Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Addition within 10

Active learning works for addition within 10 because young students develop number sense through hands-on exploration and movement. Using physical objects and collaborative tasks helps them see relationships between numbers, which builds a foundation for flexible thinking and algebraic reasoning.

• NCCA Curriculum Specifications
• NCCA: Primary - Number

• 15–20 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 20 min · Pairs

Inquiry Circle: The Mystery Box

Place a known number of items in a box, then add some 'secret' items behind a screen. Tell the students the new total. In pairs, they must use counters to figure out how many were added.

Design a strategy to quickly add two small numbers.

Facilitation Tip

During The Mystery Box, place all objects in the box beforehand so students focus only on the missing quantity, not on the setup.

What to look for

Present students with a collection of 5-7 small objects (e.g., counters, buttons). Ask them to select two groups of objects, combine them, and then use the 'counting on' strategy to find the total. Observe and note which students can accurately apply the strategy.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Simulation Game
• 20 min · Small Groups

Simulation Game: The Human Balance Scale

Two students hold 'buckets' (bags). The teacher puts 5 blocks in one and 2 in the other. A third student must figure out how many more to add to the second bucket to make the 'scale' level.

Explain how counting on is different from counting all.

Facilitation Tip

For The Human Balance Scale, have students physically move to balance the scale while saying the equation aloud to connect actions with symbols.

What to look for

Give each student a card with an addition problem, such as '6 + 2 = ?'. Ask them to solve it using drawings and then write one sentence explaining how they used 'counting on' to find the answer.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: True or False?

Write '5 + 2 = 4 + 3' on the board. Students think about whether this is true, discuss with a partner how both sides can be 'the same' without being the same numbers, and share their reasoning.

Justify why we start with the larger number when counting on.

Facilitation Tip

In True or False?, give pairs only one counter per turn to ensure both students participate in the discussion.

What to look for

Pose the problem: 'Sarah has 3 apples and gets 4 more. Tom has 4 apples and gets 3 more. Who has more apples?' Facilitate a discussion where students explain their reasoning, comparing the strategies they used to solve each problem and discussing why starting with the larger number can be helpful.

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

A few notes on teaching this unit

Teachers should model both forward and backward thinking when solving missing addend problems. Avoid rushing to abstract symbols too quickly; instead, anchor learning in concrete experiences. Research shows that students benefit from hearing classmates explain different strategies, so facilitate discussions where students compare approaches like counting on and using known facts.

Successful learning looks like students confidently solving missing addend problems using both visual and verbal strategies. They should explain their thinking clearly and recognize that addition and subtraction are connected operations. Collaboration should show their ability to justify solutions with peers.

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Watch Out for These Misconceptions

• During The Human Balance Scale, watch for students who add both sides of the equation and write the total instead of balancing them.

  Have students place 5 counters on one side and ask how many more are needed on the other side to balance it before recording the equation.

• During The Mystery Box, watch for students who guess the answer without using the total provided.

  Ask students to explain how they used the total to find the missing part, guiding them to check their answer by adding it to the known addend.

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Methods used in this brief

• Inquiry Circle
• Simulation Game
• Think-Pair-Share