Schemes of work

Y7 DELTA – AUTUMN TERM 

Unit 1: Analysis of data 

To be able to find mode, median, mean and range for a set of data.   

To be able to find the mode and range from a chart or table  

To be able to display data using tally charts, tables, bar charts and bar line charts  

To be able to understand and use frequency tables.    

To be able to draw a grouped bar chart.  

To be able to compare sets of data using their averages and range  

To be able to understand and draw line graphs.  

To be able to understand and draw dual and compound bar charts  

To be able analyse and present data using spreadsheets  

Unit 2: Number skills 

To be able to find highest common factor and lowest common multiple.    

To be able to recognise prime numbers  

To be able to carry out all four operations with positive and negative numbers.  

To be able to use mental and written strategies for multiplication.   

To be able to divide a 3 digit integer by a single or 2 digit integer  

To be able to carry out calculations involving squares, cubes, square and cube roots  

To be able to estimate answers to complex calculations.    

To be able to carry out calculations involving brackets  

Unit 3: Expressions 

To be able to simplify algebraic expressions by collecting like terms  

To be able to construct expressions using four operations  

To be able to substitute integers into a simple formulae written in either words or letter symbols  

To be able to write formulae using words and letter symbols.   

To be able to identify formulae and functions and find unknowns within them  

To be able to expand expressions involving brackets.    

To be able to substitute into expressions involving powers.  

To be able to factorise an algebraic expression 

Unit 4: Fractions 

To be able to compare and simplify fractions.   

To be able to write one number as a fraction of another  

To be able to write an improper fraction as a mixed number.   

To be able to add and subtract fractions   

To be able to work with fractions, decimals and percentages   

To be able to convert between fractions and decimals using division.  

To be able to multiply and divide fractions  

To be able to work out a fraction of amounts  

To be able to carry out all four operations with mixed numbers.   

Y7 DELTA – SPRING TERM 

Unit 5: Angles and shapes 

To be able to work out unknown angles when two or more lines meet or cross at a point.    

To be able to work out unknown angles involving parallel lines.  

To be able to describe the line and rotational symmetry of triangles.   

To be able to understand how to prove that a result is true.   

To be able to use properties of a triangle to work out unknown angles, including equilateral and isosceles angles.  

To be able to describe the line and rotational symmetry of quadrilaterals.    

To be able to describe properties of quadrilaterals and to use this knowledge to solve problems involving quadrilaterals.  

To be able to work out the interior and exterior angles of a polygon  

Unit 6: Decimals 

To be able to write decimals in ascending and descending order  

To be able to round to a given number of decimal places  

To be able to add and subtract decimals  

To be able to multiply an integer by a decimal and to use place value to multiply decimals  

To be able to divide a decimal by an integer.   

To be able to divide a number by a decimals  

To be able to convert between fractions, decimals and percentages.  

To be able to compare different proportions using percentages  

To be able to calculate percentages with and without a calculator.    

To be able to calculate percentage increase and decrease.    

To be able to work backwards to solve a percentage problem  

Unit 7: Equations 

To be able write and solve simple one step equations.    

To be able to solve problems using equations  

To be able to write and solve two step equations.    

To be able to write and solve equations containing brackets  

To be able to write and solve equations with letters on both sides  

To be able to solve equations that include x2 and x3.    

To be able to use trial and improvement to find solutions to 1 decimal place  

Y7 DELTA – SUMMER TERM 

Unit 8: Multiplicative reasoning 

To be able to convert between metric and imperial units.   

To be able to use metric units  

To be able to write a ratio in its simplest term and to simplify a ratio expressed in fractions or decimals.  

To be able to share a quantity in 2 or more parts in a given ratio  

To be able to understand the relationship between ratio and proportion  

To be able to solve simple word problems involving ratio and direct proportion.    

To be able to solve simple word problems involving ratio and inverse proportion  

To be able solve problems involving ratio and proportion using the unitary method.    

To be able to write ratios in the form of 1:n and to be able to apply this skill to best buy questions  

Unit 9: Perimeter, area and volume 

To be able to calculate the area of triangles, parallelograms and trapeziums  

To be able to calculate the area and perimeter of shapes made from rectangles and triangles  

To be able to identify nets of different 3D solids.    

To be able to know the properties of 3D solids  

To be able to calculate the surface area of cubes and cuboids.  

To be able to calculate the volume of a cube and a cuboid.    

To be able to convert between cm3, ml and litres  

To be able to convert between metric measurements for area and volume  

Unit 10: Sequences and graphs 

To be able to work out the terms of an arithmetic sequence using the term-to-term rule.   

To be able to work out the given term in a simple arithmetic sequence  

To be able to work out and use expressions for the nth tern in an arithmetic sequence  

To be able to generate a sequence and predict how they will continue.   

To be able to recognize geometric sequences and work out the term to term rule  

To be able to use positive and negative co ordinates and to work out the midpoint of a line.  

To be able to draw straight line graphs.  To be able to recognize straight line graphs parallel to the axis and to be able to recognize the graphs of y = x and y = -x  

Y7 THETA – AUTUMN TERM 

Unit 1: Analysis Data 

To be able to find mode, median, mean and range for a set of data.   

To be able to find the mode and range from a chart or table  

To be able to display data using tally charts, tables, bar charts and bar line charts  

To be able to understand and use frequency tables.    

To be able to draw a grouped bar chart.  

To be able to compare sets of data using their averages and range  

To be able to understand and draw line graphs.  

To be able to understand and draw dual and compound bar charts  

To be able analyse and present data using spreadsheets  

Unit 2: Number skills 

To be able to know and use the priority of operations and laws of arithmetic  

To be able to use a written method to add and subtract whole numbers of any size  

To be able to use a written method to multiply whole numbers  

To be able to use a written method to divide whole numbers.    

To be able to round decimals to the nearest whole number.   

To be able to interpret the display on a calculator in different contexts.  

To be able to use a calculator to solve problems involving time and money  

To be able to order positive and negative numbers.   

To be able to add and subtract positive and negative numbers.   

To be able to carry out simple multiplications with negative numbers  

To be able to find highest common factor and lowest common multiple.  

To be able to recognise prime numbers  

To be able recognise and use square numbers, square roots and triangle numbers  

Unit 3: Expressions 

To be able to find outputs of simple functions  

To be able to simplify simple linear algebraic expressions by collecting like terms  

To be able to use brackets with numbers and letters.    

To be able to write expression from word descriptions using addition, subtraction and multiplication  

To be able to substitute integers into a simple formulae written in either words or letter symbols  

To be able to write formulae using words and letter symbols.  To be able to identify formulae and functions and find unknowns within them 

Unit 4: Decimals and measures 

To be able to write decimals in order of size.   

To be able to round decimals to the nearest whole number and one decimal place.   

To be able to round decimals to make estimates and approximations of calculations  

To be able to convert measurements into the same units in order to compare them.    

To be able to solve simple problems involving units of measurement in the context of length.    

To be able to convert between metric units of length, mass and capacity  

To be able to read scales on a range of measuring equipment.    

To be able to accurately interpret a calculator display.   

To be able to plot and read co ordinates in all four quadrants  

To be able to multiply decimals mentally.    

To be able to understand where to position the decimal point by considering equivalent calculations  

To be able to add and subtract decimals.    

To be able to multiply and divide decimals by single digit whole numbers  

To be able to work out the perimeter of shapes and to solve perimeter problems  

To be able to find area by counting squares and multiplication of given lengths  

To be able to choose suitable units to estimate length and area and use these to solve problems.   

To be able to understand the relationships between metric and imperial units given the conversion factor. 

Y7 THETA – SPRING TERM 

Unit 5: Fractions 

To be able to use fraction notation to describe parts of a shape.   

To be able to compare simple fractions and use a diagram to compare two or more simple fractions  

To be able to change an improper fraction to a mixed number.   

To be able to identify equivalent fractions and simply fractions by cancelling common factors  

To be able to add and subtract simple fractions.  

To be able to calculate simple fractions of a quantity  

To be able to work with equivalent fractions and decimals.    

To be able to write one number as a fraction of another  

To be able to understand percentage as “the number of parts per hundred”.    

To be able to convert a percentage to a number of hundredths or tenths.    

To be able to work with equivalent percentages, fractions and percentages  

To be able to use different strategies to calculate with percentages and to express one number as a percentage of another  

Unit 6: Probability 

To be able to use the language of probability and to be able to use a probability scale with words and with numbers 0 to 1  

To be able to list and count outcomes.    

To be able to calculate probability based on equally likely outcomes.   

To be able to calculate more complex calculations.   

To be able to calculate the probability of an event not happening.  

To be able to record data from a simple experiment.    

To be able to estimate probability based on experimental data and draw conclusions based on the results of experiments  

To be able to use probability to estimate the number of expected wins in a game.    

To be able to apply probabilities from experimental data in simple situations  

Unit 7: Ratio and proportion 

To be able to use direct proportion in simple contexts and to solve simple problems involving direct proportion.  

To be able to   use the unitary method to solve simple word problems involving direct proportion  

To be able to use ratio notation.    

To be able to reduce a ratio to its simplest form including reducing three-part ratios by cancelling.  

To be able to divide a quantity into two parts in a ratio given in words and by a given ratio.   

To be able to solve word problems involving ratio  

To be able to use ratio and measures   

To be able to use fractions to describe and compare proportions.    

To be able to understand and use the relationship between ratio and proportion  

To be able to use percentages to describe proportions and compare simple proportions.   

To be able understand and use the relationship between them   

Y7 THETA – SUMMER TERM 

Unit 8: Lines and angles 

To be able to describe and label lines, angles and triangles.    

To be able to identify angle, side and symmetry properties of triangles.  

To be able to use a protractor to measure and draw angles.    

To be able solve to problems involving angles.  

To be able to use a ruler and protractor to draw triangles accurately and to be able to solve problems involving angles and triangles  

To be able to use the rule for angles on a straight line, angles around a point and vertically opposite angles and to solve problems involving these.  

To be able to use the rule for the sum of angles in a triangle.    

To be able to calculate interior and exterior angles.  

To be able to solve angle problems involving triangles.  

To be able to identify and name types of quadrilaterals.   

To be able to use the rule for the sum of angles in a quadrilateral and to solve angle problems involving quadrilaterals  

Unit 9: Sequences and graphs 

To be able to recognize, describe and continue number sequences.  

To be able to generate terms of a sequence using a term-to-term rule and to find missing terms in a sequence  

To be able to find patterns and rules in sequences.    

To be able to describe how a patter sequence grows.    

To be able to write and use number sequences to model real life problems  

To be able to generate and plot co ordinates from a rule.    

To be able to solve problems and spot patterns in co ordinates and to find the midpoint of a line segment.  

To be able to describe and continue special sequences.    

To be able to use the term-to-term rule to work out more terms in a sequence.    

To be able to recognize an arithmetic sequence  

To be able to recognize, name and plot graphs parallel to the axes and graphs of y = x and y = -x.    

To be able to plot straight line graphs using a table of values and to draw graphs to represent relationships  

To be able to generate terms of a sequence using the position to term rule.    

To be able to use linear expressions to describe the nth term of a simple sequence  

Unit 10: Transformations 

To be able to identify congruent shapes.    

To be able to use the language or enlargement and to enlarge shapes using a given scale factor.    

To be able to work out the scale factor given an object and its image.  

To be able to recognize line and rotational symmetry in 2D shapes.  

To be able to identify all symmetries of 2D shapes and to be able to identify reflection symmetry in 3D shapes  

To be able to recognize and carry out reflections in a mirror line and to be able to reflect a shape on a co ordinate grid.    

To be able to describe a reflection on a coordinate grid.  

To be able to describe and carry out rotations on a coordinate grid  

To be able to translate 2d shapes.    

To be able to transform 2d shapes by combinations of rotations, reflections and translations.  

 Y7 PI – AUTUMN TERM 

Unit 1: Analysis data (same as THETA – lessons in booklet.) 

To be able to find mode, median, mean and range for a set of data.   

To be able to find the mode and range from a chart or table  

To be able to display data using tally charts, tables, bar charts and bar line charts  

To be able to understand and use frequency tables.    

To be able to draw a grouped bar chart.  

To be able to compare sets of data using their averages and range  

To be able to understand and draw line graphs.  

To be able to understand and draw dual and compound bar charts  

To be able analyse and present data using spreadsheets  

Unit 2: Number skills 

To be able to add numbers together in different ways.    

To be able to subtract numbers in different ways.    

To be able to multiply numbers.    

To be able to recognise multiples and square numbers.    

To be able to divide one number by another.    

To be able to multiply and divide by 10, 100 and 1000  

To be able to use all four operations and use these skills to solve simple ratio and proportion problems  

To be able to use simple directed numbers.   

 To be able to continue a sequence  

Unit 3: Expressions, functions and formulae 

To be able to find outputs of simple functions  

To be able to simplify an expression  

To be able to write an expression given a description in words  

To be able to substitute integers into a simple formulae written in either words or letter symbols  

To be able to write formulae using words and letter symbols  

Unit 4: Graphs 

To be able to read information from real life graphs.  

To be able to draw graphs to show change over time.  

To be able to write coordinates of points on a grid.    

To be able to plot points from their coordinates.  

To be able to plot graphs of simple functions  

To be able to draw line graphs to show relationships between quantities.    

Y7 PI – SPRING TERM 

Unit 5: Factors and multiples 

To be able to use the correct priority of operations.   

To be able to understand the rules of multiplication  

To be able to recognize multiples of 2, 5, 10 and 25 and to be able to work out other multiples.  

To be able to multiply three-digit numbers by a single digit number.    

To be able to round numbers to the nearest 100 and 1000  

To be able to divide 3-digit numbers by a single digit.   

To be able to solve problems involving multiplication and division including the use of a calculator in such problems  

To be able to find factors of numbers and to identify prime numbers  

To be able to find common factors and multiples and use this knowledge to find HCF and LCM.  

Unit 6: Decimals and measures 

To be able to use different measurements and scales to solve problems including accurate drawing of lengths.  

To be able to read and write numbers in words and figures.   

To be able to understand, compare and use decimals for tenths and hundredths.    

To be able to  read and interpret scales using decimals  

To be able to order metric units and convert between different units of measure.    

To be able to read and interpret scales and record measurements  

To be able to recognize and extend number sequences by counting in decimals.    

To be able to add and subtract decimal numbers   

To be able to round decimals to the nearest whole number and nearest tenth.    

To be able to use a calculator and interpret the display in different contexts (decimals)  

To consolidate and extend mental calculation methods, including decimals.   

To be able to multiply and divide decimal numbers  

To be able us a calculator to solve word problems involving money and round answers to 2 d.p  

Unit 7: Angles and lines 

To be able to know and recognize the following features: right angles, quarter, half and three quarter turns, parallel and perpendicular lines, compass points  

To be able to recognize acute, obtuse and reflex angles and be able to measure acute angles.    

To be able to label lines and angles  

To be able to measure obtuse angles  

To be able to estimate the size of an angle and to be able to draw accurate angles  

To be able to find missing angles on a straight line.   

To be able to find missing angles around a point  

Y7 PI – SUMMER TERM 

Unit 8: Measuring and shape 

To be able to identify triangles, squares and rectangles.   

To be able to recognize the properties of triangles, squares and rectangles  

To be able to describe the line symmetry of triangles, quadrilaterals and other shapes  

To be able to solve problems using line symmetry and describe rotational symmetry  

To be able to identify polygons and to understand line and rotational symmetry of regular polygons  

To be able to find the perimeter of square, rectangles and regular polygons.   

To be able to calculate the perimeter of shapes made from rectangles.    

To be able to solve problems involving the perimeter of squares and rectangles.  

To be able to use metric units to measure area and to calculate the area of squares and rectangles  

Unit 9: Fractions, decimals and percentages 

To be able to order fractions and use fractions to describe parts of a shape  

To be able to identify equivalent fractions.  To be able to simplify fractions by cancelling.    

To be able to change an improper fraction into a mixed number  

To be able to calculate simple fractions of an amount  

To be able to add and subtract simple fractions  

To be able to understand percentage as “the number of parts per 100”.  and write a percentage as a fraction or decimal  

To be able to calculate percentages  

Unit 10: Transformations 

To be able to reflect a shape in the mirror line  

To be able to translate a shape  

To be able draw and describe rotations  

To be able to identify congruent shapes  

YEAR 8 DELTA – AUTUMN TERM 

Unit 1: Factors and powers 

To be able to Find the prime factor decomposition of a number  

To know the prime factorisation of numbers up to 30, giving answers as powers  

To be able to use prime factor decomposition to find the HCF or LCM of  2 numbers   

To be able to establish index laws for positive powers where the answer is a positive power  

To be able to apply the index laws for multiplication and division of positive integer powers  

To be able to show that any number to the power of zero is 1  

To be able to understand that each of the headings in the place value system, to the right of the tens column, can be written as a power of ten.  

To know the prefixes associated with 109, 106, 103 (giga, mega and kilo)  

To be able to understand the effect of multiplying or dividing by any integer power of 10  

To be able to understand the order in which to calculate expressions that contain powers and brackets in both the numerator and denominator of a fraction   

To be able to round numbers to a given number of significant figures  

To be able to use numbers of any size rounded to 1 significant figure  to make standardized estimates for calculations with 1 step.  

Unit 2: Working with powers 

To be able to simplify simple expressions involving powers, but not brackets, by collecting like terms  

To know and understand the meaning of an identity and use the identity sign  

To be able to simplify expressions involving brackets and powers  

To be able to factorise expressions  

To be able to substitute positive and negative integers into linear expressions and expressions involving powers  

To be able to construct and solve equations that involve multiplying out brackets by a negative number and collecting like terms  

Unit 3: 2D shapes and 3D solids 

To be able to analyse 3D shapes informally and through cross-sections, plans and elevations  

To be able to calculate the volume and surface area of right prisms (cuboids)  

To be able to calculate the volume and surface area of right prisms (prisms)  

To be able to calculate the area and circumference of a circle  

To be able to find the volume and surface area of prisms (to include cylinders)  

To be able to use Pythagoras’ Theorem in right angled triangles  

Unit 4: Real life graphs 

To be able to solve problems involving direct proportion with a graph  

To be able to discuss and interpret real-life graphs  

To be able to interpret information from a complex real life graph, read values and discuss trends  

To be able to plot the graphs of a function derived from a real life problem  

To be able to discuss and interpret linear and non linear graphs from a range of sources  

To be able to recognise graphs showing constant rates of change, average rates of change and variable rates of change  

To be able to plot a simple straight line graph (distance-time)  

To be able to draw and use graphs to solve distance-time problems 

Y8 DELTA – SPRING TERM 

Unit 5: Transformations 

To be able to escribe and carry out translations using column vectors  

To be able to identify symmetry in 2D and 3D shapes  

To be able to describe a reflection, giving the equation of the line of reflection (Show reflection on a coordinate grid in y = x, y = –x)  

To be able to describe a rotation on a coordinate grid  

To be able to enlarge shapes (no centre given)  

To be able to enlarge shapes (centre given)  

To be able to enlarge shapes (negative and fractional SF)  

To be able to describe transformations  

To be able to combine different transformations  

Unit 6: Fractions, decimals and percentages 

To be able to convert a recurring decimal into a fraction 

To be able to calculate percentage increase and decrease  

To be able to calculate percentage change  

To be able to calculate repeated percentage change  

Unit 7: Constructions and loci 

To be able to accurately draw triangles  

To be able to construct nets of 3D shapes  

To be able to construct line and angle bisectors  

To be able to draw a locus  

Y8 DELTA – SUMMER TERM 

Unit 8: Probability 

To be able to calculate probabilities 

To be able to identify Mutually Exclusive events 

To be able to calculate Relative Frequencies 

To be able to explain and apply Experimental probability 

To be able to use Sample Space 

To be able to draw Tree Diagrams 

Unit 9: Scale drawings and measures 

To be able to use scales in maps and plans 

To be able to measure and use bearings 

To be able to draw diagrams to scale 

To be able to identify congruent and similar shapes 

To be able to solve 2D Geometrical problems 

Unit 10: Graphs 

To be able to plot straight line graphs 

To be able to find the gradient of a straight line 

To be able to find the equation of a straight line 

To be able to identify parallel and perpendicular lines 

To be able to find the inverse of a linear function 

To be able to plot and identify non-linear graphs 

 YEAR 8 THETA – AUTUMN TERM 

Unit 1: Factors and powers 

To be able to multiply and divide decimals  

To be able to complete money Calculations  

To be able to add and subtract integers – positive and negative numbers (with varying numbers of significant figures )  

To be able to calculate squares, cubes and cube roots  

To be able to find the prime factor decomposition of a number  

To be able to recall the prime factorisation of numbers up to 30, giving answers as powers  

To be able to use prime factor decomposition to find the HCF or LCM of 2 numbers   

Unit 2: Area and volume 

To be able to calculate the area of shapes (Include trapezium and parallelogram)  

To be able to sketch nets of 3D solids  

To be able to draw plans and elevations  

To be able to calculate surface areas and volume of cubes and cuboids  

To be able to convert metric units  

Unit 3: Statistics, graphs and charts 

To be able to calculate the mean from a simple frequency table, and using an assumed mean   

To be able to interpret and construct pie charts  

To be able to use two way tables   

To be able to interpret scatter graphs, draw lines of best fit and use correlation  

To be able to find the modal class of a set of continuous data   

To be able to use stem and leaf diagrams to find mode, median, mean, range   

To be able to identify misleading graphs and statistics  

Unit 4: Expressions and equations 

To be able to solve simple linear equations with integer coefficients  

To be able to construct and solve linear equations   

To be able to substitute integers into formulae and solve for missing values one- step equations   

To be able to simplify simple expressions involving powers   

To be able to multiply a single term over a bracket  

To be able to use the distributive law to take out numerical common factors  

Y8 THETA – SPRING TERM 

Unit 5: Real life graphs 

To be able to draw, use and interpret conversion graphs 

To be able to draw and interpret distance-time graphs 

To be able to draw and interpret line graphs 

Unit 6: Decimals and ratio 

To be able to round to an appropriate degree of accuracy 

To be able to order positive and negative numbers (including decimals) 

To be able to multiply decimals *May need to recap multiplication of large numbers first 

To be able to divide decimals 

To be able to use ratios involving decimals *May need to recap ratio first 

Unit 7: Lines and angles 

To be able to classify quadrilaterals 

To be able to solve geometric problems using side and angle properties of triangles and special quadrilaterals 

To be able to use alternate and corresponding angles to find unknown angles 

To be able to find the interior and exterior angles of polygons 

To be able to solve geometric problems by setting up equations and giving reasons 

Y8 THETA – SUMMER TERM 

Unit 8: Fractions 

To be able to add and subtract fractions with any size denominator 

To be able to multiply integers and fractions by fractions 

To be able to convert fractions, decimals and reciprocals 

To be able to divide integers and fractions by fractions 

To be able to use the 4 operations with mixed numbers 

Unit 9: Graphs 

To be able to recognise and use graphs that are in direct proportion 

To be able to plot straight line graphs 

To be able to find the gradient of a straight line graph 

To be able to find the equation of a straight line graph 

To be able to find the midpoint of a line segment 

Unit 10: Percentage, decimals and fractions 

To be able to find equivalent fractions and decimals 

To be able to order fractions and decimals 

To be able to find equivalent fractions, decimals and percentages 

To be able to express one number as a percentage of another 

To be able to calculate percentage increase and decrease 

To be able to find a percentage of an amount 

To be able to solve finance problems 

YEAR 8 PI – AUTUMN TERM 

Unit 1: Number properties and calculations 

To be able to add and subtract with large numbers  

To be able to multiply by single and double digits 

To understand and be able to use a formal written method of division 

To be able to calculate with negative numbers 

To be able write amounts in ratio form 

To be able to simplify a ratio 

To be able to use proportion to solve problems 

Unit 2: 3D Solids 

To be able to identify types of 2D and 3D shapes 

To be able to sketch nets of 3D solids 

To be able to calculate surface areas and volume of cubes and cuboids 

To be able to convert metric units 

Unit 3: Statistics 

To be able to group data into tables (such as tally tables) 

To be able to use questionnaire responses to complete a data collection sheet 

To be able to Interpret data from bar charts - including compound and comparative bar charts 

To be able to construct a frequency table for grouped discrete data and draw a graph 

To be able to construct compound bar graphs 

To be able to Interpret and draw simple pie charts 

Unit 4: Expression and Equations 

To be able to use arithmetic operations with algebra 

To be able to simplify more complex linear algebraic expressions by collecting like terms, e.g. x + 7 + 3x, 2b – 3a + 6b 

To be able to find outputs and inputs of simple functions expressed in words or symbols using inverse operations 

To be able to construct functions (completing a number machine) 

To be able to solve simple linear equations with integer coefficients, of the form ax = b or x +/– b = c, e.g. 2x = 18, x + 7 = 12 or x – 3 = 15 

To be able to use distributive law with brackets, with numbers 

To be able to know that expressions can be written in more than one way, e.g. 2 x 3 + 2 x 7 = 2(3 + 7) 

To be able to begin to multiply a positive integer over a bracket containing linear terms, e.g. 4(x + 3) 

Y8 PI – SPRING TERM 

Unit 5: Decimal Calculations 

To be able to add and subtract decimal numbers  

To be able to multiply decimal numbers  

To be able to order and round decimal numbers  

Unit 6: Angles 

To be able to measure angles using a protractor  

To be able to accurately draw angles with a protractor  

To be able to calculate angles around a point and vertically opposite angles  

To be able to calculate the missing angle in a triangle  

To be able to accurately construct triangles  

To be able accurately create nets  

Unit 7: Number Properties 

To be able to calculate squares and cubes  

To be able to solve calculations with brackets and indices  

To be able to find factors of whole numbers  

Find the prime factor decomposition of a number less than 100  

To be able to use the lowest common multiple (LCM) and highest common factor (HCF) to solve problems  

Y8 PI – SUMMER TERM 

Unit 8: Sequences 

Generate terms of sequences arising from practical contexts.  

Generate terms of simple sequences using term-to-term rules like +3 or –2.  

Use the words finite, infinite, ascending and descending to describe sequences.  

Understand the infinite nature of a set of integers.  

Generate terms of a more complex sequence using term-to-term rules like x 2 then +1 or ‘–1 then x2’  

Generate terms of linear sequences using term-to-term with positive or negative integers.  

Know that an arithmetic sequence is generated by a starting number a, then adding a constant number, d  

Find a term given its position in the sequences like tenth number in 4x table is 40 (one operation on n)  

Find a term of a practical sequence given its position in the sequence  

Generate terms of linear sequences using position-to-term with positive integers  

Begin to use linear expressions to describe the nth term in a one-step arithmetic sequence  

Generate and describe simple integer sequences, square and triangular numbers  

Recognise triangular numbers  

Generate and describe integer sequences such as powers of 2 and growing rectangles  

Recognise geometric sequences and appreciate other sequences that arise  

Unit 9: Fractions and percentage 

Use a diagram to compare two or more simple fractions with different denominators, and not unit fractions  

Identify equivalent fractions.  

Simplify fractions by cancelling all common factors  

Express one number as a fraction of another (halves, quarters, thirds)  

Calculate fractions of quantities and measurements – only do multiplying  

Begin to add and subtract simple fractions and those with simple common denominators  

Extend the possible fractions that can be used in mental calculations by using halving and doubling strategies.  

Add fractions by writing with a common denominator, where the denominators are 12 or less, where the answer is less than 1  

Multiply a fraction by an integer  

Calculate simple percentages  

Use percentages to compare simple proportions  

Express one given number as a percentage of another  

Unit 10: Probability 

Use the vocabulary of probability  

Use a probability scale with words  

Understand and use the probability scale from 0 to 1  

Identify all possible mutually exclusive outcomes of a single event  

Find and justify probabilities based on equally likely outcomes in simple contexts  

Know that if probability of event is p then probability of event not occurring is 1 – p  

Identify all mutually exclusive outcomes for two successive events with two outcomes in each event  

Estimate probabilities based on given experimental data  

When interpreting results of an experiment, use vocabulary of probability  

Use the language of probability to compare the choice of x/a with y/a  

Use experimentation to complete a data collection sheet e.g. throwing a dice or data-logging  

YEAR 9 DELTA – AUTUMN TERM 

Unit 1: Powers and roots 

 To be able to:  

• Find the reciprocal of simple numbers /fractions mentally  

• Know that a number multiplied by its reciprocal is 1  

• Know that the reciprocal of a reciprocal is the original number  

• Use the index laws to include negative power answers and understand that these answers are smaller than 1  

• Evaluate powers of fractions  

• Use fractional indices and write a fractional power as a root  

• Work out negative fractional powers of numbers  

• Write numbers greater than 10 in standard form  

• Write number less than 10 in standard form  

• Order numbers written in standard form  

• Complete calculations using numbers written in standard form  

• Understand / use rational / irrational numbers  

• Simplify expressions which include surds  

• Present a concise and reasoned argument using surds  

• Distinguish between exact representations of roots and their decimal approximations 

Unit 2: Quadratics 

 To be able to:  

• Generate any term of a sequence when the nth term is given  

• Generate the next term in a quadratic sequence  

• Find a term of a quadratic sequence 

• Find the nth term of a quadratic sequence

• Generate the sequence of triangle numbers by considering the arrangement of dots  

• By looking at the spatial patterns of triangular numbers, deduce the nth term  

• Multiply out brackets involving positive terms  

• Multiply out brackets involving positive and negative terms  

• Square a linear expression  

• Derive and use identities for the product of two linear expressions  

• Factorise a quadratic expression  

• Factorise a perfect square  

• Derive and use the difference of two squares  

• Solve monic quadratics (coefficient of x squared is 1) 

Unit 3: Inequalities, equations and formulae 

To be able to: 

• Solve linear inequalities 

• Represent solutions on a number line 

• To multiply both sides by a negative number 

• Apply that anything to the power of zero is 1 

• Use index laws and deduce that negative powers are less than 1 

• Identify the difference between equations, formulae and functions 

• Solve equations of the form (ax +/– b)/c = (dx +/– e)/f {One of c or f should be 1} 

• Construct and solve equations of the form (ax +/– b)/c = (dx +/– e)/f {c and f are bigger than 1} 

• Change the subject of the formula 

• Change the subject of a complex formula that involves fractions 

• Solve problems by finding a variable that is not the subject of a formula 

• Change algebraic fractions to equivalent fractions 

• Simplify complex algebraic expressions 

Unit 4: Collecting and analysing data 

To be able to:  

• Select appropriate level of accuracy of data 

• Select the range of possible methods that could be used to collect this data as primary data 

• Select and discuss the range of possible sources that could be used to collect this data as secondary data 

• From a range of  sample sizes identify the most sensible answer 

• Determine the sample size and degree of accuracy needed 

• From a small choice of options identify ways to reduce bias in a sample or questionnaire 

• Identify a random sample 

• Use stem and leaf diagrams to find mode, median, mean, range 

• Construct stem and leaf diagrams 

• Use back to back stem and leaf diagrams to compare sets of data 

• Construct a frequency diagram from a grouped frequency table, and use it to draw a frequency polygon. 

