Mini-Unit Plan-
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Indiana University Of Pennsylvania *
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Mathematics
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Feb 20, 2024
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Ms. Kalkbrenner 2
nd
Grade Adding Numbers within 1,000
Larson R. Boswell L. & Big Ideas Learning (Firm). (2019).
Big ideas math grade 2
(Teaching). Big Ideas Learning.
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I.
Rationale
The purpose of this unit is to build knowledge on a second-grade classroom, with adding numbers within 1,000. The students will develop fluency in adding two and three-digit numbers. The students will be able to apply addition skills to real-life problem situations. This topic is crucial for second graders, because adding numbers within 1,000 is foundation for the future of learning multiplication, division, and algebra. Also, it is essential to know basic addition skills with everyday activities, such as calculating money, measuring, and telling time. Lastly, the students will enhance number sense while working with larger numbers, because it builds a deeper understanding of number relationships. This unit incorporates many key elements from mathematical learning theories. One is constructivism, by building within their existing understanding and experiences. Such as using interactive tools such as base-10 blocks. It also incorporates cognitivism, which is problem-solving, including place-value, and visual aids. This unit plan is centered to be designed within understanding through student-focused strategies such as differentiated instruction, where activities will be tailored to cater to
students’ diverse abilities. It also applies to critical thinking, where addition involves understanding patterns, relationships, and logical reasoning. The purpose for society, is workforce readiness, there is employment, such as finance, engineering, etc., where
these require strong math skills to perform their jobs successfully. The principal reason is to equip the students with essential life skills. The ability to add within 1,000 is a practical skill that throughout the students’ lives they will need to use.
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II.
Lesson Plan Outlines Day 1: Lesson: Add 10 and 100: In this engaging math lesson, the students can delve into the realm of addition when they are examining the processes of adding multiples of 10 and 100 to both two-digit and three-digit numbers. Within prerequisite knowledge, the students should know basic addition and should be familiar with place value. The primary objective of this lesson is for the students will understand the concept of adding multiples of 10 and 100 to two-digit and three-digit numbers. These align with the Pennsylvania Core Standard CC.2.2.2.A.1.
To start, this lesson will start with a recap of basic addition, through interactive whiteboard presentations. Following this, the lesson body will come in, where the students will have the manipulatives of number cards and base-10 blocks to aid their understanding. The main segment of this lesson involves independent practice, where the students will practice more addition problems through their peers and others' addition challenges. It will conclude with an exit ticket
to check students understanding, as well as an informal assessment of observing, and a formal assessment of a quiz. Throughout this lesson, the students will be assessed through many different methods to ensure a grasp of this topic. Day 2: Lesson: Use a Number Line to Add Three-Digit Numbers: In this math lesson, the students are going to utilize the visual support of a number line within adding three-digit numbers. The students should already have a fundamental understanding of place value in the hundreds place and identify and interpret numbers on a number line. The primary objective of this lesson is, the
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students will learn to use a number line as a visual tool to add three-digit numbers accurately. This corresponds with the Pennsylvania Core Standard CC.2.2.3.A.3. This lesson initiates with an introduction to the significance of a number line, that emphasizes its role in simplifying the addition of larger numbers for younger students. Through the lesson body, each student will receive a number line, and work collaboratively to comprehend the practical application of this tool. Within the independent practice, students will tackle their own addition problems with the number lines. This lesson includes reviewing pivotal concepts and underscoring the benefits of integrating a number line into three-digit addition. The students will be able to assess understanding through diverse methods, ensuring a comprehensive mastery of the subject matter. Day 3: Use Models to Add Three-Digit Numbers: This lesson is focused on using models, specifically base-10 blocks to enhance the student's ability to add three-digit numbers. Students are expected to have a strong foundation in basic addition, understand the addition of two-digit numbers, and have a grasp of place values up to 100. The primary objective of this lesson is to proficiency in adding three-digit numbers. The students utilize base-10 blocks and whiteboards to work through crafted problems, it is emphasized the breakdown of hundreds, tens, and ones. Some questions guide the students through the process, including physical and drawn representations. In the closure, the lesson closes with an
exit ticket that evaluates the student's reflection on the challenges, understanding, and application of base-10 blocks in three-digit addition. Lastly, there is an informal and
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formal assessment, that covers practical applications along with the lesson. This lesson is not only to grasp the mechanics of three-digit addition, but to also comprehend the underlying concepts, and a deeper understanding of mathematical principles. Day 4: Use Partial Sums to Add Three-Digit Numbers: The students are introduced to the concept of using partial sums in this lesson plan. The prerequisite knowledge includes a solid understanding of basic addition, more particularly two-digit addition, and the ability to count by tens and ones. The primary objective for the students is to demonstrate proficiency in adding three-digit numbers using the partial sums method. This lesson guides the students through the steps of adding hundreds, tens, and ones while emphasizing the importance of zeros and regrouping. There are word problems as well as number problems that encourage the students to construct a partial sum chart. Through independent practice, the students are challenged to create and solve their own three-digit addition problems using the partial sums method. There was also an exit ticket that assessed students' comprehension and reflection on challenges they faced during the lesson. Within differentiation, there were formal and informal assessments, which the formal was a quiz, that evaluated key concepts that were covered in the lesson. Day 5: Addition within 1,000
In this lesson, the prerequisite knowledge emphasizes students' proficiency in addition within 100 and understanding place value for two and three-digit numbers.
