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# Highest and Lowest

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Age 7 to 11

Challenge Level

- Problem
- Student Solutions
- Teachers' Resources

We had just a few submissions to this challenge.

Brodie & Tully from St Patrick's School Macksville NSW in Australia sent in the following;

Highest

(4-3+5)x6=36

Lowest

6/3+4-5=1

(4-3+5)/6

Highest-1, 2, 3, 4, 5, 6

(3+4)/(2-1)x5x6=210

Lowest

(4-3)x2/1+(5-6)=1

M, T and G (Y3) from Monteney Primary School, Sheffield wrote;

M, T and G say that to make the greatest possible total you need to "multiply all the numbers together but not one" Multiplying all of the numbers 2, 3, 4, 5 and 6 together generate a total of 720.

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

If you add one to your total you get a total of 721.

720 + 1 = 721

M, T and G said that you add one to make the biggest total, because if you multiplied your total by one then your answer of 720 wouldn't change.

Ashkan from Gorsefield Primary wrote;

The highest I found was:

3 - 4 + (5 x 6) = 29.

I did 5 x 6 which = 30. Then I did 3 - 4 which is -1. Finally I did -1 + 30 = 29.

The lowest I found was:

3 - 4 + (5 / 6) = 0.167

I did 5 / 6 = 0.833. Then I did 3 - 4 = -1. Finally I did -1 + 0.833 = 0.167.

Kestrel class at Churchfields, the Village School in Wiltshire, wrote:

We decided that we had to keep the numbers in order.

At first we could use the operations as many times as we wanted.

Our highest score was 360

3 x 4 x 5 x 6 = 360 (I wonder why you didn't use the 2 as well...)

Our lowest score was -117.

3 – (4 x 5 x 6) = -117

At first we experimented with division before we realised that negative numbers were lower.

Then we decided to see what would happen if we could only use each symbol once (but we kept the numbers in order).

Our highest score was 34.5.

(3 ÷ 4 + 5) x 6 = 34.5

Our lowest score was -51.

3 – ((4 + 5) x 6) = - 51

Thank you, Kestrel class. What a good idea to decide on particular 'rules', like having the numbers in order, or using each operation once.

Thank you for all these different solutions. You may like to think about the ideas in each solution and whether you can improve on them.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?