Interpret Numerical Expressions Without Evaluating

Students describe what a numerical expression represents in words without actually computing its value. They recognize expressions as descriptions of calculations and compare the size of expressions using reasoning about operations rather than arithmetic.

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Grade 5 · Algebraic Thinking: Writing and Interpreting Expressions · question 1 of 3

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20 rungs. A star at the top.

2 × (86 + 17) = 2 × 86 +

How it is taught

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An expression names a calculation even before you compute it.

You can compare two expressions by reading their structure.

Read it: Expressions from words

"5 more than the product of 4 and 2" is 4 × 2 + 5: the product first, then 5 more. 4 × 2 = 8, and 8 + 5 = 13.

Find the first job in the words: a sum, a difference or a product.
Put that job in parentheses when it must come before × or ÷.
Read an expression as groups: 2 × (…) is 2 groups of what is inside.

"The product of 4 and 2" is 4 × 2, and "5 more than" adds 5 to it.

× already comes before +, so 4 × 2 + 5 needs no parentheses.

Counting the groups compares two expressions without working either of them out.

Write the words' jobs in order; parentheses hold the job that goes first.

Adding first: (5 + 4) × 2 = 18.

The product comes first: 4 × 2 + 5 = 13.

5 × (340 + 85) + (340 + 85) = ___ × (340 + 85) — 6. 5 groups of (340 + 85) and 1 more group make 6 groups.

Compare A: 245 + 178 and B: 3 × (245 + 178)

Today we'll compare two expressions without doing any arithmetic — just by reading them carefully.

Here's expression A: two hundred forty-five plus one hundred seventy-eight.

In words, A is just the sum of 245 and 178.

And here's expression B: three times, in parentheses, 245 plus 178.

Look closely — the same sum, 245 plus 178, hides inside B.

So B is three times that same sum — without ever adding it up.

Let's picture A as one bar, this size.

B is three of those bars stacked together — three copies of A.

So we can see that B equals three times A, just by reading the operations.

Grade 5 · Reason about expressions without computing

B is three times as large as A. We compared them without computing. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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