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 = 2, b = -3 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

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.]

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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Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.1 out of 5 based on 133 votes.

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 -1 -12 3 36 -7 -108 324 -108 30 9

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.

## 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: