Math Games

Use number facts and relationships
• Learners are able to:
- use known facts to derive others, e.g. use 7 x 6 to derive 42 ÷ 0.0006
- use powers and understand the importance of powers of 10
- show awareness of the need for standard form and its representation on a calculator
- represent standard form on a calculator
- multiply, divide and use brackets with powers
- write a number as a product of its prime factors in index form

Fractions, decimals, percentages and ratio
• Learners are able to:
- use equivalence of fractions, decimals, and percentages to select the most appropriate for a calculation
- use and interpret different representations of fractions, e.g. mixed numbers and improper fractions
- calculate a percentage increase or decrease
- express one quantity as a percentage of another
- use ratio and proportion to calculate quantities

Calculate using mental and written methods
• Learners are able to:
- use efficient written methods to add and subtract numbers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places
- multiply and divide whole numbers and decimals
- use the order of operations including brackets and powers
- use the four operations in multistep calculations involving negative numbers, using mental and written methods

Estimate and check
• Learners are able to:
- make and justify estimates and approximations of calculations
- choose the appropriate degree of accuracy to present answers

Manage money
• Learners are able to:
- calculate using foreign money and exchange rates
- understand the risks involved in different ways of saving and investing
- describe why insurance is important and understand the impact of not being insured

Number sequences
• Learners are able to:
- use the nth term rule to determine whether a number is in a sequence
- determine the position number of a given term
- distinguish between a linear and non-linear sequence

Expressions and formulae
• Learners are able to:
- show and use rules that involve the multiplication, division and use of brackets with index variables
- simplify expressions including expansion of a single bracket, including a(b + c) + d(e + f), and double brackets
- factorise algebraic expressions of two or more terms into a single bracket where there is one common factor
- rearrange formulae involving two or more variables

Functions and graphs
• Learners are able to:
- examine features of linear functions, read an intercept from a graph, and recognise positive and negative gradients
- recognise the impact of the coefficient of x on the gradient of the line

Equations and inequalities
• Learners are able to:
- construct and solve equations that include brackets () and a() + b()
- construct and solve equations where the variable appears on both sides of the equals sign
- solve equations by trial and improvement and justify the solution
- express situations as inequalities
- solve inequalities and show the solutions on a number line
- construct and interpret information graphs that relate to a variety of situations, e.g. running a bath

Shape
• Learners are able to:
- recognise similar shapes and calculate the size of missing sides with whole number scale factor
- explore properties of shapes that tessellate

Construction
• Learners are able to:
- select and use appropriate equipment to draw triangles when given sufficient angles and sides

Movement
• Learners are able to:
- rotate shapes about the origin
- describe rotations about the origin
- enlarge a shape around a centre where the scale factor is positive
- explore locus where the path is a given distance from a point, line or shape

Collect and record data Present and analyse data Interpret results
• Learners are able to:
- test hypotheses, making decisions about how best to record and analyse the information from large data sets
- construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, with the learner choosing an appropriate scale
- select and justify statistics most appropriate to the problem considering extreme values (outliers)
- examine results critically, select and justify choice of statistics recognising the limitations of any assumptions and their effect on the conclusions drawn
- use appropriate mathematical instruments and methods to construct accurate drawings
- find the mean, median, mode and range from grouped frequency tables and explain why it is an estimate

Probability
• Learners are able to:
- use the sum of all probabilities is 1 - simple cases, e.g. rolling a dice P (not 6)
- recognise that practice is different from theory and that repeated experiments may give different results
- understand that reliability/stability increases with a greater number of trials
- construct a sample space diagram and a two way table.

Length, weight/mass, capacity
• Learners are able to:
- find circumferences of circles
- derive and use PythagorasÂ’ theorem
- make links between speed, distance and time
- understand and use a variety of compound measures, including speed and density
- define upper and lower bounds of discrete measurements
- recognise that there are different considerations for continuous data

Time
• Learners are able to:
- use timetables and time zones to plan a journey

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

Area and volume Angle and position
• Learners are able to:
- find areas of circles
- calculate surface areas of cubes and cuboids
- calculate volumes of prisms and cylinders
- calculate angles on parallel lines
- calculate interior and exterior angles of polygons
- draw the relative position of objects given the bearing of one from the other
- apply understanding of bearings and scale to interpret maps and plans, and to create plans and drawings to scale

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
- 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