Additive Thinking and Strategy · Autumn Term

Bridging Through Ten

Using number bonds to ten as a bridge for adding and subtracting larger numbers.

About This Topic

Bridging through ten teaches children to use number bonds to ten for efficient mental addition and subtraction of numbers up to 100. For instance, with 8 + 7, add 2 to reach 10, then add 5 more to get 15. Children partition numbers into tens and ones, extend bonds to 20 or 100, and justify why this beats counting on. This matches Year 2 National Curriculum goals for additive reasoning and strategy choice in KS1 addition and subtraction.

The strategy builds flexible partitioning and number sense, key to additive thinking. Children assess when to bridge, count back, or find differences, connecting to unit questions on speed and bonds to 100. Regular practice fosters fluency and confidence in mental calculations.

Active learning suits this topic perfectly. Concrete tools like ten frames and counters make bonds visible, while partner discussions clarify justifications. Games turn practice into play, helping children compare strategies collaboratively and retain them long-term.

Learning Objectives

• Calculate sums and differences by partitioning numbers to bridge through ten.
• Explain the efficiency of bridging through ten compared to counting on for addition and subtraction.
• Compare and contrast the strategies of bridging through ten and direct counting for solving calculations.
• Justify the connection between number bonds to ten and number bonds to 100.
• Evaluate the most efficient strategy (bridging, counting back, finding difference) for given subtraction problems.

Before You Start

Number Bonds to 10

Why: Students must be fluent with pairs of numbers that sum to 10 to use them as a bridge.

Counting to 100

Why: A solid understanding of the number sequence up to 100 is necessary for performing calculations that extend beyond 10.

Partitioning Numbers

Why: The ability to split numbers into smaller parts (e.g., 7 into 2 and 5) is fundamental to the bridging strategy.

Key Vocabulary

Partition	To split a number into smaller parts, for example, splitting 7 into 2 and 5.
Bridge through ten	Using the number 10 as an intermediate step to make adding or subtracting easier. For example, to add 8 + 5, you can add 2 to 8 to make 10, then add the remaining 3.
Number bonds to ten	Pairs of numbers that add up to 10, such as 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5.
Counting on	Starting from the first number and counting forward one by one to find the total.
Counting back	Starting from the first number and counting backward one by one to find the difference.

Active Learning Ideas

Partner Game: Bridge Dice

Pairs roll two dice to make numbers under 20, then bridge through ten using counters on ten frames. They write the equation, explain their steps aloud, and check partner's work. Switch who rolls after five turns.

⏱ 20 min·Pairs

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Stations Rotation: Bridging Challenges

Set up three stations with ten frames, bead strings, and digit cards for additions/subtractions needing bridges. Small groups spend 7 minutes per station solving five problems and recording strategies. Rotate and share one insight at the end.

⏱ 30 min·Small Groups

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Whole Class: Strategy Share

Project bridging problems on the board. Children use mini whiteboards to solve individually, then share in a class vote: bridge, count, or difference? Discuss justifications as a group and tally results.

⏱ 25 min·Whole Class

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Individual: Bridge Journals

Children draw ten frames for given problems, partition numbers, and note why bridging works. Complete five additions and five subtractions, then self-assess speed against counting.

⏱ 15 min·Individual

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Real-World Connections

Checkout cashiers at a supermarket use mental math strategies like bridging through ten to quickly calculate change for customers. For example, if an item costs $8 and the customer pays with $10, they might think '8 to 10 is 2 dollars change'.

Construction workers might estimate materials needed for a project. If they need 17 bricks and have 8, they can quickly calculate they need 9 more by thinking '8 to 10 is 2, then 10 to 17 is 7, so 2 plus 7 is 9'.

Watch Out for These Misconceptions

Common Misconception

Bridging through ten only works for numbers close to 10.

What to Teach Instead

Children overlook its use for larger gaps, like 13 + 8. Hands-on ten frame activities show partitioning tens first, then bridging ones. Partner comparisons reveal patterns across number sizes, building flexible application.

Common Misconception

Always count back from the larger number in subtraction.

What to Teach Instead

This ignores efficient bridging or difference finding. Group strategy sorts with real problems let children test methods and discuss trade-offs. Visual models clarify when bridging saves steps.

Common Misconception

Forget to subtract the bridge amount after partitioning.

What to Teach Instead

Errors occur in adjustment steps during subtraction. Bead string demos with pauses for counting aloud reinforce the full process. Collaborative error hunts in pairs strengthen accuracy.

Assessment Ideas

Exit Ticket

Provide students with a calculation, for example, 15 - 7. Ask them to write down two ways to solve it, one using bridging through ten and one using counting back. They should also circle which method they found faster and why.

Discussion Prompt

Present the calculation 6 + 8. Ask students: 'Why is it quicker to add 4 to 6 first, then add the remaining 4, rather than counting on from 8?' Encourage them to use the term 'bridge through ten' in their explanation.

Quick Check

Write a series of calculations on the board, such as 12 - 5, 7 + 6, 18 - 9. Ask students to hold up fingers to show how many they need to add or subtract to reach the next ten for each problem. For 12 - 5, they would hold up 2 fingers (to get to 10).

Frequently Asked Questions

How do you introduce bridging through ten in Year 2?

Start with concrete ten frames and counters for bonds to 10, modelling 8 + 3 as 8 + 2 = 10, plus 1. Progress to two-digit numbers by partitioning tens. Use key questions to prompt justification, building from familiar facts to strategy choice over several lessons.

What manipulatives best support bridging through ten?

Ten frames, bead strings, and place value counters visualise bonds and partitioning clearly. They allow children to see the 'bridge' to 10 or 100. Rotate these in stations to match varied problems, ensuring all children manipulate tools repeatedly for fluency.

How does bridging through ten extend to subtraction?

Partition to bridge up to the next ten, then adjust, like 52 - 38: 52 - 2 = 50, then 50 - 36. This mirrors addition and teaches difference finding. Practice pairs problems reinforces the connection, speeding mental work within 100.

How can active learning help master bridging through ten?

Games with dice and partners make practice engaging, as children explain steps aloud and compare speeds. Stations with varied manipulatives build muscle memory for partitioning. Whole-class shares validate strategies through peer input, turning abstract mental maths into shared, memorable skills over 50-80 words of targeted play.