Mathematics · Year 2

Active learning ideas

The Bridge to Ten

Active learning makes the abstract strategy of 'bridging to ten' visible and tangible for young learners. By using hands-on materials and collaborative talk, students move beyond memorization to truly understand how numbers work together, which builds both confidence and fluency.

• ACARA Content Descriptions
• AC9M2N03

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 20 min · Pairs

Inquiry Circle: The Ten-Frame Fill

In pairs, one student chooses a number (e.g., 7) and places that many counters on a ten-frame. The second student is given a 'problem' card (e.g., +6). They must physically move enough counters to fill the first frame before starting a second frame, then explain the 'bridge' they made.

Why is ten considered a friendly number in our number system?

Facilitation Tip

During The Ten-Frame Fill, circulate and ask students to describe how the second number is being split as they fill the frame.

What to look for

Provide students with a card showing an addition problem, such as 9 + 4. Ask them to write the steps they used to solve it, specifically showing how they 'bridged to ten'. For example: '9 + 1 = 10, then 10 + 3 = 13'.

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

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Strategy Showdown

The teacher presents a problem like 9 + 4. Students think of two ways to solve it: counting on and bridging to ten. They discuss with a partner which way was faster and why, focusing on the 'jump' to the number ten.

How can knowing our number bonds to ten help us solve 8 plus 5?

Facilitation Tip

During Strategy Showdown, provide sentence stems like 'I chose this method because...' to structure peer explanations.

What to look for

Display a series of addition problems on the board that require bridging to ten (e.g., 7 + 6, 8 + 5, 9 + 3). Ask students to hold up fingers to show the number they would 'take away' from the second addend to make ten. For 7 + 6, they would hold up 3 fingers.

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

Activity 03

• Simulation Game
• 30 min · Small Groups

Simulation Game: Number Line Leaps

Using a large floor number line, students act as 'kangaroos'. To solve 28 + 5, they must first jump to the next 'watering hole' (30) and then calculate how much of their jump is left to complete. This physical movement reinforces the two-step nature of bridging.

When is bridging to ten more effective than counting on?

Facilitation Tip

During Number Line Leaps, have students announce each 'leap' out loud so you can hear when they reach the ten mark and count on.

What to look for

Pose the question: 'When would it be faster to count on from 8 to solve 8 + 5, and when would bridging to ten be a better choice?' Facilitate a class discussion where students explain their reasoning, perhaps using examples.

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

A few notes on teaching this unit

Teach this by modeling the split with real objects first, then fading support as students internalize the process. Avoid rushing to abstract recordings; ensure students can justify each step using materials. Research shows that students who verbalize their thinking while using manipulatives develop stronger number sense than those who only write equations.

Students will confidently break numbers to reach ten, explain their steps aloud, and apply the strategy to solve similar problems. You’ll see students stopping to check their work, using materials purposefully, and sharing ideas with peers without relying on counting by ones.

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Watch Out for These Misconceptions

• During The Ten-Frame Fill, watch for students who fill the frame and stop without adding the leftover part of the second number.

  Prompt them to point to the empty spaces and say, 'How many are still outside the frame? Now add those to ten.' Gently cover the filled frame with your hand to focus attention on the leftover amount.

• During Strategy Showdown, watch for students who split the second number incorrectly or forget to subtract what they bridge.

  Have the peer 'guard' hold up a hand to block the second number and only reveal the part being added to make ten, then the rest. Say, 'Show me how much you gave away first, then what’s left.'

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Methods used in this brief

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