**"Mathematical reasoning"**

## Year 11- 12 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 […]

## Years 6 -12 Sandwich Puzzle

*By toni On 18 April, 2020 · Leave a Comment*

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

Arrange these six digits in a list so that:

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

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

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

[…]

## Years 4 – 12 The answer is 2020, what is the question?

*By toni On 1 January, 2020 · Leave a Comment*

Is it correct to say “twenty twenty” or should we say “two thousand and twenty” or are both correct? Why?

People say “twenty twenty” so do the 2 twenties mean – 20 thousands, 20 hundreds, 20 tens or 20 units?

You can be a creative mathematician, you can be someone who has […]

## Grades 4 to 8 How many sums?

*By toni On 1 January, 2018 · Leave a Comment*

1 + 2018 = 2019. How many other ways can you put positive whole numbers into the boxes to make the sum correct?

Explain your answer.

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

## Years 6 – 10 Magic 13837

*By toni On 20 November, 2017 · 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.

Inspired by Jain www.jainmathemagics.com

## Years 4 – 9 Command The Robot 2

*By toni On 16 October, 2017 · 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 […]

## Years 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 […]

## Years 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 […]

## Years 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 the POWERFUL THINKING 4 Worksheet.

[…]

## Grades 9 to 11 – 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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