# Module 4 - Math 4A - Course Guide

## Module Overview:

In this module students will learn about how to multiply using clustering and how to use regrouping in multiplication. They will learn about how to multiply with arrays and how to multiply large numbers many different ways. Students will learn about long division, dividing using grouping, using an area model to solve division problems, and how to apply division strategies. Students will become familiar with the parts of fractions and writing fractions.

## Module Materials:

Lesson # Lesson Title Material(s)
1 Clustering Scissors
2 Regrouping Multiplication Math Notebook
3 Multiplying with Arrays Graph paper
4 Applications of Multiplication Math Notebook
5 Long Division Math Notebook
6 Dividing Using Grouping Math Notebook
7 Area Model Graph paper Markers
8 Application of Division Strategies Math Notebook
9 Fraction Parts Scissors
10 Fraction Shape Crayons or Markers
11 Writing Fractions Math Notebook

Module Objectives:

Lesson # Lesson Title Objective(s)
1 Clustering
1. Multiply numbers using clustering
2 Regrouping Multiplication
1. Multiply numbers using re-grouping.
3 Multiplying with Arrays
1. Multiply numbers using the arrays model.
4 Applications of Multiplication
1. Apply any of the multiplication strategies to solve real-life problems.
5 Long Division
1. Divide numbers using a traditional algorithm.
6 Dividing Using Grouping
1. Divide numbers using groups for the divisor.
7 Area Model
1. Divide numbers using area models.
8 Application of Division Strategies
1. Apply any of the division strategies to solve real-life problems.
9 Fraction Parts
1. Define fraction; numerator; denominator; fraction bar.
10 Fraction Shape
1. Identify the number of shaded parts and the number of equal parts in a shape (circle; rectangle).
11 Writing Fractions
1. Write a fraction using mathematical notation and using words.

Module Key Words:

Key Words
multiplication
clustering
commutative
re-grouping
array
math
large numbers
division
quotient
dividend
divisor
division bracket
grouping
area model
fraction
equivalent
numerator
denominator
fraction bar
Fraction Line
Modeling

Module Assignments:

Lesson # Lesson Title Page # Assignment Title
1 Clustering 7 Clustering with Tiles Activity
2 Regrouping Multiplication 4 Re-grouping Activity
3 Multiplying with Arrays 8 Array Practice
4 Applications of Multiplication 2 Applications Practice
7 Area Model 7 Modeling Practice
10 Fraction Shape 3 Modeling Fractions Practice

## Learning Coach Notes:

Lesson # Lesson Title Notes
1 Clustering In this lesson have your student complete the practice activity first before looking at the answer key. Be sure to monitor this. When they check their answers using the key have them circle what they got wrong and talk about why they got it wrong and make corrections.
2 Regrouping Multiplication In this lesson have your student complete the practice activity first before looking at the answer key. Be sure to monitor this. When they check their answers using the key have them circle what they got wrong and talk about why they got it wrong and make corrections. In their Math notebook have your student describe regrouping and the write the steps to multiplying four digit numbers.
3 Multiplying with Arrays This lesson will have your student using graph paper there is a downloadable version to print if you do not have graph paper on hand. In this lesson have your student complete the practice activity first before looking at the answer key. Be sure to monitor this. When they check their answers using the key have them circle what they got wrong and talk about why they got it wrong and make corrections.
4 Applications of Multiplication In this lesson have your student complete the practice activity first before looking at the answer key. Be sure to monitor this. When they check their answers using the key have them circle what they got wrong and talk about why they got it wrong and make corrections. In their math notebook have your student write down the strategies they used to solve the problems in this lesson.
5 Long Division In their Math notebook have your student write down the 4 steps to solving a long division problem and have them diagram the parts of a division problem.
6 Dividing Using Grouping In their Math notebook have them describe how to use grouping strategies to solve division problems.
7 Area Model This lesson will have your student using graph paper there is a downloadable version to print if you do not have graph paper on hand. In this lesson have your student complete the practice activity first before looking at the answer key. Be sure to monitor this. When they check their answers using the key have them circle what they got wrong and talk about why they got it wrong and make corrections.
8 Application of Division Strategies In this lesson your student will be given practice problems to solve using any of the division strategies they have learned. Sit with them while they solve the problem. Do not allow them to click on the answer until after they have solved the problem and discussed what strategy they used to solve the problem with you. When they have finished solving the problem and discussed their strategy allow them to click on the answer to compare. In their Math notebook have your student write down the division strategies they can use to solve division problems.
9 Fraction Parts One of the activities in this lesson ask the student to practice writing fractions. As your student writes the fractions have them identify for you the numerator and the denominator in each fraction they write.
10 Fraction Shape Give your student 5 fractions and ask them to create a model for each fraction in their Math notebook.
11 Writing Fractions Write 5 fractions in your students math notebook and have them read them and label the parts. Then say a fraction and ask your student to write the fractions you tell them.

