# HYC Stage 7

**Stage 7 Unit 1 - Numbers and the number system - Hegarty maths**

Find multiples and factors of a number. 27, 33

Find HCF and LCM of two or more numbers. 31, 34

Understand the meaning of prime factors and write a number as a product of prime factors. 29, 30

Solve problems using HCF and LCM. 36

Investigate square and cube numbers, other powers and their roots. 99 - 101

Understand and use the index laws. 102

**Stage 7 Unit 2- Counting and comparing**

Investigate negative numbers. 37

Order fractions. 60

Order values given as positive or negative integers, decimals, percentages or fractions. 14, 37, 46

Compare numbers using correct inequality notation. 7, 8

**Stage 7 Unit 3 - Calculating**

Add and subtract integers and decimals 18, 19, 47

Multiply integers and decimals 21, 48

Dividing using short division. 22

Calculating division with decimals or have a decimal answer 49, 50

Understanding inverse operations 14, 177

Recall and apply BIDMAS. 24

**Stage 7 Unit 4 - Visualising and Construction**

What is all this notation? 456

Investigating parallel and perpendicular lines 456

Identifying symmetry

Drawing and describing regular polygons

Construction of a triangle with ruler and compass 683

**Stage 7 Unit 5 - Investigating properties of shapes**

Know the names and properties of special triangles 455, 456, 666

Know and use the definitions of faces, vertices, and edges of 3D shapes

Visualise 3D nets

Know and use the sum of the angles of a triangle to find a missing angle 477, 485

Know and use the sum of the angles of a qudrilateral to find a missing angle 477, 560

**Stage 7 Unit 6 - Algebraic Proficiency**

Know the meaning of an expression, term, formula, equation and a function. 154

Use algebraic notation to represent variables. 151

Simplify algebraic expressions by collecting like terms. 156, 157

Substitution into a expression /formula. 155, 189

Expand single brackets. 160

Use a mapping diagram (function machine).

**Stage 7 Unit 7 - Exploring fractions, decimals and percentages**

Write one quantity as a fraction of another where the fraction is less than 1. 62

Write one quantity as a fraction of another where the fraction is greater than 1. 62

Write a fraction in it’s lowest terms by cancelling common factors. 61

Convert between mixed numbers and improper fractions. 64

Understand that percentage means ‘number of parts per hundred’. 82, 83

Write a percentage as a fraction. 82

Write a quantity as a percentage of another. 84

**Stage 7 Unit 8 - Proportional reasoning**

Understand how to user ratio notation 328

Converting between different units of measurement 695, 709, 743

Simplify a ratio and recognise when in lowest terms 329

Solve problems that involve dividing in a ratio 332 - 334, 739 - 742

**Stage 7 Unit 9 - Pattern sniffing**

Use a term-to-term rule to generate a linear sequence. 197

Use a term-to-term rule to generate a non-linear sequence. 197

Find the term-to-term rule for a sequence. 197

Describe a number sequence. 197

Solve problems involving the term-to-term rule for a sequence. 197

**Stage 7 Unit 10 - Measuring space**

Use a ruler to accurately measure lines.

Use a protractor to accurately measure angles. 458

Convert fluently between metric units of length. 692, 693

Convert fluently between metric units of mass. 695, 696

Convert fluently between metric units of volume/capacity. 702, 703

Convert fluently between metric units of time. 709, 710

Convert fluently between metric units of money. 743

Solve practical problems that involve converting between units. 694, 711, 714

**Stage 7 Unit 11 - Investigating angles**

Identify angles at a point, angles on a straight line and vertically opposite angles. 477 - 480

Identify known angle facts in more complex geometrical diagrams. 456, 479

Use knowledge of angles to calculate missing angle in diagrams. 477 - 479

Use the angle sum of a triangle to find missing angles. 477, 480

Find missing angles in isosceles triangles. 485

**Stage 7 Unit 12 – Calculating fractions, decimals and percentages**

Add and subtract proper fractions, improper fractions and mixed numbers. 65, 66

Multiply proper fractions, improper fractions and mixed numbers. 68, 69

Divide a proper fraction by a proper fraction. 70

Divide improper fractions and mixed numbers. 64, 70

Use a calculator to find a percentage of an amount. 86, 87

Use a calculator to increase or decrease an amount by a percentage. 89, 90

Compare two quantities using percentages. 98

Calculate percentage change. 97

**Stage 7 Unit 13 – Solving equations and inequalities**

Choose the required inverse operation when solving an equation. 177

Identify the correct order of undoing the operations in an equation. 177

Solve one step equations when the solution is a whole number or fraction. 178

Solve two-step equations when the solution is whole number or fraction. 179, 180

Solve two-step equations involving brackets when the solution is whole number. 183

Solve three-step equations when the solution is whole number or fraction. 184

Solve three-step equations involving brackets when the solution is whole number or fraction. 183, 184

Check the solution to an equation by substitution. 183, 184

**Stage 7 Unit 14 – Calculating Space**

Recall and apply the area formulae for rectangles, triangles and parallelograms. 554

Calculate the area of compound shapes. 556, 557

Calculate missing lengths in shapes when the area is given. 554, 555

Recall and apply the area formula for a trapezium. 559

Understand the meaning of surface area. 584

Calculate the surface area of cubes and cuboids. 584

Calculate missing lengths in 3D shapes when the surface area or volume is known. 584, 568

**Stage 7 Unit 15 - Checking, Approximating and Estimating**

Round values to any number of decimal places. 56

Identify the first significant figure in a number. 130

Round to 1 significant figure. 130

Understand estimation as a process of finding a rough answer to a calculation and its value to check answers are sensible. 131

Use estimation to find the rough value of a calculation by rounding values to 1SF. 131

Use inverse operations to check the solutions to calculations. 177

**Stage 7 Unit 16 – Mathematical Movement**

Identify the equation of lines that are parallel to the x-axis and the y-axis and draw them. 205

Identify the lines y=x and y=-x and draw them. 205

Reflect 2D shapes in the lines y = x and y = -x. 639, 640

Describe a reflection when given the object and image. 639

Accurately perform and describe translations using vector notation. 637

Accurately rotate 2D shapes using a centre of rotation. 648, 649

Describe a rotation stating all necessary information. 648, 649

**Stage 7 Unit 17 – Presentation of data**

Know what is meant by continuous and discrete data. 393

Interpret and construct frequency tables. 402, 404, 410

Construct and interpret pictograms, bar charts, vertical line charts and tables and know their appropriate use. 425, 426

Construct and interpret comparative bar charts. 426

Interpret pie charts and know their appropriate use. 427

Draw pie charts when the total frequency is not a factor of 360°. 427

Choose appropriate graphs or charts to represent data.

**Stage 7 Unit 18 – Measuring Data**

Find the mode for a set of data. 404

Find the median for a set of data, including when there is an even number of values. 409

Calculate the mean and use it to identify the missing number in a set of data. 405

Calculate the mean from a frequency table. 417

Find the mode and median from a frequency table. 415, 416

Understand the range as a measure of spread and calculate it for a set of data. 410

Analyse and compare sets of data. 404, 405, 409, 410

Appreciate the limitations of different statistics.