Homework Book 1
Peter Derych, Kevin Evans, Keith Gordon, Michael Kent, Trevor Senior, Brian Speed
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Contents 1 1.1 1.2 1.3 1.4 1.5
2 2.1 2.2 2.3 2.4
3 3.1 3.2 3.3 3.4
4 4.1 4.2 4.3 4.4 4.5
5 5.1 5.2 5.3 5.4 5.5 5.6
6 6.1 6.2 6.3 6.4 6.5 6.6
How to use this book
5
Using numbers
6
Timetables, charts and money Positive and negative numbers Adding negative numbers Subtracting negative numbers Multiplying negative numbers
6 8 9 10 11
Sequences
12
Function machines Sequences and rules Finding missing terms Other sequences
12 13 14 16
Perimeter, area and volume
20
Perimeter and area Perimeter and area of rectangles Perimeter and area of compound shapes Volume of cubes and cuboids
20 21
Decimal numbers
27
Multiplying and dividing by 10, 100 and 1000 Ordering decimals Estimates Adding and subtracting decimals Multiplying and dividing decimals
27 28 29 30 31
Working with numbers
33
Square numbers and square roots Rounding Order of operations Long and short multiplication Long and short division Calculations with measurements
33 34 35 36 37 38
Statistics
40
Mode, median, range The mean Statistical diagrams Collecting data Grouped frequency Data collection
40 41 42 44 46 48
23 25
7 7.1 7.2 7.3 7.4
8 8.1 8.2 8.3 8.4 8.5
9 9.1 9.2 9.3 9.4 9.5
Algebra
50
Expressions and substitution Simplifying expressions Using formulae Writing formulae
50 52 53 55
Fractions
56
Equivalent fractions Comparing fractions Adding and subtracting fractions Mixed numbers and improper fractions Calculations with mixed numbers
56 57 58
Angles
63
Measuring and drawing angles Calculating angles Angles in a triangle Angles in a quadrilateral Properties of triangles and quadrilaterals
63 65 67 68
10 Coordinates and graphs 10.1 10.2 10.3 10.4 10.5 10.6
Coordinates From mappings to graphs Naming graphs Naming sloping lines Lines of the form x + y = a Graphs from the real world
11 Percentages 11.1 11.2 11.3 11.4 11.5
Fractions, decimals and percentages Fractions of a quantity Percentage of a quantity Percentages with a calculator Percentage increases and decreases
69 71 71 72 73 74 75 76
79 80 81 82 83 85
Probability words Probability scales Experimental probability
85 86 87
Contents
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12 Probability 12.1 12.2 12.3
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13 Symmetry 13.1 13.2 13.3 13.4
Line symmetry Rotational symmetry Reflections Tessellations
14 Equations 14.1 14.2 14.3 14.4
Finding unknown numbers Solving equations Solving more complex equations Setting up and solving equations
15 Interpreting data 15.1 15.2 15.3
4
Pie charts Comparing mean and and range Statistical surveys
90 90 91 93 95 97 97 97 98 99
16 3D shapes 16.1 16.2 16.3
Naming and drawing 3D shapes 107 Using nets to construct 3D shapes 109 3D investigations 112
17 Ratio 17.1 17.2 17.3 17.4
107
Introduction to ratio Simplifying ratios Ratios and sharing Solving problems
113 113 114 116 117
101 101 103 105
Contents
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How to use this book Welcome to Maths Frameworking 3rd edition Homework Book 1 Maths Frameworking Homework Book 1 accompanies Pupil Books 1.1, 1.2 and 1.3 and has hundreds of practice questions at different levels to help you consolidate what you have learned in class. Key features enable easy navigation through the book: indicators help you find the right questions for your level and question type icons help you find and practise key skills. These are the key features:
Numbered topics match the Pupil Books so you can find the right sections easily.
The level of difficulty of the questions corresponds to the three different year 1 Pupil Books: 1.1
1.2
1.3
Challenge yourself with extended Brainteaser activities.
