AC9MFN04_E1
Recognise numbers represented in physical or virtual ten frames and explain the parts that form the whole, such as recognising 7 as 5 and 2 more.
About This Foundation Maths Topic
Part-part-whole understanding helps children recognise that a whole number can be separated into smaller parts and that those parts can be combined again to make the same whole.
For example, a collection of 7 objects can be seen as 5 and 2, 4 and 3, or 6 and 1. Recognising these relationships supports flexible number thinking and prepares students for addition, subtraction and mental computation.
In this chapter, students use ten frames, counters, number bonds, dice and dominoes to partition and combine collections to 10. Students describe the parts and the whole using spoken mathematical language.
These activities support the Australian Curriculum Version 9.0 content descriptor AC9MFN04 and its associated elaborations.
Australian Curriculum Alignment
AC9MFN04
Partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts.
AC9MFN04_E2
Partition collections of up to 10 objects in different ways and describe the part-part-whole relationship.
AC9MFN04_E3
Represent part-part-whole relationships to 10 using physical or virtual materials, including standard number arrangements on dice and dominoes.
AC9MFN04_E4
Explore number groupings in First Nations Australians’ counting systems and apply these groupings to form, partition and quantify collections to 10.
Learning Intentions
Students will learn to:
- recognise a whole collection and the smaller parts within it;
- partition collections of up to 10 objects in different ways;
- combine two parts to make a whole;
- recognise quantities shown on ten frames without counting every object;
- identify familiar number arrangements on dice and dominoes;
- describe number relationships using part-part-whole language;
- recognise that the order of the parts does not change the whole;
- represent the same number in more than one way.
Student Success Criteria
I can break a collection into two parts.
I can put two parts together to make a whole.
I can name the parts and the whole.
I can show more than one way to make a number.
I can recognise numbers shown on a ten frame.
I can recognise number groups on dice and dominoes.
I can explain how the parts make the whole.
Key Vocabulary
part
whole
part-part-whole
partition
combine
number bond
ten frame
subitise
collection
altogether
make
same
Teacher Guide
Recommended Materials
- counters, buttons, blocks or bottle caps;
- physical or printable ten frames;
- number cards from 0 to 10;
- part-part-whole mats;
- number bond templates;
- dice and dominoes;
- small hoops, plates or sorting trays;
- two-coloured counters;
- connecting cubes in two colours.
Suggested Teaching Sequence
- Begin with collections of up to five objects. Separate each collection into two visible groups.
- Introduce the words part and whole. Explain that two smaller parts can be combined to make the whole collection.
- Use a part-part-whole mat with two circles for the parts and one larger circle for the whole.
- Ask students to partition the same collection in several different ways.
- Introduce ten frames and encourage students to recognise five as a useful benchmark.
- Use dice and domino arrangements to help students recognise familiar groups without counting every dot.
- Record the relationships using drawings, objects and number bond diagrams.
- Encourage students to explain their thinking using complete mathematical sentences.
Teacher Questions
- What is the whole number?
- What are the two parts?
- How many objects are in each part?
- How many are there altogether?
- Can you split the collection another way?
- What number do the two parts make?
- How did the ten frame help you recognise the number?
- What groups can you see on the dice or domino?
- Does changing the order of the parts change the whole?
- Can you prove your answer using counters?
Common Misconceptions
Counting only one part as the whole
Physically move both parts into the whole section of a part-part-whole mat and count the complete collection.
Believing the parts must be equal
Show examples such as 7 being partitioned into 5 and 2, 6 and 1, or 4 and 3.
Believing there is only one way to partition a number
Ask students to find as many different ways as possible to make the same whole.
Counting every dot instead of subitising
Briefly show familiar arrangements and ask students to describe the groups they noticed, such as 5 and 2.
Thinking that reversing the parts changes the whole
Compare 4 and 2 with 2 and 4 using the same six counters. Emphasise that both arrangements make 6.
Foundation Part-Part-Whole Activities
Activity 1: Build a Ten Frame
Show a number on a ten frame using counters. Ask students to identify the full group of five and the additional counters.
For example, students may describe 7 as 5 and 2 more.
Curriculum connection: AC9MFN04_E1
Activity 2: Flash the Ten Frame
Briefly display a ten frame and then hide it. Students say how many counters they saw and explain the groups they noticed.
Encourage statements such as: I saw 5 and 3 more, so there were 8.
Curriculum connection: AC9MFN04_E1
Activity 3: Shake and Spill
Place two-coloured counters in a cup. Shake and spill them onto the table.
Students count each colour and describe the relationship, such as: 8 is 5 red and 3 yellow.
Curriculum connection: AC9MFN04_E2
Activity 4: Split the Collection
Give students a collection of counters and two hoops or plates. Ask them to divide the collection between the two parts.
Students repeat the activity to find several ways to partition the same whole.
Curriculum connection: AC9MFN04_E2
Activity 5: Find Every Number Bond
Choose a whole number up to 10. Students use counters to find all possible two-part combinations.
For 6, students might find 0 and 6, 1 and 5, 2 and 4, and 3 and 3.
Curriculum connection: AC9MFN04_E2
Activity 6: Domino Number Bonds
Students choose a domino, identify the dots on each side and determine the total number of dots.
Record each domino as two parts and one whole using a number bond diagram.
Curriculum connection: AC9MFN04_E3
Activity 7: Roll and Combine
Roll two dice. Students subitise or count each die, then combine the two parts to find the whole.
Limit the total to 10 by using dice labelled 0 to 5 if required.
Curriculum connection: AC9MFN04_E3
Activity 8: Match the Number Bond
Prepare cards showing ten frames, dominoes, dice patterns, number bond diagrams and collections of objects.
Students match cards that represent the same whole number and explain the parts they can see.
Curriculum connection: AC9MFN04_E3
Activity 9: Number Groupings on Country or Place
Collect safe natural objects such as leaves, seed pods, stones or sticks from the local environment with appropriate permission.
Students group and regroup collections to 10, describing how the smaller groups form the whole collection.
First Nations Australian knowledge should be presented respectfully, accurately and in consultation with suitable local or authoritative sources where possible.
Curriculum connection: AC9MFN04_E4
Differentiation
Support
- begin with whole numbers no greater than five;
- use large counters and clearly divided part-part-whole mats;
- allow students to physically move the parts into the whole;
- use a five frame before introducing a ten frame;
- provide sentence starters and visual number bond templates;
- use familiar dice arrangements with small quantities.
Extension
- find every possible two-part partition of a number;
- include zero as one of the parts;
- partition collections into three parts;
- record combinations using numerals and addition symbols;
- compare two different partitions of the same whole;
- ask students to create number-bond puzzles for a partner;
- ask students to identify a missing part.
Mathematical Sentence Starters
The whole is _____.
One part is _____ and the other part is _____.
_____ and _____ make _____.
I can see _____ and _____ more.
I partitioned _____ into _____ and _____.
I made the same whole another way using _____ and _____.
The parts changed, but the whole stayed _____.
I recognised the number because _____.
Assessment Ideas
Observe whether the student can:
- identify the whole collection;
- partition a collection into two parts;
- combine two parts to make the whole;
- describe the two parts using number language;
- find more than one way to partition the same number;
- recognise quantities shown on a ten frame;
- recognise familiar dice and domino arrangements;
- explain how the parts form the whole.
Quick Exit Ticket
- Show 7 on a ten frame.
- Partition 7 into two parts.
- Show a different way to partition 7.
- Explain how both pairs of parts make the same whole.
Printable Teacher and Student Resources
Use the buttons below to open the available AC9MFN04 teaching materials and printable activities in a new browser tab.
Resources open in a new tab. Browser PDF settings may affect whether a file opens in the browser or downloads.
Home Learning Ideas
Families can practise part-part-whole relationships using familiar objects such as toys, socks, pegs, buttons, fruit, blocks or spoons.
Choose a collection of up to 10 objects and divide it into two groups. Ask the child to identify each part and then combine the groups to find the whole.
Ask questions such as:
- How many objects are there altogether?
- How many are in each part?
- What number do the two parts make?
- Can you split the collection another way?
- Can you find all the ways to make this number?
- What happens if we swap the two parts?