Beal High School Mathematics Department Scheme of Work for years 7 and 8 Version for web site March 2008 Note: This SoW covers levels 4 to 7. teachers will often dip in to level 8, especially as extension work to stretch more able students. You can see Level 8 topics Year 9 Scheme of work
Term 1- Area and Volume Understand compound measures average speed and density Calculate lengths, areas and volumes in plane shapes and right prisms Know the volume of a prism Convert between metric units including area, volume and capacity measures Know the area and perimeter of a trapezium and a kite. Know the area of composite shapes Know the area and circumference of a circle Know the surface area and volume of a cuboid and shapes made from cuboids Calculate metric and imperial conversions. Estimate distance Find the area and perimeter of squares, rectangles, triangle and parallelogram Know the surface area and volume of a cube Read accurately from a ruler and from other scales. Change from one metric unit to another Find the perimeter of shapes with measurements given and by measuring lengths of sides Make 3D models as instructed (by linking given faces or edges) from multilink cubes Find the area of regular shapes by counting squares. Find approximate area of irregular shapes by counting squares Count cubes to find volume of a cuboid
Term 1 Place value and indices Multiply and divide whole and decimal numbers by decimals Calculate Upper & Lower Bounds of measurements or rounded numbers Understand and use Significant figures Use rounding methods to estimate answers to complex expressions Select and justify appropriate degrees of accuracy Multiply and Divide by Negative Numbers Multiply and divide numbers by 0.1, 0.01, 0.001 Round numbers to a given number of decimal places Use a calculator to solve number problems and interpret the answers Find approximate values for square and cube roots by trial and improvement Know and use the Laws of indices for multiplication and division Understand and use decimal Place Value and Ordering Multiply and Divide Decimals by multiples of powers of 10 Round positive whole numbers to the nearest 10, 100, 1000 Round decimals to the nearest whole number and to one decimal place Do Long division and long multiplication without using a calculator Order, add and subtract positive and negative numbers. Number lines Understand and use Brackets and Order of operations (BODMAS) Use place value of whole numbers. Read, write and order whole numbers and decimals (including the use of decimal notation in money) Add and subtract 2 and 3 digit numbers, multiply and divide 2 digit numbers by 1 digit numbers Mentally add, subtract, multiply and divide whole numbers Round to the nearest 10, 100 and 1000 Term 1
Term 1 - Sequences and equations Find the nth term of a quadratic sequence Solve simultaneous equations (algebraic method) Write sequences given nth term. Find the nth term of linear sequence Solve polynomial equations by trial and improvement (e.g. x 3 + x = 20) Form and solve equations with unknowns on both sides Use letters symbols and distinguish their different roles in Algebra Simplify expressions by collecting like terms Solve two step linear equations Generate expressions from word problems Generate terms of a sequence given a term-to-term rule e.g. Each term is double the one before Add with letters Simplify expressions with one letter Understand number patterns and generating sequences
Term 1 Statistical Graphs and Averages Draw a line of best fit for a scatter diagram and interpolate values from either axis Draw frequency polygon. Compare distributions using frequency polygons Understand Line graphs for time series. Give and test a hypothesis to a situation Find mean, median and mode for continuous data Draw and interpret scatter diagrams. Draw and interpret histograms with equal class width intervals Draw and interpret frequency diagrams using continuous data Draw and interpret stem-and-leaf diagrams and pie charts Use mean, median and mode and range to compare different sets of data (ungrouped) Consider the validity of different data collection sheets. Interpret graphs and diagrams (including pie charts) and draw conclusions Find mean, median and mode from discrete data Complete tally charts and frequency tables Draw and interpret frequency diagrams using discrete data Draw and interpret line graphs. Read simple pie charts Find range and mode from a list of data
