 8 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 8 and 6 to get 14 is the opposite of 14 minus 6, leaving 8 or the opposite of 14 minus 8, leaving 6 Question 5. 6 + 6 = ___
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12 – 6 = ___ Answer : 6 + 6 = 12 12 – 6 = 6 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 6 and 6 to get 12 is the opposite of 12 minus 6, leaving 6 Question 6. 5 + 6 = ___ 11 – 6 = __ 11 – 5 = ___ Answer : 5 + 6 = 11 11 – 6 = 5 11 – 5 = 6 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 5 and 6 to get 11 is the opposite of 11 minus 6, leaving 5 or the opposite of 11 minus 5, leaving 6 Question 7. 9 + 8 = ___ 17 – 9 = ___ 17 – 8 = ___ Answer : 9 + 8 = 17 17 – 9 = 8 17 – 8 = 9 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 9 and 8 to get 17 is the opposite of 17 minus 9, leaving 8 or the opposite of 17 minus 8, leaving 9 Question 8. 7 + 9 = ___ 16 – 9 = ___ 16 – 7 = ___ Answer : 7 + 9 = 16 16 – 9 = 7 16 – 7 = 9 Explanation :
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Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 7 and 9 to get 16 is the opposite of 16 minus 9, leaving 7 or the opposite of 16 minus 7, leaving 9 Question 9. Number Sense Find the sums. Write a related subtraction equation for each addition equation. Answer : 4 + 9 = 13 and 13 – 4 = 9 7 + 5 = 12 and 12 – 7 = 5 Explanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 4 and 9 to get 13 is the opposite of 13 minus 4, leaving 9 Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 7 and 5 to get 12 is the opposite of 12 minus 7, leaving 5 Question 10. Modeling Real Life You have 13 colors of modeling clay. You use 7 of them to make a sculpture. How many colors are not used? Answer : Number of colors with me = 13 Number of colors used = 7 Number of colors not used = 13 – 7 = 6 colors Question 11. Modeling Real Life There are 7 more snails than caterpillars. There are 4 caterpillars. How many snails are there?
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Answer : Number of caterpillars = 4 Number of snails = 7 more snails than caterpillars. = 7 + 4 = 11 Question 12. You have 6 bears. Some are brown. The rest are black. You have more brown bears than black bears. How many brown and black bears can you have? Show how you know: Answer : Option 1 and Option 4 Explanation : Number of bears = 6 brown bears > black bears we cant say the exact number of black or brown bears but as per options we can solve Option 1 – 5 brown and 1 black satisfy the condition. Option 4 – 4 brown and 2 black satisfy the condition. brown bears > black bears Lesson 2.7 Get to 10 to Subtract Explore and Grow How can you use the number line to find the missing number?
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Answer : Explanation : Number of linking arrows represent the subtrahend of above equation = 4 Show and Grow Get to 10 to subtract.
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Question 1. Answer : Explanation : The subtrahend 6 is written as 3 + 3 so that the Minuend 13 is subtracted with 3 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 2. Answer :
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Explanation : The subtrahend 8 is written as 2 + 6 so that the Minuend 12 is subtracted with 2 to get 10. then 6 is subtracted from 10 , we get difference as 4. Question 3. 14 – 8 = ? 10 – __ = __ So, 14 – 8 = ___. Answer : 14 – 8 14- (4 + 4) 10 – 4 = 6 So, 14 – 8 = 6 Explanation : The subtrahend 8 is written as 4 + 4 so that the Minuend 14 is subtracted with 4 to get 10. then 4 is subtracted from 10 , we get difference as 6. Question 4. 16 – 7 = ? 10 – __ = __ So, 16 – 7 = ___ Answer : 16 – 7 16 – (6 + 1 ) 10 – 1= 9 So, 16 – 7 = 9 Explanation : The subtrahend 7 is written as 6 + 1 so that the Minuend 16 is subtracted with 6 to get 10. then 1 is subtracted from 10 , we get difference as 9. Apply and Grow: Practice Get to 10 to subtract. Question 5. 12 – 6 = ?
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10 – __ = __ So, 12 – 6 = __ Answer : 12 – 6 = 12 – (2 + 4 ) 10 – 4 = 6 So, 12 – 6 = 6 Explanation : The subtrahend 6 is written as 2 + 4 so that the Minuend 12 is subtracted with 2 to get 10. then 4 is subtracted from 10 , we get difference as 6. Question 6. 13 – 7 = __ 10 – __ = __ So, 13 – 7 = ___ Answer : 13 – 7 = 13 – (3 + 4) 10 – 4 = 6 So, 13 – 7 = 6 Explanation : The subtrahend 7 is written as 3 + 4 so that the Minuend 13 is subtracted with 3 to get 10. then 4 is subtracted from 10 , we get difference as 6. Question 7. 15 – 9 = ? 10 – __ = ___ So, 15 – 9 = ___ Answer : 15 – 9 = 15 – (5 + 4) 10 – 4 = 6 So, 15 – 9 = 6 Explanation : The subtrahend 9 is written as 5 + 4 so that the Minuend 15 is subtracted with 5 to get 10. then 4 is subtracted from 10 , we get difference as 6. Question 8. 14 – 6 = ? 10 – __ = __ So, 14 – 6 = __ Answer : 14 – 6 = 14 – ( 4 + 2 ) 10 – 2 = 8 So, 14 – 6 = 8
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Explanation : The subtrahend 6 is written as 4 + 2 so that the Minuend 14 is subtracted with 4 to get 10. then 2 is subtracted from 10 , we get difference as 8. Question 9. 13 – 8 = ___ Answer : 13 – 8 = 13 – ( 3 + 5 ) 10 – 5 = 5 So, 13 – 8 = 5 Explanation : The subtrahend 8 is written as 3 + 5 so that the Minuend 13 is subtracted with 3 to get 10. then 5 is subtracted from 10 , we get difference as 5. Question 10. 12 – 4= ___ Answer : 12 – 4 = 12 – ( 2 + 2 ) 10 – 2 = 8 So, 12 – 4 = 8 Explanation : The subtrahend 4 is written as 2 + 2 so that the Minuend 12 is subtracted with 2 to get 10. then 2 is subtracted from 10 , we get difference as 8. Question 11. 17 – 9 = __ Answer : 17 – 9 = 17 – ( 7 + 2 ) 10 – 2 = 8 So, 17 – 9 = 8 Explanation : The subtrahend 9 is written as 7 + 2 so that the Minuend 17 is subtracted with 7 to get 10. then 2 is subtracted from 10 , we get difference as 8. Question 12. 15 – 8 = __ Answer : 15 – 8 = 15 – ( 5 + 3 ) 10 – 3 = 7 So, 15 – 8 = 7 Explanation :
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The subtrahend 8 is written as 5 + 23 so that the Minuend 15 is subtracted with 5 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 13. 12 – 7 = ___ Answer : 12 – 7 = 12 – ( 2 + 5 ) 10 – 5 = 5 So, 12 – 7 = 5 Explanation : The subtrahend 7 is written as 2 + 5 so that the Minuend 12 is subtracted with 2 to get 10. then 5 is subtracted from 10 , we get difference as 5. Question 14. 13 – 4 = ___ Answer : 13 – 4 = 13 – ( 3 + 1 ) 10 – 1 = 9 So, 13 – 4 = 9 Explanation : The subtrahend 4 is written as 3 + 1 so that the Minuend 13 is subtracted with 3 to get 10. then 1 is subtracted from 10 , we get difference as 9. Question 15. __ = 12 – 3 Answer : 12 – 3 = 12 – ( 2 + 1 ) 10 – 1 = 9 So, 12 – 3 = 9 Explanation : The subtrahend 3 is written as 2 + 1 so that the Minuend 12 is subtracted with 2 to get 10. then 1 is subtracted from 10 , we get difference as 9. Question 16. __ = 16 – 7 Answer : 16 – 7 = 16 – ( 6 + 1 ) 10 – 1 = 9 So, 16 – 7 = 9 Explanation : The subtrahend 7 is written as 6 + 1 so that the Minuend 16 is subtracted with 6 to get 10. then 1 is subtracted from 10 , we get difference as 9.
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Question 17. ___ = 14 – 9 Answer : 14 – 9 = 14 – ( 4 + 5 ) 10 – 5 = 5 So, 14 – 9 = 5 Explanation : The subtrahend 9 is written as 4 + 5 so that the Minuend 14 is subtracted with 4 to get 10. then 5 is subtracted from 10 , we get difference as 5. Question 18. __ = 12 – 9 Answer : 12 – 9 = 12 – ( 2 + 7 ) 10 – 7 = 3 So, 12 – 9 = 3 Explanation : The subtrahend 9 is written as 2 + 7 so that the Minuend 12 is subtracted with 2 to get 10. then 7 is subtracted from 10 , we get difference as 3. Question 19. Number Sense How can you get to 10 to find 13 −5? Answer : 13 – 5 = 13 – ( 3 + 2 ) 10 – 2 = 8 So, 13 – 5 = 8 Explanation : The subtrahend 5 is written as 3+ 2 so that the Minuend 13 is subtracted with 3 to get 10. then 2 is subtracted from 10 , we get difference as 8. Think and Grow: Modeling Real Life A first-aid kit has 16 bandages. You use 7 of them. How many bandages are left? Equation:
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Answer : Number of bandages = 16 Number of used bandages = 7 Number of bandages not used = 16 – 7 = 9 Show and Grow Question 20. There are 12 elephants at a watering hole. 5 of them leave. How many elephants are left? Answer : Number of Elephants at watering hole = 12 Number of Elephants left the watering hole = 5 Number of Elephants at Watering hole now = 12 – 5 = 7 Question 21. DIG DEEPER! There are 17 hot-air balloons on the ground. 5 of them take off at 1:00. 4 more take off at 1:30. How many balloons are still on the ground? Explain how you found the number of balloons still on the ground. ______________________________________ ______________________________________ Answer : Number of hot-air balloons on the ground = 17 Number of balloons take off at 1 : 00 = 5 Number of balloons take off at 1 : 30 = 4 Number of balloons left on ground = 17 – 5 – 4 = 8 Get to 10 to Subtract Homework & Practice 2.7
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Get to 10 to subtract Question 1. Answer : Explanation : The subtrahend 5 is written as 2+ 3 so that the Minuend 12 is subtracted with 2 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 2. Answer :
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Explanation : The subtrahend 6 is written as 5+ 1 so that the Minuend 15 is subtracted with 5 to get 10. then 1 is subtracted from 10 , we get difference as 9. Question 3. 16 – 8 = ? 10 – __ = __ So, 16 – 8 = __ Answer : 16 – 8 16 – (6 + 2 ) 10 – 2 = 8 So, 16 – 8 = 8 Explanation : The subtrahend 8 is written as 6+ 2 so that the Minuend 16 is subtracted with 6 to get 10. then 2 is subtracted from 10 , we get difference as 8. Question 4. 13 – 9 = ? 10 – __ = ___ So, 13 – 9 = ___ Answer : 13 – 9 13 – ( 3 + 6 ) 10 – 6 = 4 So, 13 – 9 = 4 Explanation : The subtrahend 9 is written as 3+ 6 so that the Minuend 13 is subtracted with 3 to get 10. then 6 is subtracted from 10 , we get difference as 4. Question 5. 14 – 5 ___ Answer : 14 – 5 14 – (4 + 1 )
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10 – 1 = 9 So, 14 – 5 = 9 Explanation : The subtrahend 5 is written as 4+ 1 so that the Minuend 14 is subtracted with 4 to get 10. then 1 is subtracted from 10 , we get difference as 9. Question 6. 16 – 7 = ___ Answer : 16 – 7 16 – (6 + 1 ) 10 – 1 = 9 So, 16 – 7 = 9 Explanation : The subtrahend 7 is written as 6 + 1 so that the Minuend 16 is subtracted with 6 to get 10. then 1 is subtracted from 10 , we get difference as 9. Question 7. 12 – 8 = __ Answer : 12 – 8 12 – (2 + 6 ) 10 – 6 = 4 So, 12 – 8 = 4 Explanation : The subtrahend 8 is written as 2+ 6 so that the Minuend 12 is subtracted with 2 to get 10. then 6 is subtracted from 10 , we get difference as 4. Question 8. 13 – 8 = __ Answer : 13 – 8 13 – (3 + 5 ) 10 – 5 = 5 So, 13 – 8 = 5 Explanation : The subtrahend 8 is written as 3+ 5 so that the Minuend 13 is subtracted with 3 to get 10. then 5 is subtracted from 10 , we get difference as 5. Question 9. __ = 16 – 9 Answer : 16 – 9 16 – (6 + 3 ) 10 – 3 = 7 So, 16 – 9 = 7
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Explanation : The subtrahend 9 is written as 6+ 3 so that the Minuend 16 is subtracted with 6 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 10. ___ = 14 – 7 Answer : 14 – 7 14 – (4 + 3 ) 10 – 3 = 7 So, 14 – 7 = 7 Explanation : The subtrahend 7 is written as 4+ 3 so that the Minuend 14 is subtracted with 4 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 11. __ = 12 – 4 Answer : 12 – 4 12 – (2 + 2 ) 10 – 2 = 8 So, 12 – 4 = 8 Explanation : The subtrahend 4 is written as 2+ 2 so that the Minuend 12 is subtracted with 2 to get 10. then 2 is subtracted from 10 , we get difference as 8. Question 12. ___ = 18 – 9 Answer : 18 – 9 18 – (8 + 1 ) 10 – 1 = 9 So, 18 – 9 = 9 Explanation : The subtrahend 9 is written as 8+ 1 so that the Minuend 18 is subtracted with 8 to get 10. then 1 is subtracted from 10 , we get difference as 9. Question 13. Number Sense Complete each equation. Answer : 14 – 8 = 10 – 6
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13 – 6 = 10 – 3 15 – 7 = 10 – 2 Question 14. Modeling Real Life Descartes has 18 items to sell at a garage sale. He sells 9 of them. How many items does he have left? Answer : Number items with Descartes = 18 Number of items sold = 9 Number of items left for sale = 18 – 9 = 9 Question 15. DIG DEEPER! There are 12 penguins. 5 of them leave to find food at 5:00. 3 more leave at 5:30. How many penguins are left? Answer : Number of Penguins = 12 Number of penguins left at 5 : 00 = 5 Number of penguins left at 5 : 30 = 3 Remaining Number of penguins = 12 – 5 – 3 = 4 Review & Refresh Question 16. Answer : 19 is a Odd Number . Explanation : An odd number is a number that cannot be divided into two equal groups. Question 17. Answer : 12 is a Even number . Explanation :
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An even number is a number that can be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Lesson 2.8 Practice Addition and Subtraction Explore and Grow You have 6 yellow buttons and 8 red buttons. Write four equations that describe your buttons. Answer : Number of Yellow buttons = 6 Number of Red buttons = 8 Total Number of buttons = 6 + 8 = 8 + 6 = 14 Show and Grow Question 1. 3 + 9 = ___ Answer :
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3 + 9 = 12 Question 2. 8 – 6 = ___ Answer : 2 + 6 = 8 So, 8 – 6 = 2 Question 3. 11 – 4 = ___ Answer : 7 + 4 = 11 So, 11 – 4 = 7 Question 4. 7 + 7 = __ Answer :
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7 + 7 = 14 Question 5. 9 + 8 = ___ Answer : 9 + 8 = 17 8 + 8 = 16 Explanation : 9 + 8 is one more than 8 + 8 or 9 + 8 So, 9 + 8 = 17 Question 6. 10 – 7 = __ Answer : 3 + 7 = 10 So, 10 – 7 = 3 Apply and Grow: Practice Question 7. Answer :
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Explanation : Any number added to 0 gives the number itself. Question 8. Answer : Question 9. Answer :
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Question 10. Answer : Question 11. A nswer : Question 12. Answer :
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Explanation : Any number added to 0 gives the number itself. Question 13. Answer : Question 14. Answer : Question 15. __ = 9 + 1 Answer :
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10 = 9 + 1 Question 16. __ = 4 + 5 Answer : 9 = 4 + 5 Question 17. ___ = 11 – 8 Answer : 3 = 11 – 8
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3 + 8 = 11 So, 11 – 8 = 3 Question 18. ___ = 9 – 5 Answer : 4 = 9 – 5 4 + 5 = 9 So, 9 – 5 = 4 Question 19. __ = 7 + 9 Answer : 16 = 7 + 9 Question 20. ___ = 7 – 1 Answer : 6 = 7 – 1
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1 + 6 = 7 So, 7 – 1 = 6 Question 21. ___ = 8 + 4 Answer : 12 = 8 + 4 Question 22. __ = 14 – 7 Answer : 7 = 14 – 7
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Question 23. Repeated Reasoning Find the missing addend. Explain how you solved. Answer : 8 + _____ = 13 8 + 5 = 13 Explanation : To get 13 what should be added to 8 if we add 5 to 8 we get sum 13 . Think and Grow: Modeling Real Life Show and Grow How many more students have brown hair than blonde hair? Answer : Number of students with brown hair = 14 Number of students with black hair = 9 Number of students with blonde hair = 7 Number of more students have brown hair than blonde hair = 14 – 7 = 7 Equation: 14 – 7 = 7 Therefore 7 students more students have brown hair than blonde hair How many students do not have brown hair? Equation: 9 + 7 Answer : Number of students with out brown hair = ( number of students with blonde and black hair ) = 9 + 7 = 16
