Curriculum Unit Part I and II Revised
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Barry University *
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Mathematics
Date
Apr 3, 2024
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docx
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Uploaded by CaptainMusicWildcat32
Template to be Used for Completion of Curriculum Project I and Curriculum Project II
Instructional Unit
Content Area: Grade Level: Mathematics
3
Unit Title: Unit Length/Times:
Relationship Multiplication/ Division
5 days
Unit Description:
In this unit the students will understand the important relationship between multiplication and division. When taught together the students will have a better understanding of how the two operations are the inverse of one another. Therefore, if the students have mastered multiplication, he/she has also mastered division. The students will use both operations when solving real word problems. Standards/Benchmarks:
MA.3.NSO.2.2 Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.
Objectives:
The students will use equal groups to multiply.
The students will use equal groups to divide.
The students will explain multiplication and division equations.
The students will compare multiplication to division.
Lessons in the Unit:
Day 1: Understanding Multiplication Day 2: Strategies for Multiplication
Day 3: Understanding Division
Day 4: Strategies for Division
Day 5: Multiplication/ Division Real Word Problems
Higher Order Thinking Questions:
How many groups did you form?
How many rows are in the array? How many columns are in the array?
Why did you choose the strategy that you use to solve the problem? Explain
How are multiplication and division equations alike/different? How is the number of jumps you made related to the division problem?
What is happening in the real-world problem?
What do you need to find out?
What do the quantities represent in the problem?
What will the solution represent in the problem?
Concepts:
multiplication, division, equal groups, arrays
Academic Vocabulary:
Content Specific Vocabulary: explain, apply, compare, contrast
represent, justify, facilitate, locate
multiplication, division, factors, arrays,
equal groups, rows, columns
product, quotient, divisor
dividend
End of Unit Assessment
Unit Essential Question:
What is the relationship between multiplication and division? How is addition and subtraction similar to multiplication and division?
Materials/Resources:
Counters, Grid Paper, Pencils, Textbook, Paper Bags, Number Line
Product/Evidence:
Self- Assessment Success Criteria
Differentiation:
Some students will use counters to create the model; other students will draw the model. The students will complete limited questions. Texts for Independent Reading or Read Aloud to Support Content
Informational/Non-Fiction
Fiction
The Multiplying Menace Divides by Pam Calvert
The Best of Times by Greg Tang
The Great Divide by Dayle Ann Dodds
Divide and Ride by Stuart J. Murphy
Amanda Bean’s Amazing Dream by Cindy Neuschwander
Learning Experience # 1
Standards/Objectives:
MA.3.NSO.2.2 Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.
Essential Question: What is multiplication?
Description of Activity:
Dig In:
The teacher will call out a number and students will form groups of that given size, or number. Ensure that the number can create equal groups depending on the number of students present.
Discussion:
“How many groups did you create?” “How can you tell by looking at the board?” Count how many numbers are written. “Why are all the numbers the same?”
Activity #1:
Students will receive counters. Put 24 counters into equal groups. Draw to show your groups.
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Activity: #2:
Students will create a multiplication equation and an addition equation to represent their model. The teacher and students will create a co-created anchor chart. Game: Students will compare your models with a partner. How are the models the same? How are they different?
Homework:
The students will use the counters to create their own groups. The students will write the multiplication and addition equation to represent the model. The students will create two problems
Teacher Resources:
Student Resources:
Teacher Edition Manual
Anchor Chart Paper
Magnetic Counters
Student Book
Counters
White boards
Markers
Assessment:
The game-When discussing their models, I will be able to hear the student’s collaboration. If students can explain their model using the academic language, this lets me know they have mastered the concept.
Certain pages and numbers within the student’s book- Pg. 4 and 5 problems 1-9 odd and Model Real Life
Discussion Questions in the guided activity. See question in section description of activity. Activity #2- The teacher will preview student’s model. Prior Knowledge and Experiences:
Students will need to have a good understanding of repeated addition. The students will also need to know how to use addition strategies (make a ten). Gradual Release Model (I do, We do, They do, You do):
I do: Introduce multiplication with counters, creating an anchor chart as a visual model for the students. We do: Put the counters into groups, while creating a co-created anchor chart. They do: The multiplication and addition game.
You do: The students will create their own number and display the multiplication and addition equation, using their white boards. Differentiation:
The teacher and student anchor will help provide the ELL and ESE students a visual model when complete the math task. The teacher will ask the following questions: How many groups are there? How many are in each group? What is the total? The students will also use their read, yellow, green cards, red means I need help immediately. Yellow means come back and check with me, and green means I do not need any assistance. Cross-Curricular Connections:
Language Arts: Amanda Bean’s Amazing Dream by Cindy Neuschwander; Read the book aloud to students. Invite students to take turns coming up
to the front of the room and constructing multiplication equations from the illustrations. Alternatively, you can make photocopies of some of the illustrations in the book to distribute to students and have them identify and construct the equations. This book is great for the first lesson of the chapter because it emphasizes the importance of learning and mastering multiplication.
