What do you notice about the connections between the equations: ☐ × 8 + 1 = 9 etc. and the calculations: (9 – 1) ÷ 8 [...]]]>

What is the [...]]]>

The table below has been jumbled up. Match the graphs labelled f1 to f9 to their equations in the table below and to the descriptions of the transformations of $f(x) = \frac{1}{x}$

Download the worksheet, cut up a copy of [...]]]>

AB = BC= CD = AE

BE is parallel to CF

EI is parallel to FJ

GE is parallel to AD

Can you find the side lengths of the different shapes?

Justify your answers.

The area of JGK is 20 cm².

Can [...]]]>

Each player has 5 counters, bottle tops, buttons or stones that look different from the counters used by the other player.

To win the player must be the first to get his or her 5 counters [...]]]>

Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .

2. What do you notice about the difference between squares of consecutive numbers?

Compare the differences between squares of numbers that differ by 1 [...]]]>

What is the value of x?

Click here to download the USE AREA TO FIND x worksheet.

Click here for the Notes for Teachers.

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Draw a circle with any radius you choose, and then draw 4 tangents making a quadrilateral with the circle inside touching the quadrilateral at 4 points.

Measure the edge lengths of the quadrilateral ABCD.

What do you [...]]]>

These straight lines form a family and the curves that you see, called envelopes, are tangent to each line in the family.

Draw two base lines and mark the same number of points at equal distances along each line. Join the outermost point on one base [...]]]>

1. What type of an equation is this?

2. Remember the general form of an equation of this nature: $y={a x }^{ 2 }-bx-c$

When $a > 0$ the graph is $\cup$ shaped and when $a < 0$ it is $\cap$ shaped. What is the situation in our problem?

[...]]]>Explain your reasoning.

Click here for teacher’s notes

]]>Each student should have a stage 3 Sierpinski triangle of edge length about 6.5 cm and a colouring pen, and should colour their triangle as shown by the black filling in the small diagram.

The class will make poster of a stage [...]]]>

2. What is the area enclosed by the stage 2 squareflake? What about the stages 3 and 4 squareflakes?

3. If replacing each line segment on the edge with the zig-zag is [...]]]>

Take a large piece of backing paper, and either draw an equilateral triangle with edges of length 27 cm or cut a triangle from coloured paper and stick it on [...]]]>

She lined them up and put green icing on every second biscuit.

She put a red cherry on every third biscuit and a white chocolate button on every fourth biscuit.

How many biscuits had no decoration? How [...]]]>

The smallest pyramid is made from [...]]]>

You will need a cut-out paper circle (about 12cm diameter).

Use a circle that does not show the centre. Fold your circle along a diameter. Mark the ends A and B. Now unfold your circle and then fold again along a different diameter and mark the [...]]]>Shade the hexagons where the number inside is odd all in one colour. Using a contrasting colour, [...]]]>