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Skills available for Wales year 8 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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Curriculum for Wales: Progression step 4, Year 8 Curriculum for Wales: Progression step 4, Year 8
National Curriculum: Key Stage 3 Year 8 National Curriculum: Key Stage 3 Year 8

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1 Developing numerical reasoning

1.1 Identify processes and connections
- 1.1.1 transfer mathematical skills across the curriculum in a variety of contexts and everyday situations
- 1.1.2 select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks
  - Multi-step word problems (8-Q.2)
  - Guess-and-check word problems (8-Q.4)
- 1.1.3 prioritise and organise the relevant steps needed to complete the task or reach a solution
- 1.1.4 choose an appropriate mental or written strategy and know when it is appropriate to use a calculator
- 1.1.5 use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys
- 1.1.6 identify, measure or obtain required information to complete the task from a range of sources, including text
- 1.1.7 identify what further information might be required and select what information is most appropriate
- 1.1.8 select appropriate mathematics and techniques to use
- 1.1.9 estimate and visualise size when measuring and use the correct units
  - Estimate metric measurements (8-R.1)
  - Estimate imperial measurements (8-R.9)
- 1.1.10 develop and evaluate mathematical strategies and ideas creatively
- 1.1.11 consider connections between mathematical skills and contextualise these within extended tasks
1.2 Represent and communicate
- 1.2.1 explain results and procedures precisely using appropriate mathematical language
- 1.2.2 refine methods of recording calculations
- 1.2.3 use appropriate notation, symbols and units of measurement, including compound measures
- 1.2.4 select and construct appropriate charts, diagrams and graphs with suitable scales
- 1.2.5 interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading
- 1.2.6 evaluate different forms of recording and presenting information, taking account of the context and audience
  - Choose the best type of graph (8-GG.15)
- 1.2.7 generalise in words, and use algebra, to describe patterns that arise in numerical, spatial or practical situations
  - Write variable expressions for arithmetic sequences (8-T.8)
1.3 Review
- 1.3.1 select and apply appropriate checking strategies
- 1.3.2 interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible
- 1.3.3 verify and justify results or solutions, including discussion on risk and chance where relevant
- 1.3.4 interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data
- 1.3.5 draw conclusions from data and recognise that some conclusions may be misleading or uncertain
  - Interpret charts to find mean, median, mode and range (8-HH.2)
  - Identify representative, random and biased samples (8-HH.8)
- 1.3.6 justify numerical and algebraic results, making appropriate connections
  - Apply multiplication and division rules (8-K.8)
  - Write equivalent expressions using properties (8-U.15)
- 1.3.7 explain and justify strategies, methods, reasoning and conclusions in a variety of different ways, including orally, graphically, in writing (both in mathematical notation and without), and using appropriate digital literacy equipment
- 1.3.8 appreciate the difference between mathematical explanation and experimental evidence; recognise inconsistencies and bias
  - Identify representative, random and biased samples (8-HH.8)

