Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M5N10
Numeracy Progression: Number patterns and algebraic thinking: P5
At this level, students create, follow and modify algorithms involving a sequence of steps and decisions to experiment with multiplication and division, factors and multiples, and the relationship of these to divisibility. Students use digital tools such as spreadsheets and calculators to apply algorithms for divisibility, and describe and explain any emerging number patterns.
These algorithms can be based on a variety of activities such as implementing tests for divisibility of a number by a onedigit number. Students create and modify their own algorithms as a set of instructions, using lists, tables and flowcharts, and share them with classmates to follow, provide feedback on, and refine.
Teaching and learning summary:
 Create and follow and algorithms involving a sequence of steps and decisions.
 Use lists, tables or flowcharts to create and algorithms as a set of instructions that classmates can follow.
 Use digital tools to generate sequences of numbers involving multiples and describe and explain emerging patterns.
 Use digital tools such as spreadsheets and calculators to model and explore algorithms for divisibility tests.
 Refine and adapt algorithms based on feedback from classmates.
Students:
 use an algorithm that involves a sequence of steps and decisions
 make a simple modification to a given algorithm
 test whether a number is divisible by another number.
Some students may:
 have difficulty following algorithms represented using a list, table or diagram.
 not yet be able to identify or apply the process of decision in an algorithm.
Provide relevant examples for students to explore and follow algorithms to better understand their use and how they work. As they become more familiar with algorithms students can start to refine algorithms to make them more efficient.
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 apply an algorithm for determining whether a number is divisible by 3.
 We are learning to modify an existing algorithm to solve a different problem of the same kind.
Why are we learning about this?
Learning how to modify an existing process to tackle similar processes is an important problemsolving strategy in real life. A range of problems involve sharing equally, and divisibility tests enable us to know when this can be done exactly for singledigit divisors. Divisibility also plays a key role in security and codes.
What to do
1. Divide each of the following numbers by 3 and identify which ones divide exactly, that is, where there is no remainder:
12, 123, 1,234, 12,345, 123,456, 1,234,567, 12,345,678, 123,456,789
Below is an algorithm for deciding whether a number is divisible by 3 (can be divided exactly by 3) or not.
Step 1 
Read the number. 
Step 2 
Add (sum) its digits together. 
Step 3 
Check if the sum of the digits is a multiple of 3. 
Step 4 
· If the answer is yes, then the number is divisible by 3. · If the answer is no, then the number is not divisible by 3. 
The following example shows this applied to the number 12,345.
Step 1 
12,345 
Step 2 
1 + 2 + 3 + 4 + 5 = 15 
Step 3 
Is 15 a multiple of 3? Yes, because 3 × 5 = 15. 
Step 4 
12,345 is divisible by 3. 
The actual division gives 12,345 ÷ 3 = 4,115 exactly, there is no remainder.
Apply the algorithm to decide which of the following numbers are divisible by 3, and then use a calculator to carry out the actual division and check whether there is a remainder or not:
a. 4,325
b. 32,694
c. 6,456
d. 53,437
e. 343
2. A number is divisible by 6 if it is an even number that is also divisible by 3. Extend the previous algorithm so that it can be used to decide whether a number is divisible by 6.
Apply the extended algorithm to decide which of the following numbers is divisible by 6 and then use a calculator to carry out the actual division and check whether there is a remainder or not:
 6,936
 32,694
 6,476
 5,342
 348
3. Use an online divisibility test calculator to practise and check your application of the divisibility tests for 2, 3 and 6. Use a calculator to carry out the actual divisions and check whether there is a remainder or not.
Success criteria
I can:
 apply a simple algorithm involving a sequence of steps and decisions
 determine whether a number is divisible by 3
 determine whether a number is divisible by 6.
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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.

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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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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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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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.

Algorithms: multiplying by a value
This lesson provides ideas for exploring contexts that multiply cells in a spreadsheet by a value.
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Fix these divisibility rules
This lesson provides the divisibility rules as flowcharts. Students find which of the three flowcharts has an error.
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Magic cups
Students apply computational thinking and create an algorithm to flip pairs of cups, in exactly three moves, to have them all facing down.
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