Wales
Skills available for Wales year 10 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.
Show alignments for:
- Curriculum for Wales: Progression step 5, Year 10 Curriculum for Wales: Progression step 5, Year 10
- National Curriculum: Key Stage 4 Year 10 National Curriculum: Key Stage 4 Year 10
Actions
1 Developing numerical reasoning
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1.1 Identify processes and connections
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1.1.1 transfer mathematical skills across the curriculum in a variety of contexts and everyday situations
- Solve proportions: word problems (10-C.7)
- Percent word problems (10-D.3)
- Solve linear equations: word problems (10-F.16)
- Word problems: mixed review (10-G.1)
- Write an equation in y=mx+c form from a word problem (10-K.11)
- Solve simultaneous equations by graphing: word problems (10-L.3)
- Solve simultaneous equations using substitution: word problems (10-L.7)
- Linear inequalities: word problems (10-M.4)
- Exponential growth and decay: word problems (10-Q.4)
- Pythagoras' theorem: word problems (10-BB.2)
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1.1.2 select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks
- Evaluate numerical expressions involving rational numbers (10-B.6)
- Multi-step problems with percents (10-D.8)
- Simplify variable expressions involving like terms and the distributive property (10-E.6)
- Solve simultaneous linear inequalities by graphing (10-M.6)
- Multiply polynomials (10-S.10)
- Reflections, rotations and translations: graph the image (10-X.9)
- Area between two shapes (10-CC.8)
- Probability of independent and dependent events (10-LL.12)
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1.1.3 prioritise and organise the relevant steps needed to complete the task or reach a solution
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1.1.4 choose an appropriate mental or written strategy and know when it is appropriate to use a calculator
- Solve equations: complete the solution (10-F.13)
- Is (x, y) a solution to the simultaneous equations? (10-L.1)
- Solve simultaneous equations by graphing (10-L.2)
- Solve simultaneous equations by graphing: word problems (10-L.3)
- Find the number of solutions to simultaneous equations by graphing (10-L.4)
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1.1.5 use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys
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1.1.6 identify, measure or obtain required information to complete the task
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1.1.7 identify what further information might be required and select what information is most appropriate
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1.1.8 select appropriate mathematics and techniques to use
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1.1.9 estimate and visualise size when measuring and use the correct units
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1.1.10 develop and evaluate mathematical strategies and ideas creatively
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1.1.11 consider connections between mathematical skills and contextualise these
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1.2 Represent and communicate
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1.2.1 explain results and procedures precisely using appropriate mathematical language
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1.2.2 refine methods of recording calculations
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1.2.3 use appropriate notation, symbols and units of measurement, including compound measures
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1.2.4 select and construct appropriate charts, diagrams and graphs with suitable scales
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1.2.5 interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading
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1.2.6 evaluate different forms of recording and presenting information, taking account of the context and audience
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1.2.7 generalise in words, and use algebra, to describe patterns that arise in numerical, spatial or practical situations
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1.3 Review
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1.3.1 select and apply appropriate checking strategies
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1.3.2 interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible
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1.3.3 verify and justify results or solutions, including discussion on risk and chance where relevant
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1.3.4 interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data
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1.3.5 draw conclusions from data and recognise that some conclusions may be misleading or uncertain
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1.3.6 recognise that inferences drawn from data may suggest the need for further investigation
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1.3.7 justify numerical and algebraic results, making appropriate connections
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1.3.8 explain and justify strategies, methods, reasoning and conclusions in a variety of different ways, including orally, graphically, writing (both in mathematical notation and without), using appropriate digital literacy equipment
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1.3.9 appreciate the difference between mathematical explanation and experimental evidence; recognise inconsistencies and bias
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2 Using number skills
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2.1 Use number facts and relationships
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2.1.1 use and interpret numbers in standard form within calculations
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2.1.2 convert to and from standard form
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2.1.3 find the lowest common multiples and highest common factor using prime factors
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2.2 Fractions, decimals, percentages and ratio
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2.2.1 use multipliers as an efficient method when working with percentages, e.g. multiply by 1.2 to increase an amount by 20%
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2.2.2 calculate the outcome of a given repeated proportional change
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2.2.3 calculate with direct and inverse proportion
- Identify proportional relationships (10-J.1)
- Find the constant of variation (10-J.2)
- Graph a proportional relationship (10-J.3)
- Write direct variation equations (10-J.4)
- Write and solve direct variation equations (10-J.5)
- Identify direct variation and inverse variation (10-J.6)
- Write inverse variation equations (10-J.7)
- Write and solve inverse variation equations (10-J.8)
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2.2.4 use calculations with different representations of fractions
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2.3 Calculate using mental and written methods
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2.3.1 select, choose and justify selection of method, including when to use a calculator
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2.3.2 use negative numbers
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2.4 Estimate and check
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2.4.1 define upper and lower bounds of a number that has been given to a specified degree of accuracy
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2.5 Manage money
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2.5.1 understand and demonstrate the real-life process of foreign exchange
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2.5.2 consider best value of an item priced in two or more different currencies
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2.5.3 calculate compound interest
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2.5.4 make comparisons between financial products that involve short-term borrowing and investments
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2.5.5 calculate with money, including household bills
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2.5.6 make informed decisions relating to household budgeting
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2.5.7 understand and calculate income tax
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3 Using measuring skills
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3.1 Length, weight/mass, capacity
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3.1.1 find the perimeter of semicircles and quadrants, including compound shapes and cases that require a solution in terms of pi
