Mathematics · Grade 1

Active learning ideas

Finding the Unknown in Equations

Active learning helps Grade 1 students grasp early algebraic thinking because movement and collaboration make abstract equations concrete. When students manipulate objects and discuss solutions with peers, they move beyond memorization to flexible problem-solving strategies they can explain.

• Ontario Curriculum Expectations
• 1.OA.D.8

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 20 min · Pairs

Partner Work: Counter Balances

Pairs receive equation cards with a missing number, such as 5 + ? = 12. They use counters on two sides of a paper balance to find the unknown that makes both sides equal, then record the solution and explain their steps. Switch cards every 3 minutes.

Predict what number makes the equation 7 + ? = 10 true.

Facilitation Tip

When students Build Your Equation, ask them to describe why their unknown choice makes the equation true, connecting their choice to the operation.

What to look for

Present students with three equations on a whiteboard, such as 5 + ? = 9, ? - 3 = 7, and 11 + 2 = ?. Ask students to write the missing number for the first two and the answer for the third on a small whiteboard or paper and hold it up.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 25 min · Small Groups

Small Groups: Equation Puzzles

Provide puzzle pieces with numbers and operation symbols that form incomplete equations within 20. Groups assemble them on mats, determine the missing addend or minuend using ten frames, and verify by counting aloud. Discuss one group solution with the class.

Construct an equation with an unknown number that equals 12.

What to look for

Give each student a card with an equation like 6 + ? = 10. Ask them to write the missing number and then draw a picture or write one sentence explaining how they found it.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 30 min · Whole Class

Whole Class: Number Line Races

Project equations on the board, like ? - 4 = 7. Students use personal number lines to jump to solutions, then share strategies in a class chorus. Teacher calls variations for practice, tracking participation on a chart.

Explain different strategies for finding the missing number in an equation.

What to look for

Pose the equation 8 + ? = 15. Ask students to share with a partner how they would find the missing number. Then, ask a few pairs to share their strategies with the class, encouraging them to use terms like 'counting on' or 'fact family'.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 15 min · Individual

Individual: Build Your Equation

Students draw base equations like 9 + ___ = ___ and fill blanks to make true statements within 20, using counters for support. They solve three of their own and one partner's, noting the strategy used.

Predict what number makes the equation 7 + ? = 10 true.

What to look for

Present students with three equations on a whiteboard, such as 5 + ? = 9, ? - 3 = 7, and 11 + 2 = ?. Ask students to write the missing number for the first two and the answer for the third on a small whiteboard or paper and hold it up.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Teach this topic by starting with concrete tools like counters and ten-frames to build conceptual understanding before moving to abstract symbols. Avoid rushing students to written algorithms; instead, prioritize verbal explanations so they internalize the logic behind their steps. Research shows that students who articulate their strategies develop stronger number sense and are more likely to transfer skills to new contexts.

Students show mastery when they solve equations within 20 by using counting on, fact families, or inverse operations. They justify their thinking with clear language and can represent solutions using manipulatives, drawings, or written numbers.

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Watch Out for These Misconceptions

• During Partner Work: Counter Balances, watch for students who assume the unknown must be on the right side of the equation.

  Prompt them to place the unknown on either side of the balance scale and use blocks to show both positions result in the same total, reinforcing that equations balance regardless of order.

• During Equation Puzzles, listen for students who guess numbers randomly to fill the unknown in subtraction equations.

  Have them use the puzzle pieces that show the inverse relationship, like pairing 12 - ? = 8 with ? + 8 = 12, to guide their thinking systematically.

• During Number Line Races, notice if students treat addition and subtraction unknowns as unrelated operations.

  Ask them to jump forward for addition problems and backward for subtraction from the same starting point, then discuss how both moves relate to the same total.

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Methods used in this brief

• Plan-Do-Review