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Understand Grouping Symbols: Parentheses, Brackets, and Braces

Students learn the purpose and hierarchy of parentheses, brackets, and braces in numerical expressions. They recognize that these symbols indicate which operations must be performed first and understand the nesting order: parentheses inside brackets inside braces.

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Understand Grouping Symbols: Parentheses, Brackets, and Braces

Grade 5 · Algebraic Thinking: Expressions and Grouping Symbols · question 1 of 3

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20 rungs. A star at the top.

Rosa walks beside a parade float. Each float carries 7 drummers and 8 dancers. Rosa counts 4 floats just like it. How many performers are on the floats?

How it is taught

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Grouping symbols show what to compute first.

Work from the inside grouping outward.

Read it: Grouping symbols

5 + 6 × 2: × comes before +, so 6 × 2 = 12, then 5 + 12 = 17. To add first, write parentheses: (5 + 6) × 2 is 11 × 2 = 22.

  1. Work inside parentheses ( ) first, then brackets [ ], then braces { }, from the inside out.
  2. Then × and ÷, from left to right.
  3. Then + and −, from left to right.

Without parentheses, × comes first: 5 + 6 × 2 is 5 + 12.

Parentheses say "do this first": (5 + 6) × 2 adds before it multiplies.

One operation a line keeps every step easy to check.

The innermost grouping first, then × and ÷, then + and −.

Going left to right: 5 + 6 = 11, then 11 × 2 = 22.

× comes before +: 6 × 2 = 12, and 5 + 12 = 17.

(3 + 8) × 9 = ___ — 99. 3 + 8 = 11, then 11 × 9 = 99.

{[(2 + 3) × 4] − 5}

Some math expressions use parentheses, brackets, and braces. They tell us which part to do first.

Here is our expression — a brace holding a bracket holding parentheses, all nested together.

The order is always inside-out: parentheses first, then brackets, then braces.

Start with the innermost group — the parentheses.

Two plus three is five. We rewrite the expression with a five where the parentheses used to be.

Next we do the brackets — five times four.

Five times four is twenty. Now the expression is just braces around twenty minus five.

Last, the braces.

Twenty minus five is fifteen.

Parentheses, brackets, and bracesWhich part do we do first?Inside out: ( ) → [ ] → { }{[(2+3)×4]−5}{[5×4]−5}{20−5}=15ANSWER15innermost first
Grade 5 · Working from the innermost group out

The whole expression equals fifteen. Always work from the innermost group outward!

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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