I. Mind–map’ numbers’. When you read this ‘mind-map’, you’ll meet words that are new to you. First try to guess their meaning and then look them up in a dictionary.

II. Answering and explaining

Quiz I

1. Which of the following numbers has the greatest value?

   1. -8.3

   2. |-7.7|

   3. 2

   4. |4.5|

   5. 6.8

Quiz II

1. If m and n are negative integers, which of the following must be true?

   1. m + n < 0

   2. mn > 0

   3. mn > n

1. I only

2. II only

3. I and II

4. I and III

5. I, II and III

2. If v and w are both odd integers, which of the following could be an even integer?

   1. vw

   2. v + w + 1

   3. v/w

   4. 2(v + w)

   5. 2v +w

Answers and explanations

Quiz I

1. B is correct. The question asks for the greatest value, so you want the number farthest to the right on a number line. The two absolute values convert to 7.7 and 4.5. Of all five numbers, 7.7 is the greatest, so B is the best answer.

Quiz II

1.E is correct. Adding two negative numbers will just result in an even smaller (further to the left) negative number. So m + n < 0 and I is true. You know that a negative multiplied by a negative results in a positive number. So mn > 0 and II is true. This also means that mn is greater than any negative number, including n. Therefore mn > n and III is true. So the answer is E.

2. D is correct. You know that an odd integer multiplied by an odd integer results in an odd integer. So vw is odd and you can eliminate A. An odd integer plus an odd integer results in an even integer. So v + w is even, but v + w + 1 is odd and you eliminate B. Dividing an odd integer by an odd integer gives you either an odd integer, such as 15/5=3, or a non-integer, such as 17/5=3 2/5. So eliminate C. An even number times an odd is even, so 2v is even. Adding an even to an odd is odd, so 2v + w is odd and you should cross off E. As we saw earlier, v +w is even and multiplying by 2 keeps it even. (Even if v + w were odd, multiplying by 2 would make it even.) So D is the best answer.

III. Playing a trick with numbers

Write down your house number or your telephone number or the total amount of the coins in your pocket

Multiply this by 2.

To this add 5.

Multiply that by 50.

Then add your age.

Now add 365 (days in year).

Then subtract 615.

The last two numbers will be your age, and the other numbers will be your house address, total amount of coins in your pocket or whatever you decided upon.

IV. The ‘Terribly Stressed‘ game

Count from 11 to 31 – but only say every second number (for example 1,3,5).

1. Count backwards from 29 to 17.

2. Count backwards from 113 to 91

Practice set 8

addends minuend

3 + 2 = 5 the sum 6 – 2 = 4 the difference

subtrahend

multiplicand dividend divisor

3 х 2 = 6 the product 7 ÷ 2 = 3 the quotient and the part

Multiplier which is left is a remainder 1

I. Use this mind-map ‘Four basic operations in Mathematics’ as a topic activator to speak about the basic operations in Arithmetic

II. Complete the crossword with words referring to the basic operations of Arithmetic. The first letter of words is given for you

1M

2R

3D

4 Q

5A

6M

7A

8D

9D

10S

11P

12M

13D

14F

15M

16M

17S

1. The number by which we multiply

2. The result which we obtain in the operation of subtraction

3. The number to be divided

4. The result of division

5. The elementary branch of mathematics

6. The inverse operation of division

7. The number to be added

8. The process of finding how many parts of a number is contained in another one

9. Ten _____ by three is equal to seven

10. The number to be increased

11. The result of multiplication

12. The number from which we subtract

13. The _____ of nine and six is three

14. Numbers to be multiplied

15. The sign of subtraction

16. The number which is multiplied in the operation of multiplication

17 The process of finding the difference of two numbers