2 Using number skills

2.1 Use number facts and relationships
- 2.1.1 recognise and apply key mental facts and strategies
- 2.1.2 use known facts to derive others, e.g. use 7 x 6 to derive 0.7 x 6
  - Multiply and divide decimals by powers of ten (8-C.8)
- 2.1.3 use the terms cube, cube root and reciprocal
  - Reciprocals (8-G.1)
  - Cube roots of perfect cubes (9-F.21)
- 2.1.4 express cube numbers using powers
  - Understanding indices (8-L.1)
  - Evaluate indices (8-L.2)
- 2.1.5 express repeated multiplications as powers, e.g. 7 x 7 x 7 x 7 x 7 x 7 = 7?
  - Understanding indices (8-L.1)
2.2 Fractions, decimals, percentages and ratio
- 2.2.1 use equivalence of fractions, decimals, percentages and ratio to select the most appropriate for a calculation
  - Convert between decimals and fractions or mixed numbers (8-D.8)
  - Convert between percents, fractions and decimals (8-O.2)
- 2.2.2 simplify a calculation by using fractions in their simplest terms
  - Write fractions in lowest terms (8-D.1)
- 2.2.3 express recurring decimals using correct notation
- 2.2.4 calculate a percentage, fraction, decimal of any quantity with a calculator where appropriate
- 2.2.5 calculate the outcome of a given percentage increase or decrease
  - Percent of change (9-J.13)
  - Percent of change: word problems (9-J.14)
- 2.2.6 express one quantity as a percentage of another
- 2.2.7 simplify ratios including those given in different units
- 2.2.8 use ratio and proportion to calculate quantities, including cases where the 'total' is not given
- 2.2.9 add, subtract, multiply and divide fractions
2.3 Calculate using mental and written methods
- 2.3.1 use efficient written methods to add and subtract numbers with up to 2 decimal places
  - Add and subtract decimals (8-C.1)
  - Add and subtract decimals: word problems (8-C.2)
- 2.3.2 use efficient methods for multiplication and division of whole numbers and decimals, including decimals such as 0.6 or 0.06
- 2.3.3 use the order of operations including brackets
- 2.3.4 multiply and divide with negative numbers using mental methods
2.4 Estimate and check
- 2.4.1 use rounding to estimate answers to a given number of significant figures
  - Round decimals (8-B.4)
  - Estimate sums, differences and products of decimals (8-C.9)
- 2.4.2 present answers to a given number of significant figures
2.5 Manage money
- 2.5.1 carry out calculations relating to VAT, saving and borrowing
- 2.5.2 appreciate the basic principles of budgeting, saving (including understanding compound interest) and borrowing
- 2.5.3 calculate using foreign money and exchange rates

3 Using measuring skills

3.1 Length, weight/mass, capacity
- 3.1.1 find circumferences of circles
  - Circumference of circles (8-BB.10)
- 3.1.2 use the common units of measure, convert between related units of the metric system and carry out calculations
- 3.1.3 use rough metric equivalents of imperial units in daily use
  - Convert between metric and imperial units (8-R.12)
- 3.1.4 recognise measurements that are discrete and those that are continuous
- 3.1.5 interpret conversion graphs
3.2 Time
- 3.2.1 interpret fractions of a second appropriately
- 3.2.2 interpret time expressed as decimals and fractions and enter them appropriately on a calculator
- 3.2.3 use timetables and time zones to calculate travel time for a multi-stage journey
3.3 Temperature
- 3.3.1 convert temperatures between appropriate temperature scales
3.4 Area and volume Angle and position
- 3.4.1 calculate areas of compound shapes (e.g. consisting of rectangles and triangles) and volumes of simple solids (e.g. cubes and cuboids)
  - Area of compound figures (7-HH.11)
  - Volume of cubes and cuboids (8-BB.17)
- 3.4.2 find areas of circles
  - Circumference of circles (8-BB.10)
- 3.4.3 devise and use formulae to calculate the area of trapezia and kites
  - Area of trapeziums (8-BB.5)
- 3.4.4 calculate volumes of prisms constructed from cuboids, e.g. within an L-shaped cross-section
- 3.4.5 explore angles on parallel lines
  - Transversals of parallel lines: name angle pairs (8-Z.15)
- 3.4.6 understand exterior angles of triangles
- 3.4.7 know and use the angle properties of quadrilaterals
  - Find missing angles in triangles and quadrilaterals (8-Z.7)
- 3.4.8 find horizontal and vertical distances using coordinates
  - Distance between two points (8-S.4)
- 3.4.9 use bearings to describe the location of one object in relation to another
- 3.4.10 use compass bearings and grid references to specify location

4 Using geometry skills

4.1 Shape
- 4.1.1 classify quadrilaterals
  - Classify quadrilaterals (8-Z.5)
- 4.1.2 explore the tessellation of two shapes
- 4.1.3 recognise shapes that will or will not tessellate
4.2 Construction
- 4.2.1 recognise and draw accurate nets of prisms
  - Nets of three-dimensional figures (8-AA.2)
- 4.2.2 represent 3D shapes on isometric paper and draw plans and elevations of 3D shapes made out of cubes
- 4.2.3 construct triangles given three lengths, using a ruler and compasses
- 4.2.4 identify sets of lengths that cannot form a triangle
4.3 Movement
- 4.3.1 explore symmetrical properties of 3D shapes; identify planes of symmetry
- 4.3.2 enlarge shapes on square paper where the scale factor is a positive whole number
  - Dilations: graph the image (9-Z.11)
  - Dilations: find the coordinates (9-Z.12)

