Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
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
Grouping symbols tell a reader which part of a calculation to do first. Fifth graders meet three kinds: parentheses ( ), brackets [ ] and braces { }. They all do the same job, and the different shapes simply make nested groups easier to read. In 2 × [5 + (9 - 3)], the innermost group 9 - 3 is worked first, then the bracket 5 + 6, and finally the multiplication outside, giving 22.
Students learn that moving or removing a pair of parentheses can change the value of an expression completely. 20 - (6 + 4) is 10, but (20 - 6) + 4 is 18. Being able to evaluate an expression with grouping symbols, and to place symbols so that an expression reaches a target value, builds the careful, structured reading of expressions that algebra in sixth grade depends on. Work at this grade stays with whole numbers and simple fractions or decimals, and focuses on the meaning of the symbols rather than on long chains of rules.
Students who read 4 + 3 × 5 as 7 × 5 = 35 have ignored that multiplication comes first. Rewriting it as 4 + (3 × 5) shows the hidden grouping and gives 19.
Some students think brackets mean multiply or braces mean add. All three symbols only group; the operation is always written separately.
In {2 + [3 × (1 + 1)]}, starting with the braces leads to confusion. Find the deepest pair of symbols first and work outward one layer at a time.
In 2(6 + 1) the 2 still multiplies the group even with no × sign shown. If this notation appears, ask students to rewrite it as 2 × (6 + 1).
Evaluate 3 × [12 - (2 + 4)] + 5.
Answer: 3 × [12 - (2 + 4)] + 5 = 23.
A useful routine is to underline the innermost group, rewrite the expression with that group replaced by its value, and repeat. Each line of work then gets shorter, which makes errors easy to spot. Puzzle tasks such as placing one pair of parentheses in 8 + 4 × 3 - 1 to make 35 build flexible thinking about structure.
Assessment items often show two students' work on the same expression and ask which is correct, or ask for the value of a nested expression in a multiple-choice format with distractors built from left-to-right errors.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 30
Work inside the parentheses first: 8 - 3 = 5. Then 6 × 5 = 30.
Answer: C) 3
Innermost first: 1 + 3 = 4. The bracket is 2 × 4 = 8. Then 24 ÷ 8 = 3.
Answer: 19
With no grouping symbols, multiply before adding: 2 × 7 = 14, then 5 + 14 = 19. Working left to right would wrongly give 49.
Answer: A) Around 4 + 2
10 - (4 + 2) = 10 - 6 = 4. Grouping 10 - 4 instead gives 6 + 2 = 8, and putting parentheses around everything changes nothing, so the value stays 8.
Answer: 4
5 - 1 = 4. Then 3 × 4 = 12. Then 20 - 12 = 8. Finally 8 ÷ 2 = 4.
Answer: C) 2 + 5 × 3
4 × 3 + 1 = 13 and 5 × 3 - 2 = 13. 2 × (5 + 3) = 2 × 8 = 16. 2 + 5 × 3 = 2 + 15 = 17, because the multiplication is done first, so it has the greatest value.
A full lesson with slides, activities and an exit ticket on parentheses, brackets and braces, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.OA.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn parentheses, brackets and braces into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. In fifth grade math they all group part of an expression. Using different shapes for nested groups simply makes it easier to see which closing symbol matches which opening one.
It focuses on grouping symbols and evaluating expressions with them. Students also apply the convention that multiplication and division come before addition and subtraction, but exponents in expressions are a sixth grade topic.