大象传媒

Problem 3 - The Wall

Problem 3 is all about working with decimals and fractions.

Maths teacher Chris Smith and pupils from Grange Academy are here to explain.

The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.

So here's the challenge:

A street artist likes to get people thinking, so his latest work is a number puzzle within a pyramid.

In this pyramid, four of the bricks are marked with numbers and a fifth contains a question mark.

The numbers on a particular brick can be found by adding the numbers on the two bricks underneath it.

So, the sum of 0.8 and 陆 should be written on the pink brick.

What number should be on the brick marked with a question mark?

Need a hint?

  • It's tricky to add decimals and fractions - can you make this easier?
  • Could you try drawing it out and adding the answers you know help?
  • Can you work your way up the pyramid and then back down?

Solution

Worked out the answer? Here's how you can do it.

The bottom left brick has changed from the fraction of 1/2 to 0.5

Step 1

This problem involves decimals and fractions - it's probably easier if we convert the fractions to decimals first.

So let's change 陆 to 0.5

The bottom left brick has changed from the fraction of 1/2 to 0.5
An addition sign appears between 0.5 and 0.8 and the sum of that is 1.3 which is written above on the pink brick

Step 2

Then 0.5 + 0.8 will give us 1.3 for the pink brick.

To find out the value of the brick with the question mark, we鈥檙e going to have to work our way round to it.

An addition sign appears between 0.5 and 0.8 and the sum of that is 1.3 which is written above on the pink brick
An addition sign appears between 0.8 and 0.15 and we get the sum of those as 0.95 in the brick above.

Step 3

We can change 3/20 to 0.15 and add that with 0.8 to get 0.95.

An addition sign appears between 0.8 and 0.15 and we get the sum of those as 0.95 in the brick above.
An addition sign appears between 1.3 and 0.95 to show how we will get the value of the brick above.

Step 4

If we then do 0.95 + 1.3, we will get 2.25

An addition sign appears between 1.3 and 0.95 to show how we will get the value of the brick above.
The top brick of the pyramid, 3.4 has a subtract sign appear between it and the brick below with the value of 2.25 - giving the value of the other supporting brick as 1.15

Step 5

Now that we have one part of the value of the top brick, we can subtract this to find the value of the brick next to it.

So, 3.4 - 2.25 means the other brick must be 1.15

The top brick of the pyramid, 3.4 has a subtract sign appear between it and the brick below with the value of 2.25 - giving the value of the other supporting brick as 1.15
The yellow brick on the right of the second bottom row has a value of 0.2

Step 6

Next 1.15 subtract 0.95 to gives us 0.2

The yellow brick on the right of the second bottom row has a value of 0.2
The yellow brick in the bottom right corner which had the question mark now reads 0.05 after we worked out its value by doing the brick above (0.2) minus the supporting brick 0.15

Step 7

0.2 subtract 0.15 gives us 0.05.

So the value of the brick with the question mark is 0.05

The yellow brick in the bottom right corner which had the question mark now reads 0.05 after we worked out its value by doing the brick above (0.2) minus the supporting brick 0.15

Maths Week Scotland 2023. list

Try out all the daily challenges from Maths Week Scotland 2023.

Maths Week Scotland 2023

Maths Week Scotland 2022. list

Try out all the daily challenges from Maths Week Scotland 2022.

Maths Week Scotland 2022

Maths Week Scotland 2021. list

Want more maths challenges? Here are all the problems from 2021.

Maths Week Scotland 2021