Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

Solving for the Unknown in Equations

Active learning helps second-year students connect concrete representations to abstract symbols when solving for unknowns. Manipulatives and movement build number sense that transfers to written equations. Students who act out problems visualize part-whole relationships more clearly than with symbols alone.

• NCCA Curriculum Specifications
• NCCA: Primary - Algebra
• NCCA: Primary - Problem solving

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Escape Room
• 30 min · Pairs

Manipulative Mats: Frame Fillers

Prepare mats with printed equations and frames. Students use counters to model and fill blanks, such as placing 7 counters for 5 + ___ = 12. Pairs explain their steps before swapping mats to check work.

What number is missing? 5 + ___ = 12

Facilitation Tip

During Frame Fillers, circulate and ask students to verbalize their counting strategy aloud to reinforce number bonds.

What to look for

Present students with equations like 7 + ___ = 15 and ___ - 3 = 8. Ask them to write the missing number on a whiteboard or paper and hold it up. Observe for accuracy and speed.

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

Activity 02

• Escape Room
• 40 min · Small Groups

Balance Scale Equations

Use real or paper balance scales. Students place number cards on both sides to solve for unknowns, like 5 + ___ balancing 12. Groups test predictions, adjust, and record balanced equations.

How can you find the missing number in ___ + 4 = 9?

Facilitation Tip

When using Balance Scale Equations, remind partners to take turns placing counters and reading the scale aloud to maintain focus on equality.

What to look for

Give each student a card with a number story like: 'Sarah had some stickers. She got 6 more and now has 14 stickers. How many did she start with?' Ask students to write an equation using a frame for the unknown and then solve it.

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

Activity 03

• Escape Room
• 35 min · Whole Class

Number Story Relay

In lines, each student adds to a group story with a missing number equation, like starting with 'I baked ___ cookies, ate 4, 9 left.' Next student solves and continues. Whole class shares final stories.

Can you write a number story that has a missing part?

Facilitation Tip

In Number Story Relay, collect stories first to identify common misconceptions before students solve them in groups.

What to look for

Pose the equation 10 - ___ = 4. Ask students to explain in their own words how they found the missing number. Encourage them to share different strategies, such as counting on or using subtraction facts.

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

Activity 04

• Escape Room
• 25 min · Pairs

Equation Hunt Cards

Scatter cards with equations around the room. Students hunt in pairs, solve using frames on clipboards, and justify answers with drawings. Collect and review as a class.

What number is missing? 5 + ___ = 12

What to look for

Present students with equations like 7 + ___ = 15 and ___ - 3 = 8. Ask them to write the missing number on a whiteboard or paper and hold it up. Observe for accuracy and speed.

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

A few notes on teaching this unit

Teach missing addends and subtrahends as the same concept by rewriting subtraction as addition with a missing addend. Avoid teaching rules like 'subtract when the blank is after the equals sign.' Use real contexts to show that equations represent relationships, not just answers. Research shows that students who model problems with manipulatives before symbols develop stronger algebraic foundations.

Success looks like students using counting strategies or known facts to determine missing numbers without guessing. They explain their reasoning and match equations to real situations. Flexibility with position of the unknown shows deep understanding of equality.

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Watch Out for These Misconceptions

• During Frame Fillers, watch for students adding the two known numbers to find the missing one, such as saying 5 + 4 = 9 so blank is 9.

  Prompt students to place counters on the mat and adjust the scale until both sides match, revealing subtraction as the inverse operation. Ask, 'What number makes both sides equal?'

• During Equation Hunt Cards, watch for students assuming the blank can only appear at the end of the equation.

  Have students sort cards by the position of the blank and explain their counting strategy, using cubes to visualize part-whole relationships in different positions.

• During Number Story Relay, watch for students treating subtraction stories as separate from addition families.

  Guide students to rewrite subtraction stories as missing addend equations, such as '___ - 3 = 8' becoming '___ + 3 = 11.' Use group discussion to correct misconceptions.

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Methods used in this brief

• Escape Room