Question

A farmer sets up two corn mazes for a fall festival, as shown in this model.



Which equivalent expressions are represented by the model? Check the three that apply.

(3 points)
Responses

15+5
15 plus 5

5(3+1)
5 times open paren 3 plus 1 close paren

3+(5+1)
3 plus open paren 5 plus 1 close paren

(5)(3)+(5)(1)
5 times 3 plus 5 times 1

3(5+1)
3 times open paren 5 plus 1 close paren
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Answer 1

To determine which equivalent expressions are represented by the model of the corn mazes, let's analyze the expressions provided:

1. **15 + 5**
- This expression is just a sum of two numbers. It does not represent the combination of the parts of the maze in a distributive manner.

2. **5(3 + 1)**
- This expression uses the distributive property, suggesting that we have 5 times the result of (3 + 1). This can represent the total area if it breaks down the components consistently.

3. **3 + (5 + 1)**
- This expression adds 3 to the sum of 5 and 1. It does not show a multiplication nor does it seem to structure the maze efficiently.

4. **(5)(3) + (5)(1)**
- This expression applies the distributive property. We can interpret it as 5 times 3 plus 5 times 1, which effectively breaks down a multiplication and addition based on the model.

5. **3(5 + 1)**
- This expression also uses the distributive property and can appear to be a valid representation as it suggests a multiplication of 3 with the sum of 5 and 1.

Based on the reasoning above, the three equivalent expressions represented by the model are:

- **5(3 + 1)**
- **(5)(3) + (5)(1)**
- **3(5 + 1)**

Therefore, the checked responses should be these three expressions.