Term 2 Angles, Constructions, Pythagoras and Trig Know and use Pythagoras Theorem in 2D Draw the locus of an object moving according to a rule Use bearings to solve problems Calculate angles in triangles and quadrilaterals Identify and use alternate and corresponding angles (parallel lines) Identify properties of equilateral and isosceles and right angled triangles Identify interior and exterior angles of a triangle and know that exterior angle = sum of 2 int. angles Classify quadrilaterals by their geometric properties Identify regular and irregular polygons, interior and exterior angles of a polygon Read and plot co-ordinates in 4 quadrants Construct perpendicular bisector, angle bisector and perpendicular from a point using compass and ruler Find simple loci. Construct triangles using ruler and compasses (SSS, SAS, ASA) Know and use Three figure bearings Measure and draw angles with a protractor. Estimate angle size. Identify acute, reflex, obtuse angles Know and use the laws for: sum of angles at a point and straight line (including vert. opp. angles) Construct squares, rectangles and triangles Construct nets of solids Read and plot co-ordinates (positive only) Identify perpendicular, parallel, vertical and horizontal. Measure angles. Calculate angles Know the properties of triangles and rectangles Draw common 2D shapes in different orientation on grids Plot co-ordinates
Term 2 - Fractions, decimals and percentages Calculate percentage increase and decrease Find 100% (i.e. find the original amount a reverse percentage problem) Understand Equivalent Fractions. Simplify Fractions. Order Fractions. Express one quantity as a percentage of another Express one quantity as a fraction of another Add/Subtract/Multiply/Divide Fractions Convert and compare fractions/decimals/percentages Find the prime decomposition of a number Calculate HCF and LCM Change an improper fraction into a mixed fraction and vice versa Cancel down fractions to their lowest form Add and subtract simple fractions (halves, quarters, eighths) Finding percentages of quantities, using a calculator where appropriate Understand Multiples, Factors, Primes & Tests of Divisibility Find the fraction of the shape shaded Recognise and understanding simple percentages Find a fraction of an amount. Find a simple percentage of an amount Convert fractions into decimals (non-recurring) Convert fractions (with denominators that are factors of 100) into percentages
Term 2 Formulae and equations Substitute positive and negative numbers into linear expressions and those involving powers Rearrange formulae Multiply together two brackets and simplify the answer (a+b)(c+d) Factorise a linear expression Solve inequalities in one variable Multiply out single brackets Substitute positive and negative numbers into linear expressions and simple expressions involving powers Substitute positive numbers into linear expressions Remove brackets and collect like terms Use formulae written in symbols. Make up formulae in symbols using one or two operators Understand and use Rules and formulae. Use simple formulae written in words
Term 2 - Probability Understand and use Relative frequency. Use relative frequency to compare outcomes of experiments List the outcomes for two events. Calculate probabilities for two events Know the rule for the Probability of an event not happening. Use the fact that the total probability of all mutually exclusive outcomes of an experiment is 1 Use a probability scale. List outcomes one event Calculate probability using equally likely outcomes (one event) Use the vocabulary of probability likely, unlikely, impossible, etc. Calculate simple probabilities
Term 3 Ratio and proportion Compare ratios by changing them into the form m:1 Simplify a ratio given as a fraction or decimal Understand Equivalent Ratios, simplify ratios to their lowest terms Divide a quantity into parts in a given ratio using the unitary method Use ratios when interpreting or sketching maps Read & make scale drawings Solve simple problems involving ratio and direct proportion Use direct proportion in simple contexts
Term 3 Transformations, Congruence and Similarity Identify planes of symmetry Recognise similar shapes and find the lengths of unknown sides Enlarge shapes with a fractional scale factor Understand the implications of enlargement on area and volume Understand combinations of transformations Enlarge shapes using positive scale factor and centre of enlargement Rotate shapes using centre of rotation Understand Rotational Symmetry Make Transformations on shapes (translation, reflection) Understand Congruent shapes and Tessellations Reflect simple shapes in a mirror line and draw axis of reflection
Term3 Co-ordinates and Graphs Plot graphs of linear relationships given in the form ay + bx + c = 0 Solve simultaneous equations graphically Find the equation of a straight line given m and c and vice versa For a given linear relationship, generate co-ordinate pairs and plot graphs of simple linear functions using all 4 quadrants For linear equations in the form y = mx + c, identify the effect of changing m and c Draw and interpret distance-time graphs and other real life graphs Plot and interpret graphs such as y = x, y = 2x, y = x + 1 Draw and interpret conversion graphs Plot co-ordinates in all four quadrants
Term 3 Handling Data Specifying a Problem, planning and collecting data Processing and representing data Interpreting and discussing results