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CHRIS For this challenge, we’ve been given a weird diagram with straight lines, red dots, yellow dots and numbers. And we’ve got to figure out what’s going on.

There are three lines missing from this diagram. Where should they go and which ends of each line should have a yellow dot and which a red dot?

Explain your answer.

Your task is to work out where the three missing lines should go in this diagram.

PUPILS Have a go at drawing this out.

Think about the relationships between the numbers that are connected by lines. Are there any patterns?

Why are some dots red and some dots yellow?

Is there a relationship between three and nine or three and six?

What about four? What about its relationship with 2, 8 and 12?

Remember, every number might not be connected by a line.

Give it a go!

In this challenge we were given a diagram with lines and dots and we had to find the three missing lines.

We are looking for patterns between the numbers that were connected with dots and lines.

Let’s take a look at the number three.

The numbers six and nine can both be divided exactly by three.

Notice that these two lines have red dots next to the three and yellow dots next to the six and nine.

The number six is also connected to the number twelve.

Twelve can be divided exactly by six. So this fits the pattern.

Twelve is also connected to two and four.

Yellow dots at the twelve. Red dots at the two and four.

If we look at the other connected numbers we can see they fit the same pattern.

Eight can be divided by two and four exactly, four can be divided by two exactly, and ten can also be divided by two exactly.

The pattern that we’ve found is that a line leaving a number from a red dot points to a different number into which it divides exactly – marked with a yellow dot.

The first number is a factor of the second.

A factor is a number which divides exactly into another number.

And the second number is a multiple of the first number.

So it can be divided exactly by the smaller one.

The key to solving this weird picture was to figure out that multiples were important and factors were important and those dictated where the lines went.

And the red dots and the yellow dots were clues as to which ones were factors and which ones were multiples.

So to find the three missing lines we’re looking for factors and multiples to join.

Starting with the smallest number, two is a factor of six so we can join those and three is a factor of twelve.

And the final connection joins five and ten.

The numbers seven and eleven, don’t have any dots or lines.

Seven and eleven are prime numbers so they don’t have any factors except for themselves and one.

How did you get on?

Did you work it out?