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3.1.2 find a radius or diameter given a circumference
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3.1.3 use trigonometry and Pythagoras' theorem to calculate the length of a side in a right angled triangle
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3.1.4 understand and use a variety of compound measures, including speed, density and population density
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3.1.5 define upper and lower bounds of a measurement that has been given to a specified degree of accuracy
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3.1.6 construct and interpolate from conversion graphs
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3.2 Time
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3.2.1 use timetables and time zones to plan a multi-stage journey
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3.2.2 plan the optimum route from a selection of timetables
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3.4 Area and volume Angle and position
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3.4.1 apply proportional change to 2-dimensional designs
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3.4.2 find areas of semicircles and quadrants, including cases that require a solution expressed in terms of pi
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3.4.3 find a radius or diameter given an area
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3.4.4 convert between metric units of area
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3.4.5 convert between metric units of volume
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3.4.6 calculate an angle in a right angled triangle using trigonometry
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3.4.7 find the distance between two points from their coordinates
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3.4.8 find the midpoint of a line
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3.4.9 find locations given sets of bearings and/or distances
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4 Using geometry skills
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4.1 Shape
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4.1.1 recognise similar shapes and calculate the size of missing sides
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4.1.2 use the terms arc, sector, segment, chord, tangent
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4.2 Construction
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4.2.1 draw plans and elevations of any 3D solid
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4.2.2 construct perpendicular bisectors, the perpendicular from a point to a line, angles of 60° and 90°, and the bisector of an angle
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4.2.3 shade a region defined by up to two conditions
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4.3 Movement
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4.3.1 reflect shapes in horizontal and vertical lines
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4.3.2 describe reflection in horizontal or vertical lines
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4.3.3 rotate shapes about a point
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4.3.4 describe rotations and find the centre of rotation
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4.3.5 translate a shape by a vector
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4.3.6 describe a translation using vectors
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4.3.7 enlarge a shape from a centre where the scale factor is 0.5
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5 Using algebra skills
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5.1 Number sequences
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5.1.1 generate non-linear sequences given the nth term rule
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5.2 Expressions and formulae
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5.2.1 manipulate indices, e.g. (2a²) ³
- Multiplication with positive indices (10-N.3)
- Division with integer indices (10-N.8)
- Multiplication and division with integer indices (10-N.9)
- Power rule with integer indices (10-N.10)
- Evaluate expressions using properties of indices: integer indices (10-N.11)
- Identify equivalent expressions involving integer indices (10-N.12)
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5.2.2 show and use rules of indices where the power is 0 or a fraction with numerator 1
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5.2.3 substitute into a variety of expressions, including those involving powers and brackets
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5.2.4 multiply out double brackets
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5.2.5 factorise algebraic expressions of two or more terms into a single bracket, including those where there is more than one common factor
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5.2.6 rearrange formulae including whole number powers and brackets
- Properties of addition and multiplication (10-E.2)
- Distributive property (10-E.3)
- Simplify variable expressions using properties (10-E.4)
- Rearrange multi-variable equations (10-F.18)
- Power rule with integer indices (10-N.10)
- Evaluate expressions using properties of indices: integer indices (10-N.11)
- Identify equivalent expressions involving integer indices (10-N.12)
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5.2.7 distinguish between equations, formulae and expressions
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5.3 Functions and graphs
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5.3.1 generate and plot points for simple quadratic and cubic functions
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5.3.2 solve simple linear simultaneous equations graphically
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5.3.3 construct graphs and define regions to show one inequality <> ??
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5.4 Equations and inequalities
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5.4.1 solve equations by trial and improvement, and justify the solution
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5.4.2 solve linear simultaneous equations with matching coefficients
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5.4.3 draw inferences from distance–time graphs
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6 Using data skills
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6.1 Collect and record data Present and analyse data Interpret results
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6.1.1 specify and test hypotheses, taking account of sampling
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6.1.2 identify possible sources of bias in the design of collection sheets and questionnaires
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6.1.3 evaluate questionnaires and write suitable questions, including response boxes
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6.1.4 construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, with the learner choosing the most appropriate representation, including frequency polygons and lines of best fit on scatter diagrams
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6.1.5 calculate the upper quartile, lower quartile and interquartile range of a set of discrete data and use them to describe a data set
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6.1.6 use a scatter diagram to make predictions about the data from a line of best fit drawn by eye
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6.1.7 understand the effects of extrapolation and interpolation on reliability
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6.1.8 use the mean, median, mode and range from grouped frequency tables to compare distributions
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6.2 Probability
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6.2.1 know that the sum of probabilities is 1 and use this to find missing probabilities in fraction or decimal form, including where there are two equal probabilities missing
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6.2.2 compare an estimated probability from experimental results with a theoretical probability
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6.2.3 identify when to construct sample space diagrams or two way tables to solve a problem
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6.2.4 use a two way table and sample space diagram to calculate the probability of simple compound events
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6.2.5 use a two way table to calculate simple cases of x given y, e.g. find the probability that a girl travels by bus
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6.2.6 estimate the number of successes where probability is expressed as a fraction or decimal.
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