Planning tool

Students will be able to:

• follow algorithms involving a sequence of steps to generate number patterns
• use digital tools such as spreadsheets and calculators to explore algorithms
• identify, describe and explain emerging patterns in the number patterns generated
• create an algorithm as a set of instructions that a classmate can follow.

Some students may: 

• not understand that an algorithm is an ordered set of instructions
• not recognise that each step must be explicitly included in an algorithm
• be able to follow an algorithm but have difficulty describing steps and actions using written instructions with words and mathematical expressions.

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 recognise when a number is a multiple of 2, 5 or 10.
• We are learning that when multiplying an odd number by 5 the resulting number is odd.
• We are learning that when multiplying an even number by 5 the resulting number is even.

Why are we learning about this?

Algorithms are a set of steps or rules to follow to help complete a task. Following a recipe to bake a cake or following the rules of a board game are examples of how we apply algorithms in everyday life.

What to do

Create a table that has a row of the numbers from 1 to 20 across the top and a column of the numbers 2, 5 and 10 down the left.

1. Complete the first row in the table by multiplying each of the numbers across the top by 2 and placing the result into the table.

1. Describe any patterns you notice and explain them.
2. Look at the last (units) digit for each result (for instance, for 36 this is 6). List all the different last digits that you can see and comment on anything you notice.

2. Complete the second row by multiplying each of the numbers across the top by 5 and placing the result into the table.

1. Describe any patterns you notice and explain them.
2. Look at the last (units) digit for each result (for instance, for 25 this is 5). List all the different last digits that you can see and comment on anything you notice.

3. Complete the third row by multiplying each of the numbers across the top by 10 and placing the result into the table.

1. Describe any patterns you notice and explain them.
2. Look at the last (units) digit for each result (for instance, for 130 this is 0). List all the different last digits that you can see and comment on anything you notice.

4. Use your findings from questions 1, 2 and 3 to help answer these questions. For each of the numbers below, decide if they are a multiple of 2, 5 or 10. Remember, a number can be a multiple of more than one other number.

35

88

160

754

895

5. Look at your table and identify the results that are odd numbers. Colour in the squares with odd number results.

1. What do you notice?
2. Is the result odd when an even number is multiplied by 5 or when an odd number is multiplied by 5?

Success criteria

I can:

• recognise when a number is a multiple of 2, 5 or 10
• understand that when multiplying an odd number by 5 the resulting number is odd
• understand that when multiplying an even number by 5 the resulting number is even.