wyvern college mathematics department key stage 3 · pdf filewyvern college mathematics...

Wyvern College Mathematics Department

Wyvern College

Mathematics Department

Key Stage 3

Year 8 Learning Objectives


Year 8 Learning Units

In year 8 your will cover the following learning units in your mathematics lessons:

Year 8 Learning Unit Year 8 Learning Unit

Policies and Four Operations Linear Sequences

Probability Trial and Improvement

Expressions Properties of Shapes and Nets

Equations Angles

Area and Perimeter Collecting Data

Circles Displaying Data

Surface Area and Volume Indices

Averages Transformations

Real Life Graphs Bearings

Straight Line Graphs Formulae

Rounding Simultaneous Equations

Fractions/Decimals/Percentages Constructions

Percentages Pythagoras’ Theorem

Ratio


Year 8 Learning Unit Objectives On these pages you will be able to see what learning objectives you need to meet in each learning unit to reach your target level. There

are also links to enrichment activities that you can do in your spare time to apply your learning to solve problems.


Policies and Four Operations

Level Objective

4 Add and subtract whole numbers using column methods

4 Multiply whole numbers using the Gelosia method

4 Divide whole numbers using short division

5 Add and subtract all decimal numbers using column methods

5 Multiply decimal numbers using the Gelosia method

5 All division problems including decimals using short division

Enrichment NRich activities:

Countdown http://nrich.maths.org/6499

http://nrich.maths.org/6499









Probability

Level Objective

Support Use words to describe the probability of an event happening

Support Understand and use the probability scale from 0 to 1

5 Select methods based on equally likely outcomes and experimental outcomes as

appropriate

6 Find and record all mutually exclusive outcomes for single events and successive events in

a systematic way (lists and sample spaces)

6 Know that the sum of probabilities for all mutually exclusive outcomes is equal to 1

7 Calculate the relative frequency of an event given experimental data

7 Understand that relative frequency tends towards theoretical probability as the number of

trials is increased

7 Calculate the expected number of outcomes for a given event.

8 Use the AND / OR rule to solve probability problems

8 Construct and use probability trees to solve probability problems with replacement


Odds and evens http://nrich.maths.org/4308

In a box http://nrich.maths.org/919

Flippin’ discs http://nrich.maths.org/4304

Do you feel lucky? http://nrich.maths.org/7222

Two’s company http://nrich.maths.org/4311

Cosy corner http://nrich.maths.org/4313

Which spinners? http://nrich.maths.org/6123


























































Expressions

Level Objective

Support Simplify algebraic expression by collecting like terms

5 Substitution with one variable

5 Multiply out single brackets and simplify by collecting like terms

6 Factorise linear expressions by taking out common factors

7 Multiplying algebraic terms

7 Expand double brackets and simplify by collecting like terms

Enrichment Pair products http://nrich.maths.org/2278

What’s possible? http://nrich.maths.org/742

Plus minus http://nrich.maths.org/658

Multiplication square http://nrich.maths.org/2821


































Equations

Level Objective

Support Find the missing whole number represented by a box or symbol in problems using all four

operations

4 Solve simple one step equations

5 Solve one step linear equations

6 Solve two step linear equations

7 Solve linear equations with the unknown on both sides and brackets

E Solve equations involving algebraic fractions


Think of two numbers http://nrich.maths.org/1170










Area and Perimeter

Level Objective

Support Find perimeters of simple shapes and find areas by counting squares

Support Understand and use the formula for a rectangle and distinguish between area and

perimeter

6 Deduce and use formulae for the area of a triangle, kite and a parallelogram

6 Deduce lengths of shapes given the area or perimeter and known lengths

7 Calculate areas and perimeters of compound shapes

7 Calculate the area of a trapezium

7 Solve functional area and perimeter problems (wallpapering, tiling etc)


Warmsnug double glazing http://nrich.maths.org/4889

Isosceles triangles http://nrich.maths.org/2666

Pick’s theorem http://nrich.maths.org/1867


























Circles

Level Objective

Support Use mathematical names for common 3-D and 2-D shapes

Support Construct circles of a given radius accurately

5 Label the radius, diameter, centre, tangent, chord, sector, segment, arc and

circumference of a circle

6 Calculate the circumference of a circle

6 Calculate the area of a circle

7 Calculate the radius and diameter of a circle given the area or circumference

E Calculate the length of an arc

E Calculate the area of a sector


An unusual shape http://nrich.maths.org/2161

Curvy areas http://nrich.maths.org/6468

Salinon http://nrich.maths.org/2425

Arclets http://nrich.maths.org/866

Track design http://nrich.maths.org/7359

Triangles and petals http://nrich.maths.org/2095


















































Surface Area and Volume

Level Objective

Support Calculate volume of 3D shapes by counting cubes

Support Calculate the area of common 2d shapes

6 Calculate the volume of cuboids

6 Calculate the surface area of right prisms including cuboids and cylinders

7 Calculate the volume of prisms including cylinders

E Calculate the volume of cones, frustums and spheres

E Calculate the surface area of spheres, cones and frustrums


Efficient cutting http://nrich.maths.org/2664

Cola can http://nrich.maths.org/5888

Funnel http://nrich.maths.org/5890


























Averages

Level Objective

Support Understand and use the mode and range to describe sets of data

5 Understand and use the mean of discrete data and compare two simple distributions,

using the range and one of mode, median or mean.

6 Identify the positives and negatives of each measure of average and choose the most

appropriate measure to be used

7 Find the mean, median and mode from a frequency table

8 Find an estimate for the mean, the class that contains the median and the modal group

from a grouped frequency table


Litov’s mean value theorem http://nrich.maths.org/4838

How would you score it http://nrich.maths.org/6957


















Real Life Graphs

Level Objective

Support Interpret simple graphs

Support Solve calculations involving time including conversion between the 12-hour and 24-hour

clock

Support Understand and solve calculations involving gas and electricity bills and bank statements

6 Use and construct conversion graphs

6 Interpret and construct speed/time, distance/time and depth/time graphs

6 Interpret and construct graphs/ charts of other real life situations including mobile phone

tariffs, mileage charts, timetables etc


Charting success http://nrich.maths.org/7735

Charting more success http://nrich.maths.org/7759


















Straight Line Graphs

Level Objective

Support Use and interpret coordinates in the first quadrant

Support Use and interpret coordinates in all 4 quadrants

6 Plot a straight line graph given the equation of the line

6 Understand all straight line graphs take the form y=mx + c and the effect of m and c on the

graph

6 Calculate the gradient of a line

7 Find the equation of a line

7 Identifying parallel lines


How steep is the slope? http://nrich.maths.org/6603

Parallel lines http://nrich.maths.org/5609


















Rounding

Level Objective

4 Round numbers to the nearest 10, 100 and 1000

4 Round to the nearest whole number

5 Round numbers to a given number of decimal places

7 Round numbers to a given number of significant figures

7 Estimate the answers to calculations by rounding numbers to 1 significant figure

Enrichment


Fractions/ Decimals/ Percentages

Level Objective

4 Convert well known fractions, decimals and percentages

6 Convert between any fractions, decimals and percentages

6 Order fractions, decimals and percentages by size

Enrichment


Percentages

Level Objective

Support Halve numbers

Support Divide numbers by 10 and 100

4 Find 50%, 25%, 75% and 10% of whole numbers

5 Find any percentage of a number with and without a calculator

5 Express one number as a percentage of another

7 Find the outcome of a given percentage increase or decrease using multipliers

7 Calculate what percentage change has occurred

8 Calculate the results of multiple percentage changes

Enrichment


Ratio

Level Objective

Support Begin to understand simple ratio

5 Understand simple ratios

5 Solve simple problems involving ratio

5 Simplify ratios by cancelling down

6 Divide a quantity into two or more parts in a given ratio


Mixing lemonade http://nrich.maths.org/6870

Mixing paints http://nrich.maths.org/4793

Mixing more paints http://nrich.maths.org/4794


























Linear Sequences

Level Objective

Support Recognise and describe number patterns.

Support Recognise and extend number patterns and sequences

6 Generate terms of a sequence using term to term and position to term rules

6 Find the nth term of a linear sequence

6 Find the nth term from a pattern or diagram and use this to generate any given term


Charlie’s delightful machine http://nrich.maths.org/7024










Trial and Improvement

Level Objective

Support Confidently multiply, divide, subtract and add all numbers including decimals

6 Solve quadratic and cubic equations to a given number of decimal places using trial

and improvement methods

Enrichment


Properties of Shapes and Nets

Level Objective

3 Identify the names of 2D and 3D shapes

4 Identify and construct nets of common 3D shapes

4 Classifying triangles by their shape properties

6 Classify quadrilaterals by their shape properties

6 Draw plan, side and front elevations of 3D shapes

6 Construct 3D views of shapes using isometric paper


Property chart http://nrich.maths.org/2927

Shapely pairs http://nrich.maths.org/2925

Quadrilaterals game http://nrich.maths.org/2924

Marbles in a box http://nrich.maths.org/895

Nine colours http://nrich.maths.org/768










































Angles

Level Objective

Support Name the different types of angle

Support Accurately estimate, measure and draw angles

5 Know and use angle facts to solve problems including, angles around a point, angles

on a straight line, angles in a triangle, angles in a quadrilateral and vertically opposite

angles

5 Know and use angle facts to solve problems involving isosceles, equilateral triangles

and exterior angles of triangles

6 Solve geometrical problems using properties of angles, of parallel and intersecting lines

6 Calculate interior and exterior angles of polygons

6 Understand a proof that angles in a triangle add up to 180 degrees and that angles in

a quadrilateral add up to 360 degrees


Cyclic quadrilaterals http://nrich.maths.org/6624

Subtended angles http://nrich.maths.org/2845

Right angles http://nrich.maths.org/2847









http://nrich.maths.org/2845/index

















Collecting Data

Level Objective

4 Collect and record discrete data in tally charts, data capture sheets and frequency

tables

5 Ask questions, plan how to answer them and collect the data required (questionnaires)

6 Design and use two way tables

7 Suggest a problem to explore using statistical methods, frame, questions and raise

conjectures; identify possible sources of bias and how to minimise it


Statistical shorts http://nrich.maths.org/7721

Reaction timer http://nrich.maths.org/6044

Who’s the best? http://nrich.maths.org/7367

Retiring to paradise http://nrich.maths.org/7722


































Displaying Data

Level Objective

3 Construct bar charts and pictograms, where the symbol represents a group of units.

5 Interpret graphs and diagrams, including pie charts and draw conclusions

6 Construct pie charts for categorical data

7 Construct and interpret scatter diagrams

8 Construct a cumulative frequency column from a frequency table

8 Construct a cumulative frequency graph, find the median and use the graph to

estimate other values

Enrichment


Indices

Level Objective

Support Be able to find the value of square and cube numbers

7 Find the value of an index problem using the laws of indices

7 Use the laws of indices to simplify algebraic problems

8 Solve problems involving fractional and negative indices


Power countdown http://nrich.maths.org/6448










Transformations

Level Objective

Support Identify lines of symmetry

Support Reflect simple shapes in a mirror line

Support Identify all the line and rotational symmetries of 2D shapes

6 Translate a shape by a given column vector

6 Rotate a shape by a given degrees, centre and direction

6 Enlarge a shape by a whole number scale factor and given centre

6 Reflect a shape in a given line of reflection

7 Fully describe any given transformation

7 Enlarge shapes by fractional and negative scale factors from a given centre of

enlargement


Transformation game http://nrich.maths.org/5457










Bearings

Level Objective

Support Accurately measure and draw angles

3 Describe and use compass directions

6 Measure and construct 3 figure bearings

6 Describe the points in relation to each other using bearings

Enrichment


Formulae

Level Objective

5 Writing a formula from words

5 Substitution with one variable

7 Substitution with more than one variable, squares, cubes and negatives

7 Rearranging the subject of formulae where the subject appears once

Enrichment


Simultaneous Equations

Level Objective

Support Solve simple one step equations

Support Solve one step equations

Support Solve two step equations

7 Solve pairs of simultaneous equations where one variable has the same coefficient

using the elimination method

7 Solve pairs of simultaneous equations where neither variable has the same coefficient

using the eliminations method

7 Graphically solve pairs of simultaneous equations


What’s it worth? http://nrich.maths.org/1053










Constructions

Level Objective

Support Measure the length of straight lines accurately using a ruler and construct straight lines

of a given length using a ruler

Support Accurately construct SAS ASA and SSS triangles

6 Construct standard constructions including, angle bisectors, perpendicular bisectors,

perpendicular from a point on a line, perpendicular from a point to a line

6 Construct circumscribed and inscribed circles

6 Construct angles of 60 degrees

6 Using angle bisectors to construct angles of 30 degrees 45 degrees and so on

6 Construct a regular hexagon

Enrichment


Pythagoras’ Theorem

Level Objective

Support Know and use properties of isosceles, equilateral triangles, scalene and right angled

triangles

Support Work out the area of triangles

7 Find the hypotenuse of a right angled triangle using Pythagoras’ Theorem

7 Find one of the shorter sides on a right angled triangle using Pythagoras’ Theorem

7 Solve functional problems involving Pythagoras’ Theorem


Ladder and cube http://nrich.maths.org/289

Walking around a cube http://nrich.maths.org/5689

















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