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The objective is for students to practice addition within 1,000 using their place value understanding. This is aligned with the CC.2.1.2.B.3
Pennsylvania Core Standard. This lesson incorporates hands-on learning with base-10 blocks and whiteboards, this encourages the students to visualize and engage with the concepts. The lesson addresses trades and regrouping, with students being able to get the opportunity for both independent and collaborative activities. The closure of this lesson is an exit ticket that has questions for the students to reflect on the lesson, and to comprehend what they did in the lesson. The evaluation of the lesson includes a formal and informal assessment, the formal assessment includes a 4-question quiz. Overall, this lesson is designed to accommodate different learning needs through flexible grouping
and targeted instruction.
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A.
HEADING: Ms. Kalkbrenner 2
nd
Grade 45 Minutes Using Models to Add Three-Digit Numbers
B.
PREREQUISITE KNOWLEDGE: The students should have a strong grasp of basic addition. They should also possess a fundamental understanding of the addition of two-digit numbers, lastly, to be beneficial, the students should understand place value up to 100. C.
STUDENT OBJECTIVE(S): The students will be able to proficiently add three-digit numbers using visual models, specifically utilizing base-10 blocks. Standards: CC.2.2.3.A.3 – Fluent addition and subtraction within 1,000 using strategies and algorithms based on place value. D.
LIST OF MATERIALS/RESOURCES: For students: For teachers: -
Base-10 Blocks -
White Boards, markers, and erasers
-Smart Board V.
PROCEDURES: A)
Initiation/Motivation (3-5 minutes)- 1.
The students will stay seated at their desks. 2.
The teacher will start the lesson with the following word problem:
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3.
Lauren has 458 apples; her mom gave her 327 more apples. How many apples does Lauren have now? 4.
The teacher will then ask the following questions: a.
How can we use models to make adding three-digit numbers easier? b.
Using your base-10 models, how many hundreds do we need? (7) c.
How many tens blocks do we need to pull out? (7) d.
How many one-blocks do we need to pull out? (16) e.
Looking at that last number with the ones, can you make ten ones to make a trade for a ten block? (Yes) f.
So, how many ten blocks do we have now? (8)
g.
Adding up all your blocks, what is your answer? (786) B)
Lesson Body – (30 minutes) 1.
The teacher will ask a few questions as an introduction to the lesson. a.
Why do you think we are using base-10 blocks to learn about three-digit addition? b.
How do base-10 blocks visually represent hundreds, tens, and ones? 2.
Each student will receive a whiteboard, eraser, and markers, and they should already have base-ten blocks. 3.
The teacher will write down a problem on the board, the students will copy the number problem down. h.
Taylor has 692 cows on her farm, and her sister also has a farm, and needs to transport 147 cows to Taylor’s farm, how many cows does Taylor have now?
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i.
The teacher will let the students know, as well as demonstrate on the board, that the students need to draw 3 different columns one place for hundreds, another for tens, and the last one for ones. These will be the two models they use to answer the problems. Explain that in that chart the students will draw the base-10 blocks they will use for those numbers. Also, let them know to draw another chart just like that but below the base-10, write the addition problem in there. j.
Questions the teacher will ask:
1.
With your first chart, using your physical base-10 blocks as well, how many hundred blocks will you draw in that column? (7) 2.
In the second column, tens, how many ten blocks will you draw in there? (13) 3.
In your last column, which are the ones, how many blocks will you draw in there? (9)
4.
Now, I want you to look over your blocks in front of you as well as your drawings, can you make any trades? (Yes, tens to hundreds) 5.
With ten, ten blocks, we can trade it for a hundred blocks, how many hundred blocks do you have now? (8) 6.
How many ten blocks do you have now? (3)
k.
Now let’s turn over to our written addition problem chart. 7.
What is 2+7? (9)
8.
Meaning how many ones? (9) 9.
What is 9+4 (13)
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10. Meaning how many tens, remembering we must carry a one? (3) l.
Remind the students here that the trade is where they are carrying the one in the actual problem. 11. What is 6+1 and another 1? (8)
12. So, what is your answer? (839) m.
Look over your blocks, and make sure that those blocks are what you have according to the addition problem. n.
Julia has 553 soccer balls, she needs to add on 250 more, if she adds on more, how many will she have all together then? o.
Make sure the students redraw both of their charts. 1.
In your hundred’s column, how many hundreds do we have? (7)
2.
In your ten’s column, how many tens do we have? (10)
3.
In your one’s column, how many ones do we have? (3) 4.
Now, looking back at our blocks, can we make any trades? (Yes, tens for hundreds.) 5.
Now, how many hundreds and tens do we have? (8 and 0) p.
Now let’s move over to your number problem.
1.
What is 3+0? (3) 2.
What is 5+5? (10) 3.
We carried the one over so what is 5+2+1? (8) 4.
What is our answer altogether? (803)
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q.
Your elementary school wants to collect canned goods. They collected 600 cans of soup, and 386 cans of vegetables, how many canned goods did your elementary school obtain? 1.
Draw your two models. 2.
How many hundreds will we use? (9) 3.
How many tens will we use? (8)
4.
How many ones will we use? (6) 5.
Do we need to make any trades? (No) 6.
What is 6+3? (9)
7.
What is 8+0? (8) 8.
What is 6+0? (6) 9.
What is our answer? (986) r.
A charity needs to have 700 volunteers. 432 people signed up on Friday, and 193 people signed up on Saturday. Are there enough volunteers? Explain, why
yes or no. 1.
Let’s add this problem like we have been. 2.
How many hundred blocks do we need? (5) 3.
How many ten blocks do we need? (12) 4.
How many one-blocks do we need? (5) 5.
Can we make a trade on anything? (Yes, tens for hundreds) 6.
How many hundreds do we have now? (6)
7.
How many tens do we have now? (2)
8.
What’s 4+1+1? (6)
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9.
What’s 3+9? (12) 10. What’s 3+2? (5) 11. What is our answer? (625) 12. Do we have enough volunteers? (No) s.
Here is an addition problem, that you need fill in to regroup to add. 255+32___. 1.
Use your blocks to create the problem with what we have right now, then add in as we go. 2.
Now, what does regrouping mean again? (A trade) 3.
So, with this problem we see a blank in the one’s place, what would we trade these for? (tens) 4.
What number could we add with 3? (9,8,7) 5.
Let’s add 9, what’s 9+3? (12) 6.
Now, with 13 ones, we can make a trade for a ten, after we do that how many blocks do, we have left? (3)
7.
How many tens blocks do we have now? (8)
8.
Do the hundred blocks stay the same? (yes) Which is? (5)
9.
So, our answer will be? (582)
t.
To get independent practice, the students will discuss their approach to solving
problems with their base-10 blocks. The students will create their own problems in small groups and work on them together. They will also, reflect and ask each other to explain the importance of using base-10 blocks during
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independent practice. Explain how it helps them visualize the addition process. Methods of Further Differentiating Instruction –
For differentiating instruction, the students will be allowed to use alternative materials including hands-on manipulatives as well as drawing representations. During the independent practice, the students will be provided with additional guidance and support for those who need extra assistance. Also, the students will be in groups by their tables that are mixed ability for collaborative problem-solving and which promote
peer learning. C)
Lesson Closure – (10 minutes) 1.
The students will now be handed out an exit ticket, that they will complete over the next 10 minutes. The following questions will be provided on the exit ticket. a.
Share what you struggled with the most in today’s lesson for you and explain how you were able to get through it. b.
Describe how using base-10 blocks deepened your understanding of three-
digit addition. c.
Tell me the importance of place value in the context of adding three-digit numbers, referring to today’s activities. d.
Highlight one concept from today’s lesson that you found beneficial. e.
Imagine you were teaching your peers about what you learned about using base-10 blocks to add three-digit numbers. What key points would you emphasize? IV.
EVALUATION:
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A)
Informal Assessment: The students will be informally assessed during their whiteboard time as well as their independent time. The students will be observed on how they have utilized the base-10 blocks in front of them and drawing representations of them. They will be asked to create their problems and discuss the importance of the base-10 blocks with their peers. B)
Formal Assessment: The students will be participating in a 5-question quiz that includes a
word problem, a number problem, short answer problems, and applying questions. Each question will be 2 points, so the total of the quiz is 10 points.
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Name: /10 Date: Each question is worth 2 points. The total of the quiz is 10 points.
1.
Demonstrate the model for 328 + 147 using base-10 blocks. (
2 points
)
2.
Elizabeth has 426 dolls in her playhouse, her mom bought her 102 more dolls for Christmas, how many dolls does she have in her playhouse now? (Show two columns of your base-10 blocks and your number sentence) (
2 points
)
3.
Outline the process of using base-10 blocks to model three-digit addition. (
2 points
)
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4.
Explain when and why regrouping is necessary. (
2 points
) 5.
Elaborate on how place value influences three-digit addition. (
2 points
)
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Answer Key: Name: /10 Date: Each question is worth 2 points. The total of the quiz is 10 points.
1.
Demonstrate the model for 328 + 147 using base-10 blocks. (
2 points
)
2.
Elizabeth has 426 dolls in her playhouse, her mom bought her 102 more dolls for Christmas, how many dolls does she have in her playhouse now? (Show two columns of your base-10 blocks and your number sentence) (
2 points
)
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3.
Outline the process of using base-10 blocks to model three-digit addition. (
2 points
)
We can make it easier by starting with the 100s, we can draw and pull how many blocks are needed in the 100s column. Then, we can move to the 10s and place our blocks there, and lastly, move on to the ones. After doing all of that, we can see if any of the totals exceed 9, if so, we can
regroup and make a trade into another place value. 4.
Explain when and why regrouping is necessary. (
2 points
) Regrouping is necessary when the digit sum is higher than 9. It is essential to represent and calculate that one place-value column. 5.
Elaborate on how place value influences three-digit addition. (
2 points
) The position of the digit determines its values. The place value column is extremely important in the addition process.
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A. HEADING: Ms. Kalkbrenner 2
nd
Grade 45 Minutes Use Partial Sums to Add Three-Digit Numbers B.
PREREQUISITE KNOWLEDGE: The students should have a solid grasp of basic addition, more particularly two-digit addition. Also, they should be able to count by tens and ones, as their understanding on that topic will serve as a foundation for learning partial sums. C.
STUDENT OBJECTIVE(S): The students will be to demonstrate the ability to add three-digit numbers using partial sums. Standards: D.
LIST OF MATERIALS/RESOURCES: For students: For teachers: -
Number cards (0-9) -
Pencils -
White Boards, markers, and erasers
-Smart Board VI.
PROCEDURES: A)
Initiation/Motivation (3-5 minutes)- 5.
The students will stay seated at their desks. 6.
The teacher will explain that today we are going to look at partial sums.
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7.
We will start with a word problem, that the students will be guided through. 8.
The teacher will start the lesson with the following word problem: 9.
Andrea has 424 candies in her bookbag, her friend bought her 267 more candies, how many candies does she have now? 10. The teacher will then ask the following questions: u.
Starting in the hundred’s column, what are the two numbers we will add together? (4 and 2) v.
Since 4 and 2 are in the hundreds column how many zeros do we add to each number? (Two…. 400+200) w.
Now let’s move to the ten columns, what are the two numbers we will add together? (2 and 6) x.
Since 2 and 6 are in the ten columns, how many zeros will we add to those numbers? (1… 20+60) y.
Lastly, let’s move on to the one’s column, what are the two numbers that we will add? (4 and 7) z.
Do we need any zeros added? (No)
aa.
But, if we have 4+7, it is a two-digit number, 11, so which column do we put the 1 in? (ones) bb.
Which column do we put the one in? (tens) cc.
If we have 400+200, 20+60, and 4+7, what is our answer? (691)
B.
Lesson Body – (30 minutes)
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4.
The teacher will draw a chart on the board, that includes hundreds, tens, and ones,
on the top, with the numbers beneath, then on the left side, where the solutions will go, with hundreds, tens, ones, and sum. 5.
The teacher will then write down a problem on the board, the students will copy the number problem down. C.
Taylor has 234 turkeys on her farm, she wants to add more, her mother told her that she would get her 368 more turkeys to add to her farm, how many turkeys would she have now? D.
