Expected level of development
Australian Curriculum Mathematics V9: AC9M3A02, AC9M3A03
Numeracy Progression: Number patterns and algebraic thinking: P3, Additive strategies: P8, Multiplicative strategies: P5
At this level, students extend and apply knowledge of number facts to 20 for addition and subtraction, and extend to larger numbers. They demonstrate proficiency with multiplication facts for 3, 4, 5 and 10 and further develop their knowledge of related division facts.
Provide opportunities for students to develop proficiency in automatic recall of the number facts associated with a mathematical operation. Use models such as fact family triangles to record number facts for inverse operations (addition and subtraction, and multiplication and division). Use maths games that draw on additive or multiplicative thinking and use of number facts, including strategy games to reach a target number.
Explore number patterns using a hundreds chart. Students identify patterns, skip counting by 3, 4, 5 and 10. Model and explore arrays using materials such as counters or Unifix cubes to record representations.
Use calculators to explore patterns in repeated addition and subtraction. Make connections between multiplication and repeated addition, and between division and repeated subtraction. Use number lines to reinforce the connections and to explore patterns.
Teaching and learning summary:
- Describe a rule for a number pattern, then create the pattern.
- Partition using materials and part-part-whole diagrams to develop subtraction facts related to addition facts.
- Understand basic addition and related subtraction facts and use extensions to these facts.
- Use concrete or virtual manipulatives, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts.
- Use a calculator or spreadsheet to generate a list of the multiples of five to develop the multiplication and related division facts for five.
- use skip counting to continue number patterns
- recall addition and subtraction facts up to 20
- recall multiplication facts for 3, 4, 5 and 10 and their related division facts.
Some students may:
- have difficulty with basic number facts
- have limited strategies and revert to counting on fingers or similar inefficient strategies.
Provide a range of strategies through Number talks and help students make connections between addition and subtraction and between multiplication and division using materials and relevant models.
Use arrays to develop number facts. Start with a limited number of facts learned grouped according to counting patterns of twos, fours, threes, fives and tens. Then progress, adding the next grouping of facts, when students demonstrate proficiency.
View the resource Top draw teachers: Number sequences which includes a detailed section on misconceptions related to number sequences.
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 improve our recall of number facts.
Why are we learning about this?
- Having efficient strategies helps us work out more difficult maths problems.
What to do
1. Here is a problem: 9 x 13
- Which of these number facts could you use to help solve the problem?
- How can that number fact help you?
|1 x 11||12 x 12||10 x 11||10 x 13|
|2 x 10||13 x 13||11 x 11||11 x 12|
|13 x 2||11 x 2||10 x 10||1 x 13|
|4 x 13||9 x 10||1 x 3||14 x 11|
2. The fact families for 24 are:
4 x 6 = 24, 6 x 4 = 24, 24 ÷ 6 = 4, 24 ÷ 4 = 6
3. Can you think of other number facts for 24? Write as many as you can.
4. Write the fact families for 18 and for 30.
- recall basic number facts
- write fact families for two-digit numbers.
Please note: This site contains links to websites not controlled by the Australian Government or ESA. More information here.
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.
A well-developed lesson structure is important for both teacher and students.Go to resource
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.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
Spaced, interleaved and retrieval practice
These are three strategies that can be used to increase student retention and recall of their learning.Go to resource
An illustration of a teacher running a number talk with a lower primary classGo 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.
Use this interactive tool for students to practise recall and recognising patterns in multiplication facts.Resource details
reSolve: Algebra – Number sequences
Students are challenged to solve problems to generate patterns, explore strategies for addition and subtraction and apply their skills to constructing their own new patterns.Resource details
Musical number patterns: musical times
Students make some music by building up rhythms from four instruments, and make a counting rule that matches a pattern on a number line.Resource details
Multiplication and division: arrays and multiples
Use this guide to select tasks to develop multiplication and related division facts for 3, 4, 5 and 10.Resource details
Times tables shifts
This interactive task will help students become familiar with multiplication (times tables) facts, by encouraging them to think about number properties.Resource details
Circus towers: square stacks
Students work out how many acrobats are needed to form square-shaped human towers and describe how the number pattern is formed.Resource details
Students link the development of skip-counting patterns to bars on a relationship graph and then plot the skip-counting patterns on a hundreds board.Resource details
In this unit, students explore the number patterns created when tins are stacked in different arrangements and keep track of the numbers involved by drawing up a table of values.Resource details
What was in the box?
This problem is rather like a function machine, but it can be more interesting and is easily extended to challenge a wide range of pupils.Resource details
In this unit students explore and apply multiplicative thinking.Resource details
Multiplication flash cards
Students recall the multiplication and division facts for the multiples of 2, 3, 5, and 10 using flash cards.Resource details
Students recall the multiplication and division facts for the multiples of 2, 3, 5 and 10 using a game board.Resource details
In and out
Students recall the multiplication and division facts for the multiples of 2, 3, 5 and 10 using input output model.Resource details
A little bit more / A little bit less
Students derive multiplication facts from 2, 5 and 10 times tables.Resource details
By the end of Year 3, students extend and use single-digit addition and related subtraction facts and apply additive strategies to model and solve problems involving two- and three-digit numbers.