Mathematics · Grade 5

Active learning ideas

Order of Operations

Students learn best when they move beyond memorization to experience the purpose of the order of operations. Active tasks let them see how grouping symbols and operation hierarchy change outcomes, making abstract rules concrete. Relays, puzzles, and builder activities turn what could feel like a set of steps into a problem-solving challenge they own.

• Ontario Curriculum Expectations
• 5.OA.A.1

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Escape Room
• 30 min · Small Groups

Relay Race: Order of Ops Dash

Divide class into teams of four. Write expressions with grouping symbols on the board. First student solves and tags the next, who checks and solves the next. Include 8-10 expressions per round. Debrief as a class on common errors.

Explain why a consistent order of operations is necessary for evaluating expressions.

Facilitation Tip

During the Relay Race, have students write each step on a separate index card so peers can follow the chain of reasoning in real time.

What to look for

Present students with a complex expression like 5 + [ (3 x 4) - 2 ] / 2. Ask them to write down only the first step they would perform according to the order of operations and explain why. This checks their understanding of prioritizing grouping symbols.

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

Activity 02

• Escape Room
• 25 min · Pairs

Pairs Puzzle: Grouping Switcheroo

Give pairs cards with expressions missing parentheses or brackets and a target result. They insert symbols in different spots, calculate each version, and explain which works. Switch partners midway to share strategies.

Analyze how the placement of parentheses can change the value of an expression.

Facilitation Tip

In Pairs Puzzle, require students to sketch the expression with arrows showing which operation they evaluate next, making hidden steps visible.

What to look for

Give each student a target number (e.g., 10) and a set of numbers and operations (e.g., 2, 3, 4, +, x). Ask them to construct a numerical expression using all the given numbers and operations that equals the target number, using parentheses as needed. This assesses their ability to create expressions.

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

Activity 03

• Escape Room
• 35 min · Small Groups

Small Groups: Target Expression Builder

Provide groups with numbers and operations cards plus a target value. They arrange into expressions using order of operations to match it. Groups present one solution; class verifies using the rules.

Construct a numerical expression that yields a specific result using the order of operations.

Facilitation Tip

For Target Expression Builder, circulate with a clipboard to listen for students’ explanations of why their parentheses placement matters.

What to look for

Pose the question: 'Imagine two people are asked to solve 6 + 2 x 3. One person gets 24, and the other gets 12. How could this happen?' Guide students to explain the role of the order of operations in resolving such discrepancies.

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

Activity 04

• Escape Room
• 20 min · Whole Class

Whole Class: Error Detective Hunt

Project expressions with deliberate mistakes. Students signal correct order with thumbs up/down, then vote on fixes. Tally results and discuss why the standard order prevents confusion.

Explain why a consistent order of operations is necessary for evaluating expressions.

Facilitation Tip

During the Error Detective Hunt, assign each wrong answer to a team for correction and presentation to the class.

What to look for

Present students with a complex expression like 5 + [ (3 x 4) - 2 ] / 2. Ask them to write down only the first step they would perform according to the order of operations and explain why. This checks their understanding of prioritizing grouping symbols.

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teachers know students resist grouping symbols until they see them change the problem’s outcome. Start with low-floor expressions, then layer in nested symbols and multi-step problems. Avoid teaching PEMDAS as a chant; instead, build from the concrete to the abstract through visual models and collaborative reasoning. Research shows that letting students debate incorrect solutions in small groups corrects misconceptions faster than direct instruction alone.

By the end of these activities, students should apply the order of operations fluently in expressions up to three-digit numbers and nested grouping symbols. They will justify their steps using the hierarchy and use parentheses strategically to hit numerical targets. Missteps become visible through peer discussion and live feedback, leading to lasting understanding.

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Watch Out for These Misconceptions

• During Relay Race: Order of Ops Dash, watch for students scanning left to right and ignoring grouping symbols. When you see this, pause the relay and have the student demonstrate both the left-to-right and correct order side by side on the board for the team to discuss.

  During Pairs Puzzle: Grouping Switcheroo, watch for students treating parentheses, brackets, and braces as interchangeable. Ask them to build the same expression first with parentheses, then rewrite it with brackets, and finally with braces, comparing the results to see why nesting order matters.

• During Relay Race: Order of Ops Dash, watch for students performing addition before multiplication when it appears first in the expression. Redirect them by shading the multiplication and division areas in their expressions and solving those sections before addressing addition and subtraction.

  During Error Detective Hunt, watch for students who default to addition before multiplication. Assign them a problem like 8 + 2 x 5 and ask them to draw an area model to show why multiplication must come first, then revise their original approach.

• During Target Expression Builder, watch for students skipping grouping symbols or placing them randomly. Ask them to explain why their expression equals the target without parentheses, then have them add minimal parentheses to prove the necessity of grouping.

  During Small Groups: Target Expression Builder, watch for students who think all grouping symbols work the same. Provide mixed-nesting examples (e.g., 4 x [5 + (3 - 1)]) and ask groups to trace which operation gets evaluated first, second, and third to internalize the hierarchy.

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Methods used in this brief

• Escape Room