Contents. Heinemann Maths Zone Copyright Pearson Australia (a divsion of Pearson Australia Group Pty Ltd)

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1 Contents Chapter 1 Whole numbers R1.1 Mathematics in sentences R1.2 Rounding to the first digit R1.3 Operations on whole numbers R1.4 Addition of whole numbers R1.5 Consecutive numbers R1.6 Ordering R1.7 Subtracting whole numbers R1.8 Counting and number patterns R1.9 Comparing numbers R1.10 Number patterns R1.11 Division by multiples of 10 R1.12 Number sentences and equations R1.13 Division of whole numbers R1.14 Multiples of numbers R1.15 Order of operations R1.16 Rounding decimals R1.17 Adding and subtracting fractions with the same denominator R1.18 Operations with money C1.1 Estimating and rounding C1.2 Inequalities C1.3 Divisibility tests C1.4 Number patterns C1.5 Lowest common multiple C1.6 Factors C1.7 Highest common factor (HCF) C1.8 Factor trees C1.9 Factors, multiples and primes C1.10 Powers using a calculator C1.11 Whole numbers word search C1.12 Whole numbers crossword 1.1 Whole numbers 1.2 Whole numbers Assignment 1 Chapter 2 Directed numbers R2.1 Ordering R2.2 Comparing numbers R2.3 Adding whole numbers R2.4 Subtracting whole numbers R2.5 Multiplying whole numbers R2.6 Dividing whole numbers R2.7 Order of operations R2.8 Rounding to two decimal places R2.9 Addition of whole numbers R2.10 Ordering R2.11 Multiplying by multiples of 10 R2.12 Comparing decimal numbers R2.13 Number sentences R2.14 Number sequences R2.15 Number patterns R2.16 Multiples C2.1 Comparing directed numbers C2.2 Ordering directed numbers C2.3 Ascending and descending order C2.4 Adding directed numbers C2.5 Subtracting directed numbers C2.6 Simplifying addition of directed numbers C2.7 Simplifying addition and subtraction C2.8 Addition and subtraction of directed numbers C2.9 Multiplication of directed numbers C2.10 Division of directed numbers C2.11 Directed numbers word search C2.12 Directed numbers crossword 2.1 Directed numbers 2.2 Directed numbers 2.3 Directed numbers Assignment 2 Chapter 3 Fractions, decimals and R3.1 Types of fractions R3.2 Order of operations R3.3 Expressing fractions as decimals R3.4 Multiplying and dividing decimal numbers R3.5 Adding and subtracting decimal numbers R3.6 Rounding to a number of decimal places R3.7 Comparing fractions R3.8 Comparing decimal numbers R3.9 Subtraction of whole numbers R3.10 Division of whole numbers R3.11 Geometric solids C3.1 Adding and subtracting fractions

2 C3.2 Multiplying fractions C3.3 Dividing fractions C3.4 Multiplying a decimal C3.5 Division by a decimal C3.6 Converting decimal to fractions C3.7 Converting to decimals C3.8 Converting decimals to C3.9 Expressing one quantity as a percentage of another C3.10 Forming a percentage and finding a percentage C3.11 Fractions, decimals and word search C3.12 Fractions, decimals and crossword 3.1 Fractions, decimals and 3.2 Fractions, decimals and 3.3 Fractions, decimals and Assignment 3 Chapter 4 Patterns and algebra R4.1 Progressive operations R4.2 Harder sentences R4.3 Order of operations C4.1 Algebra rules C4.2 Multiplication in algebra C4.3 Substitution C4.4 Working with algebra substitution C4.5 Addition and subtraction in algebra C4.6 Dividing with pronumerals C4.7 The Distributive Law C4.8 Factorising C4.9 Finding the rule C4.10 Patterns and algebra word search C4.11 Patterns and algebra crossword 4.1 Patterns and algebra 4.2 Patterns and algebra 4.3 Patterns and algebra 4.4 Patterns and algebra Assignment 4 Chapter 5 Ratio R5.1 Converting mixed numbers to improper fractions R5.2 Finding the missing number R5.3 Simplifying fractions R5.4 Changing units R5.5 Operations with decimals R5.6 Multiplication of fractions R5.7 Rounding to two decimal places C5.1 Ratios, fractions and simplification C5.2 Simplifying ratios C5.3 Using ratio to find amounts (1) C5.4 Using ratio to find amounts (2) C5.5 Increasing and decreasing in a given ratio C5.6 Dividing an amount in a given ratio C5.7 Ratio word search C5.8 Ratio crossword 5.1 Ratio 5.2 Ratio Assignment 5 Chapter 6 Equations R6.1 What is an equation? R6.2 Simplifying multiplication and division R6.3 Substitution R6.4 Operations R6.5 Inverse operations C6.1 The language of equations C6.2 Substitution C6.3 Solving equations using backtracking C6.4 Solving equations by performing the same operation on both sides C6.5 Solving equations involving two operations C6.6 Algebraic expressions and equations C6.7 Equations word search C6.8 Equations crossword 6.1 Equations 6.2 Equations