Practise your problem solving, mathematical reasoning and financial skills with highlighted questions.
How to use this book
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2
Sequences
2.1 Function machines 1
Find the outputs for each function machine below. a
2
Input
Output
Input
Output
6
?
20
?
6
?
7
?
30
?
7
?
8
?
40
?
8
?
9
?
50
?
9
?
Make up your own diagrams to show each of these functions. Use 1, 2, 3 and 4 as your inputs. b multiply by 5
add 2
b
subtract 1
c
Input
Output
Input
Output
Input
Output
3
9
3
10
8
2
4
12
4
11
12
3
5
15
5
12
16
4
6
18
6
13
20
5
Write down the inverse function of: b multiply by 4
subtract 8
c
divide by 5 then add 2
b divide by 5
c
subtract 6
Work out the input values for these function machines. a
12
c
Describe each of these functions in words.
a 5
subtract 6
Output
a
4
c
divide by 5
Input
a 3
b
add 2
add 7
Input
Output
Input
Output
Input
Output
?
13
?
5
?
1
?
14
?
6
?
3
?
15
?
7
?
5
?
16
?
8
?
7
2 Sequences
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6
Find the output for the double function machine. a
×5+4 Input
Output
1 2 3 4
7
Draw each of these double function machines. Choose your own four input numbers for each machine. a
add 3 multiply by 2 Input
b
multiply by 4 subtract 1 Input
8
Output
Output
Draw function machines to show these general rules. 2n + 1
Use inputs 1, 2, 3, 4.
b 3n − 1
Use inputs 5, 6, 7, 8.
a
(n + 3) × 2
Use inputs 1, 3, 5, 7.
d (n ÷ 2) × 5
Use inputs 2, 4, 6, 8.
c e
10(n − 4)
Use inputs 12, 8, 4, 2.
2.2 Sequences and rules 1
Use each term-to-term rule and starting point to make a sequence with four terms in it. a
Rule
add 3
Start at 2.
b Rule
add 6
Start at 10.
c
double
Start at 3.
d Rule
multiply by 4
Start at 1.
e
Rule
add 100
Start at 50.
f
Rule
subtract 5
Start at 60.
g
Rule
divide by 2
Start at 40.
Rule
Answer: 2, 5 , __ , __
2.2 Sequences and rules
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2
Each of these sequences uses an ‘add’ rule. Write the next two terms in each sequence. Describe the term-to-term rule you have used. a c
3
4
Write down the 1st term and term-to-term rule. You could answer part a without adding the sequences. How?
Each of these sequences uses either a ‘subtract’ ‘multiply’ or ‘divide’ rule. Write the next two terms in each sequence. Describe the term-to-term rule you have used. a 1, 3, 9, 27, d 36, 28, 20, 12, …
5
b 5, 10, 15, 20, … d 20, 30, 40, 50, …
Add any two sequences from question 2, term-by-term. a b
PS
1, 3, 5, 7, … 8, 15, 22, 29, …
b 25, 20, 15, 10, … e 5, 10, 20, 40, …
c f
1000, 100, 10, 1, … 20, 10, 5, 2.5, …
For each of the sequences, find the following: i
the first three terms
ii
a c
times by 3, then add 1 add 3, then times by 4
b times by 6, then take 5 d take 2, then times by 2
the 100th term.
2.3 Finding missing terms 1
For each of the patterns below, draw the next diagram, and describe the sequence. a Diagram 1
Diagram 2
Diagram 3
Diagram 4
Diagram 4
Diagram 3
b
Diagram 1
14
Diagram 2
Diagram 3
Diagram 4
2 Sequences
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2
Draw the missing diagrams for these sequences: a
1
2
1
3
2
3
4
4
b
3
PS
4
Each of these sequences uses a ‘subtract’ rule. Copy and complete the sequences. Describe the rule used. a
40, 35, …, 25, …
b …, 91,… ,…, 73, 64,… c
a
Think about the 10th diagram in the pattern below. Work out how many:
15, 5, …, …, –25
i blue squares there will be ii orange squares there will be iii squares in total there will be. b
Can you work out the link between the three sequences?
