Mathematics · Foundation · Counting Objects to 10 · Term 1

Partitioning Numbers: Making Different Amounts

Students explore factors and multiples, and apply divisibility rules to efficiently determine factors of numbers.

• ACARA Content Descriptions
• AC9M6N02

About This Topic

Partitioning numbers helps Foundation students see that a whole can split into parts in different ways, building core number sense. They use counters or blocks to explore questions like splitting 6 into two groups or finding pairs that make 5. This aligns with Australian Curriculum AC9MFN02, where students represent numbers to 20 as combinations of smaller numbers, fostering fluency in composing and decomposing.

In the number strand, partitioning connects counting objects to early addition and subtraction. Students notice patterns, such as 5 equals 2 and 3 or 4 and 1, which prepares them for place value and flexible problem-solving. Classroom discussions reveal how these part-whole relationships appear in everyday sharing or grouping toys.

Active learning shines here through concrete materials that let students physically manipulate objects. When they build and break apart groups on ten-frames or mats, they internalize concepts that words alone cannot convey. This hands-on trial and error makes abstract ideas concrete, boosts confidence, and encourages persistence in finding all possibilities.

Key Questions

1. Can you split these 6 counters into two groups? How many different ways can you do it?
2. If I have 4 red and 3 blue blocks, how many do I have altogether?
3. Can you find two numbers that make 5 when you put them together?

Learning Objectives

• Identify all possible combinations of two numbers that sum to a given whole number up to 10.
• Demonstrate how a whole number can be partitioned into different pairs of smaller numbers using concrete materials.
• Represent the partitioning of a number up to 10 using drawings or number sentences.
• Compare different ways to partition a given number and explain if all possibilities have been found.

Before You Start

Counting Objects to 10

Why: Students need to be able to accurately count a collection of objects before they can partition them into smaller groups.

Number Recognition to 10

Why: Students must be able to recognize and name numbers up to 10 to understand the quantities they are partitioning.

Key Vocabulary

partition	To split a whole number into smaller parts or groups.
whole	The total amount or number before it is split into parts.
part	One of the smaller numbers or groups that make up a whole.
combination	A set of numbers that, when added together, equal a specific whole number.

Watch Out for These Misconceptions

Common Misconception

A number has only one way to split.

What to Teach Instead

Students often miss multiple partitions, like seeing only 3+3 for 6. Hands-on sorting with counters lets them test and list all pairs systematically. Group sharing exposes more options and builds a complete list together.

Common Misconception

Order of parts matters, so 2+3 differs from 3+2.

What to Teach Instead

This confuses addition properties. Pair activities with ten-frames show swapping parts keeps the whole same. Verbalizing during manipulation reinforces commutativity through repeated physical evidence.

Common Misconception

Parts must be equal.

What to Teach Instead

Fair sharing bias leads here. Exploration stations with varied objects encourage unequal splits. Peer teaching in rotations corrects this by comparing diverse models.

Active Learning Ideas

Counter Split Challenge: Groups of 6

Give pairs 6 counters and ask them to split into two groups in as many ways as possible, like 1 and 5 or 3 and 3. Record drawings on mini whiteboards. Share one unique split with the class.

25 min·Pairs

Part-Whole Mat Relay: Make 5

Set up mats with a whole circle (5) and two part circles. In small groups, roll dice to fill parts that sum to 5, then race to the board to draw and label. Switch roles after each turn.

30 min·Small Groups

Block Combo Hunt: 4 Red + 3 Blue

Provide connecting blocks in two colors. Individually build towers showing 4 red and 3 blue, then combine and count total. Discuss how parts make the whole.

20 min·Individual

Sharing Circle: Different Ways for 7

In a whole class circle, pass a bag of 7 objects. Each student suggests a split, like 2 and 5, and demonstrates with objects from the bag. Tally all ideas on chart paper.

35 min·Whole Class

Real-World Connections

• When sharing cookies, a child might partition a plate of 6 cookies into two groups for themselves and a friend, exploring different ways to divide them equally or unequally.
• A baker might partition a batch of 10 muffins into smaller groups for sale, perhaps 2 boxes of 5 or 5 boxes of 2, to meet customer needs.

Assessment Ideas

Quick Check

Provide students with 7 counters. Ask them to show you two different ways to partition the 7 counters into two groups. Observe if they can physically separate the counters and name the two parts for each partition.

Exit Ticket

Give each student a card with a number (e.g., 5). Ask them to draw two different ways to make that number using two parts. For example, drawing 3 dots and 2 dots, and then drawing 4 dots and 1 dot.

Discussion Prompt

Present 8 blocks on a table. Ask: 'How many different ways can we split these 8 blocks into two groups?' Encourage students to share their ideas and explain their thinking, guiding them to find all possible pairs.

Frequently Asked Questions

How to teach partitioning numbers in Foundation math?

Start with concrete objects like counters or blocks up to 10. Pose key questions such as splitting 6 into groups or combining to make 5. Use visual aids like ten-frames and part-whole mats to record explorations. Regular practice through games builds automaticity and links to addition fluency.

What are common partitioning misconceptions for beginners?

Students may think splits are unique or parts must be equal. They confuse order in sums or overlook the whole-part link. Address with manipulatives that allow testing multiple ways, followed by class charts to visualize all possibilities and correct mental models.

How can active learning help students master partitioning?

Active learning with hands-on materials turns partitioning into play. Manipulating counters or blocks lets students discover splits kinesthetically, like building 2+3=5 towers. Collaborative challenges reveal patterns peers miss alone. This engagement deepens understanding, reduces errors, and sparks joy in math exploration over rote memorization.

How does partitioning link to Australian Curriculum standards?

AC9MFN02 requires representing numbers as part combinations. Partitioning activities directly target this by exploring sums to 20. It supports subitising, counting principles, and early algebra, preparing for Year 1 operations. Track progress with student drawings of partitions to assess growth.