Difference Between Two Squares
In this activity we are going to explore the relationship between the difference in area between two squares and the side lengths of the squares.
There are two squares in the activity: the red square and the blue square.
On the right hand side of the activity there is a green rectangle that is related to the two squares.
You are going to investigate the relationship between the difference of the area of the red square and the blue square and the area of the green rectangle.
Calculate the area of the two squares, and work out the difference in area (how else could you calculate the difference in area?). Also calculate the area of the green rectangle.
What do you notice about two areas you just worked out?
Grab the red points and blue points to change the size of the two squares, and explore the relationship between these two measurements.
There are two squares in the activity: the red square and the blue square.
On the right hand side of the activity there is a green rectangle that is related to the two squares.
You are going to investigate the relationship between the difference of the area of the red square and the blue square and the area of the green rectangle.
Calculate the area of the two squares, and work out the difference in area (how else could you calculate the difference in area?). Also calculate the area of the green rectangle.
What do you notice about two areas you just worked out?
Grab the red points and blue points to change the size of the two squares, and explore the relationship between these two measurements.
Now that you have worked out a relationship between the difference in areas and the area of the rectangle, we are going to explore how the rectangle is created from the size of the squares.
What are the side lengths of the red square and the blue square? What are the side lengths of the rectangle?
By moving the red points and blue points, can you come up with an expression for the side lengths of the rectangle given by the side lengths of the red square and blue square (let a be the side length of the red square, and b be the side length of the blue square.
Can you turn all the information you have collected into an equation relating the difference of two squares to the side lengths of the rectangle?
What are the side lengths of the red square and the blue square? What are the side lengths of the rectangle?
By moving the red points and blue points, can you come up with an expression for the side lengths of the rectangle given by the side lengths of the red square and blue square (let a be the side length of the red square, and b be the side length of the blue square.
Can you turn all the information you have collected into an equation relating the difference of two squares to the side lengths of the rectangle?
Ideas for Teachers
This is a wonderful geometric exploration of the concept of Difference of Two Squares. Either use the activity with pupils after you have seen the result aalgebraically to show them the links between algebra and geometry, or get them to discover the result themselves before exploring the algebraic nature of this identity. Set the investigation as a homework and discuss the results in the next lesson, or use it as a computer based lesson. Alternatively, use the activity on the board as a starting point, and get students to do the investigation by hand (which has really nice results for a display).
This is a wonderful geometric exploration of the concept of Difference of Two Squares. Either use the activity with pupils after you have seen the result aalgebraically to show them the links between algebra and geometry, or get them to discover the result themselves before exploring the algebraic nature of this identity. Set the investigation as a homework and discuss the results in the next lesson, or use it as a computer based lesson. Alternatively, use the activity on the board as a starting point, and get students to do the investigation by hand (which has really nice results for a display).
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