Page 6 - 新思维数学学生用书7 样章

1.1 Adding and subtracting integers
How are parts d and e different from parts a, b and c?
1.1 Adding and subtracting integers
10 Estimate the answers to these questions. Round the numbers to the
nearest whole number.
a
How are parts d and e different from parts a, b and c?
b
−3.14 + 8.26
−5.93 − 6.37
c 3.2 − −6.73 d −13.29 + −5.6
11 Estimate the answers to these questions.
10 Estimate the answers to these questions. Round the numbers to the
a nearest whole number. b −82 − 47
−67 + 29
Tip
c a 688 − −512 d −243 + −514 How to use this book
−3.14 + 8.26
12 a Work out: b −5.93 − 6.37 For part i, first
−13.29 + −5.6
c i 3.2 − −6.73 ii d −5 + 4 + −3 add −3 and 4.
−3 + 4 + −5
11 Estimate the answers to these questions. −3 + 4 + −5 Then add −5 to

−3 + −5 + 4
iv
iii
a
−67 + 29
−82 − 47
b
b What do the answers to part a show? Is this true for any the answer.
c three integers? d −243 + −514 Tip
688 − −512
12 a 2 Expressions, formulae and equations For part i, first
Work out:

i
−3 + 4 + −5
Think like a mathematician ii −5 + 4 + −3 add −3 and 4.
iii −3 + −5 + 4 iv −3 + 4 + −5
13 a 6 Copy and complete this addition table. Then add −5 to
This is part of Bethan’s homework. Bethan has made a mistake in
These investigations, to be carried b b What do the answers to part a show? Is this true for any the answer.
−5
7
+
Add the four answers inside the addition table.
every answer. Explain what Bethan has done wrong. Work out the
correct answer
Add the four integers on the side and the top of the addition
c three integers?s. 4
out with a partner or in a group, table. −3
Question
Think like a mathematician
What do you notice about the answers to parts b and c? Is this
d
will help develop skills of thinking 13 a true for any addition table? Give evidence to justify your answer.
Multiply out the brackets.
Copy and complete this addition table.
b 2(6x − 3)
a 4(x + 4)
and working mathematically. b Add the four answers inside the addition table. + −5 7
d 6(2 − x)
c 3(2 − 5x)
Add the four integers on the side and the top of the addition
c
How did you do the investigation in part d? Could you improve your method? 4
Solution
table. a 4(x + 4) = 4x + 8 b 2(6x − 3) = 12x – 3 −3
What do you notice about the answers to parts b and c? Is this
d
14 Three integers are equally spaced on a number line. Two of the integers are −3 and 7.
c 3(2 − 5x) = 6 + 15x
d 6(2 − x) = 12 − 6x = 6x
true for any addition table? Give evidence to justify your answer.
Questions to help you think a What is the other integer? Is there more than one possible answer?
b Compare your answer with a partner’s. Critique each other’s method.
Look again at Question 6. What method did you use to answer this question?
about how you learn. How did you do the investigation in part d? Could you improve your method?
Summary checklist
Do you think this was the best method or would you use a different method if
you had to answer the question again?
I can add positive and negative integers.
I can subtract positive and negative integers.
14 Three integers are equally spaced on a number line. Two of the integers are −3 and 7.
When I
a 7 What is the other integer? Is there more than one possible answer?
Arun looks at these four expressions.
expand the brackets
b Compare your answer with a partner’s. Critique each other’s method.
in all of these expressions,
2(12x + 15)
3(10 + 8x)
This is what you have Summary checklist 6(5 + 4x) the answers are all the
same.

4(6x + 26)

Is Arun correct? Explain your answer
learned in the unit. I can add positive and negative integers. 11
and show your working.
I can subtract positive and negative integers.
Think like a mathematician
1 Integers 8 Discuss with a partner the answers to these questions.
Questions that cover what you a When you expand the brackets in the expressions 3(4b + 5) and 3(5 + 4b),
do you get the same answer?
Check your progress
b
When you expand the brackets in the expressions 2(5c − 1) and 2(1 − 5c),
have learned in the unit. If you 1 Work out: do you get the same answer? 11
b
a 3 − 7 Give evidence to justify your answers.
−3 + −7
can answer these, you are ready c −2 × (2 − −4) d (−9 + −6) ÷ 3
2 a Find two integers that add up to 2 and multiply to make −15.
to move on to the next unit. 3 b Find two integers that add up to 3 and multiply to make −70.
Find the missing numbers.
a 5 × = −8 − 7 b −12 ÷ = 4 + −6
4 48 Find all the common factors of 16 and 24.
5 a Find all the multiples of 6 between 50 and 70.
At the end of several units, 6 b Find the lowest common multiple of 6 and 15.
Find the highest common factor of 26 and 65.
a
there is a project for you to 7 b Simplify the fraction 26 . 3 Project 1 Mixed-up properties
65
The integer N is less than 100. N and N are both integers.
a Explain why N must be a square number.
carry out, using what you 8 Project 1
b
Find the value of N.
The number 96*32 has a digit missing.
have learned. You might make a b Explain why the number is divisible by 4.
Find the missing digit if the number is divisible by 3.
Mixed-up properties
c
Find the missing digit if the number is divisible by 11.
something or solve a problem. Here are nine property cards:
9
Copy and complete the following.
1 3 = 1 2
Their difference is a Their highest common Their product has
4 3 = 8 2
3 = 2
factor of their sum factor (HCF) is 1 exactly 4 factors
3
2
16 =
Their sum is a Their lowest common
Their difference is prime
square number multiple (LCM) is 12
They are both They are both prime Their product is a
factors of 30 cube number
Here are six number cards:
2 3 4 5 6 7
28
Can you find a way to arrange the property cards and the number cards in a grid, so
that each property card describes the pair of numbers at the top of the column and
on the left of the row?
For example, the cell marked * could contain the card ‘They are both prime’ because
2 and 5 are both prime.
Can you find more than one way to arrange the 5
4 5 7 cards?
Which cards could go in lots of different places?
2 *
Which cards can only go in a few places?
Could you replace the six numbers with other
3
numbers and still complete the grid?
6
29
29