Mathematics · 3rd Year

Active learning ideas

Mental Math: Bridging and Compensation

Active learning helps students move beyond memorized procedures by letting them test strategies in real time. For mental math with bridging and compensation, physical or visual representations make abstract ideas concrete, so students can see why 38 + 25 becomes 40 + 23 instead of just following a rule.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Operations

• 20–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Think-Pair-Share
• 30 min · Small Groups

Bridging Board Game

Students roll two dice and use bridging through ten to add the numbers. They move their game piece along a number line, explaining their bridging steps. The first to reach the end wins.

Explain how changing a number to a nearby multiple of ten can make mental addition easier.

Facilitation Tip

During The Problem Solvers' Lab, rotate to pairs to ensure every student contributes at least one idea before the group moves on.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Compensation Challenge Cards

Provide cards with addition problems. Students must solve each problem using a compensation strategy, writing down both the adjusted calculation and the final answer. They can work individually or in pairs.

Analyze why different people use different mental paths to reach the same sum.

Facilitation Tip

While students role-play as Math Storytellers, listen for the moment they translate the story into numbers out loud so you can reinforce the connection.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 20 min · Whole Class

Mental Math Relay

Divide the class into teams. Present an addition problem to the first student in each line. They solve it using bridging or compensation and run to tag the next teammate, who solves the next problem. The first team to finish wins.

Assess when it is faster to calculate mentally than to write it down.

Facilitation Tip

During the Gallery Walk, place a green dot next to bar models that show correct bridging or compensation so students can self-check as they move.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teachers direct students to use the language of ‘splitting’ and ‘adjusting’ when they explain their steps aloud. Avoid rushing to the answer by asking, ‘How did you decide to split the number first?’ before any calculations. Research shows that when students verbalize their moves, they internalize the flexibility they need for mental math.

Successful learning looks like students explaining their mental steps aloud, using bar models to justify their choices, and switching strategies when one method feels less efficient. They should also catch errors by checking their answers against the problem’s context before declaring them final.

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Watch Out for These Misconceptions

• During The Problem Solvers' Lab, watch for students grabbing numbers without first acting out the scenario with counters or drawings.

  Prompt them to model the story with objects or sketches, then ask, ‘What did the action in the story tell you to do with the numbers? How does the bar model show that?’

• During role play as Math Storytellers, watch for students declaring answers without checking if the context makes sense.

  After each performance, ask the class, ‘Does this answer fit the story? How can we tell?’ so students practice explaining why 3.2 buses is impossible.

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Methods used in this brief

• Think-Pair-Share