Write Numerical Expressions from Word Descriptions

Students translate verbal descriptions of calculations into numerical expressions using numbers, operation symbols, and grouping symbols where appropriate. They learn to identify key words and phrases that indicate specific operations.

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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.

Vic counts 11 bones and 6 shells in a display case at the museum. There are 5 cases that look exactly alike. Which of these expressions matches all the items?

5×(11+6)

5+11×6

11+6×5

5×11+6

How it is taught

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A numerical expression uses numbers and operation marks, not an equal sign.

Words like sum, product, and difference tell which mark to write.

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.

Write "9 more than the product of 7 and 8" as an expression, then find its value: ___ — 65. 7 × 8 + 9: 7 × 8 = 56, then 56 + 9 = 65.

Add 8 and 5, then multiply the sum by 3 → (8 + 5) × 3

Words can tell us what to do in math. Let's learn how to turn a description into an expression!

Grade 5 · Turning words into math expressions

Here's our description: add eight and five, then multiply the sum by three.

First clue: 'add eight and five.' The word 'add' means we use a plus sign.

So we write: eight plus five.

Next clue: 'multiply by three.' The word 'multiply' means we use a times sign.

But look closely — it says multiply THE SUM by three. 'The sum' means we have to add first.

Parentheses tell us 'do this first.' We put them around eight plus five.

Now we multiply that whole sum by three.

Let's check. Inside the parentheses first: eight plus five is thirteen.

Then thirteen times three equals thirty-nine.

Our expression is open-paren eight plus five close-paren times three. Words turned into math — 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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