5 Using algebra skills

5.1 Number sequences
- 5.1.1 use algebra to express the nth term rule of a linear sequence
  - Write variable expressions for arithmetic sequences (8-T.8)
- 5.1.2 use the nth term rule to find particular terms
- 5.1.3 use the nth term rule to generate a sequence
  - Evaluate variable expressions for arithmetic sequences (8-T.6)
5.2 Expressions and formulae
- 5.2.1 know that a x a = a²
- 5.2.2 know that 2a x a = 2a²
- 5.2.3 substitute positive and negative whole numbers into one and two step expressions
- 5.2.4 simplify expressions involving the addition and subtraction of two or more variables, including those where one or more of the simplified variables is negative
  - Add and subtract like terms (8-U.9)
- 5.2.5 expand a single bracket
  - Multiply using the distributive property (8-U.11)
- 5.2.6 rearrange formulae involving two variables
5.3 Functions and graphs
- 5.3.1 express output generated from function machines, taking into account the order of operations
- 5.3.2 generate and plot points for linear functions
5.4 Equations and inequalities
- 5.4.1 solve equations including those where the solution is a negative, a fraction or a decimal and those that include brackets ()
- 5.4.2 give a set of solutions from an inequality with two boundaries and show them on a number line
- 5.4.3 express a set of numbers as an inequality
- 5.4.4 complete and interpret simple information and distance–time graphs, showing an understanding of gradients within the context of the question

6 Using data skills

6.1 Collect and record data Present and analyse data Interpret results
- 6.1.1 plan how to collect data to test hypotheses
- 6.1.2 construct a wide range of graphs and diagrams to represent discrete and continuous data
- 6.1.3 construct frequency tables for sets of data in equal class intervals, selecting groups as appropriate
  - Create frequency charts (8-GG.10)
- 6.1.4 construct graphs to represent data including scatter diagrams to investigate correlation
  - Identify trends with scatter plots (8-HH.10)
- 6.1.5 interpret diagrams and graphs to compare sets of data
- 6.1.6 find the mean, median, mode and range from ungrouped frequency tables
- 6.1.7 use mean, median, mode and range to compare two distributions (continuous data)
6.2 Probability
- 6.2.1 show that the sum of all probabilities = 1
- 6.2.2 recognise that some outcomes cannot occur simultaneously, e.g. a coin cannot show heads and tails at the same time
  - Probability of mutually exclusive events and overlapping events (8-II.3)
- 6.2.3 know that events that have two outcomes are not necessarily equally likely
  - Probability of mutually exclusive events and overlapping events (8-II.3)
- 6.2.4 complete a sample space diagram and a two way table
  - Compound events: find the number of outcomes (8-II.7)
  - Find the number of outcomes: word problems (8-II.9)
- 6.2.5 estimate the number of successes of an event, e.g. rolling a fair dice 300 times, how many 3s would be expected?
  - Use collected data to find probabilities and make predictions (8-II.)
  - Make predictions using theoretical probability (8-II.5)

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1 Developing numerical reasoning

1.1 Identify processes and connections

1.1.1 transfer mathematical skills across the curriculum in a variety of contexts and everyday situations

1.1.2 select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks

1.1.3 prioritise and organise the relevant steps needed to complete the task or reach a solution

1.1.4 choose an appropriate mental or written strategy and know when it is appropriate to use a calculator

1.1.5 use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys

1.1.6 identify, measure or obtain required information to complete the task from a range of sources, including text

1.1.7 identify what further information might be required and select what information is most appropriate

1.1.8 select appropriate mathematics and techniques to use

1.1.9 estimate and visualise size when measuring and use the correct units

1.1.10 develop and evaluate mathematical strategies and ideas creatively

1.1.11 consider connections between mathematical skills and contextualise these within extended tasks