Vocabulary:
Multiplication, Repeated Addition, Factors, Equal Groups, Equation
Learning Experience # 2
Standards/Objectives:
MA.3.NSO.2.2 Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.
Essential Question: What is the relationship between multiplication and repeated addition?
Description of Activity:
Dig In: Teacher will choose 12 students
. Students will try to form lines, with an equal number of students in each line, to see if they can form an array.
Discussion: Is it possible to have two equal lines? Is it possible to have four equal lines? Is it possible to have five equal lines?
Activity #1:
Students will receive counters. Put 36 counters into equal rows. Draw to show your groups. Teacher and students will discuss arrays (rows and columns).
Activity: #2:
Students will create a multiplication equation and an addition equation to represent their model. The teacher and students will create a co-created anchor chart. Students will draw the array using the grid paper.
Game: Students will compare your models with a partner. How are the models the same? How are they different?
Exit Ticket:
The students will each receive a card with a number on it. The students will create an array using their number. The students must create the multiplication and repeated addition equation. Teacher Resources:
Student Resources:
Teacher Edition Manual
Anchor Chart Paper
Magnetic Counters
Student Book
Counters
White boards
Markers
Grid Paper
Assessment:
The game: When discussing their models, I will be able to hear the student’s collaboration. If students can explain their model using the academic language, this lets me know they have mastered the concept.
Certain pages and numbers within the student’s book- Pages 11and 12 problems 1-9 odd and Model Real Life
Discussion Questions-See question in section description of activity.
Exit Ticket-Array Exit Ticket
Prior Knowledge and Experiences:
Students will need to have a good understanding of repeated addition. The students will also need to know how to use addition strategies (make a ten). Gradual Release Model (I do, We do, They do, You do):
I do: Introduce multiplication with counters, creating an anchor chart as a visual model for the students. We do: Put the counters into equal rows, while creating a co-created anchor chart. They do: The multiplication and addition game.
You do: The students will create a model using the exit ticket.
Differentiation:
The teacher and student anchor will help provide the ELL and ESE students a visual model when complete the math task. The students will also use their read, yellow, green cards, red means I need help immediately. Yellow means come back and check with me, and green means I do not need any
assistance. The teacher will ask the prompting questions: How many columns did you draw? How many rows? What is the total?
Cross-Curricular Connections:
Art: Provide students with a multiplication equation that has a product less than 50. Have students cut out an outline of a skyscraper and represent their multiplication equation in square window arrays. Students should write the repeated addition equation that corresponds to their multiplication equation.
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Vocabulary:
Multiplication, Repeated Addition, Factors, Arrays, Rows, Columns, and Equation
Learning Experience # 3
Standards/Objectives:
MA.3.NSO.2.2 Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.
Essential Question: What is division?
Description of Activity:
Dig In: Students will be placed in groups. Each group will receive 24 counters, and prize bags with various number written on them (2, 3, 4, or 6). Discussion: “Was each group able to fill the same number of bags? Why?”
Activity #1: The students will put 24 counters into equal groups of 4. Draw to show your groups. The students will create division equation to represent the model. The teacher will model repeated subtraction for the students. Activity: #2:
Using the students will use the same counters and place counters into equal groups of 6. The teacher and the students will create a co-
created anchor chart. The students will use the anchor chart as model when working independently. Turn and Talk: How does changing the size of the groups change the number of equal groups?
Exit Ticket:
If 7 represents the number of equal groups, what does the equation 35 ÷ 5 = 7 tell you?
Teacher Resources:
Student Resources:
Teacher Edition Manual
Anchor Chart Paper
Magnetic Counters
Student Book
Counters
White boards
Markers
Assessment:
Turn and Talk- See the question in the section Description of Activity
Certain pages and numbers within the student’s book- page 29 and 30 2-10 even only and Real Life Model
Discussion Questions- See the question in the section Description of Activity
Exit Ticket-Section Description of Activity. Prior Knowledge and Experiences:
Students will need to have a good understanding of repeated subtraction. The students will also need to know how to use subtraction strategies (counting up or down). Gradual Release Model (I do, We do, They do, You do):
I do: Introduce multiplication with counters, creating an anchor chart as a visual model for the students. We do: Put the counters into equal groups, turn and talk discussions.
They do: The division and repeated subtraction, while creating a co-created anchor chart.
You do: The students will explain the exit ticket activity.
Differentiation:
The teacher and student anchor will help provide the ELL and ESE students a visual model when complete the math task. The students will also use their read, yellow, green cards, red means I need help immediately. Yellow means come back and check with me, and green means I do not need any
assistance. Demonstrate the Build Understanding example by distributing 12 counters into cups 4 at a time. Continue placing 4 counters in each cup until all counters have been used. Then count the number of cups that contain counters.
Cross-Curricular Connections:
Language Arts: Have each student create a riddle about animals and the number of legs they have. For example, “There are 12 legs in the pond. How
many ducks are there?” Once the riddles are written, without students’ names on a piece of paper, put all the riddles in a bag for students to pick one out and solve. Allow students to draw, use counters, or a number line to solve. Then have them write a division equation to show their answer.
