Five Steps to 50
2 out of 3
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Problem
Five Steps to 50 printable sheet
Watch this silent video to see this challenge being attempted.
Can you work out the rules?
This challenge is about counting on and back in steps of 1 and 10.
Roll a dice twice to establish your starting number - the first roll will give you the tens digit and the second roll will give you the ones digit.
You can then make five jumps to get as close to 50 as possible. You can jump forwards or backwards in jumps of 1 or 10.
Compare your strategy with someone else.
How far from 50 were you? Could you get even closer?
Which numbers can get you to 50? Which can't?
How do you know?
Getting Started
Begin by rolling the dice and establishing your starting number.
Then decide whether you need to make any jumps of 10 to get close to 50.
Then make any jumps of 1.
Remember than you can go forwards and backwards!
Student Solutions
Year 4 from Tidcombe Primary School sent in the following:
Abbie, Olive, Edith and Piran all noticed the diagonal pattern when they plotted the numbers that worked on a hundred square. They also noticed that something slightly changed the pattern in the middle. Daisy noticed that the numbers in the 2s column worked if they had an even number of tens but 2 didn't work because it was too far away from 50. Olive noticed that this pattern changed from column to column, for example in the 1s column, only the numbers with an odd number of tens worked. Fleur noticed that: when you find a number that you can get to 50 in 5 steps, if you subtract that number from 100, then you get another number that you can get to 50 in 5 steps.
Here is a solution which is based on a similar idea. This pupil also used a hundred square to very effectively represent which numbers he could, and could not, reach when taking five steps to fifty. In the image below,
Black = Works and can be rolled with a 1-6 die
Blue = Works and can't be rolled with a 1-6 die
Red = Doesn't work
He says:
Another way of thinking about this problem is that you can move five spaces across or down.
Can you follow his reasoning?
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this activity?
This activity provides a context for practising counting on in 1s and 10s (and later 100s). Children will also be invited to find out how far from 50 they end up so they will be practising finding the difference between two numbers. It encourages children to find more than one way of getting to a solution.
Possible approach
It would be good to start the lesson by practising counting on and back in 1s and 10s. You may also remind children how they can use a 100 square or number track to support this.
Children could work in pairs to attempt the challenge. You might want to generate starting numbers for the whole class, and see which pair can get closest. Bring together different approaches, which will include different ways of recording as well as different steps.
Learners may need reminding that sometimes it is helpful to go beyond the target and then count back.
Key questions
How far away from 50 are you?
Could you get any closer? How do you know?
How would it be different if you swapped a jump of 1 for a jump of 10? Or a jump of 10 for a jump of 1?
Possible extensions
Learners can encouraged to investigate all of the possible starting numbers and record which can and which can't reach 50.
Another possible extension is to generate a three-digit starting number and aim for the target of 500, making jumps of 1, 10 or 100.
Possible support
A 100 square or number line will be useful for some children.