Math Games

Classifying 2D shapes
• Identify and write clear definitions of triangles in terms of their sides and angles, distinguishing between:
- equilateral triangles
- isosceles triangles
- right-angled triangles
• Identify and write clear definitions of quadrilaterals in terms of their sides and angles, distinguishing between:
- parallelogram
- rectangle
- square
- rhombus
- trapezium
- kite

Similar and congruent 2D shapes
• Identify and describe the properties of congruent shapes
• Identify and describe the properties of similar shapes

Solving problems
• Solve geometric problems involving unknown sides and angles in triangles and quadrilaterals, using known properties and definitions.

Classifying 3D objects
• Describe, name and compare the 5 Platonic solids in terms of the shape and number of faces, the number of vertices and the number of edges

Building 3D models
• Revise using nets to create models of geometric solids, including:
- cubes
- prisms
- pyramids

Geometry of straight lines. Angle relationships
• Recognize and describe pairs of angles formed by:
- perpendicular lines
- intersecting lines
- parallel lines cut by a transversal

Geometry of straight lines. Solving problems
• Solve geometric problems using the relationships between pairs of angles described above

Transformations
• Recognize, describe and perform transformations with points on a co-ordinate plane, focusing on:
- reflecting a point in the X-axis or Y-axis
- translating a point within and across quadrants
• Recognize, describe and perform transformations with triangles on a co-ordinate plane, focusing on the co-ordinates of the vertices when:
- reflecting a triangle in the X-axis or Y-axis
- translating a triangle within and across quadrants
- rotating a triangle around the origin

Enlargements and reductions
• Use proportion to describe the effect of enlargement or reduction on area and perimeter of geometric figures

Constructions
• Accurately construct geometric figures appropriately using a compass, ruler and protractor, including:
- bisecting lines and angles
- perpendicular lines at a given point or from a given point
- triangles
- quadrilaterals
• Construct angles of 30°, 45°, 60° and their multiples without using a protractor

Investigating properties of geometric figures
• By construction, investigate the angles in a triangle, focusing on:
- the sum of the interior angles of triangles
- the size of angles in an equilateral triangle
- the sides and base angles of an isosceles triangle
• By construction, investigate sides and angles in quadrilaterals, focusing on:
- the sum of the interior angles of quadrilaterals
- the sides and opposite angles of parallelograms

Area and perimeter
• Use appropriate formulae to calculate perimeter and area of:
- squares
- rectangles
- triangles
- circles
• Calculate the areas of polygons, to at least 2 decimal places, by decomposing them into rectangles and/or triangles
• Use and describe the relationship between the radius, diameter and circumference of a circle in calculations
• Use and describe the relationship between the radius and area of a circle in calculations

Calculations and solving problems
• Solve problems, with or without a calculator, involving perimeter and area of polygons and circles
• Calculate to at least 2 decimal places
• Use and describe the meaning of the irrational number Pi (π) in calculations involving circles
• Use and convert between appropriate SI units, including: mm² <-> cm² <-> m² <-> km²

Surface area and volume
• Use appropriate formulae to calculate the surface area, volume and capacity of:
- cubes
- rectangular prisms
- triangular prisms
• Describe the interrelationship between surface area and volume of the objects mentioned above

Calculations and solving problems
• Solve problems, with or without a calculator, involving surface area, volume and capacity
• Use and convert between appropriate SI units, including:
- mm² <-> cm² <-> m² <-> km²
- mm³ <-> cm³ <-> m³
- ml (cm³) <-> l <-> kl

Develop and use the Theorem of Pythagoras
• Investigate the relationship between the lengths of the sides of a right-angled triangle to develop the Theorem of Pythagoras
• Determine whether a triangle is a right-angled triangle or not if the length of the three sides of the triangle are known
• Use the Theorem of Pythagoras to calculate a missing length in a right-angled triangle, leaving irrational answers in surd form

Collect data
• Pose questions relating to social, economic, and environmental issues
• Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines)
• Distinguish between samples and populations, and suggest appropriate samples for investigation
• Design and use simple questionnaires to answer questions with multiple choice responses

Organize and summarize data
• Organize (including grouping where appropriate) and record data using
- tally marks
- tables
- stem-and-leaf displays
• Group data into intervals
• Summarize data using measures of central tendency, including:
- mean
- median
- mode
• Summarize data using measures of dispersion, including:
- range
- extremes

Represent data
• Draw a variety of graphs by hand/technology to display and interpret data including:
- bar graphs and double bar graphs
- histograms with given and own intervals
- pie charts
- broken-line graphs

Interpret data
• Critically read and interpret data represented in:
- words
- bar graphs
- double bar graphs
- pie charts
- histograms
- broken-line graphs

Analyse data
• Critically analyse data by answering questions related to:
- data categories, including data intervals
- data sources and contexts
- central tendencies (mean, mode, median)
- scales used on graphs
- samples and populations
- dispersion of data
- error and bias in the data

Report data
• Summarize data in short paragraphs that include
- drawing conclusions about the data
- making predictions based on the data
- identifying sources of error and bias in the data
- choosing appropriate summary statistics for the data (mean, median, mode, range)
- the role of extremes in the data

Probability
• Consider a simple situation (with equally likely outcomes) that can be described using probability and:
- list all the possible outcomes
- determine the probability of each possible outcome using the definition of probability
- predict with reasons the relative frequency of the possible outcomes for a series of trials based on probability
- compare relative frequency with probability and explains possible differences

Mental calculations
• Revise multiplication of whole numbers to at least 12 x 12

Ordering and comparing whole numbers
• Revise prime numbers to at least 100

Properties of whole numbers
• Revise:
- The commutative; associative; distributive properties of whole numbers
- 0 in terms of its additive property (identity element for addition)
- 1 in terms of its multiplicative property (identity element for multiplication)
• Recognize the division property of 0, whereby any number divided by 0 is undefined

Calculations using whole numbers
• Revise calculations using all four operations on whole numbers, estimating and using calculators where appropriate

Calculation techniques
• Use a range of techniques to perform and check written and mental calculations of whole numbers including:
- long division
- adding, subtracting and multiplying in columns
- estimation
- rounding off and compensating
- using a calculator

Multiples and factors
• Revise:
- Prime factors of numbers to at least 3-digit whole numbers
- LCM and HCF of numbers to at least 3-digit whole numbers, by inspection or factorisation

Solving problems
• Solve problems involving whole numbers, including
- comparing two or more quantities of the same kind (ratio)
- comparing two quantities of different kinds (rate)
- sharing in a given ratio where the whole is given
- increasing or decreasing of a number in a given ratio
• Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:
- profit, loss, discount and VAT
- budgets
- accounts
- loans
- simple interest
- hire purchase
- exchange rates

Exponents. Mental calculations
• Revise:
- Squares to at least 122 and their square roots
- Cubes to at least 63 and their cube roots

Exponents. Comparing and representing numbers in exponential form
• Revise compare and represent whole numbers in exponential form
• Compare and represent integers in exponential form
• Compare and represent numbers in scientific notation, limited to positive exponents

Exponents. Calculations using numbers in exponential form
• Establish general laws of exponents, limited to:
- natural number exponents
- a to the m power x an = a to the m power + n
- a to the m power ÷ an = a to the m power – n, if m > n
- (a to the m power)n = a to the m power x n
- (a x t)n = an x tn
- a° = 1
• Recognize and use the appropriate laws of operations using numbers involving exponents and square and cube roots
• Perform calculations involving all four operations with numbers that involve the squares, cubes, square roots and cube roots of integers
• Calculate the squares, cubes, square roots and cube roots of rational numbers

Exponents. Solving problems
• Solve problems in contexts involving numbers in exponential form

Counting, ordering and comparing integers
• Revise:
- counting forwards and backwards in integers for any interval
- recognizing, ordering and comparing integers

Calculations with integers
• Revise addition and subtraction with integers
• Multiply and divide with integers
• Perform calculations involving all four operations with integers
• Perform calculations involving all four operations with numbers that involve the squares, cubes, square roots and cube roots of integers

Properties of integers
• Recognise and use commutative, associative and distributive properties of addition and multiplication for integers
• Recognize and use additive and multiplicative inverses for integers

Solving problems
• Solve problems in contexts involving multiple operations with integers

