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(1) Select Upper Primary or Lower Secondary […]
1. What do you see in this picture?
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 […]
You are going to investigate quadrilaterals that have inscribed circles as shown in the diagram.
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 […]
1. ENVELOPE PATTERNS WITH STRAIGHT LINES
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 […]
Graph $y={ x }^{ 2 }-2x-1$ .
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?
[…]
Which is longer, the dashed portion of the square or the circumference of the circle?
Explain your reasoning.
Click here for teacher’s notes
Start by watching the video https://youtu.be/B2dkNPaTmDY
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 […]
1. If the red square has area 1 square unit. What is the area enclosed by the stage 1 squareflake?
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 […]
John plans to get the minimum possible Diamond Razor Mesh fencing material, as a security measure to discourage entry into his dam. He finds out that the rectangular shape drawn around the dam picture can help. The dimensions are given in algebraic form, in metres. Find an expression for the area of this […]
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