3 6.3 Equations Assignment 6 Chapter 7 Cartesian graphs R7.1 The number plane R7.2 Working with rules C7.1 Plotting points C7.2 Finding the rule C7.3 Plotting linear graphs C7.4 Cartesian graphs word search C7.5 Cartesian graphs crossword 7.1 Cartesian graphs 7.2 Cartesian graphs Assignment 7 Chapter 8 Measurement R8.1 Substitution R8.2 Converting units R8.3 Perimeter R8.4 Solving simple linear equations R8.5 Working with time C8.1 Circumference using π C8.2 Perimeter using circumference C8.3 Areas of rectangles and triangles C8.4 Area of a parallelogram C8.5 Perimeter, circumference and area C8.6 Finding the area of part of a shape C8.7 Measurement word search C8.8 Measurement crossword 8.1 Measurement 8.2 Measurement 8.3 Measurement Assignment 8 Chapter 9 Space R9.1 Drawing and labelling R9.2 Scale factors R9.3 Finding angles R9.4 Polygons R9.5 Compass points C9.1 Congruent figures C9.2 Similar figures C9.3 Similar triangles C9.4 Exterior angle of a triangle C9.5 Drawing solids C9.6 Space word search C9.7 Space crossword 9.1 Space 9.2 Space Assignment 9 Chapter 10 Chance and data R10.1 Frequency tables R10.2 Dividing a circle into sectors R10.3 Line graphs R10.4 Theoretical probability C10.1 Histograms C10.2 Averages C10.3 Frequency tables and averages C10.4 Theoretical probability C10.5 Chance and data word search C10.6 Chance and data crossword 10.1 Chance and data 10.2 Chance and data Assignment 10 Worksheet solutions Chapter 1 Worksheet Solutions Chapter 2 Worksheet Solutions Chapter 3 Worksheet Solutions Chapter 4 Worksheet Solutions Chapter 5 Worksheet Solutions Chapter 6 Worksheet Solutions Chapter 7 Worksheet Solutions Chapter 8 Worksheet Solutions Chapter 9 Worksheet Solutions Chapter 10 Worksheet Solutions

4 Mathematics in sentences R1.1 Mathematics can be expressed in sentences, but it is more accurate to use equations and expressions = 6 is an equation is an expression. 1 Complete each of the following sentences. (a) is an with terms. (b) = 60 is an (c) 5 (8 + 3) = 55 is an. 2 Rewrite each of the following sentences using mathematical symbols. The first one has been done for you. (a) Twenty minus eight equals twelve = 12 (b) Five is subtracted from 100 and the result is ninety-five. 100 = (c) Eight plus five times six equals thirty-eight = 38 (d) Three times four is twelve. = (e) Five boxes of twenty balls is one hundred. = (f) Fifteen is six more than nine. = Calculate mathematical answers for the following sentences. (a) How old is Helen if she is three years older than her brother Timothy who is fourteen? =... (b) If a poultry farm produces twenty dozen eggs a day, how many will it produce in a week? =... (c) How many boxes will be needed to store thirty-six tennis balls if six balls can fit in one box? =... (d) How many days are there in Spring if it can be said to occur from 1 September to 30 November? =... (e) If you had seven dollars, and bought a magazine for $2.95 and a newspaper for one dollar, how much money would you have left? =... (f) If your family has two dogs and a cockatoo as pets, how many legs do your pets have all together? (2...) + ( 1...) =...

5 Number patterns C1.4 1 Complete each of the following number patterns. (a) 8, 11,,, 20, 23 (b) 19, 28,, 46,, (c) 15, 25,,, 55, (d) 1300, 1400,,, 1700, (e) 26, 28, 30,,, (f) 147, 153, 159,,, 2 Complete each of the following number patterns. (a) 3, 6,, 24,, (b) 2, 4,,, 32, 64 (c) 40,, 160,, 640, (d) 10, 100, 1000,,, (e) 32, 16,,, 2, (f) 3, 9, 27,, 243, 3 Complete each of the following number patterns. (a) 7, 14,, 56,, 224 (b) 1, 4,, 64,, 1024 (c) 10, 30,, 270,, (d) 5, 35,,,, (e) 128, 64,, 16,, (f) 21, 63, 189,,, 4 Complete the pattern in each of the following by adding or subtracting the same number each time. (a) 6,, 10, 12,, (b) 61, 68,, 82,, 96 (c) 75,, 225,, 375, (d) 16, 14,, 10,, 6 (e) 8, 6,,, 0, (f) 2600,, 2200,, 1800, (g) 100, 125, 150,,, 225, (h) 180,, 150,, 120,

6 Whole numbers The following questions refer to Exercises 1.1 to 1.3 in your textbook. If you are unsure of how to do a question, try looking at a worked example or other information in the section shown under the question number. Show all working in the space provided. Name: Class: Due date: Parent s signature/comment: If a car uses 8 L of petrol for every 100 km that it travels, find how many litres it would use for a trip of: 1.2 (a) 600 km Use rounding to the first digit to estimate the answer to: (b) 1050 km 2 Find the difference between 7243 and and then multiply the result by the quotient of 816 and Simplify the following: Round each of the following numbers to the 7 first digit (a) 69 Simplify the following: (2 + 5) (b) Estimate by rounding to the first digit: Circle those of the following numbers that are divisible by Heinemann Maths Zone Copyright Pearson Australia (a divsion of Pearson Australia Group Pty Ltd)

7 Assignment 1 1 If a car uses 10 L of petrol for every 120 km that it travels, how far would each of the following tanks of petrol take it? (a) 20 L (b) 5 L (c) 35 L 2 What is the sum of 52 and 83 added onto the product of 52 and 83? 3 Use rounding to the first digit to find estimates for these multiplications. (a) (b) (c) (d) Choose the best estimate for the following division: A 180 B 280 C 200 D 300 E Simplify: (a) (b) (c) 6( ) State whether each of the following is True or False. (a) 5 + (4 3) 2 > (5 + 4) 3 2 (b) (6 3) < 6 (3 + 5) 4 (c) 7 + (4 5) + 1 < (5 + 1) 7 State True or False for each of the following. (a) 7345 is divisible by 5. (b) 4759 is divisible by 3. (c) 333 is divisible by 6. (d) is divisible by 9. 8 Write the next three terms in each sequence. (a) 12, 16, 20,...,...,... (b) 100, 80, 60,...,...,... (c) 1, 3, 9, 27,...,...,... 9 Find the lowest common multiple (LCM) of: (a) 8 and 14 (b) 6 and 10 (c) 15 and 24 (d) 9 and Find the highest common factor (HCF) for each of these pairs of numbers. (a) 56, 72 (b) 64, 48 (c) 28, 84 (d) 45, Express each of these numbers as a product of its prime factors. (a) 36 (b) 44 (c) 56 (d) Evaluate: (a) 81 (b) 144 (c) (d) Arrange these numbers in ascending order (from smallest to largest). 3 2, 20 3, 10 2, 2 3, 30 2, Evaluate without using a calculator. (a) 3 27 (b) (c)