Questions the teacher will ask:
13. Let’s start with our hundreds place, what two numbers are we adding together? (2 and 3) 14. Now, with those two numbers being in the hundreds place, how many zeros would we add onto the back of the 2 and 3? (2 zeros, 200, and 300) 15. Moving onto the tens place, what two numbers are we adding together? (3 and 6)
16. Knowing that the 3 and the 6 are in the tens place, how many zeros do we need to add to those two numbers? (one zero, 30 and 60)
17. Lastly, in the one’s place, what two numbers are we adding? (4 and 8)
18. Looking at our one’s place, when we add 4+8, it is a double-digit number, so the answer is 12, where do we put the 1? (tens place) 19. Now, what column would we put the 2? (one’s place) E.
Now, instead of a word problem, write the column on the board and put the problem, 593+184. Have the students tell you where to place each number.
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F.
Now we will ask the following questions: 1.
Let’s start with 593, which column do we put the 5 in? (hundreds) 2.
What column do we put the 9 in? (tens) 3.
What column do we put the 3 in? (ones) 4.
Now looking at 184, which column do we put the 1 in? (hundreds)
5.
What column do we put the 8 in? (tens) 6.
What column do we put the 4 in? (ones) 7.
Now let’s find our partial sums. Which two numbers are we adding together in the hundreds place? (5 and 1) 8.
How many zeros do we need to add to 5 and 1 for being in the hundreds place? (two zeros, 500 and 100)
9.
Which two numbers are we adding in the tens place? (9 and 8)
10. Being in the tens place, how many zeros do we need to add? (1 zero, 90 and 80)
11. Lastly, what two numbers are we adding in the ones place? (4 and 3) 12. Let’s go back to our tens place, it exceeds over 9, so what does that mean we have to do again? (regroup, so carry a 1)
13. The answer being 17, where do we put the 7? (tens place) 14. Where do we put the 1? (hundreds place) 15. Now we have, 500+100, 90+80, and 3+4, what is our answer? (777)
G.
Let’s try a problem without our columns. H.
The problem is 532+129. 1.
What is the value of the hundreds place in the number 532? (5 hundreds)
2.
What is the value of the tens place in the number 532? (30 tens)
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3.
What is the value of the ones place in the number 532? (2 ones)
4.
What is the value of the hundreds place in the number 129? (One hundred)
5.
What is the value of the tens place in the number 129? (20 tens)
6.
What is the value of the ones place in the number 129? (9 ones)
7.
Can you break down 532 into the sum of its partial sums? (500 hundreds +30 tens +2 ones)
8.
Can you break down 129 into partial sums? (100 hundreds + 20 tens + 9 ones)
9.
What is the sum of the hundreds in 532 and 129? (500+100=600) 10. What is the sum of the tens in 532 and 129? (30+20=50) 11. What is the sum of the ones in 532 and 129? (2+9+11) 12. How can you combine the partial sums of hundreds, tens, and ones to find the sum of 532+129? (600+50+11=661) I.
Let’s look at another problem, 448+312. 1.
What is the value of the hundreds place in 448? (4 hundreds) 2.
What is the value of the tens place in 448? (40 tens) 3.
What is the value of the ones place in 448? (8 ones) 4.
What is the value of the hundreds place in 312? (3 hundreds) 5.
What is the value of the tens place in 312? (10 tens)
6.
What is the value of the ones place in 312? (2 ones) 7.
Can you break down 448 into the sum of its partial sums? (400 hundreds+40 tens+8 ones)
8.
Can you break down 312 into the sum of its partial sums? (300 hundreds+10 tens+2 ones)
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9.
What is the sum of the hundreds in 448 and 312? (400+300=700) 10. What is the sum of the tens in 448 and 312? (40+10=50) 11. What is the sum of the ones in 448 and 312? (8+2=10) 12. How can you combine the partial sums of hundreds, tens, and ones to find the sum of 448+312? (700+50+10=760) J.
Now, we are going to go back to our columns, we will dig deeper, and you are going to try and find the missing digits, then find the sum. We have ___ 4 and 5 + 3 ___ 3. Here’s how the column should start out looking like: Hundreds
Tens
Ones _______
4
5
3
____
3
7
0
0
1
1
0
8
1.
Alright, so looking at our chart, we have a few sections filled out, but one is filled out, which section is that? (Ones) 2.
What two numbers are being added together in the ones? (5+3=8) 3.
Let’s start from the beginning and look at our hundreds, below the hundreds we have the number 7, what could we add to 3 to get 7? (4)
4.
Now, moving to the tens place, in that row, we see a 1 in the hundreds and a 1 in the tens place, what do we think that means? (We carried one (regrouped))
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5.
So if we have the 4 in the tens place, what number could we add to 4 to get to the number 11? (Think, let’s look to our side, if 4 means 40, there is a 70 there so what number could we use?) (7)
6.
So, no we can add 40+70 to the side, right? (Yes)
7.
Now let’s look at all of our partial sums together, we have 400+300 which is? 700, we
have 40+70 which is? 110, and we have 5+3 which is? 8. 8.
So now, let’s put it all together, what is our number sentence? (700+110+8)
9.
What is our answer? (818)
K.
To get independent practice, to challenge the students, they will be able to create their three-digit addition problems and solve them by using partial sums. When creating these problems, they will solve them themselves, but also will collaborate with a peer, and exchange their problems with another peer. They can review each other’s work and provide feedback to each other. Methods of Further Differentiating Instruction –
For differentiating instruction, the students who need additional support, may be provided, or be offered simplified problems, first before progressing to more complex ones. As in other lessons, the students are based in groups that are a mix of learning needs and are based on their comfort level with the partial sum method. Also, number lines may be provided on students' desks. B)
Lesson Closure – (10 minutes) 2.
The students will now be handed out an exit ticket, that they will complete over the next 10 minutes. The following questions will be provided on the exit ticket.
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f.
Why is understanding place value so important when using the partial sums method? g.
What did you find challenging, and what strategies helped you understand the partial sums method better? h.
Why might breaking down a three-digit number into hundreds, tens, and ones,
be a helpful strategy in addition? i.
Explain the partial sums method. How does it help in adding the digit numbers?
IV.
EVALUATION: A)
Informal Assessment: The students will be informally assessed during the warm-up, to see if they are readily prepared for this lesson. They will also be observed during their independent practice, where they will be needed to pay attention to their strategies, use of
partial sums, and ability to articulate their reasoning. Lastly, observation will be used during their peer discussions during their independent practice, to see their comprehension levels and misconceptions. B)
Formal Assessment: The students will be formally assessed with a short quiz of 4 questions that is 8 points altogether, making each question on the quiz worth 2 points. This quiz is to assess the key concepts that were covered in this lesson.
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Name: /8
Date: Each question is worth 2 points. The total of the quiz is 8 points. 1.
Break down the steps involved in finding partial sums during addition with the problem, 256+187. (
2 points
)
2.
Which one does not belong? If the answer is 581, which expression does NOT belong with the other THREE
? Circle and explain your answer. (
2 points
)
200 + 300 + 50 + 20 + 5 + 6 581
500 + 70 + 11 500 + 80 + 5 +6
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3.
Use the column chart, like we did in the lesson, and solve the problem, 357+234 (
2 points
)
Hundreds Tens
Ones Hundreds: Tens: Ones: Sum 4.
Use the partial sum strategy, to solve this problem. 451+401. Write your steps below: (
2 points
)
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Answer Key: 1.
Break down the steps involved in finding partial sums during addition with the problem, 256+187. (
2 points
)
200+100 = 300
50+80=130
6+7= 13
300+130+13=443
2.
Which one does not belong? If the answer is 581, which expression does NOT belong with the other THREE
? Circle and explain your answer. (
2 points
)
200 + 300 + 50 + 20 + 5 + 6 581
500 + 70 + 11 500 + 80 + 5 +6 That is the expression that does not fit, because it equals 891, and the rest of the expressions equals 581. 3.
Use the column chart, like we did in the lesson, and solve the problem, 357+234 (
2 points
)
Hundreds Tens
Ones 3
5
7
2
3
4
Hundreds: 5
0
0
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Tens: 0
8
0
Ones: 0
1
1
Sum 5
9
1
4.
Use the partial sum strategy, to solve this problem. 451+401. Write your steps below: (
2 points
)
In 451: In 401: Hundreds: 400
hundreds: 400
Tens: 50 Tens: 0
Ones: 1 Ones: 1 400 hundreds+400 hundreds= 800 hundreds
50 tens+0 tens= 50 tens
1 one+1 ones= 2 ones
800+50+2=852
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III.
Misconceptions: In this mini-unit plan, there could be some misconceptions that arise when students are learning about place value and addition within 1,000. When adding, some students may have confusion with the regrouping, or carrying. For example, when adding 398 and 267, a student may incorrectly regroup the tens without understanding why. To address this, the base-ten blocks
come in, to break down the regrouping process. It is important to emphasize the transition from ones to tens and from tens to hundreds. Also, the students may lack an understanding of working backward. For example, if you had the number 540, the student may struggle to decompose that number into hundreds, tens, and ones. This is where you will use a reverse-problem-solving problem and incorporate activities where they decompose numbers into place values. Also, the trading part of addition might cause the students to struggle. For example, if there were numbers to add 485 and 297, they might struggle with the idea of trading in both the tens and one’s places simultaneously. What you can do is, visualize the trading with base-ten blocks. These base-ten blocks can illustrate the process of trading in different places. There could
also be an overreliance on memorization of these concepts. For example, a student may memorize certain addition problems without understanding the underlying concepts. This is a problem for when more complex problems come in. To address this misconception, it is important to emphasize understanding over memorization. The students should be able to explain
their thought processes when solving problems.
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IV.
Manipulative Activity
Lesson: Use Models to Add Three-Digit Numbers
Base-ten blocks are a great concrete representation of abstract mathematical concepts. The students can physically manipulate these blocks and touch the different units of, ones, tens, and hundreds. It is a great visual for students who have different learning styles, and this
helps with their multisensory approach to enhance comprehension. Lastly, while using the base ten blocks, the students can build a strong foundation in place value which is a fundamental concept in mathematics. The Website SplashLearn has great resources for teaching students different concepts in mathematics. This specific one is a five-step lesson with three questions in each section of adding within 1,000. The students will first create a base of hundreds plus another set of hundreds just with numbers. Then, it will get into using the base-ten blocks to determine the answer to the problem. Then, they will go on by moving the blocks that represent each number. As shown below, is what the front page of the lesson looks like, as well as one example where base-ten blocks are shown in a different lesson. This is a great interactive tool
that gets the students to learn content through technology in a fun way, rather than just from their teacher.
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References: https://www.splashlearn.com/s/math-games/add-3-digit-and-3-digit-numbers-using-
model
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V.
Differentiation copies ready for students: Think-Tac-Toe – Understanding place-value and addition within 1,000. Select one row, column, or diagonal and complete each assignment on a separate sheet of paper. Knowledge Identify and list the place value digits that are given in the number 465. Comprehension
Explain the difference between the hundreds, tens, and one’s places with using your own words, within the number 583. Application
Apply your understanding of place-value, by composing and decomposing the numbers 45 and 456. Analysis
With the number 364, identify and explain the place values of each digit in 364. Synthesis
Use your base ten blocks and a visual representation of solving the problem 474+530.
Evaluation
Evaluate the effectiveness of different addition strategies, and out of these strategies, which method do you find the
most efficient? Why? Evaluation
Critique and justify different solution methods, that other peers in the class had used to solve addition problems within 1,000. Application
Mary had 436 chickens, she needs to buy 482 more, when buying the other chickens, how many will she have in all? Show your work. Analysis
Compare and contrast the place value systems that are within two- and three-digit numbers. Copy that identifies learning styles, levels of Bloom’s Taxonomy, and solutions. Knowledge Knowledge is the ability to recall or remember information the students had previously learned. This level
of Bloom’s, involve recognizing, listing, describing, and identifying. Learning Style: Mastery Learners
Solution: The digit “4” is in the hundreds place, the digit “6” is in the tens place,
the digit “5” is in the ones place. Comprehension
Comprehension is when the students develop an understanding of information,
concept, and being able to interpret into their own words. This involves explaining ideas and concepts. Learning Style: Understanding Learners
Solution: 583 is a three-digit
number, the 5 is in the hundreds place, the 8 is in the tens place, and the 3 is Application
Application is the ability of the students to use their learned knowledge in new and concrete situations. This involves applying principles and rules to solve problems or
tasks. Learning Style: Mastery Learners
Solution: 45 as 40+5. 456 as 400+50+6.
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in the ones place. Analysis
Analysis is when the students break the information down into parts, and examine the relationships between them, and understand how they can contribute. This involves organizing, comparing, and contrasting.
Learning Style: Self-Expressive Learners Solution: The digit “3” represents 300, the digit “6”
represents 60, and the digit “4” represents 4.
Synthesis
Synthesis is when the students will create new ideas. This involves solutions,
designs, or proposals.
Learning Style: Self-
Expressive Learners
Solution: Students will have
their visual representation of the problem, as well as use their base 10 blocks. Evaluation
Evaluation is when the students will make judgements about value, materials, or methods on criteria. It involves assessing the effectiveness, appropriateness, or significance of something. Learning Style: Interpersonal Learners Solution: Some students may prefer a number line.
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Evaluation
Evaluation is when the students will make judgements about value, materials, or methods on criteria. It involves assessing the effectiveness, appropriateness, or significance of something. Learning Style: Interpersonal Learners Solution: They will identify errors and provide feedback and assess their peer’s solution. Application
Application is the ability of the students to use their learned knowledge in new and concrete situations. This involves applying principles and rules to solve problems or
tasks. Learning Style: Mastery Learners
Solution: Analysis
Analysis is when the students break the information down into parts, and examine the relationships between them, and understand how they can contribute. This involves organizing, comparing, and contrasting.
Learning Style: Self-Expressive Learners Solution: Two-digit numbers are numbers 10 to 99; three-digit numbers are the numbers 100 to 999.
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VI.
Quiz
Unit Quiz (Base-ten blocks will be given out) Name:
Date:
1.
Multiple choice:
What is the value of the digit ‘5’ in the number 753? (1 point) a) 5
b) 50
c) 500
2.
Short Answer: (1 point for correction decomposition into hundreds, tens, and ones)
Decompose the number 468 into hundreds, tens, and ones using place-
value blocks. 3.
Fill in the Blank: (
1 point)
246 + _______ = 543 4.
Matching (
Each correct match, 1 point each, total 3 points)
Match each addition problem to its correct sum: a)
312 + 189
i) 824
b)
467 + 325 ii) 501
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c)
548 + 276 iii) 792 5.
Word Problem: (Correct answer 1 point, shown work, 1 point, 2 points total)
Charlie has 427 apples, and his friend gave him 359 more apples. How many apples does Charlie have now? (Show your work) 6.
Problem-Solving: (1 point correct answer, 1 point shown work, 2 points total)
Laura wants to buy a doll that costs $285. She already has $150. How much more money does she need to buy the toy? (Show your work)
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7.
True/False: (1 point)
Regrouping is only necessary when adding three-digit numbers. 8.
Extended Response: (Clear explanation and correct example: 2 points)
Tell me how understanding place value helps you understand adding numbers within 1,000. Give me an example you can think of. 9.
Real-Life Scenario: (1 point for correct answer, 1 point for shown work, 2 total)
In the zoo, there are 248 lions and 397 kangaroos. How many legs do the lions and kangaroos have altogether? (Show your work) 10.
Performance Task: (Correct representation using base-ten drawings and clear explanation: 2 points)
Use base-ten blocks to show the addition problem of 536 and 278. Draw your base-ten blocks and explain the steps you took.
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Rubric:
15-17 points: Excellent understanding and application of the mini plan.
11-14 points: Good understanding of some areas for improvement.
9-13 points: Basic understanding, need additional practice.
0-8 points: Limited understanding, further review and support needed.
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Unit Quiz (Answer Key) (Base-ten blocks will be given out) Name:
Date:
11.Multiple choice:
What is the value of the digit ‘5’ in the number 753? (1 point) d) 5
e)
50
f) 500
12.
Short Answer: (1 point for correction decomposition into hundreds, tens, and ones)
Decompose the number 468 into hundreds, tens, and ones using place-
value blocks. 400 (for hundreds), 50 (for tens), 3 (for ones)
13.
Fill in the Blank: (
1 point)
246 + ___297
____ = 543 14.
Matching (
Each correct match, 1 point each, total 3 points)
Match each addition problem to its correct sum: d)
312 + 189
i) 824
e)
467 + 325 ii) 501
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f)
548 + 276 iii) 792 15.
Word Problem: (Correct answer 1 point, shown work, 1 point, 2 points total)
Charlie has 427 apples, and his friend gave him 359 more apples. How many apples does Charlie have now? (Show your work) 16.
Problem-Solving: (1 point correct answer, 1 point shown work, 2 points total)
Laura wants to buy a doll that costs $285. She already has $150. How much more money does she need to buy the toy? (Show your work)
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17.
True/False: (1 point)
Regrouping is only necessary when adding three-digit numbers. False 18.
Extended Response: (Clear explanation and correct example: 2 points)
Tell me how understanding place value helps you understand adding numbers within 1,000. Give me an example you can think of. It allows us to group numbers efficiently. For example, in 348+267, knowing 3 hundreds, 4 tens, and 8 ones, then 2 hundreds, 6 tens, and 7 ones. It allows us to add the ones, then tens, then hundreds. 19.
Real-Life Scenario: (1 point for correct answer, 1 point for shown work, 2 total)
In the zoo, there are 248 lions and 397 kangaroos. How many legs do the lions and kangaroos have altogether? (Show your work) 20.
Performance Task: (Correct representation using base-ten drawings and clear explanation: 2 points)
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Use base-ten blocks to show the addition problem of 536 and 278. Draw your base-ten blocks and explain the steps you took. Students may have different variations to this problem.
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