Addition Strategies: Bridging Ten

Active learning works for bridging ten because students need physical and visual experiences to internalize the abstract idea that adding and subtracting are connected. When they see numbers moving on a line or rearranging objects, the inverse relationship becomes clear in a way that memorization cannot achieve.

• 2nd Year
• Foundations of Mathematical Thinking
• 3 activities
• 15 min–25 min

Learning Objectives

1. Calculate the sum of two single-digit numbers by bridging through ten.
2. Explain the strategy of bridging ten to add two numbers, using a number line or manipulatives.
3. Compare the efficiency of bridging ten versus direct counting for specific addition problems.
4. Identify the nearest multiple of ten when adding numbers that cross the ten boundary.

Inquiry Circle

⏱ 25 min·Small Groups

Inquiry Circle: Fact Family Triangles

Give groups sets of three numbers (e.g., 12, 8, 4). They must work together to create four different number sentences (two addition, two subtraction) and present them to the class using a large triangle poster.

Prepare & details

How does making ten help you add 8 and 5?

Facilitation Tip: During Fact Family Triangles, ask students to rotate roles so each child experiences building, solving, and explaining the triangle at least once.

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

Role Play

⏱ 15 min·Whole Class

Role Play: The Number Swap

Two students hold large number cards (e.g., 6 and 9) with a '+' sign between them. They show the total. Then they physically swap places to show that the total remains the same. They then try this with a '-' sign to see why it doesn't work.

Prepare & details

Can you show how to use bridging ten to add 7 + 6?

Facilitation Tip: For The Number Swap, model exaggerated facial expressions and gestures to highlight the moment when the number 'swap' changes the operation’s direction.

Setup: Open space or rearranged desks for scenario staging

Materials: Character cards with backstory and goals, Scenario briefing sheet

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Inverse Detectives

Provide a subtraction problem like 18 - 5 = 13. Pairs must come up with an addition 'check' to prove the answer is correct. They then create their own 'secret' subtraction for another pair to solve and check.

Prepare & details

What is 9 + 4? Can you draw it on a number line?

Facilitation Tip: In Inverse Detectives, provide sentence stems like 'I know 8 + 5 = 13 because 13 - 8 = 5' to guide precise language.

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

Teachers should avoid rushing to abstract symbols; instead, use number lines and counters to anchor every step. Research shows that students who verbalize their thinking while moving objects develop stronger mental models. Emphasize the language of 'making ten' and 'taking from ten' to reinforce the bridge between addition and subtraction.

What to Expect

Students will confidently use bridging ten to solve addition problems and immediately recognize the corresponding subtraction fact. They will explain their steps aloud and connect their process to the part-whole model, showing they understand why the strategy works.

Watch Out for These Misconceptions

Common Misconception

During The Number Swap, watch for students who reverse the order of numbers without noticing the operation changes. Have them act out the swap with counters so they see 'giving away' is different from 'joining'.

What to Teach Instead

Use the physical counters in The Number Swap to show that if you start with 3 sweets and take away 10, you are trying to remove more than you have, which is impossible.

Common Misconception

During Fact Family Triangles, watch for students who treat the three numbers as unrelated. Ask them to place each number in the triangle’s corners and label the sides that show addition and subtraction to reveal the shared parts.

What to Teach Instead

Use the part-whole bar models in Fact Family Triangles to circle the three numbers and draw arrows between the same numbers in the addition and subtraction equations.

Assessment Ideas

Quick Check

After Fact Family Triangles, present students with addition problems like 7 + 5 and 9 + 3. Ask them to write the corresponding subtraction facts and note which ten they bridged.

Discussion Prompt

During Inverse Detectives, pose the question: 'How does making ten help you add 8 and 5?' Circulate and listen for students to reference the number line or counters, then invite volunteers to share their drawings.

Exit Ticket

After The Number Swap, give each student a card with an addition problem such as 6 + 7. Ask them to solve it using bridging ten and draw the jumps on a number line on the back of the card before leaving the room.

Extensions & Scaffolding

• Challenge students to create their own bridging ten word problems using the numbers 11 to 19, then trade with a partner to solve.
• For students who struggle, give them a pre-drawn number line with the 'bridge' at ten already marked to scaffold their jumps.
• Deeper exploration: Invite students to investigate three-digit bridging, such as 28 + 15, and present their solutions to the class using place-value mats.

Key Vocabulary

Bridging Ten	An addition strategy where you first add to reach the next multiple of ten, then add the remaining amount.
Number Line	A visual representation of numbers in order, used to model addition and subtraction by making jumps.
Multiple of Ten	A number that can be divided by ten with no remainder, such as 10, 20, 30, etc.
Addend	One of the numbers being added together in an addition problem.