Without a calculator copy and complete:

$$4\times4=16$$
$$3\times3 = 9$$
$$2\times2 =$$
$$1\times1 =$$
$$0\times0 =$$
$$-1\times-1 =$$
$$-2\times$$
$$-3\times$$
$$-4\times$$
$$-5\times$$

If a = 4, b = -6 and c = -6
find the values of:

$$a + b$$
$$ac$$
$$b - c$$
$$abc$$
$$a + b + c$$
$$bc^2$$
$$(bc)^2$$
$$a^2b^3$$
$$c(b - a)$$
$$b^a$$

## A Mathematics Lesson Starter Of The Day

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Topics: Starter | Negative Numbers | Number

• Transum,
•
• Have you ever tried to explain to pupils why a negative number multiplied by a negative number gives a positive result? It is difficult to find a real world example that makes this concept clear. My favourite method is to use the pattern or sequence generated in the left frame above. Most pupils take this as a good explanation for the product of negatives result. The right frame above is simply a chance to put this knowledge into practice with some directed number questions.
• Stafford,
•
• A negative x a negative:
The way I explain it to the kids if they're struggling to get it is to ignore the minus signs and do the multiplication. So -5 x -8 do as 5x8=40. If you then put 1 minus on the answer it becomes -40. But we have 2 minuses to include so it'll be 40 and we know that a minus and a minus together make a + (I always do adding/subtracting before multiplying/dividing).
• RER, Paris
•
• Great resource, however some of the questions on the left hand side are incomplete eg 0x then there is no other number. Perhaps this could be amended. The same is true if you ask for different numbers.

[Transum: Thank you for your comments. The left column is intended to be an unfinished sequence of calculations that the pupils should complete. By seeing the patterns in the sequence the pupils might gain a better understanding of directed number.]
• Transum,
•
• My octogenarian mother put on odd slippers today. She thought that was a very negative thing to do. If her slippers were the same it would be a more positive thing!

If you remember that you'll have a good way of remembering what happens for division and multiplication. If the numbers have different signs (one positive and the other negative) then the result will be negative. If the signs are the same (either both positive or both negative) the result will be positive.

This notion is for multiplying and dividing only. For adding and subtracting directed numbers refer to the Number Line.

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Previous Day | This starter is for 15 January | Next Day

 4  x 4 = 163  x 3 = 92  x 2 = 41  x 1 = 10  x 0 = 0-1  x -1 = 1-2  x -2 = 4-3  x -3 = 9-4  x -4 = 16-5  x -5 = 25 -2 -24 0 144 -8 -216 1296 -3456 60 1296

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

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...

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...

## 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...

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

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 search box and some items chosen and recommended by Transum Mathematics to get you started.

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=January15

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=Negative

For Students:

For All: