Math Games

Use number facts and relationships
• Learners are able to:
- recognise and apply key mental facts and strategies
- use known facts to derive others, e.g. use 7 x 6 to derive 0.7 x 6
- use the terms cube, cube root and reciprocal
- express cube numbers using powers
- express repeated multiplications as powers, e.g. 7 x 7 x 7 x 7 x 7 x 7 = 7?

Fractions, decimals, percentages and ratio
• Learners are able to:
- use equivalence of fractions, decimals, and percentages to select the most appropriate for a calculation
- simplify a calculation by using fractions in their simplest terms
- express recurring decimals using correct notation
- calculate a percentage, fraction, decimal of any quantity with a calculator where appropriate
- calculate the outcome of a given percentage increase or decrease
- express one quantity as a percentage of another
- simplify ratios including those given in different units
- use ratio and proportion to calculate quantities
- add, subtract, multiply and divide fractions

Calculate using mental and written methods
• Learners are able to:
- use efficient written methods to add and subtract numbers with up to 2 decimal places
- use efficient methods for multiplication and division of whole numbers and decimals, including decimals such as 0.6 or 0.06
- use the order of operations including brackets
- multiply and divide with negative numbers using mental methods

Estimate and check
• Learners are able to:
- use rounding to estimate answers to a given number of significant figures
- present answers to a given number of significant figures

Manage money
• Learners are able to:
- carry out calculations relating to VAT, saving and borrowing
- appreciate the basic principles of budgeting, saving (including understanding compound interest) and borrowing
- calculate using foreign money and exchange rates

Collect and record data Present and analyse data Interpret results
• Learners are able to:
- plan how to collect data to test hypotheses
- construct a wide range of graphs and diagrams to represent discrete and continuous data
- construct frequency tables for sets of data in equal class intervals, selecting groups as appropriate
- construct graphs to represent data including scatter diagrams to investigate correlation
- interpret diagrams and graphs to compare sets of data
- find the mean, median, mode and range from ungrouped frequency tables
- use mean, median, mode and range to compare two distributions (continuous data)

Probability
• Learners are able to:
- show that the sum of all probabilities = 1
- recognise that some outcomes cannot occur simultaneously, e.g. a coin cannot show heads and tails at the same time
- know that events that have two outcomes are not necessarily equally likely
- complete a sample space diagram and a two way table
- estimate the number of successes of an event, e.g. rolling a fair dice 300 times, how many 3s would be expected?

Identify processes and connections
• Learners are able to:
- transfer mathematical skills across the curriculum in a variety of contexts and everyday situations
- select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks
- prioritise and organise the relevant steps needed to complete the task or reach a solution
- choose an appropriate mental or written strategy and know when it is appropriate to use a calculator
- use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys
- identify, measure or obtain required information to complete the task
- identify what further information might be required and select what information is most appropriate
- select appropriate mathematics and techniques to use
- estimate and visualise size when measuring and use the correct units
- develop and evaluate mathematical strategies and ideas creatively
- consider connections between mathematical skills and contextualise these within extended tasks

Represent and communicate
• Learners are able to:
- explain results and procedures precisely using appropriate mathematical language
- refine methods of recording calculations
- use appropriate notation, symbols and units of measurement, including compound measures
- select and construct appropriate charts, diagrams and graphs with suitable scales
- interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading
- evaluate different forms of recording and presenting information, taking account of the context and audience
- generalise in words, and use algebra, to describe patterns that arise in numerical, spatial or practical situations

Review
• Learners are able to:
- select and apply appropriate checking strategies
- interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible
- verify and justify results or solutions, including discussion on risk and chance where relevant
- interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data
- draw conclusions from data and recognise that some conclusions may be misleading or uncertain
- justify numerical and algebraic results, making appropriate connections
- 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
- appreciate the difference between mathematical explanation and experimental evidence; recognise inconsistencies and bias

Shape
• Learners are able to:
- classify quadrilaterals
- explore the tessellation of two shapes
- recognise shapes that will or will not tessellate

Construction
• Learners are able to:
- recognise and draw accurate nets of prisms
- represent 3D shapes on isometric paper and draw plans and elevations of 3D shapes made out of cubes
- construct triangles given three lengths, using a ruler and compasses
- identify sets of lengths that cannot form a triangle

Movement
• Learners are able to:
- explore symmetrical properties of 3D shapes; identify planes of symmetry
- enlarge shapes on square paper where the scale factor is a positive whole number

Length, weight/mass, capacity
• Learners are able to:
- find circumferences of circles
- use the common units of measure, convert between related units of the metric system and carry out calculations
- use rough metric equivalents of imperial units in daily use
- recognise measurements that are discrete and those that are continuous
- interpret conversion graphs

Time
• Learners are able to:
- interpret fractions of a second appropriately
- interpret time expressed as decimals and fractions and enter them appropriately on a calculator
- use timetables and time zones to calculate travel time

Temperature
• Learners are able to:
- convert temperatures between appropriate temperature scales

Area and volume Angle and position
• Learners are able to:
- calculate areas of compound shapes (e.g. consisting of rectangles and triangles) and volumes of simple solids (e.g. cubes and cuboids)
- find areas of circles
- devise and use formulae to calculate the area of trapezia and kites
- calculate volumes of prisms constructed from cuboids, e.g. within an L-shaped cross-section
- explore angles on parallel lines
- understand exterior angles of triangles
- know and use the angle properties of quadrilaterals
- find horizontal and vertical distances using coordinates
- use bearings to describe the location of one object in relation to another
- use compass bearings and grid references to specify location

Number sequences
• Learners are able to:
- use algebra to express the nth term rule of a linear sequence
- use the nth term rule to find particular terms
- use the nth term rule to generate a sequence

Expressions and formulae
• Learners are able to:
- know that a x a = a²
- know that 2a x a = 2a²
- substitute positive and negative whole numbers into one and two step expressions
- simplify expressions involving the addition and subtraction of two or more variables, including those where one or more of the simplified variables is negative
- expand a single bracket
- rearrange formulae involving two variables

Functions and graphs
• Learners are able to:
- express output generated from function machines, taking into account the order of operations
- generate and plot points for linear functions

Equations and inequalities
• Learners are able to:
- solve equations including those where the solution is a negative, a fraction or a decimal and those that include brackets ()
- give a set of solutions from an inequality with two boundaries and show them on a number line
- express a set of numbers as an inequality
- complete and interpret simple information and distance - time graphs, showing an understanding of gradients within the context of the question