100 square jigsaw
Can you complete this jigsaw of the 100 square?
Problem
Use the interactivity below to complete the 100 square jigsaws. There are four different versions to try. If you would prefer to work away from a screen, you could print off the pieces to cut out for puzzle 1, puzzle 2, puzzle 3 and puzzle 4.
How are you going about this task? What are you looking for?
Getting Started
How do the numbers appear on a hundred square?
You could start by finding the piece with the lowest number on it. Where should that go?
How about the piece with the highest number, which square should that go over?
You might need to count both forwards and backwards to help you complete the square!
Student Solutions
Well done to everybody who solved these jigsaws. Lots of children sent us pictures of their finished jigsaws, but only a few children explained how they completed the 100 squares.
Joseph from Wolfson Hillel Primary School in the UK gave this advice:
Start from the top and work your way to the bottom.
Dynel from Whitegrove Primary School in the UK had a different strategy:
I started with 0. Because it was at the bottom, I put it at the bottom of the square. Then I put 1 next to it. And the rest just fell in place.
Thank you both for explaining your strategies! I wonder if it's easiest to start at the top of the square or at the bottom? Does it depend on the square?
Jeremy from Thailand sent in some step-by-step pictures showing how he solved the second puzzle. Have a look at Jeremy's solution and see if you can work out why he placed each piece in that order. Thank you for sending in this solution, Jeremy - it's interesting to see the step-by-step pictures.
Dhruv sent us some step-by-step pictures for the first puzzle:
I started with an edge piece and worked my way round.
Thank you for sending in these pictures, Dhruv. Your method is really clear.
We didn't have many ideas sent in about how to solve these jigsaws, so if you have any more ideas you'd like to share then please email us.
Teachers' Resources
Why do this problem?
This jigsaw is a great way to reinforce children's understanding of the sequences contained within a hundred square. It could be used as an exploratory tool for children who haven't met the 0-99 hundred square before (puzzles 2 and 4 in the interactivity), or it could play a part in assessing their understanding of it, if they have already met it.
Possible approach
This problem featured in an NRICH Primary webinar in September 2021.
You could use one of the jigsaws as a whole class activity on an interactive whiteboard, inviting children to explain how they would start, and going on to complete the task altogether.
Alternatively, you could introduce a jigsaw to the whole group and then ask them to complete it in pairs, either on computers/tablets or by printing off and cutting out the sheets (Puzzle 1, Puzzle 2, Puzzle 3 and Puzzle 4) of the grid and pieces.
The conversations they have amongst each other as they work will be well worth listening in on!
Key questions
What are you looking out for?
Which piece has the lowest number on it?
Which has the highest number?
How might that help us to complete the jigsaw?
Where will the smallest number go? How do you know?