Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Finding the Unknown in Subtraction

Active learning helps students grasp finding the unknown in subtraction because it turns abstract symbols into concrete experiences. Moving, talking, and testing ideas with partners makes the relationship between addition and subtraction visible and memorable for first-year learners.

• NCCA Curriculum Specifications
• NCCA: Primary - Algebra

• 15–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 25 min · Pairs

Partner Relay: Missing Subtrahend Dash

Pairs line up at the board with subtraction cards like 10 - ? = 5. One partner solves by counting up from 5 to 10, writes the answer, and tags the next partner for a new card. Switch roles halfway; discuss checks as adding back.

Compare how finding a missing part in subtraction is similar to finding a missing part in addition.

Facilitation Tip

During Partner Relay: Missing Subtrahend Dash, circulate to listen for students explaining their thinking aloud, especially when they hit equations like 4 - ? = 6.

What to look for

Present students with three equations: 15 - ? = 8, ? - 6 = 9, and 10 - 3 = ?. Ask them to solve for the missing number in the first two and identify the difference in the third. Collect their answers to gauge understanding of finding the unknown and identifying parts of a subtraction sentence.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: Unknown Spot Puzzles

Set up three stations: number lines for missing minuends, counters for subtrahends, and part-whole mats for mixed. Small groups spend 10 minutes per station solving and recording three equations each, then share one strategy with the class.

Design a method to check if your missing number is correct.

Facilitation Tip

For Station Rotation: Unknown Spot Puzzles, place a variety of equations at each station so students practice both missing minuends and subtrahends.

What to look for

Give each student a card with a problem like 'Sarah had 18 stickers. She gave some to her friend and now has 11. How many stickers did she give away?'. Ask students to write the equation (18 - ? = 11), solve it, and then write one sentence explaining how they checked their answer.

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

Activity 03

• Problem-Based Learning
• 20 min · Whole Class

Whole Class Prediction Board

Display equations like 7 - 9 = ? on the board. Students predict outcomes via thumbs up/down or sticky notes, then test with counters as a group. Reveal patterns and vote on checking methods.

Predict what happens if you try to subtract a larger number from a smaller one.

Facilitation Tip

On Whole Class Prediction Board, pause after each prediction to ask students to justify their guesses before revealing the answer.

What to look for

Pose the question: 'Imagine you have 7 apples and want to give some away so you have 3 left. How many do you give away? Now, imagine you have some apples, give away 4, and have 5 left. How many did you start with?'. Ask students to compare how they found the missing number in each case and discuss if the process felt similar or different.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 15 min · Individual

Individual Equation Builders

Students get equation frames with two knowns and one blank, using beads or drawings to find the unknown. They create two originals for a partner to solve, then check together.

Compare how finding a missing part in subtraction is similar to finding a missing part in addition.

Facilitation Tip

When using Individual Equation Builders, have students use two-color counters to model the equation and physically separate the parts.

What to look for

Present students with three equations: 15 - ? = 8, ? - 6 = 9, and 10 - 3 = ?. Ask them to solve for the missing number in the first two and identify the difference in the third. Collect their answers to gauge understanding of finding the unknown and identifying parts of a subtraction sentence.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start with concrete models using counters or number bonds to show how subtraction relates to addition, then move to pictorial representations before symbols. Avoid rushing to abstract symbols; students need time to internalize the part-whole relationship. Research shows that students who verbalize their strategies during partner work develop stronger number sense and fewer misconceptions about missing values.

Students will confidently identify missing numbers in subtraction equations and explain their reasoning using manipulatives or drawings. They will check solutions by reversing the operation and share strategies with peers during discussions.

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Watch Out for These Misconceptions

• During Partner Relay: Missing Subtrahend Dash, watch for students assuming no solution exists for 5 - 8.

  Have partners use counters to model 5 - 8 by grouping five counters and trying to subtract eight. Then ask them to explain why this doesn't work in real life and focus their attention on equations where the minuend is larger.

• During Station Rotation: Unknown Spot Puzzles, watch for students assuming the missing number is always the smallest.

  Ask students to explain how they know the missing number in ? - 4 = 3 isn't smaller. Encourage them to write the related addition equation (3 + 4 = ?) to see the larger sum as the missing minuend.

• During Whole Class Prediction Board, watch for students skipping the check step after solving.

  Model adding the difference back to the subtrahend on the board to confirm the minuend. Then ask students to do the same on their individual boards before sharing answers.

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Methods used in this brief

• Problem-Based Learning
• Stations Rotation