Planning tool

Students:

• follow algorithms involving a sequence of steps and decisions to generate number patterns using addition or multiplication
• use digital tools such as spreadsheets and calculators to model and explore algorithms
• identify, describe and explain emerging patterns in the number patterns generated
• use flowcharts or lists to 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 realise that each step must be explicitly included in an algorithm
• have difficulty describing steps and actions using written instructions with words and mathematical expressions.

To support and build understanding, provide opportunities to explore algorithms in different formats such as a list of steps or as a flowchart. As students follow an algorithm, they will begin to understand their use and see how they are helpful.

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 generate a sequence of numbers using a spreadsheet.
• We are learning to analyse and describe the number sequence ‘multiplying by 11’.
• We are learning to use our findings to predict the next 10 numbers in the given sequence.

Why are we learning about this?

Algorithms are a set of steps or rules to follow to help complete a task. The process for adding 3-digit numbers, for example 345 + 259, is an example of an algorithm. Computer programmers write algorithms that instruct computers how to complete a task.

What to do

1. Using a spreadsheet, create a table that has two columns like the one shown below. Fill the left column with the numbers 0 to 39.

In cell B2, enter the formula ‘=A2*11’ and press ENTER. You should now see the number 0 in B2. 

2. Use the ‘fill down’ function to generate a sequence for ‘multiply by 11’ from 0 to 39. (Hint: Move your cursor to the bottom right of cell B2, until you see a solid cross, hold the mouse down and drag your cursor all the way down to 39.)                        

3. Analyse the sequence generated from input numbers 0 to 9. Describe any pattern you notice. Can you explain why this pattern is generated when multiplying by 11?

4. Now analyse these two sections of the sequence: 10 to 19 and 20 to 29. Describe how the patterns in these two sections are similar and how they are different from each other.

5. Look at the section from 30 to 39. Is this pattern similar to the one you described in part c?

6. Use your findings from parts c and d to predict what you think the sequence will be from 40 to 49. Write it down on a piece of paper.

7. Check your results from part e by extending your table to 49 in the left column and extending the sequence in the right column.

Success criteria:

I can:

• generate a number sequence using a spreadsheet
• analyse and describe the number sequence ‘multiplying by 11’
• use my findings to predict the next 10 numbers in the given sequence.