Complete the Square
3 out of 3
Complete the squares - but be warned some are trickier than they look!
Problem
Complete the Square printable sheet
Can you complete these squares?
This activity has been adapted from one of BEAM's free Maths of the Month resources, which unfortunately are no longer available.
Getting Started
What do you know about squares? Can this help you finish the diagrams?
It might be easier to print off this sheet and then use a pencil and ruler to complete the squares.
Student Solutions
Jamie from Great Hilton High School sent in some pictures of his solutions. He says
When trying to make a square, there are 2 rules to follow, which are:
1. All the sides need to be the same size.
2. There must be 4 perpendicular angles (or right angles).
To complete the squares, see how many grid squares 1 line takes up and rotate the line 90 degrees. Keep doing this until you get a full square.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem is excellent for helping to reinforce the properties of squares and in particular for highlighting the fact that a square is a square no matter what orientation it is in.
Possible approach
You could introduce this activity by showing the children a square piece of paper. Put the square on the board so that its sides are parallel to the sides of the board and ask the class what shape it is. How do they know? Then, invite one pupil to come up and pin the square on the board in a different way. Is the shape still a square? You might find that an interesting discussion ensues! It is common for children to call a tilted square a "diamond" but the earlier we can encourage them to avoid this, the better.
Once pupils have tried the problem, they could show each other their completed squares and discuss the drawings before sharing them with you and/or the whole class. Playing the game Seeing Squares would be a good way to end this lesson.
Key questions
What do you know about squares?
What do you need to add to this to make it a square?
Possible extension
You could give some learners a grid (for example 3 by 3 small squares) and challenge them to draw all possible squares on it, if all corners have to be on the grid.
Possible support
Children may need rulers to convince themselves that the sides of the shape they have drawn are (or are not!) the same. Turning the page also helps!