1.2 Represent and communicate

1.2.1 explain results and procedures precisely using appropriate mathematical language

1.2.2 refine methods of recording calculations

1.2.3 use appropriate notation, symbols and units of measurement, including compound measures

1.2.4 select and construct appropriate charts, diagrams and graphs with suitable scales

1.2.5 interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading

1.2.6 evaluate different forms of recording and presenting information, taking account of the context and audience

1.2.7 generalise in words, and use algebra, to describe patterns that arise in numerical, spatial or practical situations

1.3 Review

1.3.1 select and apply appropriate checking strategies

1.3.2 interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible

1.3.3 verify and justify results or solutions, including discussion on risk and chance where relevant

1.3.4 interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data

1.3.5 draw conclusions from data and recognise that some conclusions may be misleading or uncertain

1.3.6 justify numerical and algebraic results, making appropriate connections

1.3.7 explain and justify strategies, methods, reasoning and conclusions in a variety of different ways, including orally, graphically, in writing (both in mathematical notation and without), and using appropriate digital literacy equipment

1.3.8 appreciate the difference between mathematical explanation and experimental evidence; recognise inconsistencies and bias

2 Using number skills

2.1 Use number facts and relationships

2.1.1 recognise and apply key mental facts and strategies

2.1.2 use known facts to derive others, e.g. use 7 x 6 to derive 0.7 x 6

2.1.3 use the terms cube, cube root and reciprocal

2.1.4 express cube numbers using powers

2.1.5 express repeated multiplications as powers, e.g. 7 x 7 x 7 x 7 x 7 x 7 = 7?

2.2 Fractions, decimals, percentages and ratio

2.2.1 use equivalence of fractions, decimals, percentages and ratio to select the most appropriate for a calculation

2.2.2 simplify a calculation by using fractions in their simplest terms

2.2.3 express recurring decimals using correct notation

2.2.4 calculate a percentage, fraction, decimal of any quantity with a calculator where appropriate

2.2.5 calculate the outcome of a given percentage increase or decrease

2.2.6 express one quantity as a percentage of another

2.2.7 simplify ratios including those given in different units

2.2.8 use ratio and proportion to calculate quantities, including cases where the 'total' is not given

2.2.9 add, subtract, multiply and divide fractions

2.3 Calculate using mental and written methods

2.3.1 use efficient written methods to add and subtract numbers with up to 2 decimal places

2.3.2 use efficient methods for multiplication and division of whole numbers and decimals, including decimals such as 0.6 or 0.06

2.3.3 use the order of operations including brackets

2.3.4 multiply and divide with negative numbers using mental methods

2.4 Estimate and check

2.4.1 use rounding to estimate answers to a given number of significant figures

2.4.2 present answers to a given number of significant figures

2.5 Manage money

2.5.1 carry out calculations relating to VAT, saving and borrowing

2.5.2 appreciate the basic principles of budgeting, saving (including understanding compound interest) and borrowing

2.5.3 calculate using foreign money and exchange rates

3 Using measuring skills

3.1 Length, weight/mass, capacity

3.1.1 find circumferences of circles

3.1.2 use the common units of measure, convert between related units of the metric system and carry out calculations

3.1.3 use rough metric equivalents of imperial units in daily use

3.1.4 recognise measurements that are discrete and those that are continuous

3.1.5 interpret conversion graphs

3.2 Time

3.2.1 interpret fractions of a second appropriately

3.2.2 interpret time expressed as decimals and fractions and enter them appropriately on a calculator

3.2.3 use timetables and time zones to calculate travel time for a multi-stage journey

3.3 Temperature

3.3.1 convert temperatures between appropriate temperature scales

3.4 Area and volume Angle and position

3.4.1 calculate areas of compound shapes (e.g. consisting of rectangles and triangles) and volumes of simple solids (e.g. cubes and cuboids)

3.4.2 find areas of circles

3.4.3 devise and use formulae to calculate the area of trapezia and kites

3.4.4 calculate volumes of prisms constructed from cuboids, e.g. within an L-shaped cross-section