The image you uploaded appears to be a worksheet titled "DECOMPOSING ADDENDS, AREA MODELS, AND DISTRIBUTIVE PROPERTY TO MULTIPLY." The task involves solving multiplication problems using the distributive property and area models. Below is an explanation of how to approach such problems:
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Problem Overview
The worksheet likely asks students to:
1. Decompose numbers (break them into smaller parts).
2. Use area models to visualize multiplication.
3. Apply the distributive property to simplify calculations.
####
Example Problem:
Let's assume one of the problems on the worksheet is:
$$
7 \times 24
$$
####
Step-by-Step Solution:
1.
Decompose the Numbers:
- Break down the larger number (24) into smaller, more manageable parts. For example:
$$
24 = 20 + 4
$$
2.
Apply the Distributive Property:
- Use the distributive property to rewrite the multiplication:
$$
7 \times 24 = 7 \times (20 + 4)
$$
- Distribute the 7 across the sum:
$$
7 \times (20 + 4) = (7 \times 20) + (7 \times 4)
$$
3.
Calculate Each Part:
- Compute each multiplication separately:
$$
7 \times 20 = 140
$$
$$
7 \times 4 = 28
$$
4.
Add the Results:
- Add the two products together:
$$
140 + 28 = 168
$$
5.
Verify with an Area Model:
- Draw a rectangle where the length is 7 and the width is 24. Divide the width into two parts: 20 and 4.
- Calculate the area of each smaller rectangle:
- Rectangle 1: \( 7 \times 20 = 140 \)
- Rectangle 2: \( 7 \times 4 = 28 \)
- Add the areas:
$$
140 + 28 = 168
$$
####
Final Answer:
$$
\boxed{168}
$$
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General Explanation for Similar Problems:
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Decomposition: Always break down the larger number into simpler parts (e.g., tens and ones).
-
Distributive Property: Rewrite the multiplication as a sum of simpler multiplications.
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Area Models: Use visual aids to help understand the decomposition and verify the calculations.
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Practice: Repeat the process for different numbers to build fluency.
If you have a specific problem from the worksheet that you'd like me to solve in detail, please provide it, and I can walk through it step by step!
Parent Tip: Review the logic above to help your child master the concept of sentence fragment run on worksheet.
