1

2

3

4

5

• Arrange the numbers 1 to 5 in the squares so that the total of the row is the same as the total of the column
• How many different ways are there of doing this?
• What do you notice about the different ways of solving this problem?

## A Mathematics Lesson Starter Of The Day

Topics: Starter | Arithmetic | Investigations | Puzzles

• Mairi Salters, Burwell VC Primary School
•
• I copy the pages onto a flipchart on the electronic whiteboard. That way the class can take their time at it, as we use it as a half-hour settling in activity rather than a starter to the numeracy lesson proper. I use it with a Year 4 clsas, so a lot of the starters are too advanced for them. However, they have got on well with the ones we have used. Would be delighted to see similar written specically for KS2!
• J.Hesmer, Filsham Valley
•
• I found this an awful starter, it was incredebly difficult for my YEAR 7 group!
• L Martin, Canterbury
•
• I tried it with my Year 7s. They did it in 20 seconds flat. We extended it to algebra, to prove it.
• L. Northern, Hayle School
•
• We had a long discussion, we found out that:
1. The middle number has to be odd
2. If all the numbers are odd or all the numbers are even, it will always work
3. When you chose a middle number, you have to have the smallest and largest above it, and the middle numbers either side.
We thought it was a good problem.
Hayle School Year 7 maths class.
• Susan, Australia
•
• This lead beautifully into an activity about surface area - using the net.
• Nick, Holy Trinity, Weymouth
•
• We found 24 combinations after doing some methodical thinking
Mrs Penn, Mr Corben and Year 5.
• Snowdon, Mrs Peters
•
• Our Year 4,5 and 6 class really enjoyed this activity to start the day. Everybody was able to attempt the task and lots of children were successful!!
• Alison, Australia
•
• I did this with my year 5/6 class and they loved it. It allowed all of the students to find at least one combination, while it extended the other to find more.
• Louise, Bolton
•
• This starter was great. I did it with my YEAR 2 children and they found lots of ways to make different totals, using their reasoning skills to say why they could change the positions of the numbers. They loved it!
• Transum,
•
• Thanks so much for all the comments. Don't forget to click on the link towards the bottom of this page to find the student version of this activity which has a number of different levels extending this puzzle for the those who enjoy a challenge.
•
• An engaging starter to provoke mathematical reasoning and critical thinking.
Although my students are weak mathematically, they were all able to have a degree of success and began to discuss possible theories.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

Previous Day | This starter is for 3 June | Next Day

We found 24 different solutions. Are there any more?

 4 1 3 5 2

 4 5 3 1 2

 4 2 5 3 1

 4 3 5 2 1

 5 3 1 4 2

 5 4 1 3 2

 5 2 3 4 1

 5 4 3 2 1
 2 1 5 4 3

 2 4 5 1 3

 3 2 1 5 4

 3 5 1 2 4

 3 1 5 4 2

 3 4 5 1 2

 4 2 1 5 3

 4 5 1 2 3
 1 2 3 4 5

 1 4 3 2 5

 1 2 5 3 4

 1 3 5 2 4

 2 3 1 4 5

 2 4 1 3 5

 2 1 3 5 4

 2 5 3 1 4

Can you prove that the centre number has to be odd?

You may want to print out this page, cut out each answer and arrange them into groups. This may help you spot patterns.

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

## Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

## How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

## Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

## Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

## Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

## The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

## Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more...

## A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more...

## Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone. more...

Click the images above to see all the details of these gift ideas and to buy them online.

## Maths T-Shirts

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Educational Technology on Amazon

Here is the URL which will take them to a multi-level version of this activity.

Transum.org/go/?to=Plus

For Students:

For All: