## Grade 7-10 Powerful Thinking 1

*By toni On September 17, 2016 · Leave a Comment*

What patterns can you see in the last digits for these numbers?

Can you explain why all these numbers are multiples of 5?

What about the 99th powers ?

What can you find out about ?

What other patterns with powers can you find that have special properties?

Click here for […]

## Grades 8 -10 Powerful Thinking 2

*By toni On September 16, 2016 · Leave a Comment*

Will the first number be a power of 10 for any value of n?

What can you say about the values of n that make the second number a power of 10?

Are there any other pairs of integers between 1 and 10 which have similar properties?

Click here for Notes […]

## Grades 9 and 10 Powerful Thinking 3

*By toni On September 15, 2016 · Leave a Comment*

1. Imagine the first number is written out in full. How many zeros would there be at the end? Why? Can you find the answer without doing the whole calculation?

2. Work out a few values of the second number with n = 1, 2, 3 and 4 . Can you show numbers […]

## Grades 10 Powerful Thinking 4

*By toni On September 14, 2016 · Leave a Comment*

Is this number divisible by 5?

Investigate other big powers?

Make up some similar numerical expressions involving powers that have interesting properties.

What about

?

Click here for Notes for Teachers.

## Grades 9 to 12 Tri-Fold

*By toni On September 13, 2016 · Leave a Comment*

Take any triangle and label it ABC with A as the largest angle. Fold the triangle along PQ, PS and QT where the points P and Q are the midpoints of AB and AC and PS and PT are perpendicular to BC.

What do you notice? Why does this happen? Will it […]

## Grades 7 to 9 Angle Sum

*By toni On September 8, 2016 · Leave a Comment*

For any triangle you can construct a line through one of the vertices parallel to the opposite edge.

Using what you know about angles and parallel lines prove that the angles of the triangle add up to 180 degrees.

## Grades 7 to 9 Fraction Jig-saw

*By toni On September 7, 2016 · Leave a Comment*

You will need to download and print out this jigsaw (or draw the pieces on squared paper), and cut up the pieces into squares (don’t cut along the diagonal lines!).

Now try to put the square pieces together without rotating any of them (so that in the finished jigsaw all the […]

## Grades 9 to 12 – Dating Made Easier

*By toni On August 30, 2016 · Leave a Comment*

If a sum invested gains 10% each year how long will it be before it has doubled its value?

If an object depreciates in value by 10% each year how long will it take until only half of the original value remains?

Why aren’t these two answers the same?

Is there a rate, used […]

## Grades 7 to 12 Transformation Art

*By toni On August 27, 2016 · Leave a Comment*

The wall painting on the house in this photo shows geometric transformations.

Assuming that the parts of the design that look the same are identical and that they only appear different because of the perspective in the photo, describe in detail all the transformations and symmetries that you see in the different […]

## Grades 9 to 12 Handshakes

*By toni On August 26, 2016 · Leave a Comment*

Everyone in the class must shake hands with everyone else and say hello. Everyone must join in. How many handshakes will there be altogether?

This will be difficult to count, especially if you have a large class. Try the problem in small groups and then compare different methods for finding the answers, or try it […]

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