Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M4N05
Numeracy Progression: Number and place value: P7, Multiplicative strategies: P7
At this level, students solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits.
Use relevant materials such as place value charts, place value expanders and virtual manipulatives to explore the effect of multiplying by 10. Make explicit that multiplying by 10 moves the digits one place to the right. Discuss the use of zero.
Take the opportunity to introduce digital tools to explore the effect of multiplying or dividing numbers by 10 first, then multiples of 10, for example, 100 and 1,000. A spreadsheet can be a useful tool to automate the process using a few simple formulas. A possible starting point is to have a spreadsheet for students to use that has a formula set up to multiply by 10. Use this to show them how to create their own spreadsheet to explore emerging patterns, for example, when dividing by 10, 100 or 1000.
Teaching and learning summary:
 Use relevant materials to explore the effect of multiplying by 10.
 Introduce digital tools to explore the effect of multiplying or dividing numbers by multiples of 10.
Students:
 describe patterns of multiplying or dividing numbers by multiples of 10
 use efficient computational strategies to solve problems that include multiplying or dividing numbers by multiples of 10.
Some students may:
 believe you should you just add a zero when multiplying by 10. This approach is limited in its usefulness and can cause problems when dealing with decimal numbers. Provide challenges to this line of thinking and present a decimal number. For example, 3.5 x 10 isn’t 3.50, because simply inserting a zero on the end gives exactly the same value.
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 develop understanding of multiplying and dividing natural numbers by multiples of 10.
Why are we learning about this?
 This builds number sense and helps us find efficient ways to solve problems.
What to do
 Create a series of cards that match answers to the numbers in the grid.
 Each equation should be written with a multiple of 10, either multiplication or division. For example, an answer for 300 could be 3,000 ÷ 10 or 30 x 10.
 Create 30 cards and play bingo with a friend.
 Whoever is first to get a row and then fill the whole card is the winner.
300  9,000  4  90 
30  7  50  500 
0.5  60  600  100 
1  1,000  9  700 
5. Create a series of cards that match answers to the numbers in the grid above.
Each equation should be written with a multiple of 10, either multiplication or division.
For example, an answer for 300 could be 3000 ÷ 10 or 30 x 10.
3,000 ÷ 10  30 × 10  
Success criteria
I can:
 use my knowledge of multiples of 10 when multiplying and dividing numbers.
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Teaching strategies
A collection of evidencebased 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.

Concrete, Representational, Abstract (CRA model)
The CRA model is a threephased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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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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Collaborative learning
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.
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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.

Multiply by 10, 100 and 1,000
Use this spreadsheet to show students how to automate the multiplication of a number by 10, 100 and 1,000.
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Multiply and divide by 10 and 100
Use this guide to develop lessons for students to multiply natural numbers by multiples of 10.
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An easy way to multiply by 10?
In this interactive, students click through a series of mathematical statements related to multiplying by 10. They are challenged to decide whether or not the statement is true, and why.
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Activities on the Gattegno chart
In this investigation, students use a Gattegno chart to gain awareness of place value and the inverse relationship between multiplication and division.
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Multiplying by ten
In this activity, students use multiplication by ten to find an amount ten times bigger than a given amount.
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Tens time
In this activity, students explore what happens to whole numbers when they are divided by 10 and 100.
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