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.

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

Learning Objectives

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

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

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

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.

Prepare & details

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.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.'

Assessment Ideas

Exit Ticket

After The Ten-Frame Fill, give each student a slip with 7 + 6. Ask them to write the steps they took to solve it using the ten-frame, showing how they split the 6.

Quick Check

During Number Line Leaps, display 9 + 4. Ask students to hop to 10 first, then shout out how many more hops they took. Listen for '1 to reach ten, then 3 more' to confirm bridging.

Discussion Prompt

After Strategy Showdown, pose the question: 'If you were adding 6 + 6, would you bridge to ten or count on? Why?' Facilitate a brief turn-and-talk before sharing responses.

Extensions & Scaffolding

• Challenge: Provide three-digit problems like 28 + 5 and ask students to apply bridging to ten in the ones place.
• Scaffolding: Give students a strip of paper with 10 circles to represent the ten-frame, pre-filled to the needed amount.
• Deeper exploration: Have students create their own word problems where bridging to ten is the most efficient strategy.

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.