Expected level of development
Australian Curriculum Mathematics V9: AC9MFN06
Numeracy Progression: Multiplicative strategies: P1
At this level, students develop the foundations of multiplicative thinking. They represent practical situations that involve equal sharing and grouping with physical and virtual materials and use counting or subitising strategies.
Activate prior knowledge by drawing on students’ lived experiences of sharing and their idea of what constitutes a ‘fair share’. Provide opportunities for students to develop their multiplicative thinking by creating groups of objects from a collection using virtual and physical materials. Use a range of ways to represent equal sharing and grouping.
Use regular number talks to practise subitising small collections and to develop other counting strategies. Connect these skills to multiplicative contexts. Make explicit two ways to share, using examples such as the following:
- When the number of the group is known, the size of each group can be found (partition), for example, when sharing 12 apples between 4 people, how many does each person get?
- When the size of the group is known, the number of groups can be found. This process can be viewed as repeated subtraction, for example: We have 10 toys; 2 toys are to be placed into each gift box. How many boxes do we need?
Teaching and learning summary:
- Explore multiplication and division with materials, stories, role-play, games and regular classroom talks.
- Ensure a playful culture of learning where mistakes and struggle are seen as valuable to learning.
- Connect multiplication and division to everyday situations.
- share collections equally by dealing
- make equal groups and count by ones to determine the total
- represent sharing and grouping.
Some students may:
- have difficulty working out what mathematical operation or strategy to use to work out a number story connected to sharing. Use concrete materials to share out small collections that can be shared equally. Talk through representations that demonstrate sharing and grouping.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
- We are learning to describe situations that use multiplication and division.
Why are we learning about this?
- We use multiplication and division in everyday life.
What to do:
1. When engaged in creative play, notice situations involving sharing into equal groups. Consider questions like:
- There are 6 pieces of fruit. How can we share the pieces fairly between all 3 of us? I see there are 6 buttons. What if I took these 2 away, how many would be left?
- I notice there are 4 gumnuts. What if you shared them equally with your friend - how many would we each get?
2. Read storybooks and notice situations involving equal groups and sharing. Model curiosity and pose questions such as:
- Each character has two apples. How many apples altogether?
- I see 5 buttons in the story. Could we share 5 buttons equally between the two of us? Why or why not?
3. Link multiplication and division to everyday situations. Use examples such as the following:
- When out walking, notice small collections to count or subitise, for example: There are some birds. How many birds altogether? How did you count them?
- Collect natural materials like leaves or gumnuts. Talk about how many in the collection. And then think about different ways they could be shared. Can this collection be shared equally between 2 people? What might that look like? What about sharing equally between 3 people? Is that possible? Why or why not?
- When drawing pictures, notice and describe multiplicative aspects such as the number of legs on multiple people. How many people have you drawn? How many legs does each person have? What’s the total number of legs altogether?
- share small collections equally by dealing
- think about certain sharing situations as being fair or unfair
- make equal groups and count or describe how many in each group.
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A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.Go to resource
Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.Go to resource
Culturally responsive pedagogy
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.Go to resource
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.Go to resource
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.Go to resource
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.Go to resource
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
In this task, different scenarios are used to draw attention to different ways of thinking about the idea of division.Go to resource
Let's share to be fair
Use this video lesson to guide students to share 20 green grapes equally between four people.Go to resource
Handfuls: thinking multiplicatively
In this task, presented as a video, students play ‘Handfuls: thinking multiplicatively’, for example bears and numbers of paws (each bear has 4).Go to resource
Use this task to help students understand the process of division as sharing.Go to resource
Find my pattern: doubling, sharing and grouping
Use this guide to introduce practical contexts to group and share items.Go to resource
By the end of Foundation, students can represent practical situations that involve quantifying, equal sharing, adding to and taking away from collections to at least 10.