Problem Analysis and Solution Explanation
The image contains a math worksheet from "Eureka Math" Lesson 1 Homework, focusing on understanding multiplication as equal groups. Let's break down each problem and explain the solution:
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Problem 2:
Question: The picture below shows 3 groups of hot dogs. Does the picture show \(3 \times 3\)? Explain why or why not.
Image Description: There are 3 boxes, and each box contains 3 hot dogs.
Solution:
- The picture shows 3 groups (boxes), and each group contains 3 hot dogs.
- This can be represented as \(3 \times 3\), which means 3 groups of 3.
- Therefore, the total number of hot dogs is \(3 \times 3 = 9\).
Answer: Yes, because there are 3 hot dogs per group.
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Problem 3:
Question: Draw a picture to show \(4 \times 2 = 8\).
Solution:
- To represent \(4 \times 2\), we need to draw 4 groups, with 2 items in each group.
- The student drew:
1. Two circles, each containing 4 items (representing \(2 \times 4 = 8\)).
2. Four separate items (circles) grouped together (representing \(4 \times 2 = 8\)).
Explanation:
- The first drawing shows 2 groups of 4, which is \(2 \times 4 = 8\).
- The second drawing shows 4 groups of 2, which is \(4 \times 2 = 8\).
- Both representations are correct and demonstrate the commutative property of multiplication (\(a \times b = b \times a\)).
Answer: The drawings correctly represent \(4 \times 2 = 8\).
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Problem 4:
Question: Circle the pencils below to show 3 groups of 6. Write a repeated addition and a multiplication sentence to represent the picture.
Image Description: There are 18 pencils arranged in 3 groups.
Solution:
- The student circled the pencils to form 3 groups, with 6 pencils in each group.
- The repeated addition sentence is:
\[
6 + 6 + 6 = 18
\]
- The multiplication sentence is:
\[
3 \times 6 = 18
\]
Explanation:
- The total number of pencils is 18, which is the result of adding 6 pencils three times.
- Alternatively, it can be expressed as multiplying the number of groups (3) by the number of pencils per group (6).
Answer:
- Circled groups of pencils.
- Repeated addition: \(6 + 6 + 6 = 18\)
- Multiplication: \(3 \times 6 = 18\)
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Final Answer:
\[
\boxed{Yes, 3 \times 3; 4 \times 2 = 8; 6 + 6 + 6 = 18, 3 \times 6 = 18}
\]
Parent Tip: Review the logic above to help your child master the concept of lesson 1 home work 4 2.
