Bridging Through Ten

Active learning works for bridging through ten because children need to see numbers flexibly and manipulate them in space. Moving beads, rolling dice, and recording in journals helps them internalize why bridging saves steps compared to counting on. These hands-on experiences turn abstract number bonds into concrete strategies they can trust.

• Year 2
• Mathematics
• 4 activities
• 15 min–30 min

Learning Objectives

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

Think-Pair-Share

⏱ 20 min·Pairs

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.

Prepare & details

Justify why it is often faster to make a ten before adding the rest of a number.

Facilitation Tip: During Bridge Dice, remind partners to pause after each roll and say the bridge steps out loud before recording.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Stations Rotation

⏱ 30 min·Small Groups

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.

Prepare & details

Explain how knowing our bonds to 10 helps us find bonds to 100.

Facilitation Tip: In Bridging Challenges, circulate with a checklist to note which students still count on first and which bridge automatically.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Think-Pair-Share

⏱ 25 min·Whole Class

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.

Prepare & details

Assess when it is better to count back and when it is better to find the difference.

Facilitation Tip: During Strategy Share, invite two students who used different methods to compare their written steps at the board.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Think-Pair-Share

⏱ 15 min·Individual

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.

Prepare & details

Justify why it is often faster to make a ten before adding the rest of a number.

Facilitation Tip: In Bridge Journals, model one full example with crossed-out adjustments so students see the revision process.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Teaching This Topic

Teach bridging through ten by starting with ten frames and bead strings to build visual anchors. Move quickly to verbal rehearsal so students internalize the steps before writing. Avoid letting children rely on counting on as a default by routinely asking, 'Could we bridge here to save time?' Research shows that children who verbalize their steps while moving manipulatives develop stronger mental strategies.

What to Expect

Successful learning looks like children confidently partitioning numbers, explaining each step in bridging, and justifying their choice of method over counting. They should articulate when bridging through ten is efficient and apply it across different calculations without prompting. Partners should debate methods and recognize patterns in their work.

Watch Out for These Misconceptions

Common Misconception

During Partner Game: Bridge Dice, watch for students who only bridge when the second number is 1 or 2 away from ten.

What to Teach Instead

After each roll, ask students to explain how they partitioned the second number and why they chose that bridge size, even if it feels large. Partners should challenge each other to justify their bridge choice before recording.

Common Misconception

During Station Rotation: Bridging Challenges, watch for students who subtract the bridge amount incorrectly in subtraction problems.

What to Teach Instead

Have students use a number line strip in the station to physically move back the bridge amount, then pause to recount the steps aloud before recording the final answer.

Common Misconception

During Individual: Bridge Journals, watch for students who forget to subtract the bridge amount after partitioning.

What to Teach Instead

Model crossing out the bridge amount in the journal example and ask students to do the same in their own work. Circulate to check that they adjust the tens or ones correctly after bridging.

Assessment Ideas

Exit Ticket

After Partner Game: Bridge Dice, give each student the calculation 24 - 9. Ask them to write two methods, circle the faster one, and explain why bridging through ten helped them solve it quickly.

Discussion Prompt

After Whole Class: Strategy Share, present the calculation 16 + 7. Ask students to explain to a partner why bridging through 20 saves time compared to counting on from 7. Circulate to listen for the phrase 'bridge through ten' and the correct partitioning steps.

Quick Check

During Station Rotation: Bridging Challenges, write three calculations on the board: 23 - 7, 15 + 8, 32 - 6. Ask students to hold up fingers to show the bridge amount for each, then discuss their answers with a partner before moving to the next station.

Extensions & Scaffolding

• Challenge: Provide larger numbers like 47 + 39 and ask students to solve using bridging through 50 or 100, explaining their choice of bridge.
• Scaffolding: Give a partially completed Bridge Journal page with the first partition filled in, so students focus on the bridge and adjustment steps.
• Deeper exploration: Ask students to create their own bridging word problem and trade with a partner to solve, then compare methods in pairs.

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.