Untitled Lesson

CALCULATING WITH POSITIVE AND
NEGATIVE INTEGERS

SOLUTIONS

TASK 1

Using the number line

1st integer

Operation

2nd integer

1st integer ± 2nd integer

Jumps on the number line

2

+

4

+2 + 4 = 6

–5

+

6

–5 + 6 = 1

5

–

–4

5 – –4 =9

–1

–

3

–1 – 3 = –4

6

+

–7

6 + –7 = –1

TASK 2

Complete the number sentence

1

2 + –5 = –3

2 2 – –3 = 5

3

2 + –3 = –1

4

4 + –4 = 0

5 4 – –2 = 6

6

4 + –2 = 2

7

–3 + 6 = 3

8 –3 – –7 = 4

9

–3 + 8 = 5

FINDING COMMON FACTORS

TASK 1

Sort factors

Fill in each diagram by entering all the factors of the given pair of numbers into the correct spaces.

1

2

3

4

For each pair above, give its highest common factor (HCF).

HCF of 10 and 15 = __________

HCF of 18 and 42 = __________

HCF of 35 and 70 __________

HCF of 14 and 45 __________

WHAT IS THE NUMBER?

TASK 1

Shared factors

1

Write three numbers smaller than 160 that I could be
thinking of.

Next to each number list allits factors.

1st number could be ________

Factors: __________________________________

2nd number could be ________

Factors: __________________________________

3rd number could be ________

Factors: __________________________________

Compare the numbers and the lists of factors. Record what you notice.

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

2 A mystery number has a factor of 12. What other numbers must also be its factors?

_________________________________________________________________________

TASK 2

Who am I?

Each problem below has more than one answer. Find them all.

1 I am less than 100. I have the factors 2, 3 and 7. Who am I?

_________________________________________________________________________

2 I have exactly two factors. I am bigger than 70 and smaller than 80. Who am I?

_________________________________________________________________________

3 I have more than two factors. I am odd. I am between 46 and 54. Who am I?

_________________________________________________________________________

4 I have an odd number of factors. I am smaller than 20. Who am I?

_________________________________________________________________________

I’m thinking of a number that

has the factors 5 and 6.

TASK 2

Explore factors

1 Can you find two numbers that have no common factors? Explain your answer.

______________________________________________________________________________

______________________________________________________________________________

2 Two numbers are even. What must be one of their common factors?

______________________________________________________________________________

3 A mystery number is even. How would you find its second largest factor?

______________________________________________________________________________

______________________________________________________________________________

4 A mystery number is odd. Will its second largest factor be more than half or less than half of the

number? Explain using examples.

______________________________________________________________________________

______________________________________________________________________________

5 List three pairs of numbers that have a common factor of 7. Do not repeat any number.

______________________________________________________________________________

______________________________________________________________________________

6 Two mystery numbers have a common factor of 6. What other two numbers, other than 1, must

also be common factors? Explain using examples.

______________________________________________________________________________

______________________________________________________________________________

7 All the factors of 6 are also factors of 42. Enter a number to complete each sentence. There are

many correct answers to both questions.

a All the factors of 10 are also factors of __________.

b 24 and ________ have no common factors except 1.