Generated with Monsha

Distributive Property and Area Models Practice Worksheets

Smart Worksheet · Grade 4 · English

Distributive Property and Area Models Practice Worksheets

Worksheet 1: Exploring Area Models and Algebraic Notation

Name: ​​​​​​​​​​​​​​​​​​​​​​​​​ Date: ​​​​​​​​​​​​​​​​​​​​


Activity 1: Guided Area Model and Algebraic Steps (Easy)

Follow the example from class to solve

. Fill in each missing value to complete the area model and the algebraic notation method.
Step 1: Decompose the double-digit number into tens and ones:



Step 2: Complete the partial products inside the area model table:
​
Width:

​
Width:

​
Height:

​
​

​
​

​
Step 3: Use the Algebraic Notation Method to write out the distributive steps and find the total:














Activity 2: Equivalent Expressions Multiple Choice (Easy)

Choose the correct option for each question. Circle your answer.
  1. Which expression shows
    
    broken apart using the distributive property?
  • A.
    
  • B.
    
  • C.
    
  • D.
    
  1. Which sum represents the partial products for
    
    ?
  • A.
    
  • B.
    
  • C.
    
  • D.
    
  1. A student evaluated
    
    by computing
    
    . What is the correct total product?
  • A.
    
  • B.
    
  • C.
    
  • D.
    
  1. Which expression correctly applies the distributive property to
    
    ?
  • A.
    
  • B.
    
  • C.
    
  • D.
    


Activity 3: Partitioning and Partial Products (Moderate)

Decompose the 2-digit number, fill in the area model values, and complete the algebraic notation steps for each problem.

Part A:


  1. Decompose:
    
  1. Complete the Area Model:
​
Width: Tens ( )
Width: Ones ( )
Height:

​
​

​
​

​
  1. Algebraic Notation:










Part B:


  1. Decompose:
    
  1. Complete the Area Model:
​
Width: Tens ( )
Width: Ones ( )
Height:

​
​

​
​

​
  1. Algebraic Notation:











Activity 4: Error Analysis – Spot the Mistake (Moderate)

Read each student's work. Identify where they made a mistake, explain their error, and provide the correct solution.
Problem 1: Marcus tried to solve

:



  • Explain Marcus's error:

  • Write the correct algebraic steps and final product:

Problem 2: Elena tried to solve

:



  • Explain Elena's error:

  • Write the correct algebraic steps and final product:



Activity 5: Real-World Application – The Community Garden (Moderate)

A rectangular section of a community garden measures

wide by

long. The gardeners want to find the total area in square feet.
  1. Sketch or label the area model dimensions for the garden plot:
​
Width: Tens ( )
Width: Ones ( )
Height:

​
Area:
Area:
  1. Show your work using the Algebraic Notation Method:









  1. Write your final answer as a complete sentence:


Worksheet 2: Deepening Algebraic Notation and Problem Solving

Name: ​​​​​​​​​​​​​​​​​​​​​​​​​ Date: ​​​​​​​​​​​​​​​​​​​​


Activity 6: Multi-Step Algebraic Notation (Moderate)

Solve each problem by showing the full three-line algebraic notation method. Do not skip any steps.
  1. Solve
    
    :
  • Line 1 (Decompose): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  • Line 2 (Partial Products): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  • Line 3 (Total Sum): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  1. Solve
    
    :
  • Line 1 (Decompose): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  • Line 2 (Partial Products): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  • Line 3 (Total Sum): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  1. Solve
    
    :
  • Line 1 (Decompose): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  • Line 2 (Partial Products): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  • Line 3 (Total Sum): ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​


Activity 7: True or False with Justification (Moderate)

Write True or False on the blank. If the statement is false, explain why or write the corrected equation.
  1. 
    ​​​​​​​​​​​​
  • Justification: ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  1. 
    ​​​​​​​​​​​​
  • Justification: ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  1. 
    ​​​​​​​​​​​​
  • Justification: ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  1. 
    ​​​​​​​​​​​​
  • Justification: ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​


Activity 8: Decomposing in Two Different Ways (Challenging)

The distributive property allows us to decompose numbers into any convenient addends, not just tens and ones. Solve

using two distinct decompositions.
Method 1: Standard Place Value (Tens and Ones)
Decompose

into

:






Method 2: Friendly Numbers
Decompose

into

:






Reflection:
Why do both methods give the exact same product? Which method did you find easier to compute in your head, and why?



Activity 9: Multi-Step Real-World Problem (Challenging)

A school librarian orders

boxes of chapter books. Each box contains

books.
  1. Write a single-by-double-digit multiplication expression for the total number of books:
  1. Draw an area model layout in the box below to represent this problem:
​
Width: Tens (
​​​​​​
)
Width: Ones (
​​​​​​
)
Height:

Partial Area:
​​​​​​​​​​​​
Partial Area:
​​​​​​​​​​​​
  1. Use the Algebraic Notation Method to calculate the total number of books ordered:

  1. Extension: The librarian wants to distribute all the books equally onto
    
    empty display shelves. How many books will be placed on each shelf? Show your work:



Activity 10: Distributive Detective – Missing Values (Challenging)

Find the missing numbers to make each distributive property equation true. Write the correct number in each blank.
  1. 
  1. 
  1. 
  1.