**"Exponents"**

## Grades 7 to 9 Making Six

*By toni On 12 January, 2017 · Leave a Comment*

Insert signs and symbols to make each line a true equation.

Hint: You can use square roots and cube roots.

As an extension you could investigate the factorial sign on your calculator and use factorials to answer the same questions for 0 0 0 = 6 and 1 1 1 = […]

## Grades 9-11 Exponents

*By Ben Walker On 24 November, 2016 · Leave a Comment*

Working either in small groups or as a whole-class activity, you will be given two sets of small cards. On one set expressions, such as 68 ÷ 64, are given. In the other set single values, such as 64, are given. Work out the value of the cards using the laws of exponents or by […]

## Grade 7-10 Powerful Thinking 1

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

What pattern can you see in the last digits of the powers of 2?

What about the last digits of the powers of 3?

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

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

What about […]

## Grades 8 -10 Powerful Thinking 2

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

Investigate the last digits of the numbers in the picture when n = 1, 2, 3 , 4 and 5. What do you notice? Does this pattern continue? Why?

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

What can you say about the values of n […]

## Grades 9 and 10 Powerful Thinking 3

*By toni On 15 September, 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 to 12 Powerful Thinking 4

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

Is this number divisible by 5?

Hint: Just look at the last digits of powers. What values do they take?

Investigate other big powers?

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

What about even bigger powers

?

Click here for Notes for Teachers.

This problem […]

## Grades 9 to 12 – Dating Made Easier

*By toni On 30 August, 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 […]

Download copies of these shapes here and cut out the 16 small triangles.

Arrange the 16 pieces into a larger triangle so that the numbers on matching edges are the same, for example .

## Grades 9 to 11 – How Many Factors?

*By toni On 18 January, 2012 · 3 Comments*

What can you say about numbers that have exactly 2 factors?

What can you say about numbers that have exactly 3 factors?

Give some examples of numbers with 4 factors. What do they have in common?

Give some examples of numbers with 5 factors. What do they have in common?

What about numbers […]

## Grade 10 – Water Lilies

*By toni On 16 January, 2012 · Leave a Comment*

There are some water lilies in a lake.

The area that they cover doubles in size every day.

After 17 days the whole lake is covered with water lilies.

How long did it take them to cover half the lake?

Click here for the Notes for […]

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