Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M7N03
Numeracy Progression: Additive strategies: P9, Multiplicative strategies: P9, Number and place value: P10
At this level, students will represent natural numbers in expanded notation using place value and powers of 10. Students learn the connection between exponent notation and its expanded form. By understanding how powers of ten are sequenced, students make connections with scale and consolidate representation.
As students move towards Year 8, they will establish and apply the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers.
Be aware that students are introduced to complete science investigations that may involve measuring, collecting and analysing data. The application of place value and its value in scientific inquiry and communication is valuable.
It is important to encourage students to engage with concrete or pictorial representations before moving to the abstract and symbolic representation of the index form.
Students should understand and be comfortable using the following terms and notation:
 base
 index
 expanded form
 index form.
Teaching and learning summary:
 Demonstrate the connection between expressing numbers in their expanded form.
 Encourage fluency with conversions between basic numerals in their expanded form.
 Demonstrate notation of powers and use corresponding terminology.
Students:
 use exponent notation to expand and contract numbers
 convert between natural numbers in expanded form and powers of 10
 are fluent with place value
 sequence powers of 10 for big and small numbers.
Some students may:
 often make the mistake of multiplying the base by the index instead of multiplying the base by itself for the number of times represented by the index. Students who make this error will say, for example, 3^{2}= 6 (instead of 9).
 incorrectly think that multiplying by an index number of zero will give the answer zero.
 get confused between having a negative on the index number and a negative on the base.
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
 I am learning about positive indices, negative indices and zero indices.
 I am learning that exponents are used to write repeated multiplication.
Why are we learning about this?
Exponential notation is an effective way to write what could be a longer complicated multiplication problem.
What to do
 Go to the number slider and print it out.
 Find some scissors and first cut out the large orange box and then cut out the white box below it.
 Fold the orange box along the dotted line backwards so that the white boxes are facing you.
 Cut out the nine white boxes to make small windows underneath the words that say Tenthousands, Thousands, Hundreds, Tens etc.
 Fold the orange box backwards so the windows are facing up.
 Cut out the white rectangular piece that was below the orange box, and then slide it into the slider.
To the left
 Pick two numbers and write one of them in the Ones box and the other in Tenths box. I’ve chosen 1 and 0.
 What happens when you pull your white strip from the left? I get 10. What about you? What did you get?
 Slide your numbers to the left for a second time. Hmm … I better add another zero to make it a proper number around the decimal point. Mine becomes 100. What about your number?
 Keep pulling from the left and adding zeroes, or any number you want. What is happening to your number?
 Is it getting bigger of smaller?
To the right
 Return the numbers back to their original positions.
 What happens to your numbers when you slide the strip to the right? Mine became .10 What happens when you slide the strip two positions to the right, and then three positions and then four? What do you think is happening to your number?
 Is it getting bigger of smaller?
 What operation are you using time when you slide your number to the left?
 What operation are you using when you slide your number to the right?
Success criteria
 I can understand the significance of exponents to shorten big numbers or small numbers.
 I can work with both positive and negative exponents on a number line.
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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.

Worked examples
A worked example is not just a preworked question that is given to the students. There are several types of worked examples and ways of using them.
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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 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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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.

Index notation
Use this resource to investigate indices with a certain base. Worked examples and teacher guidance is provided.
Resource details 
Place value
This resource progressively shows the small steps required in learning place value through to ordering.
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Multiples, factors and powers
This comprehensive resource covers multiplicative thinking in arithmetic and gives teacher guidance and worked examples for multiples, factors and powers.
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Assessment
By the end of Year 7, students can represent natural numbers in expanded notation using place value and powers of 10. Students make connections between exponent notation and its expanded form.

A question of scale
This activity focuses on representing very small numbers and very large numbers as exponents. By connecting numbers to real objects, students make connections.
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Multiplying powers of ten
Students can complete the formative and summative assessment task working with powers of ten.
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Geogebra: multiplying powers of ten
This interactive connects exponents with their expanded form and assesses students' understanding of sequencing with big and small numbers.
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