Sets of Four Numbers

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Age

7 to 11

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

Problem

Miss Brown was working with Becky's group on numbers that share a certain property. She wrote twelve numbers on the board.

"You can all find a different set of just four numbers that go together," she said, "And they must have a proper mathematical name. They can't be just a set of numbers that you like!"

The children stared at the numbers. Alan put up his hand. "Like odd numbers?" he suggested.

"That's the right idea," said Miss Brown, "but you can't choose just odd numbers because there are more than four of them. You must use all the numbers in my list which fit your set. Anyone else got an idea?"

Becky put her hand up. "Numbers in the $5$ times table? There are four of those."

"That's right. But what would be a good name for them?"

"Multiples of $5$?" suggested Becky.

"Good," said Miss Brown and she wrote on the board:

There are ten children in Becky's group.

Can you find a set of numbers for each of them?

Are there any other sets?

Student Solutions

There were so very many interesting ideas sent in for this challenge. Well done everyone!

We had solutions from:

Nadia and Lasata from Bentworth Primary

Anna, Jemma, Madeleine, Jessica and Linzi from Park View Community School

Phoebe, Joseph and Leigh from Newark Hill Primary School

Wiliam from Toot Hill

Chajicka and Demi-lee from Ricards Lodge High School

Hannah and Georgia from Penrhos College

Elm Park Maths Club

Year 8 at Dyffryn Taf

William from Barnton Community Primary School

Aman from Davidson Primary

Connie from Blackheath High School

Jaylyn

Year 5 maths club at Queens College Prep School

Hamish, Samuel and Rory from Rutherglen Primary School

Class 5S from Tenby Junior School

Ryan, Robbie and Georgia at Orchard Junior School

Vishaal from Brompton Manor

Shannon from St Julian's

Aporva

SHS Challenge Groupat Sutton High Junior School

Becky, Jacob and Katie from Tudhoe Grange

Simon from Dartford Grammar School

SaiSankalp from Roan Forest Elementary

Grace at Ninelands Primary School

Year 4/5 from Salisbury Heights (South Australia)

Samir from By Brook Valley

Year 6KM at Newton Primary School

Wazidur at Harrowden Middle School

Harry and Guy from St Michael's

Jessica from Jane Ryan School

Cameron, Kane, Jonathan, Aimee and Imogen from Falkland Primary School

Miss Parker's Class Aberdyfi

YemYem2 from Newstead

Imman from Foxborough

Oswald and Jimmy from Doncaster Gardens Primary School

Mark, Mekeela, Hannah, Sophie, Alexander, Jamie, Tom and Paula at Gledhow Primary School

Kelsey from Archbishop Beck

Kate, Alexander, Olivia and Thomas from Culford Prep

Mrs Lydford's Y6 Maths group from Balgowan Primary School

Norwich Numpties

Year 6 from Talycopa Primary

Miss Rowcliffe's Maths Class at Upton Heath Primary School

Mukul from The Grammar School at Leeds

Mrs Ferris' Maths Group at Wolfson Hillel Primary

Catherine, Kate, Lucinda and Ceciley from Wimbledon High School

Henry

Jazz and James from Woodstock C.E. Primary School

P5 and P6 Richmond School Ballygawley, Northern Ireland

Below you will see most of the ideas presented together, as there were many overlapping ideas:

Well done to everyone!

Teachers' Resources

Sets of Four Numbers

Miss Brown was working with Becky's group on numbers that share a certain property. She wrote twelve numbers on the board.

There are ten children in Becky's group.

Can you find a set of numbers for each of them?

Are there any other sets?

Why do this problem?

This problem can be used at any time when learners are looking at varied properties of numbers. There are a large number of possibilities so the problem can be as challenging as you want!

Possible approach

Here are two suggestions of ways you could start the lesson.

Firstly, you could begin by writing down some numbers on the board and asking for those with the same properties. These eight numbers, for example, could be used: $5, 9, 12, 16, 20, 24, 30, 35$. Remember that in the problem that there must be four, and only four, numbers in a certain category. In this list there are five even numbers to help in making this point. Alternatively, you could begin with the problem itself as given.

In both cases it will be necessary to make sure that learners know that there must only be four numbers chosen from the list and that each number can be used in as many sets as they want. They should also find a title for their set such as "multiples/factors of ... " or "single digit numbers".

After the introduction learners could work in pairs on the problem so that they are able to talk through their ideas with a partner.

At the end of the lesson you could write all the different categories that have been found on the board, or on paper on a designated section of the classroom walls. You should have many more than just ten. The advantage of creating a wall display is that it can become interactive, with learners continuing to add to the list over the coming week.

Key questions

Are there just four numbers that share this property in the list, or are there more than four?

Is this number odd or even?

Which multiplication tables will you find this number in?

What properties does this number have? Are there any others like it?

Can you think of a number that has many factors that you could try? Let's see if any of the numbers on our list are factors of that number.

Have you thought of a title for this set?

Possible extension

Learners could be challenged to find two or more criteria for the same set of numbers.

Possible support

You could suggest writing down the numbers and then underlining all the even numbers in, for example, red. Then circling the multiples of three in another colour and so on. This should highlight several sets of four numbers.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Sets of Four Numbers

Problem

Getting Started

Student Solutions

Teachers' Resources

Sets of Four Numbers

Why do this problem?

Possible approach

Key questions

Possible extension

Possible support