Without a calculator copy and complete:

$$4\times2=8$$
$$3\times1 = 3$$
$$2\times0 =$$
$$1\times-1 =$$
$$0\times-2 =$$
$$-1\times-3 =$$
$$-2\times$$
$$-3\times$$
$$-4\times$$
$$-5\times$$

If a = 6, b = -3 and c = -4
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.

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.

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This starter has scored a mean of 3.1 out of 5 based on 249 votes.

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

 4  x 2 = 83  x 1 = 32  x 0 = 01  x -1 = -10  x -2 = 0-1  x -3 = 3-2  x -4 = 8-3  x -5 = 15-4  x -6 = 24-5  x -7 = 35 3 -24 1 72 -1 -48 144 -972 36 729

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.

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## Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I'd taught Maths" is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

## Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

 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: