A sample 5th grade problem from the Common Core resources of the New York-based Lake Shore Central School District:

**Operations and Algebraic Thinking:
**

**5.OA1: Write and Interpret numerical expression.
**

Maxwell bought a new pair of skis for $350. He put $110 down and received a student discount of $30. His mother gave him 1/2 of the balance for his birthday. Which of these expressions could be used to find the amount Maxwell still owes on the skis?

A. 350−110+30÷2

B. 350−(110−30)÷2

C. [350−(110−30)÷2]

D. [350−(110+30)]÷2

Answer: ________

**Extra Credit:**

Besides “write and interpret numerical expression,” what other skills does this problem involve? Consider the ESL student, the language-impaired student, or the student on the autistic spectrum, and:

1. Idiosyncratic meanings that override literal meaning: “put money down;” “balance.”

2. Knowledge of transactional “schema”: the special discount; the down payment.

**A rewrite that more specifically measures 5.OA1:**

A pair of skis costs $350. Students get a price reduction of $30. A student has $110. His mother gives him 1/2 of what he still needs to buy the skis. Which of these expressions shows the amount he now needs?

A. 350−110+30÷2

B. 350−(110−30)÷2

C. [350−(110−30)÷2]

D. [350−(110+30)]÷2

Answer: ________

## 1 comment:

I'd also argue the problem is ambiguous. What was the original price of the skis?

Was it $350, and after the $30 discount he "paid" $320, or, as I think the wording actually suggests, since it says he paid $350, the discount was already taken, and the original price was $380.

You don't pay for a discount; a discount reduces the price before you pay.

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