Algebra with pictures

Puzzle ONE

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Puzzle TWO

The following shape is made from four identical rectangles

Simplify

Puzzle THREE

A smaller square of side b and area b is placed in a larger square of side a and area a.

Collect the green areas ie the “like terms” and make one simple shape from them.
Draw the simple area and write down the expression for its area.

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Puzzle FOUR

The area of the of a trapezium = average width × height.

= (short width + long width) × height.

Factorise

This is an alternative method to that shown in Question 3. The answers should be the same

Hint:

Draw the simplest area possible formed by combining the two trapeziums and write and expression for the combined area.

Puzzle FIVE

Write down TWO expressions for the total area of the largest square.

Equate the two expressions for the total area.

Simplify.

The Chinese called this theorem Kou Ku Sian. (Short side, long side hypotenuse)

By which Greek name is the theorem more commonly known?

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Puzzle SIX

This illustrates an ancient technique for solving quadratic equations called

“completing the square”

The area that needs to be added to complete the square is shown in grey.

Solve the equation

Does the geometrical method find all the solutions? Yes / No.

Explain.

Have fun and let me know how easy this is to read.

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