Browse

Numerical Expressions Worksheets

13 free PDFsUS Letter PDFsAnswer key includedNo login

Write expressions from words, describe expressions in words, interpret them without calculating, and evaluate them with parentheses, brackets and braces.

Download the numerical expressions worksheets

Write and read expressions

From words to expressions and back.

Interpret expressions

How many times as large, without calculating.

Evaluate with brackets and braces

Work from the innermost group out.

Print at 100% (actual size) for the cleanest tracing lines.

About these numerical expressions worksheets

A numerical expression is a math phrase made of numbers and operation signs, like 2 × (8 + 7). It has a value but no equal sign. In 5th grade, children learn to write an expression for a description ("add 8 and 7, then multiply by 2"), to say an expression in words, and to read what an expression means without working it out.

Grouping symbols show what to do first. Fifth graders use parentheses ( ), brackets [ ] and braces { }, working from the innermost group out: 2 × {5 + [3 × (4 − 1)]} = 2 × {5 + [3 × 3]} = 2 × {5 + 9} = 28.

These pages cover writing, reading and interpreting expressions, then evaluating expressions with brackets and braces, writing each step. Every page has an answer key on page 2 that shows the steps.

Standards

  • CCSS.MATH.CONTENT.5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
  • CCSS.MATH.CONTENT.5.OA.A.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

How to use them

  1. Start with Write Numerical Expressions. Underline the step that happens first in the words.
  2. Use Numerical Expressions in Words to go the other way.
  3. Interpret Numerical Expressions asks children to compare without calculating. Ask them to explain how they know.
  4. Then evaluate with brackets and braces, one step per line.

Teaching tips

  • "Add 8 and 7, then multiply by 2" needs parentheses: 2 × (8 + 7). Without them, 2 × 8 + 7 is a different number.
  • Start with the innermost grouping symbol and work out.
  • 3 × (18,932 + 921) is three times as large as 18,932 + 921, whatever the sum is.

Questions teachers and parents ask

What is a numerical expression?

Numbers joined by operation signs, like (12 + 4) ÷ 2. It has a value but no equal sign.

What is the difference between an expression and an equation?

An equation has an equal sign and says two things are the same. An expression is just one side: a calculation to do.

What order do you use for brackets and braces?

Work inside the innermost group first, then the next group out: parentheses, then brackets, then braces. Inside each group, multiply and divide before you add and subtract.