Five steps to 50
Problem
Five Steps to 50 printable sheet
This challenge is about counting on and back in steps of 1, 10 and 100.
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 units 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 or 100.
Compare your strategy with a friend.
Did you jump forwards or backwards?
Can you land on 50 exactly?
How far from 50 were you?
Could you do it another way?
Could you get even closer?
Which numbers can get you to 50?
Which can't?
Roll the dice again and have another go!
For example:
I roll a dice and get a 2 then a 3, so my starting number is 23.
I make the following jumps to get as close to 50 as possible:
Starting number is 23
Jump one is +10 to get me to 33
Jump two is +10 to get me to 43
Jump three is +10 to get me to 53
Jump four is -1 to get me to 52
Jump five is -1 to get me to 51
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
Five Steps to 50
Five Steps to 50 printable sheet
This challenge is about counting on and back in steps of 1, 10 and 100.
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 units 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 or 100.
Compare your strategy with a friend.
Did you jump forwards or backwards?
Can you land on 50 exactly?
How far from 50 were you?
Could you do it another way?
Could you get even closer?
Which numbers can get you to 50?
Which can't?
Roll the dice again and have another go!
For example:
I roll a dice and get a 2 then a 3, so my starting number is 23.
I make the following jumps to get as close to 50 as possible:
Starting number is 23
Jump one is +10 to get me to 33
Jump two is +10 to get me to 43
Jump three is +10 to get me to 53
Jump four is -1 to get me to 52
Jump five is -1 to get me to 51
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 could even count on in 10s and then change to counting in 1s. You may also remind children how they can use a 100 square or number track to support this.
A possible starting point for the activity is using the same idea but with a different target number. You could choose 40 as the target, use a dice to generate a start number and then give the children five steps to get as close as possible. Children could work in pairs.
As a class you could collate different approaches. This will include different ways of recording as well as different steps. A discussion could then focus on which series of jumps got closest to 40. They may need reminding that sometimes you need to go beyond the target and then count back. How do you know you're closer to 40? Remind the class about finding the difference between numbers.
As children attempt the main task, they may explore different ways of moving from the same given starting number or they may generate their own starting point. Encourage discussions about different approaches. The class might be encouraged to try all of the two-digit numbers and record which can and which can't reach 50.
Some children may move onto the extension tasks (below).
Key questions
What is the difference between the numbers?
Do any other pairs of numbers have the same difference?
Can you spot a pattern?
Possible extensions
Extension 1: This time generate a three-digit starting number and get as close as you can to the target of 500. You can then make five jumps forwards or backwards of 1 or 10 or 100. What numbers can get you to your target in five steps? Which can't?
Extension 2: Working with either two- or three-digit numbers, establish your own target number. Which do you think will be most reachable? Which will be least reachable? Have a go and find out!
Possible support
A 100 square or number line/track will be useful for some children.