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Question 24. How many fewer students have hazel eyes than brown eyes? Answer : Number of students with Blue Color= 8 Number of students with Brown color = 12 Number of students with Hazel Color = 4 Number of students fewer have hazel eyes than brown eyes = 12 – 4 = 8 DIG DEEPER! How many students do not have brown eyes? Answer : Number of students do not have brown eyes = students with blue color and Hazel color = 8 + 4 = 12 Practice Addition and Subtraction Homework & Practice 2.8 Question 1. 3 + 5 = ___ Answer : 3 + 5 = 8 Question 2. 5 + 7 = ___ Answer : 5 + 7 2 + 3 + 7 = 2 + 10 = 12 Explanation : To make addend 7 as 10 we should add 3 to the 7 so write addend 5 as 2 + 3 . then add 3 + 7 we get , 10 and then later add 2 to 10 we get sum , 12 .
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Question 3. 13 – 6 = ___ Answer : Explanation : The subtrahend 6 is written as 3+ 3 so that the Minuend 13 is subtracted with 3 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 4. 12 – 8 = ___ Answer : Explanation : The subtrahend 8 is written as 2+ 6 so that the Minuend 12 is subtracted with 2 to get 10. then 6 is subtracted from 10 , we get difference as 4. Question 5. 6 + 0 = __ Answer : 6 + 0 = 6 Explanation : Any number added to 0 gives the sum the number itself . Question 6. 15 – 8 = ___ Answer :
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Explanation : The subtrahend 8 is written as 5+ 3 so that the Minuend 15 is subtracted with 5 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 7. Answer : Question 8.
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Answer : Question 9. Answer : Question 10. Answer : Explanation : Any number subtracted with 1 gives the difference of previous number . Question 11. ___ = 5 + 5
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Answer : 5 + 5 = 10 Question 12. ___ = 3 – 0 Answer : 3 – 0 = 3 Explanation : Any number subtracted with 0 gives the difference the number itself . Question 13. Number Sense Which expressions have a sum or difference that is greater than 10? Question 14. Modeling Real Life How many fewer students choose a sandwich than pizza? Answer : Number of students chooses sandwich = 9 Number of students chooses pasta = 4 Number of students chooses pizza = 15 Number of fewer students chooses a sandwich than pizza = 15 – 9 = 4 Therefore 4 fewer students chooses a sandwich than pizza . DIG DEEPER! How many students do not choose pizza? Answer : Number of students do not choose pizza = number of students who chooses
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sandwich and pasta = 9 + 4 = 13 Therefore, Number of students do not choose pizza = 13 Question 15. Circle groups of 4. Write a repeated addition equation to match. Answer : Explanation : Number of birds = 16 Number of groups = 4 Number of birds in each group = 16 ÷ 4 = 4 Therefore, 4 + 4 + 4 + 4 = 16 each group contains 4 birds . Lesson 2.9 Problem Solving: Addition and Subtraction Explore and Grow Model the story. You have 5 puzzle pieces. Your friend has 9. How many more pieces does your friend have than you? Answer : Number of puzzles with me = 5
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Number of puzzles with my friend = 9 Number of more pieces does my friend have than me = 9 – 5 = 4 Show and Grow Question 1. You have 7 more keychains than your friend. You have 15 keychains. How many keychains does your friend have? Answer : Number of key chains with me = 15 Number of key chains with my friend = You have 7 more keychains than your friend = 15 -7 = 8 Explanation : Apply and Grow: Practice Question 2. Some friends are at a community pool. 7 more join them. Now there are 12. How many friends were there to start?
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Answer : Number of friends at community pool = x Number of friends joined = 7 Number of friends now at pool = 15 = x + 7 x + 7 = 15 x = 15 – 7 = 8 Therefore, Number of friends at community pool = 8 Question 3. Some friends are playing miniature golf. 8 of them leave. There are 6 left. How many friends were there to start? Answer : Number of friends playing golf = x Number of friends left = 8 Number of friends now playing golf = 6 Number of friends at the start = x- 8 = 6 x= 8+ 6 = 14 Therefore, 14 friends were there to start. Question 4. YOU BE THE TEACHER Newton has 5 fewer fish than Descartes. Newton has 8 fish. Your friend uses a bar model to find how many fish Descartes has. Is your friend correct? Explain.
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Answer : Yes he is correct Explanation : Number of fishes with Newton = 8 Number of fishes with Descartes = Newton has 5 fewer fish than Descartes. that means Descartes 5 more fishes than Newton = 8 + 5 = 13 Think and Grow: Modeling Real Life 15 kids play at a park. 6 of them leave. 9 more kids come to the park. How many kids are at the park now? Answer : Number of kids playing in the park = 15 Number of kids left the park = 6 Number of kids remaining in the park = 15 – 6 = 9 Number of kids joined the park = 9 Total number kids now in the park = 9 + 9 = 18 Question 5. You have 13 baseball cards. You give 5 away. Then you get 4 more. How many baseball cards do you have now?
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Answer : Number of base balls cards with me = 13 Number of base balls cards given away = 5 Number of base balls cards remaining with me now = 13 – 5 = 8 Number of base balls cards added = 4 Total Number of base balls cards now = 8 + 4 = 12 Question 6. DIG DEEPER! There are 7 adult lions and some cubs in a pride. The pride has 13 lions in all. 3 more cubs are born. How many cubs are in the pride now? Explain how you solved this problem. Answer : Number of Adults lions = 7 Number of Lions = 13 Number of cubs are more than 3 Number of cubs = 13 – 7 = 6 Therefore, Number of cubs in the pride = 6 Problem Solving: Addition and Subtraction Homework & Practice 2.9 Question 1. You have 3 more movies than your friend. You have 10 movies. Your friend has 5 video games. How many movies does your friend have?
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Answer : Number of movies with me = 10 You have 3 more movies than your friend Number of movies with my friend = 10 – 3 = 7 Question 2. Some friends are at a skating rink. 6 more join them. Now there are 11. How many friends were there to start? Answer : Number of Friends at skating rink = x Number of friends joined = 6 Number of Friends now at skating rink = 11 Number of Friends at skating rink = 11 – 6 = 5 Therefore, 5 friends were there to start Question 3. Structure There are 9 bananas in a bunch. A monkey eats some. There are 5 bananas left. Which picture shows how many bananas the monkey ate?
