Mathematics · 2nd Year

Active learning ideas

Addition Strategies: Bridging Ten

Active learning works for bridging ten because students need physical and visual experiences to internalize the abstract idea that adding and subtracting are connected. When they see numbers moving on a line or rearranging objects, the inverse relationship becomes clear in a way that memorization cannot achieve.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Understanding and recalling facts

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 25 min · Small Groups

Inquiry Circle: Fact Family Triangles

Give groups sets of three numbers (e.g., 12, 8, 4). They must work together to create four different number sentences (two addition, two subtraction) and present them to the class using a large triangle poster.

How does making ten help you add 8 and 5?

Facilitation Tip

During Fact Family Triangles, ask students to rotate roles so each child experiences building, solving, and explaining the triangle at least once.

What to look for

Present students with addition problems like 7 + 5 and 9 + 3. Ask them to write down the steps they used to solve each, specifically noting how they 'bridged ten'.

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

Activity 02

• Role Play
• 15 min · Whole Class

Role Play: The Number Swap

Two students hold large number cards (e.g., 6 and 9) with a '+' sign between them. They show the total. Then they physically swap places to show that the total remains the same. They then try this with a '-' sign to see why it doesn't work.

Can you show how to use bridging ten to add 7 + 6?

Facilitation Tip

For The Number Swap, model exaggerated facial expressions and gestures to highlight the moment when the number 'swap' changes the operation’s direction.

What to look for

Pose the question: 'How does making ten help you add 8 and 5?' Facilitate a class discussion where students share their strategies, perhaps using drawings or manipulatives to illustrate their points.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Inverse Detectives

Provide a subtraction problem like 18 - 5 = 13. Pairs must come up with an addition 'check' to prove the answer is correct. They then create their own 'secret' subtraction for another pair to solve and check.

What is 9 + 4? Can you draw it on a number line?

Facilitation Tip

In Inverse Detectives, provide sentence stems like 'I know 8 + 5 = 13 because 13 - 8 = 5' to guide precise language.

What to look for

Give each student a card with an addition problem, such as 6 + 7. Ask them to solve it using the bridging ten strategy and draw it on a number line on the back of the card.

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

A few notes on teaching this unit

Teachers should avoid rushing to abstract symbols; instead, use number lines and counters to anchor every step. Research shows that students who verbalize their thinking while moving objects develop stronger mental models. Emphasize the language of 'making ten' and 'taking from ten' to reinforce the bridge between addition and subtraction.

Students will confidently use bridging ten to solve addition problems and immediately recognize the corresponding subtraction fact. They will explain their steps aloud and connect their process to the part-whole model, showing they understand why the strategy works.

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Watch Out for These Misconceptions

• During The Number Swap, watch for students who reverse the order of numbers without noticing the operation changes. Have them act out the swap with counters so they see 'giving away' is different from 'joining'.

  Use the physical counters in The Number Swap to show that if you start with 3 sweets and take away 10, you are trying to remove more than you have, which is impossible.

• During Fact Family Triangles, watch for students who treat the three numbers as unrelated. Ask them to place each number in the triangle’s corners and label the sides that show addition and subtraction to reveal the shared parts.

  Use the part-whole bar models in Fact Family Triangles to circle the three numbers and draw arrows between the same numbers in the addition and subtraction equations.

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Methods used in this brief

• Inquiry Circle
• Role Play
• Think-Pair-Share