Square surprise
Why do you think that the red player chose that particular dot in this game of Seeing Squares?
Age
5 to 11
Challenge level
Problem
This problem is based on the game Square It, which you can find in Seeing Squares.
Players take it in turns to click on a dot on the interactive grid. The first player's dots will be blue and the second player's (or computer's) will be red. The winner is the first to have four dots of their own colour that can be joined by straight lines to form a square.
Have a go at playing the game a few times against the computer to get a feel for it.
Here is a picture taken part-way through a game. It is blue's turn next.
Where would you go if you were the blue player?
Click on the 'Show' button below to see which dot the blue player chose.
Are you surprised?
Why do you think the blue player made that move?
Players take it in turns to click on a dot on the interactive grid. The first player's dots will be blue and the second player's (or computer's) will be red. The winner is the first to have four dots of their own colour that can be joined by straight lines to form a square.
Have a go at playing the game a few times against the computer to get a feel for it.
Here is a picture taken part-way through a game. It is blue's turn next.
Image
Where would you go if you were the blue player?
Click on the 'Show' button below to see which dot the blue player chose.
Are you surprised?
Why do you think the blue player made that move?
Image
Getting Started
Student Solutions
Yousef from Emirates International School in Egypt wrote:
In order to solve this, you have to consider all options of where the blue dot will go. A way to do this is by removing all the red dots then considering the spaces where the blue one could be then replacing the red dots again.
So in the end, it seems that the dot will have to go in one space.
Majid from Essex Primary sent in this:
If I were the blue player, I would put it anywhere as the pink does not have a chance to make a square. When a chance is in sight for the pink, I would put it on the t dot on the bottom row. That would be a square but it would just be orientated, in the shape of a diamond.
(It is interesting you refer to a 'diamond'. Is this shape a square?)
The computer might block you, so to be on the safe side you would put it on the 3rd dot on the bottom row as shown here.
Scout from James Allen's Prep School sent in the following:
When the computer conquers (in red) three corners I must click the fourth corner otherwise the computer could/would make a square.
The computer double traps you when it can (has two sets of three lined up so wherever you click you still lose). To win I would try to double trap the computer.
In order to solve this, you have to consider all options of where the blue dot will go. A way to do this is by removing all the red dots then considering the spaces where the blue one could be then replacing the red dots again.
So in the end, it seems that the dot will have to go in one space.
Majid from Essex Primary sent in this:
Image
The computer might block you, so to be on the safe side you would put it on the 3rd dot on the bottom row as shown here.
Scout from James Allen's Prep School sent in the following:
When the computer conquers (in red) three corners I must click the fourth corner otherwise the computer could/would make a square.
The computer double traps you when it can (has two sets of three lined up so wherever you click you still lose). To win I would try to double trap the computer.
Teachers' Resources
Square Surprise
This problem is based on the game Square It, which you can find in Seeing Squares.Players take it in turns to click on a dot on the interactive grid. The first player's dots will be blue and the second player's (or computer's) will be red. The winner is the first to have four dots of their own colour that can be joined by straight lines to form a square.
Have a go at playing the game a few times against the computer to get a feel for it.
Here is a picture taken part-way through a game. It is blue's turn next.
Image
Where would you go if you were the blue player?
Click on the 'Show' button below to see which dot the blue player chose.
Are you surprised?
Why do you think the blue player made that move?
Image
Why do this problem?
This problem will present many learners with something unexpected, thereby capturing their curiosity and providing a context in which to consolidate their knowledge of properties of squares.Possible approach
Use the interactive to play a few games of Square It with the whole class playing against you or the computer. The aim at this point is simply for learners to become familiar with the rules of the game rather than necessarily beginning to think about possible strategies for winning.Once you feel they have got the idea of the game, show the group the first image, explaining that it is blue's turn to go. Give them a few moments of individual thinking time to consider what they would do if they were the blue player. Invite them to discuss their thoughts with a partner.
Bring everyone together again and explain that you are going to show them the game after blue had taken his/her next turn. Try not to say any more before revealing the image. (You may need to check that everyone has noticed which dot has been chosen.) Listen and watch out for learners' reactions. You could choose one or two students to share why they were surprised by what they saw.
Give time for pairs of learners to talk about why the blue player chose that dot. In a plenary you could invite some pairs to explain how they know that a square has been formed by the blue player. Try to discourage use of the word 'diamond' to describe a tilted square. You may want to find something that is square shaped e.g. a square piece of paper and physically orientate it in different ways to make the point that it does not stop being a square if it is not held with horizontal and vertical sides.
Key questions
Which dot would you choose if you were blue? Why?Which dot did the blue player select?
Why do you think s/he chose that spot?