Write 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.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A numerical expression is a compact record of a calculation. Fifth graders learn to translate in both directions: from words such as "add 8 and 7, then multiply by 2" into 2 × (8 + 7), and from an expression back into a description of what it does. The parentheses matter, because the words say the adding happens before the multiplying.
The second half of the skill is reading an expression for its structure instead of rushing to a number. A student who looks at 3 × (418 + 96) should be able to say it is three times as large as 418 + 96 without working anything out. Likewise, (250 - 50) ÷ 4 is one fourth of the difference between 250 and 50. Seeing an expression as an object with parts, a factor of 3 applied to a sum, is the habit that later lets students simplify algebraic expressions and reason about equations instead of only computing.
"Multiply by 2 the sum of 8 and 7" is often written 2 × 8 + 7. The phrase "the sum of" signals a group, so the expression needs parentheses: 2 × (8 + 7).
When asked how 4 × (39 + 17) compares to 39 + 17, some students compute both. Point out that the question is about structure: four groups of the same sum must be four times as big.
In the phrase "subtract 3 from 10" the starting amount is 10, so the expression is 10 - 3. Acting it out with counters helps students hear the order.
Students may read (60 + 20) ÷ 4 as four times the sum. Dividing by 4 makes the sum one fourth as large, so the result is smaller than 60 + 20.
Write an expression for "subtract 6 from 20, then multiply the result by 3". Then describe how its value compares with 20 - 6.
Answer: 3 × (20 - 6), which is three times as large as 20 - 6 (it equals 42).
Card sorts work well here: one set of cards shows phrases, another shows expressions, and students match them, then argue about near-misses such as 2 × 8 + 7 versus 2 × (8 + 7). Asking students to write their own word description for an expression is a strong check of understanding.
Test items commonly offer four expressions and ask which matches a description, or ask how one expression compares with another in size. Large or awkward numbers are deliberately used so that structural reasoning is quicker than calculating.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: A) 5 × (9 + 4)
The adding happens first, so 9 + 4 is grouped in parentheses, and then the whole sum is multiplied by 5: 5 × (9 + 4).
Answer: D) It is 6 times as large
The expression is 6 groups of the same sum, so it is 6 times as large. No calculation is needed.
Answer: 5
The expression is (30 - 5) ÷ 5. Inside the parentheses 30 - 5 = 25, and 25 ÷ 5 = 5.
Answer: B) Add 48 and 12, then divide by 3
The parentheses show 48 + 12 is done first, and then the sum is divided by 3.
Answer: 64 (also accepted: 64 stickers)
Each pack has 10 + 6 = 16 stickers, and 4 packs give 4 × 16 = 64 stickers.
Answer: D) 7 × (85 - 19)
85 - 19 is a positive number, and 7 times a positive number is larger than the number itself.
A full lesson with slides, activities and an exit ticket on writing and interpreting expressions, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.OA.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn writing and interpreting expressions into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It means explaining what an expression represents, such as 'three times the sum of 18,932 and 921', and comparing expressions by their structure, without working out the final number.
No. Fifth grade expressions use numbers only. Writing expressions with letters standing for numbers is introduced in sixth grade.