Expected level of development
Australian Curriculum Mathematics V9: AC9M5A02
Numeracy Progression: Multiplicative strategies: P7, Number patterns and algebraic thinking: P5
At this level, students are given opportunities to explore mathematical equations involving multiplication and division.
Introduce relevant number problems that involve students applying multiplicative strategies to solve mathematical problems with an unknown value. The aim is to develop students’ use of flexible strategies for multiplication and division, for example, working out how long it will take to save $100 when saving $4 a week. Show how to record the data in a table and look for patterns. Support students to write a mathematical statement or equation that describes the pattern. When developing an equation, for example, 4n = 100 where n is the number of weeks, show what happens when values are changed. Make explicit inverse operations (25 x 4 = 100 and 100 ÷ 4 = 25).
Use physical materials such as Unifix cubes to build stacks. Compare larger stacks with multiples of smaller unit stacks to look for patterns. For example, compare a stack of 32 and a stack of 4. Write these as statements showing relationship between multiplication and division. Look for opportunities to demonstrate associative and commutative properties of multiplication and show that these do not work for division. Relate number stories to match the mathematical statements.
Use arrays to recognise and explain distributive property. For example, when given the equivalent number sentence
5 x 17 = 5 x 10 + 5 x 7 students can reason whether this is true.
Teaching and learning summary:
- Use number stories to form equations and find unknown values.
- Use materials, diagrams and arrays to demonstrate that multiplication is associative and communitive but division is not.
- Investigate equivalent number sentences involving multiplication to find unknown values.
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.
Learning intention
- We are learning to look for patterns to help solve mathematical problems.
Why are we learning about this?
- Algebraic thinking can help us to solve problems.
What to do
1. Look at this pattern. It is a seating arrangement for people to sit around tables.
- What do you notice?
- Draw what you think will be the next arrangement.
2. Complete this table to show the number of tables and number of people.
3. See if you can write a rule to find the number of people for a given number of tables.
| Number of tables |
Number of people |
| 1 | 4 |
| 2 | 6 |
| 3 | |
| 4 | |
| 5 | |
| 10 | |
| 20 |
Success criteria
I can:
- describe patterns in arrangements and data
- write a rule to describe a repeating pattern to solve problems.
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Teaching strategies
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.
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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Concrete, Representational, Abstract (CRA)
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.
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Number Talks
An illustration of a teacher running a number talk with a lower primary class
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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Teaching resources
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.
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Multiplier-unknown scaling problems
Use this task to support students to apply their knowledge of basic multiplication facts and connect multiplication and division as inverse operations.
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Applying multiplication and division to rates
The purpose of this activity is to support students to find the multiplicative ‘operator’ that connects numbers in two rates to find an unknown value.
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Multiplicand-unknown scaling problems
This activity supports students to apply division to identify the initial stack size in scaling situations.
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Multiply multiples 3
This problem can be used to reinforce learning about equations being balanced common factors.
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Multiplication and division symbols, expressions and relationships
This unit develops an understanding of multiplication and division, including the inverse relationship between the two operations, and when and how to use them in problem-solving situations.
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