Foundations of Mathematical Thinking · 1st Class · Addition of Numbers to 20 · Autumn Term

Subtraction of Numbers to 20

Investigate subtraction of positive and negative integers, fractions, and decimals, using various methods and understanding 'subtracting a negative'.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.1
• NCCA: Junior Cycle - Strand 3: Number - N.1.2

About This Topic

Mental Strategies and Doubles focuses on giving students a 'toolbox' for quick calculation. In 1st Class, the NCCA curriculum moves students away from counting on fingers toward more sophisticated mental methods. Learning doubles (like 6+6) and near-doubles (6+7) allows children to use known facts to solve unknown problems. This builds computational fluency and reduces the cognitive load during complex tasks.

Strategies like 'bridging through ten' (e.g., solving 8+5 by doing 8+2+3) are also introduced. These methods encourage students to see numbers as flexible and decomposable. Students grasp these concepts faster through structured discussion and peer explanation, where they share the different 'shortcuts' they used to arrive at an answer, validating that there is often more than one way to solve a problem.

Key Questions

1. What does it mean to take away some objects from a group?
2. How can you use counters or a number line to find the answer to a subtraction?
3. Can you tell a take-away story using objects from the classroom?

Learning Objectives

• Calculate the difference between two numbers up to 20 using concrete materials.
• Represent subtraction problems involving numbers up to 20 on a number line.
• Explain the meaning of taking away objects from a set to find a difference.
• Compare the results of subtraction problems solved using different strategies, such as counting back or using a number line.

Before You Start

Counting to 20

Why: Students need to be able to count reliably to 20 to understand the quantities involved in subtraction problems up to 20.

One-to-One Correspondence

Why: This foundational skill is necessary for accurately representing and manipulating quantities when subtracting.

Key Vocabulary

Subtract	To take away a number or quantity from another number or quantity.
Difference	The result when one number is subtracted from another.
Take away	To remove a part from a whole; this is a common phrase used to describe subtraction.
Number line	A line with numbers placed at intervals, used to visualize mathematical operations like addition and subtraction.

Watch Out for These Misconceptions

Common Misconception

Relying solely on finger counting for every sum.

What to Teach Instead

While fingers are a great tool, they can slow down progress. Use 'timed challenges' in pairs where students are encouraged to use a 'near double' trick instead of counting. Peer modeling of faster strategies helps motivate students to try new mental tools.

Common Misconception

Thinking that 'doubling' only applies to small numbers.

What to Teach Instead

Students often stop using doubles once they pass 5+5. Use hands-on modeling with base-ten blocks to show that doubling 10 or 20 follows the same pattern. Collaborative investigations into 'big doubles' help expand their mental limits.

Active Learning Ideas

Stations Rotation: The Strategy Circuit

Set up stations for different mental tricks: one for 'Doubles' using mirrors, one for 'Adding 9' (add 10, subtract 1), and one for 'Near Doubles' using ladybird spots. Students rotate and practice each specific mental shortcut.

40 min·Small Groups

Think-Pair-Share: How Did You Get There?

The teacher presents a problem like 7 + 8. Students solve it mentally, then explain their specific strategy to a partner (e.g., 'I doubled 7 and added 1' or 'I made a ten'). This surfaces different ways of thinking.

15 min·Pairs

Simulation Game: The Human Number Line

Students stand on a large number line. To solve 9 + 6, the '9' student explains how they can 'jump' to 10 first and then add the remaining 5. This physical 'bridging' makes the mental strategy visible and concrete.

20 min·Whole Class

Real-World Connections

• When a baker has 15 cookies and sells 7, they use subtraction to find out how many cookies are left to decorate.
• A child with 12 building blocks uses subtraction to determine how many are remaining after giving 5 to a friend.

Assessment Ideas

Exit Ticket

Provide students with 10 counters. Ask them to show 15 take away 6. Have them write the number sentence and the answer on a slip of paper.

Quick Check

Draw a number line from 0 to 20 on the board. Pose a subtraction problem, such as 18 - 5. Ask students to come up and demonstrate how to solve it by jumping backward on the number line.

Discussion Prompt

Present a scenario: 'There were 11 birds on a branch, and 4 flew away.' Ask students: 'What does it mean to take away the birds? How can we find out how many birds are left?' Encourage them to use objects or drawings to explain their thinking.

Frequently Asked Questions

What are 'near doubles' and why are they taught?

Near doubles are sums like 6+7. If a child knows 6+6=12, they can easily figure out that 6+7 is just one more (13). The NCCA curriculum emphasizes this because it uses existing knowledge to solve new problems, which is much faster than counting from one.

How can I help my child stop counting on their fingers?

Encourage the use of 'ten frames' or 'number strings' to visualize groups. Active learning games that reward using a specific strategy (like 'making a ten') help them see the efficiency of mental math. Practice doubles daily until they are automatic.

What is 'bridging through ten'?

It is a mental strategy where you use ten as a landing point. For 8+5, you add 2 to get to 10, then add the remaining 3 to get 13. It is a foundational skill for 1st Class that makes adding across the tens boundary much easier.

What are the best hands-on strategies for teaching mental math?

Using visual aids like Rekenreks (bead strings) or ten-frames is highly effective. In a student-centered classroom, peer-teaching is powerful; when one student explains their 'shortcut' to another, it reinforces the logic for both. Games that require quick strategy selection also help build fluency.