Diagram 1
PS
Diagram 2
Diagram 3
5
What will be the 10th term for each sequence in question 3?
6
Find two terms between each pair of numbers to form a sequence. Describe the termto-term rule you have used. a 2, … , … , 8 d 24, … , … , 3 g
7
16, … , … , 2
b 5, … , … , 14 e 13, …, …., −2 h 1000, … , … , 1
c f
6, … , … , 18 9, 90, …, …, 90 000
i
8, …, …, 1, 1 2
What will be the next two terms in each of the sequences in question 6?
2.3 Finding missing terms
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8
For the following sequences, write down the number of matches in the first four diagrams and work out how many matches there are in the 10th and 20th diagrams. a
Diagram 1
Diagram 2
Diagram 3
Diagram 4
b
Diagram 1
Diagram 2
Diagram 3
Diagram 4
Brainteaser A garden path is to be paved as shown below. There need to be five pink hexagons in total. a b c d e f g
How many yellow hexagons will there be? What is the rule that governs how many of tiles of each type there are? Yellow hexagon tiles cost £12.99 each, but pink ones are £2 more. What will the total cost be? An alternative pattern is to use octagonal tiles. Draw a sketch of the path with five central octagons. How many of each tile will be used? What are the rules now? Octagonal tiles are all £1 cheaper than hexagonal ones. Which of the two patterns will cost least?
2.4 Other sequences 1
The sequence of square numbers is shown below. a b c
16
What type of number do you add each time to make the next square number? What will the next square number be? What is the: i 10th square number ii 15th square number?
2 Sequences
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1
1+3
4+5
9+7
16 + 9
2
The numbers below are referred to as triangle numbers. a b c
What type of number is added each time to continue the sequence? What is the next triangle number in the sequence below? What is the: i 10th triangle number ii 12th triangle number? 1
PS
+2=3
+3=6
+ 4 = 10
+ 5 = 15
+ 6 = 21
3
A full-size snooker table uses 15 red balls in a triangle. How many are along each side of the triangle?
4
The diagram below shows yellow beads in a triangle pattern arranged with blue beads also in a triangular pattern. Look at the resulting shape. What can you say happens when you add two consecutive triangle numbers to each other? 22 = 1 + 3
=4
32 = 3 + 6
=9
42 = 6 + 10 = 16
2.4 Other sequences
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5
Find at least three different sequences that begin 2, 3, 5, ‌ Explain why each sequence works.
6
The Chinese first discovered this amazing triangular pattern many centuries ago. When European mathematician Blaise Pascal popularised it, it became known as Pascal’s triangle. 1 1 1 1 1 1 1 1
a b c d e
PS
7
5
6 10
15 21
1 3 10
20 35
1 4
1 5
15 35
1 6
21
1 7
1
Can you see how each row of the triangle is derived from the previous line? What will the next row be? Add up the numbers in each horizontal row. What number sequence is revealed? How would you describe the number sequence in the 2nd diagonal? What name is given to the number sequence in the 3rd diagonal?
The diagram shows some dominoes arranged in a pattern.
a b c d
18
3 4
6 7
1 2
Draw the next column of dominoes in the pattern. Write down the total number of spots in each of the four columns of dominoes. Divide each of these totals by 3 and write down the new sequence of numbers. Write down the next two numbers in the sequence you obtained in part c.
2 Sequences
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Brainteaser A gardener buys roses and decides to plant them one metre apart in triangles.
1 rose
3 roses
6 roses
a Draw a picture of a similar pattern using ten roses. b How many roses would he need if the triangle had four roses along each side? c He decides to form a triangular pattern using 15 roses. How long is each side of his triangle? d He counts the number of equilateral triangles that can be drawn with five roses down the side and how many can be drawn with four roses down the side.
five roses on each side – 1 arrangement
four roses on each side – 3 arrangements
He continues by counting triangles with three roses on each side. How many equilateral triangles can be drawn?
2.4 Other sequences
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