Follow and create algorithms: Year 5: Planning tool

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 one-digit 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 problem-solving 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 single-digit 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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