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

Addition of Integers and Rational Numbers

Explore addition of positive and negative integers, fractions, and decimals, using various models and strategies.

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

About This Topic

Combining and Partitioning is the heart of early arithmetic. In 1st Class, students move from simply counting all objects to 'counting on' from a larger number and breaking totals apart into smaller components. This topic covers the NCCA Number strand's focus on addition and subtraction, emphasizing that these are inverse operations. Understanding that 7 can be 5+2 or 4+3 gives students the flexibility to solve problems in multiple ways.

By partitioning numbers, children develop a deeper sense of number bonds and the 'part-part-whole' relationship. This is essential for mental math and later work with larger numbers. This topic is most effective when students use collaborative problem-solving, where they are given a total and must work together to find all the different ways to 'break' that number apart using physical objects.

Key Questions

1. What happens to the total when you add more objects to a group?
2. How can you use a number line to help you add two numbers together?
3. Can you show that adding 5 and 3 gives the same answer as adding 3 and 5?

Learning Objectives

• Calculate the sum of two positive integers up to 20 using manipulatives and number lines.
• Compare the results of adding numbers in different orders to demonstrate the commutative property of addition.
• Identify and explain the part-part-whole relationship in addition problems involving numbers up to 20.
• Represent addition problems using concrete objects and pictorial models.

Before You Start

Counting and Cardinality

Why: Students need to be able to count objects accurately and understand that the last number counted represents the total quantity.

Number Recognition

Why: Students must be able to identify and read numerals up to 20 to engage with addition problems of this scope.

Key Vocabulary

Addend	A number that is added to another number in an addition problem. For example, in 5 + 3 = 8, both 5 and 3 are addends.
Sum	The result when two or more numbers are added together. In 5 + 3 = 8, the sum is 8.
Number Line	A straight line marked with a series of numbers at intervals, used to visualize mathematical operations like addition.
Part-Part-Whole	A model that shows how two smaller numbers (parts) combine to make a larger number (whole) through addition.

Watch Out for These Misconceptions

Common Misconception

Thinking subtraction always means 'taking away'.

What to Teach Instead

Subtraction can also mean 'finding the difference' or 'comparing.' Use two towers of blocks of different heights. Instead of taking blocks away, ask students to find how many more one has. Peer discussion helps them see that the math is the same even if the action is different.

Common Misconception

Believing that the order of numbers doesn't matter in subtraction.

What to Teach Instead

Students often try to subtract the smaller number from the larger one regardless of the order (e.g., seeing 2 - 5 and saying 3). Use physical objects to show that if you have 2 sweets, you cannot give away 5. This hands-on limit makes the rule memorable.

Active Learning Ideas

Inquiry Circle: The Part-Part-Whole Lab

Groups are given a 'whole' number (e.g., 12) and a pile of cubes. They must find as many ways as possible to split the 12 cubes into two hoops. They record each combination as a number sentence to see the patterns.

30 min·Small Groups

Role Play: The Number Shop

One student is the 'Shopkeeper' with a set number of items (the whole). A 'Customer' buys some (a part), and the class must figure out how many are left (the other part). This makes the abstract concept of subtraction a concrete social interaction.

20 min·Small Groups

Think-Pair-Share: Story Sums

The teacher provides a simple equation like 5 + 3 = 8. Partners must come up with a real-life story to match it (e.g., 5 birds on a fence, 3 more fly down). They share their stories to see how the same math applies to different situations.

15 min·Pairs

Real-World Connections

• When a baker is preparing cookies, they might add 5 chocolate chip cookies to a tray and then add another 3 chocolate chip cookies. They use addition to find the total number of cookies on the tray.
• A child playing with building blocks might count 7 red blocks and then add 4 blue blocks. They use addition to determine the total number of blocks they have for their tower.

Assessment Ideas

Quick Check

Present students with a collection of 15 counters. Ask them to show two different ways to partition the 15 counters into two groups and record the addition sentence for each. For example, 10 + 5 = 15 and 8 + 7 = 15.

Exit Ticket

Give each student a card with a number sentence, such as '6 + 4 = ?'. Ask them to solve the problem using a number line drawn on the back of the card and write the sum. Then, ask them to write one sentence explaining what happens to the total when you add more objects to a group.

Discussion Prompt

Pose the question: 'Can you show that adding 5 and 3 gives the same answer as adding 3 and 5?' Allow students to use manipulatives or draw pictures to demonstrate their thinking. Facilitate a class discussion where students share their findings and explain the concept of the commutative property.

Frequently Asked Questions

What is 'partitioning' in 1st Class math?

Partitioning is simply breaking a number into smaller parts. For example, 10 can be partitioned into 8 and 2. It is a vital skill in the NCCA curriculum because it helps children understand how numbers are built and prepares them for adding larger numbers by breaking them into tens and units.

How do I teach the relationship between addition and subtraction?

Use 'fact families.' Show that if 3 + 4 = 7, then 7 - 4 = 3. Active learning through 'triad cards' (where three numbers are linked) helps students see these connections. Doing this with physical objects like counters ensures they see the groups joining and separating.

How can active learning help students understand partitioning?

Active learning turns partitioning into an exploration. Instead of memorizing facts, students use collaborative investigations to 'break' numbers apart physically. This hands-on approach allows them to see that the total remains the same even when the parts change, which builds a much stronger conceptual foundation than worksheets alone.

What are 'part-part-whole' models?

It is a visual diagram (usually three circles) showing how two parts combine to make a whole. It is a key tool in 1st Class for solving word problems. Students can use it to find a missing part or a missing total by placing physical objects in the circles.