Common fractions. Calculations with fractions
• Revise:
- addition and subtraction of common fractions, including mixed numbers
- finding fractions of whole numbers
- multiplication of common fractions, including mixed numbers
• Divide whole numbers and common fractions by common fractions
• Calculate the squares, cubes, square roots and cube roots of common fractions

Common fractions. Calculation techniques
• Revise:
- convert mixed numbers to common fractions in order to perform calculations with them
- use knowledge of multiples and factors to write fractions in the simplest form before or after calculations
- use knowledge of equivalent fractions to add and subtract common fractions
• Use knowledge of reciprocal relationships to divide common fractions

Common fractions. Solving problems
• Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers

Common fractions. Percentages
• Revise:
- finding percentages of whole numbers
- calculating the percentage of part of a whole
- calculating percentage increase or decrease
• Calculate amounts if given percentage increase or decrease
• Solve problems in contexts involving percentages

Common fractions. Equivalent forms
• Revise equivalent forms between:
- common fractions (fractions where one denominator is a multiple of the other)
- common fraction and decimal fraction forms of the same number
- common fraction, decimal fraction and percentage forms of the same number

Decimal fractions. Ordering and comparing decimal fractions
• Revise:
- ordering, comparing and place value of decimal fractions to at least 3 decimal places
- rounding off decimal fractions to at least 2 decimal place

Decimal fractions. Calculations with decimal fractions
• Revise:
- addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places
- division of decimal fractions by whole numbers
• Extend multiplication to 'multiplication by decimal fractions' not limited to one decimal place
• Extend division to 'division of decimal fractions by decimal fractions'
• Calculate the squares, cubes, square roots and cube roots of decimal fractions

Decimal fractions. Calculation techniques
• Use knowledge of place value to estimate the number of decimal places in the result before performing calculations
• Use rounding off and a calculator to check results where appropriate

Decimal fractions. Solving problems
• Solve problems in context involving decimal fractions

Decimal fractions. Equivalent forms
• Revise equivalent forms between:
- common fraction and decimal fraction forms of the same number
- common fraction, decimal fraction and percentage forms of the same number

Numeric and geometric patterns. Investigate and extend patterns
• Investigate and extend numeric and geometric patterns looking for relationships between numbers, including patterns:
- represented in physical or diagram form
- not limited to sequences involving a constant difference or ratio
- of learner's own creation
- represented in tables
- represented algebraically
• Describe and justify the general rules for observed relationships between numbers in own words or in algebraic language

Functions and relationships. Input and output values
• Determine input values, output values or rules for patterns and relationships using:
- flow diagrams
- tables
- formulae
- equations

Functions and relationships. Equivalent forms
• Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented:
- verbally
- in flow diagrams
- in tables
- by formulae
- by equations

Algebraic language
• Revise the following done in Grade 7:
- recognize and interpret rules or relationships represented in symbolic form
- identify variables and constants in given formulae and/or equations
• Recognize and identify conventions for writing algebraic expressions
• Identify and classify like and unlike terms in algebraic expressions
• Recognize and identify coefficients and exponents in algebraic expressions

Expand and simplify algebraic expressions
• Use commutative, associative and distributive laws for rational numbers and laws of exponents to:
- add and subtract like terms in algebraic expressions
- multiply integers and monomials by:
- divide the following by integers or monomials:
- simplify algebraic expressions involving the above operations
• Determine the squares, cubes, square roots and cube roots of single algebraic terms or like algebraic terms
• Determine the numerical value of algebraic expressions by substitution

Equations
• Revise the following done in Grade 7:
- set up equations to describe problem situations
- analyse and interpret equations that describe a given situation
- solve equations by inspection
- determine the numerical value of an expression by substitution.
- identify variables and constants in given formulae or equations
• Use substitution in equations to generate tables of ordered pairs
• Extend solving equations to include:
- using additive and multiplicative inverses
- using laws of exponents

Interpreting graphs
• Revise the following done in Grade 7:
- analyse and interpret global graphs of problem situations, with a special focus on the following trends and features:
• Extend the focus on features of graphs to include:
- maximum or minimum
- discrete or continuous

Drawing graphs
• Draw global graphs from given descriptions of a problem situation, identifying features listed above
• Use tables or ordered pairs to plot points and draw graphs on the Cartesian plane