**"Mathematical reasoning"**

## How many sums?

*By toni On 1 January, 2024 · Leave a Comment*

Put positive whole numbers into the boxes to make the sum correct.

Here is one way to do it. How many other ways can you find? Explain your answer.

Now answer the same question for the year you were born.

Click here for the HOW MANY SUMS Notes […]

## The answer is 2024 but what is the question?

*By toni On 30 December, 2023 · Leave a Comment*

You can be a creative mathematician, you can be someone who has your own mathematical ideas. Find your own interesting facts about 2024 and calculations that have the answer 2024.

What different questions can you find with 2024 as the answer? For example you might ask: ‘What is (20 + 24) + […]

## Sandwich Puzzle

*By toni On 24 November, 2021 · Leave a Comment*

Suppose you have two 1s, two 2s and two 3s.

Arrange these six digits in a list so that:

between the two 1s there is one digit giving 1?1,

between the two 2s there are two digits giving 2??2,

between the two 3s there are three digits giving 3???3.

[…]

## Magic 13837

*By toni On 20 January, 2021 · Leave a Comment*

Try the ages of your family and friends.

What happens?

Can you explain it?

Does this work for very old people over the age of 99? Why or why not?

Click here to download the MAGIC 13837 worksheet.

Click here for the Notes for Teachers for Years 6-10.

## Command The Robot 2

*By toni On 3 October, 2020 · Leave a Comment*

Watch this turtle. Describe his path.

What commands would you give to make the turtle do this?

This activity will help you to start writing programs to command the robot even if you have never done anything like this before and you know nothing about coding. The LOGO language is simple to […]

## Quadratic sequences

*By Kwethemba Moyo On 30 April, 2020 · Leave a Comment*

A sequence is defined by the formula an = n2 – 2n + 1.

(a) Calculate the first 8 terms of the sequence.

(b) Calculate the first difference between the terms.

(c) Calculate the second difference between the terms.

(d) What can you say about the results you obtained?

Please click Guide for Home […]

## 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 […]

## 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 […]

## 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 or

?

Click here for the POWERFUL THINKING 4 Worksheet.

[…]

## Right Time

*By toni On 18 January, 2012 · Leave a Comment*

The hour and minute hands of my clock are at right angles.

How many degrees does each hand move forward in one minute? How long will it be before they are at right angles again?

Be careful, it will not be at half past three!

See the AIMSSEC Notes for Teachers.

This problem […]

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