Foundations of Mathematical Thinking · 2nd Year · Operations and Algebraic Patterns · Autumn Term

Addition Strategies: Bridging Ten

Students learn and apply strategies for adding numbers by bridging through ten.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Understanding and recalling facts

About This Topic

Understanding the relationship between addition and subtraction is a cornerstone of algebraic thinking in the NCCA Primary Mathematics Curriculum. Instead of seeing these as two isolated skills, 2nd Year students explore them as inverse operations. They learn that if 7 + 8 = 15, then 15 - 7 must be 8. This 'fact family' approach builds computational fluency and reduces the memory load for basic facts.

Students also investigate the commutative property of addition (the idea that 4 + 5 is the same as 5 + 4) and contrast it with subtraction, where order matters. This distinction is vital for preventing common errors in vertical subtraction later on. Students grasp this concept faster through structured discussion and peer explanation, where they 'prove' these relationships using concrete sets of objects.

Key Questions

1. How does making ten help you add 8 and 5?
2. Can you show how to use bridging ten to add 7 + 6?
3. What is 9 + 4? Can you draw it on a number line?

Learning Objectives

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

Before You Start

Counting to 20

Why: Students must be able to count reliably to and from numbers within 20 to use bridging ten effectively.

Number Bonds to Ten

Why: Understanding how numbers make ten (e.g., 3 + 7 = 10) is crucial for the first step in the bridging ten strategy.

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.

Watch Out for These Misconceptions

Common Misconception

Thinking that 10 - 3 is the same as 3 - 10.

What to Teach Instead

Students often apply the commutative property of addition to subtraction. Use physical objects to show that if you have 3 sweets, you cannot give away 10. This hands-on demonstration makes the 'order matters' rule in subtraction concrete.

Common Misconception

Seeing addition and subtraction as completely unrelated tasks.

What to Teach Instead

This leads to students struggling with subtraction even if they know addition facts. Use part-whole bar models to show that the same three numbers are always involved, helping them see the 'bridge' between the two operations.

Active Learning Ideas

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.

25 min·Small Groups

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.

15 min·Whole Class

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.

20 min·Pairs

Real-World Connections

• Cashiers use bridging ten when making change. For example, to give 8 euro change from 10 euro, they might think '2 to get to 10, then 6 more', totaling 8.
• Construction workers might estimate materials needed. If they need 7 bricks and then 6 more, they might quickly calculate '7 plus 3 is 10, plus 3 more is 13 bricks'.

Assessment Ideas

Quick Check

Present students with addition problems like 7 + 5 and 9 + 3. Ask them to write down the steps they used to solve each, specifically noting how they 'bridged ten'.

Discussion Prompt

Pose the question: 'How does making ten help you add 8 and 5?' Facilitate a class discussion where students share their strategies, perhaps using drawings or manipulatives to illustrate their points.

Exit Ticket

Give each student a card with an addition problem, such as 6 + 7. Ask them to solve it using the bridging ten strategy and draw it on a number line on the back of the card.

Frequently Asked Questions

What are 'Fact Families' and why are they important?

Fact families are groups of related addition and subtraction facts using the same three numbers (e.g., 2+3=5, 3+2=5, 5-3=2, 5-2=3). They are important because they help students understand the logic of math, making it easier to solve problems and check their work.

How can active learning help students understand inverse operations?

Active learning strategies like 'The Number Swap' allow students to physically experience the properties of operations. When they move their bodies to represent numbers, they internalize that addition is flexible while subtraction is rigid. This physical movement creates a stronger mental map than simply writing equations on a page.

How do I explain that subtraction is the 'opposite' of addition?

Use the 'undoing' analogy. If addition is building a tower of blocks, subtraction is taking them down. If you add 5 blocks and then take 5 away, you are back where you started. This concept of 'undoing' is the foundation of algebra.

Why does my child struggle with 15 - 8 but knows 7 + 8 = 15?

They may not yet see the connection between the two. Encourage them to 'think addition' when they see a subtraction sign. Ask, '8 plus what makes 15?' This shifts the focus to a relationship they already know, building confidence.