## Module Guiding Questions:

When a student starts a lesson ask them questions to check for prior knowledge and understanding and to review concepts being taught. At the end of the lesson ask the questions again to see if their answer changes.

Lesson Title Question
Clustering
1. What is clustering?
Regrouping Multiplication
1. What is re-grouping in multiplication?
2. What is the commutative property?
Multiplying with Arrays
1. What is an array?
Applications of Multiplication
1. What are the different ways you can multiply large numbers?
Long Division
1. How do you solve long division problems?
Dividing Using Grouping
1. How do you divide using grouping?
Area Model
1. What is an area model?
2. What does it mean that division is known as the inverse of multiplication?
Application of Division Strategies
1. What are some strategies you can use to solve division problems?
Fraction Parts
1. What are the parts of a fraction?
Fraction Shape
1. How does modeling help with understanding fractions?
Writing Fractions
1. How do you write fractions?

## Module Video Questions:

When a student watches a video take time to ask them questions about what they watched. Suggested questions for the videos in this module are listed here. Suggestion: Have the student watch the entire video first all the way through. Then have them watch the video a second time, as they watch it pause the video and ask the questions.

Lesson Title Video Question
Clustering Maths Mansion
1. What are the problems the kids have to solve to get out of the Maths Mansion?
2. Can you solve them before the kids do?
Regrouping Multiplication Four Digit Multiplication
1. What are the steps involved in multiplying four digit numbers?
Multiplying with Arrays 1001 Naughts
1. How are arrays used to multiply in this video?
Multiplying with Arrays Completing Multiplication Sentences Using Arrays
1. How does an array represent multiplication sentences?
Long Division Division and Multiplication - Beads
1. How can beads teach us the properties of division?
Long Division Division Procedures
1. What are the steps to long division?
Dividing Using Grouping Dividing Using Grouping
1. What is a grouping strategy?
Area Model Understanding the Relationship Between the Remainder and the Divisor
1. How can you use base ten blocks to understand the relationship between the remainder and the divisor?
Application of Division Strategies Dividend, Divisor and Quotient
1. What is the dividend?
2. What is the divisor?
3. What is the quotient?
Application of Division Strategies Division Word Problems
1. What are the steps to solving a word problem?
2. What are some strategies you can use to solve division word problems?
Fraction Parts Fractions for Food
1. What food was broken into fractions?
Fraction Parts Parts of a Whole
1. What is a fraction?
2. What is the numerator of a fraction?
3. What is the denominator of a fraction?
Fraction Shape Modeling Fractions
1. Describe how you model fractions.
Writing Fractions Read and Write Fractions
1. What is a fraction?
2. What is the denominator?
3. What is the numerator?
4. How do you read a fraction?
5. How do you write a fraction?

## Module Suggested Read Aloud Books:

Take time to read to your student or have them read aloud to you. Read a different book each day. While reading the book point out concepts being taught. You may purchase these books or find them at your local library. Suggested things to discuss while reading the book:

• What is the main idea?
• What are three things new you learned?
• How does this book relate to what you are learning about?

# Book Author Lexile Level
1 Amanda Bean's Amazing Dream Cindy Neuschwander AD520L
2 How Do You Count a Dozen Ducklings? Seon Chae
3 Bean Thirteen Matthew McElligott 470L
4 The Lion's Share Matthew McElligott 550L
5 Full House: An Invitation to Fractions Dayle Ann Dodds 530L
6 A Fraction's Goal ― Parts of a Whole Brian P. Cleary 620L

## Module Outing:

Take some time to apply what your student is learning to the real world. Suggested outings are below.

# Outing