Without a calculator copy and complete:

$$7\times3=21$$

$$6\times2 = 12$$

$$5\times1 =$$

$$4\times0 =$$

$$3\times-1 =$$

$$2\times-2 =$$

$$1\times \;$$

$$0\times \;$$

$$-1\times \;$$

$$-2\times \;$$

If $$a = 3, b = -4, c = -6$$
find the values of:

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

## 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.]
• 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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## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

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