Vocabulary:
Division, Quotient, Divisor, Dividend, Number of Groups, Number of Rows, Equations
Learning Experience # 4
Standards/Objectives:
MA.3.NSO.2.2 Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.
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MA.3.AR.2.1 Restate a division problem as a missing factor problem using the relationship between multiplication and division.
Essential Question: What is the relationship between multiplication and division?
Description of Activity:
Dig In: The teacher will show the students two factors, using the fact family triangle card.
Students will
solve the equation. The teacher will show the students one factor and the product. The students will write the missing factor.
Discussion: “How did you figure out the missing factor?”. The teacher hopes a student will say division, if not teacher will pose question: “Could I think about a division equation to find the missing number? Explain
Activity #1: YouTube video https://www.youtube.com/watch?v=i31rRt5m1-4
The teacher and the students will create a co-created anchor chart. The students will use the anchor chart as model when working independently. Activity: #2:
The students will use 24 counters to make an array. Draw the array. Write a multiplication equation and a division equation for the array. The students will compare their array to their shoulder partner. How are they the same? How are they different?
Exit Ticket:
Draw an array to find 2 × 7. Write the other 3 facts in the fact family. Explain how an array helps you write a multiplication equation and a division equation.
Teacher Resources:
Student Resources:
Teacher Edition Manual
Anchor Chart Paper
Magnetic Counters
Video
Fact Family Cards
Student Book
Counters
White boards
Markers
Assessment:
Turn and Talk- See section Description of Activity questions under subheading: Discussion Exit Ticket- See section Description of Activity
Prior Knowledge and Experiences:
Students will need to have a good understanding of multiplication. The students will need to start practicing multiplication fluency.
Gradual Release Model (I do, We do, They do, You do):
I do: Introduce multiplication with two factors, relate the product to the dividend in division.
We do: YouTube Video and co-created anchor chart.
They do:
Create the array and discuss how multiplication and division are related. Activity 2.
You do: The students will explain the exit ticket activity.
Differentiation:
The teacher and student anchor will help provide the ELL and ESE students a visual model when complete the math task. The students will also use their read, yellow, green cards, red means I need help immediately. Yellow means come back and check with me, and green means I do not need any
assistance. Draw a family tree and ask students to describe how different individuals are related. Remind them that fact families in math are also related. Ask them which operation is related to division.
Cross-Curricular Connections:
Art: Have students draw a shape with four sections, such as a flower with four petals or a tree with four branches. Provide students with four equations of a fact family with various pieces missing. Students put one equation on each of the four sections of their shape and write the three numbers that form the fact family in the middle of the shape.
Vocabulary:
Division, Quotient, Divisor, Dividend, Number of Groups, Number of Rows, Equations, Multiplication, Factors, Number in Each Group, Array
Learning Experience # 5
Standards/Objectives:
MA.3.NSO.2.2 Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers.
MA.3.AR.2.1 Restate a division problem as a missing factor problem using the relationship between multiplication and division.
Essential Question: How is multiplication and division alike and different?
Description of Activity:
Dig In: The teacher will provide the students with a real-world problem. The students will work together to find the answer.
Discussion: The teacher will discuss the three-read strategy with the students. Compare your strategy to your partner’s strategy.
How are they the same? How are they different?
Activity #1: The teacher and the students will work through two or three real word problems, practicing the three-read strategy and thinking logically about which operation will be used. Exit Ticket:
The students will be given a real word problem. The student will solve the problem using multiplication or division. Teacher Resources:
Student Resources:
Teacher Edition Manual
Anchor Chart Paper
Three-Read Strategy Anchor Chart
Student Book
Clip Boards
Assessment:
Turn and Talk- See section: Description of Activity subheading: Discussion
Weekly Formative- The students will complete a formative with a total of 6 problems. Prior Knowledge and Experiences:
Students will need to have a good understanding of multiplication and division. The students need to understand what the question is asking (previous real word application problems using simple numbers). Students must be able to understand certain vocabulary within the problem.
Gradual Release Model (I do, We do, They do, You do):
I do: Three-Read Strategy
We do: Three-Read Strategy creating an anchor chart.
They do:
Complete problems 2, 3, and 5 in math book.
You do: The students will complete math formative.
Differentiation:
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The teacher and student anchor will help provide the ELL and ESE students a visual model when complete the math task. The students will also use their read, yellow, green cards, red means I need help immediately. Yellow means come back and check with me, and green means I do not need any
assistance. The students will keep a notebook of phrases that signal division as they complete the exercises. Continue to repeat the three read strategy
questions. Cross-Curricular Connections:
Physical Education: While at PE the coaches will have the students solve multiplication and division equations while warming up.
Vocabulary:
Division, Quotient, Divisor, Dividend, Number of Groups, Number of Rows, Equations, Multiplication, Factors, Number in Each Group, Array
Resources
B.E.S.T. Standards for Math Grade 3