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Answer : Number of Bananas = 9 Number of Bananas left = 5 Number of Bananas eaten by Monkey = 9 – 5 = 4 Picture 4 shows 4 Bananas . Question 4. Modeling Real Life You make 4 snow angels and Newton makes 5. Descartes makes 3 more snow angels. How many snow angels are there in all? Answer : Number of snow angels made by me = 4 Number of Snow angels made by Newton = 5 Number of Snow angels made by Descartes = 3 Total Number of Snow angels = 4 + 5 + 3 = 12 Question 5. Modeling Real Life Newton has 9 glitter pens. Descartes has 2 fewer than Newton. How many glitter pens do they have in all? Answer : Number of Glitter pens with Newton= 9 Number of Glitter pens with Descartes = Descartes has 2 fewer than Newton = 9
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– 2 = 7 Number of Glitter pens in all = 9 + 7 = 16 Review & Refresh Question 6. Which two shapes combine to make the shape on the left? Answer : Triangle and semi-circle combine to make the above shape . Fluency and Strategies within 20 Performance Task Question 1. You and your friend check out books from the library as shown in the table. a. You have one more adventure book than science books. How many books do you have in all? Answer : Number of History books with me = 5 Number of science books with me = 7 Number of Adventure books with me = one more adventure books than science books = 7 + 1 = 8 Total Number of Books with me N= science + History + Adventure = 7 + 5 + 8 = 20 b. You and your friend have the same number of books. Your friend has more science books than history books. Your friend has an even number of adventure books. How many science books and adventure books does your friend have? Answer : Total Number of books with me = Total Number of books with my friend = 20 Science books > History books Number of history books with my Friend = 8 Number of Science books with my friend let it be = 10
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Number of books remaining = 20 – 8 – 10 = 2 Number of Adventure books = 2 even number So, all the given conditions are satisfied . c. How many books do you and your friend have in all that are not history books? Answer : Number of History books with me and my friend = 5 + 8 = 13 Number of Books with me and my friend = 20 + 20 = 40 Number of books in all that are not history books = 40 – 13 = 27 Books. d. You return 3 books on Monday and 6 books on Thursday. How many books do you have left? Answer : Number of books with me = 20 Number of books returned on Monday = 3 Number of books returned on Thrusday = 6 Number of books left now = 20 – 3 – 6 = 20 – 9 = 11 Books. Fluency and Strategies within 20 Activity To Play: Place your cube on 0. Roll a die to see how many spaces to move. Write an equation that matches on the Joey Jump Add or Subtract Recording Sheet.
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Continue until you reach the food and then return to the pouch. Fluency and Strategies within 20 Chapter Practice 2.1 Add in Any Order Question 1. Answer :
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Explanation : Changing the Order of addends doesn’t change the sum. The Expressions 7 + 2 and 2 + 7 have the sum 9 . Question 2. Number Sense Complete each equation. Answer : Explanation : Changing the Order of addends doesn’t change the sum. The Expression a + b = b +a = c ,the sum . 2.2 Use Doubles Find the sum. Write the double you used. Question 3. 6 + 5 = ___ ___ + ___ = ___ Answer : 6 + 5 = 11 5 + 5 = 10 Explanation : Doubles plus 1 6 + 5 is equal to 5 + 5 and 1 more. Question 4. 8 +9 = ___
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___ + ___ = ___ Answer : 8 + 9 = 17 8 + 8 = 16 Explanation : Doubles plus 1 8 + 9 is equal to 8 + 8 and 1 more. Question 5. Answer : Explanation : Changing the Order of addends doesn’t change the sum. The Expressions 3 + 2 and 2 + 3 have the sum 5 . Question 6. Answer :
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Explanation : Changing the Order of addends doesn’t change the sum. The Expressions 7 + 8 and 8 + 7 have the sum 15 . 2.3 Add Three Numbers Question 7. Answer : Explanation : Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 8, 0 give the sum 8 and then adding the another addend 6 to the sum 8. Gives the sum 14.
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Question 8. Answer : Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 1, 3 give the sum 4 and then adding the another addend 9 to the sum 4. Gives the sum 13. Question 9. Answer : Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 8, 8 give the sum 16
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and then adding the another addend 4 to the sum 16. Gives the sum 20. Question 10. 4 + 8 + 8 = ___ Answer : Explanation: Addends are represented in circle and Sum is represented in square. First adding two addends 8, 8 give the sum 16 and then adding the another addend 4 to the sum 16. Gives the sum 20. Question 10. Structure Write the missing addends. Answer :
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2.4 Make a ten to Add Make a 10 to add Question 11. Answer : Explanation : To make addend 9 as 10 we should add 1 to the 9 so write addend 8 as 1 + 7 . then add 9 + 1 we get , 10 and then later add 7 to 10 we get sum , 17 .
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Question 12. Answer : Explanation : To make addend 7 as 10 we should add 3 to the 7 so write addend 6 as 3 + 3 . then add 7 + 3 we get , 10 and then later add 3 to 10 we get sum , 13 . Question 13. 9 + 6 = ___
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Answer : Explanation : To make addend 9 as 10 we should add 1 to the 9 so write addend 6 as 1 + 5 . then add 9 + 1 we get , 10 and then later add 5 to 10 we get sum , 15 . Question 14. 4 + 7 = ___ Answer : Explanation : To make addend 4 as 10 we should add 6 to the 4 so write addend 7 as 6 + 1 . then add 4 + 6 we get , 10 and then later add 1 to 10 we get sum , 11 . 2.5 Count On and Count Back to Subtract
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Question 15. 12 – 8 = __ Answer : Start at 12 and count back to 8 . The arrow ends at 4 showing the difference . So, 12 – 8 = 4 Start at 8 count on to 12. So, 12 – 8 = 4 Question 16. 14 – 5 = ___ Answer : Start at 14 and count back to 5 . The arrow ends at 9 showing the difference . So, 14 – 5 = 9 Start at 5 count on to 14. So, 14 – 5 = 9
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Question 17. 17 – 9 = ___ Answer : Start at 17 and count back to 9 . The arrow ends at 8 showing the difference . So, 17 – 9 = 8 Start at 9 count on to 17. So, 17 – 9 = 8 2.6 Relate Addition and Subtraction Question 18. 7 + 6 = __ 13 – 6 = ___ 13 – 7 = ___ Answer : 7 + 6 = 13 13 – 6 = 7 13 – 7 = 6
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E xplanation : Addition and subtraction are inverse operations because one operation can “undo” the other operation. Adding 7 and 6 to get 13 is the opposite of 13 minus 7, leaving 6 or the opposite of 13 minus 6, leaving 7. 2.7 Get to 10 to Subtract Get to 10 to subtract Question 19. Answer : Explanation : The subtrahend 4 is written as 2+ 2 so that the Minuend 12 is subtracted with 2 to get 10. then 2 is subtracted from 10 , we get difference as 8.
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Question 20. Answer : Explanation : The subtrahend 8 is written as 5 + 3 so that the Minuend 15 is subtracted with 5 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 21. 16 – 9 = ___ Answer : 16 – 9 = 16 – ( 6 + 3 ) 10 – 3 = 7 So, 16 – 9 = 7 Explanation : The subtrahend 9 is written as 6+ 3 so that the Minuend 16 is subtracted with 6 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 22. 14 – 7 = ___ Answer : 14 – 7 = 14 – ( 4 + 3 ) 10 – 3 = 7
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So, 14 – 7 = 7 Explanation : The subtrahend 7 is written as 4 + 3 so that the Minuend 14 is subtracted with 4 to get 10. then 3 is subtracted from 10 , we get difference as 7. 2.8 Practice Addition and Subtraction Question 23. 8 + 3 = ___ Answer : 8 + 3 = 11 Question 24. 13 – 7 = ___ Answer : 12 – 4 = 12 – ( 2 + 2 ) 10 – 2 = 8 So, 12 – 4 = 8 Explanation : The subtrahend 5 is written as 2+ 3 so that the Minuend 12 is subtracted with 2 to get 10. then 3 is subtracted from 10 , we get difference as 7. Question 25. Answer :
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Question 26. Answer : Question 27. Answer : Question 28.
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Answer : Question 29. __ = 5 + 8 Answer : 5 + 8 3 + 2 + 8 3 + 10 = 13 So, 5 + 8 = 13 Explanation : To make addend 8 as 10 we should add 2 to the 8 so write addend 5 as 3 + 2 . then add 2 + 8 we get , 10 and then later add 3 to 10 we get sum , 13 . Question 30. __ = 12 – 5 Answer : 12 – 5 = 12 – ( 2 + 3 ) 10 – 3 = 7 So, 12 – 5 = 7 Explanation : The subtrahend 5 is written as 2+ 3 so that the Minuend 12 is subtracted with 2 to get 10. then 3 is subtracted from 10 , we get difference as 7. 2.9 Problem Solving: Addition and Subtraction Question 31. Some friends are playing laser tag. 4 of them leave. There are 8 left. How many friends were there to start?
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Answer : Number of friends playing = x Number of friends left = 4 Number of friends left = 8 = x-4 x= 8 + 4 = 12
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