Additive Thinking and Strategies · Term 2

The Bridge to Ten

Developing strategies to cross ten efficiently when adding single and double digit numbers.

About This Topic

Bridging to ten is a pivotal mental strategy where students use their knowledge of 'rainbow facts' (pairs that make ten) to solve addition problems that cross a ten-boundary. For example, to solve 8 + 5, a student breaks the 5 into 2 and 3, adding the 2 to the 8 to reach 10, then adding the remaining 3 to get 13. This is a key requirement of the Australian Curriculum (AC9M2N03) as it moves students away from inefficient 'counting on' strategies.

Mastering this 'friendly number' approach builds the foundation for all future mental computation. It requires students to be flexible with numbers and understand the composition of digits. This topic comes alive when students can use ten-frames and counters to physically 'fill the bucket' of the first ten before starting on the next, making the abstract mental jump a visible reality.

Learning Objectives

• Calculate the sum of two single-digit numbers where one number is greater than five, using the bridging to ten strategy.
• Explain the process of breaking down a single-digit addend to reach ten when solving addition problems.
• Compare the efficiency of bridging to ten versus counting on for addition problems crossing the ten boundary.
• Identify number pairs that sum to ten (rainbow facts) to facilitate bridging strategies.
• Demonstrate the bridging to ten strategy using manipulatives like ten-frames and counters.

Before You Start

Counting to 100 by Ones, Twos, Fives, and Tens

Why: Students need a solid understanding of number sequence and magnitude to effectively manipulate numbers when bridging.

Number Bonds to Ten

Why: This is the foundational knowledge required to identify the 'part' of the second addend that will complete the ten.

Understanding Addition as Combining

Why: Students must grasp the concept of addition as joining sets to understand how breaking apart and recombining numbers works.

Key Vocabulary

Bridging to Ten	A mental math strategy where students use their knowledge of number bonds to ten to solve addition problems that go over ten. For example, to solve 7 + 5, a student makes 10 by adding 3 to 7, then adds the remaining 2 from the 5 to make 12.
Number Bonds to Ten	Pairs of numbers that add up to ten, such as 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. These are also known as 'rainbow facts'.
Ten-Frame	A rectangular frame with ten empty squares, used to help visualize numbers up to ten and understand place value and addition strategies.
Addend	One of the numbers being added together in an addition problem. In the problem 8 + 5, both 8 and 5 are addends.

Active Learning Ideas

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.

⏱ 20 min·Pairs

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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.

⏱ 15 min·Pairs

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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.

⏱ 30 min·Small Groups

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Real-World Connections

Construction workers often need to quickly estimate quantities. For example, if a builder needs 14 bricks and has 8, they can quickly calculate they need 6 more by thinking '8 plus 2 is 10, then 4 more makes 6'.

Bakers preparing large batches of cookies might need to add ingredients. If a recipe calls for 15 eggs and they have 8 in the carton, they can mentally calculate they need 7 more eggs by bridging to ten: '8 plus 2 is 10, plus 5 more makes 7'.

Watch Out for These Misconceptions

Common Misconception

Counting on fingers and losing track of the count.

What to Teach Instead

This happens when students don't trust their number bonds. Active modeling with ten-frames shows that 8+5 is 'obviously' 13 because 2 fills the frame and 3 are left over, removing the need for finger counting entirely.

Common Misconception

Adding the whole second number to the 'ten' (e.g., 8+5 becomes 10+5=15).

What to Teach Instead

Students forget to subtract the 'bridge' amount from the second number. Peer teaching, where one student 'guards' the second number and only gives away what is needed to reach ten, helps clarify that the second number is being split.

Assessment Ideas

Exit Ticket

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'.

Quick Check

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.

Discussion Prompt

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.

Frequently Asked Questions

When should I move a student from counting on to bridging?

Once a student is fluent with their number facts to ten (e.g., they know 7+3 instantly), they are ready. If they are still counting 7+3 on their fingers, they will find bridging too cognitively heavy. Focus on 'rainbow facts' first.

What are 'friendly numbers' in Year 2?

Friendly numbers are multiples of ten (10, 20, 30...). They are 'friendly' because they are easy to add to. Bridging is the process of getting to the nearest friendly number to make the rest of the calculation simple.

How can active learning help students understand bridging to ten?

Active learning strategies like 'Number Line Leaps' turn a mental process into a physical one. By physically stopping at the 'ten' (the watering hole), students internalise the two-step logic. Collaborative games also allow students to hear the 'mental talk' of their peers, which is often more relatable than a teacher's explanation.

Is bridging to ten useful for subtraction too?

Absolutely. It is often called 'bridging back to ten'. For 13 - 5, students take away 3 to get to 10, then take away the remaining 2. It is the exact same logic in reverse and is highly efficient.