• Compare two distributions using the shape of the distributions – frequency polygons. 

• Construct and use frequency polygons to compare sets of data 

• Estimate the range of a large set of grouped data 

• Calculate an estimate of the mean of a large set of grouped data 

• Estimate the mean from a frequency polygon 

• Identify the class that contains the median of a set of grouped data from a table 

• Calculate possible values of the set of data given summary statistics 

• Find quartiles from raw data and present data in a box plot 

• Find the lower and upper quartiles of a set of grouped data using a cumulative frequency chart and box and whisker diagram 

• Draw a grouped frequency graph 

• Estimate the median of a set of grouped data using a cumulative frequency chart 

• Find the interquartile range of a large set of grouped data using a cumulative frequency chart 

• Interpret / construct histograms 

Y9 DELTA – SPRING TERM 

Unit 5: Multiplicative reasoning 

 To be able to:  

• Set up equations to show direct proportion  

• Recognise sets of data that are proportional  

• Given a relationship (as proportion) graphically or in words, extend beyond known values (e.g. off lines of chart, or above pairs of values given  

• Check by drawing graphs whether two variables are in direct proportion  

• Understand direct proportion as equality of ratio  

• Use algebraic methods to solve problems involving variables in direct proportion  

• Use expressions of the form y is proportional to x  

• Use expressions of the form y is proportional to x 

• Use expressions of the form y is proportional to x2  

• Identify data that is proportional to the inverse of a variable  

• Understand / use inverse proportion 

• Recognise the formulae for length of arcs in a circle  

• Recognise the formulae for area of sectors in a circle  

• Use the formulae for length of arcs and area of sectors of circles to solve problems  

Unit 6: Non-linear graphs 

To be able to:   

• Construct a table of values, including negative values of x for a quadratic function such as y = ax2  

• Recognise the graph of a quadratic function  

• Construct a table of values, including negative values of x for a function such as y = ax2 + b  

• Find the line of symmetry and write down the turning point of a quadratic graph  

• Explain the effect on a quadratic graph of changing the parameter 

• Solve simple quadratic equations graphically, e.g. x2 – 10 = 0, 2x2 – 15 = 0  

• Construct a table of values, including negative values of x for a function such as y = ax2 + bx and y = ax2 + bx + c  

• Solve quadratic equations such as ax^2 + bx = 0 graphically and relate the solutions to quadratic factorisation  

• Solve quadratic equations such as x2 + bx + c = 0 graphically and relate the solutions to quadratic factorisation  

• Construct a table of values, including negative values of x for a function such as y = ax3  

• Recognise the graphs of y = x^2, y = 3x^2 + 4, y = x^3  

• Recognise graphs of functions of the form y = ax2 + b and y = ax3  

• Identify maxima, minima and lines of symmetry on quadratic and cubic graphs  

• Construct models of real-life situations by drawing graphs and constructing algebraic equations  

• Sketch / interpret graphs of reciprocal functions  

• Recognise and use reciprocal graphs and graphs for inverse proportion  

Unit 7: Accuracies and measures 

To be able to:  

• Solve problems using constant rates and related formulae.  

• Extend to simple conversions of compound measures (e.g. convert 2 m/s to km/hr)  

• Solve problems using average rate of change and related formulae   

• Solve problems using constant rates and related formulae  

• Extend to simple conversions of compound measures 

• Identify the upper and lower bounds of a measurement by calculating +/– half of the unit used for rounding  

• Identify upper and lower bounds for rounding of discrete and continuous data  

• Calculate simple error intervals using inequality notation a < x <= b  

• Calculate the lower and upper bounds of area measurement  

• Calculate the upper and lower bounds of compound measures  

• Determine upper and lower bounds in complex problems 

• Solve problems by understanding upper and lower bounds 

Y9 DELTA – SUMMER TERM 

Unit 8: Graphical Solutions 

To be able to:  

• Understand the steps required to solve a pair of simultaneous equations of the form ax + y = b, y = ax  

• Understand the steps required to solve a pair of simultaneous equations, when they are solved by addition. Equations are of the form ax + y = b, x – y = c  

• Understand the steps required to solve a pair of simultaneous, when they are solved by subtraction. Equations are of the form ax + y = b, x + y = c  

• Rearrange equations of the form ax+by=c to compare gradients and y- intercept  

• Recognise that linear functions can be rearranged to give y explicitly in terms if x, e.g. rearrange y + 3x – 2 = 0 in the form y = 2 – 3x  

• Find the equation of the line between two points  

• Understand the steps required to solve a pair of simultaneous equations, when they are solved by multiplication. Equations are of the form ax + y = b, x +/– cy = d  

• Identify the solution of simultaneous equations on a graph  

• Solve inequalities in two variables by using linear graphs  

• Solve more complex inequalities in two variables by using linear and quadratic graphs  

Unit 9: Trigonometry 

To be able to:  

• Understand that the ratio of any two sides is constant in similar right-angles triangles  

• Understand that the ratio of any two sides is constant in similar right-angles triangles 

• Understand that the ratio of any two sides is constant in similar right-angles triangles  

• Begin to use the trigonometric ratios to find the size of an angle in a right-angled triangle  

• Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle, using straight-forward algebraic manipulation, e.g. calculate the adjacent (using cosine), or the opposite (using sine or tangent ratios)  

• Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle, using more complex algebraic manipulation, e.g. the hypotenuse (using cosine or sine), or adjacent (using the tangent ratio)  

• Use the appropriate ratio to find a length, or angle, and hence solve a two-dimensional problem  

• Use sine / cosine / tangent of any size of angle and Pythagoras’ theorem when solving problems in 3D  

• Sketch graphs of sine / cosine / tangent functions for any angle, generating/interpreting them  

Unit 10: Probability 

To be able to:  

• Calculate probabilities from two-way tables with more than two columns / rows each way   

• Use the language of probability to compare the choice of x/a with x/b  

• Use the language of probability to compare the choice of x/a with y/b   

• Calculate the probability of a combination of events or single missing events of a set of mutually exclusive events using sum of outcomes is one  

• Calculate estimates of probability from experiments or survey results   

• Use experimental probabilities to predict outcomes  

• Identify all mutually exclusive outcomes for two successive events    

• Compare experimental and theoretical probabilities  

• Enumerate sets and combinations of sets systematically, using tabular, grid and Venn diagrams   

• Identify conditions for a fair game  

• Use P(A and B) = P(A) × P(B) for two independent events  

• Complete and use tree diagrams to calculate probabilities  

YEAR 9 THETA – AUTUMN TERM 

Unit 1: Indices and standard Form  

To be able to:  

• Establish index laws for positive powers where the answer is a positive power  

• Understand which part of an expression is raised to a power  

• Be able to simplify expressions containing powers  

• Solve word problems using square roots and cube roots  

• Apply the index laws for multiplication and division of integer powers  

• Make and justify estimates and approximations of calculations involving more than two operations and BIDMAS  

• Understand the order in which to calculate expressions that contain powers and bracket 

• Know the prefixes associated with 1012, 109, 106, 103, 10-2, 10-3, 10-6, 10-9, 10-12  

• Know that any number to the power of zero is 1 

• Write and order numbers in standard index form  

Unit 2: Expressions and formulae 

To be able to:  

• Substitute integers into simple expressions involving small powers  

• Substitute integers into formulae to give equations and solve 

• Derive complex algebraic expressions and formulae 

• Change the subject of a formula  

• Apply the index laws including negative power answers  

• Simplify expressions involving brackets and powers    

• Use the distributive law to take out single term algebraic factors  

• Multiply out brackets and collect like terms 

• Change algebraic fractions to equivalent fractions  

• Simplify algebraic expressions 

Unit 3: Dealing with data  

To be able to:  

• Select the range of possible methods that could be used to collect primary data   

• Determine suitable sample size and degree of accuracy needed   

• Design and use a data collection sheet for continuous grouped data   

• Discuss factors that may affect the collection of data   

• Design tables recording discrete and continuous data  

• From a small choice of options identify ways to reduce bias in a sample 

• Find the modal class of a large set of data  

• Calculate estimate of mean from large sets of grouped data  

• Identify key features of data sets described in either line graphs or scatter graphs – including exceptions and correlation  

• Use a line of best fit, drawn by eye, to estimate the missing value in a two variable data set  

• Construct and use frequency polygons to compare sets of data 

• Write a report to show results of a survey 

Unit 4: Multiplicative reasoning 

To be able to:  

• Enlarge 2D shapes, given a centre of enlargement and a positive whole number scale factor  

• Find the centre of enlargement by drawing lines on a grid 

• Enlarge 2D shapes, given a negative and fractional scale factor  

• Solve 'original value' problems using inverse operation  

• Calculate percentage change, using the formula actual change / original amount × 100 – where formula is recalled  

• Round numbers to a given number of significant figures  

• Solve problems using compound measures  

• Solve problems using constant rates and related formulae  

Y9 THETA – SPRING TERM 

Unit 5: Constructions 

To be able to:  

• Use and interpret maps and scale drawings  

• Analyse 3D shapes through cross-sections, plans and elevations  

• Identify alternate and corresponding angles on the same diagram  

• Use straight edge and compass to construct the mid-point and perpendicular bisector of a line segment  

• Use straight edge and compass to construct the bisector of an angle  

• Use straight edge and compass to construct the perpendicular from a point to a line segment  

• Use straight edge and compass to construct the perpendicular from a point on a line segment 

• Use straight edge and compass to construct a triangle, given three sides (SSS)  

• Use straight edge and compass to construct a triangle, given right angle, hypotenuse and side (RHS)  

• Construct nets of triangular prism, pyramid and wedge shape using SSS or RHS for the triangular sections  

• Draw and interpret loci  

Unit 6: Equations, Inequalities and Proportion 

 To be able to :   

• Construct and solve equations with the unknown on both sides  

• Construct and solve equations including brackets, powers and fractions 

• Convert recurring decimals to fractions 

• Solve difficult equations using trial and improvement 

• Solve linear inequalities  

• Represent solutions to inequalities on a number line 

• Set up equations to show direct proportion  

• Recognise data sets that are proportional  

• Use algebra to solve problems involving proportion 

• Solve linear simultaneous equations  

Unit 7: Circles, Pythagoras and Prisms 

To be able to:   

• Know the names of parts of a circle  

• Use the formula for the circumference of a circle  

• Round to an appropriate number of decimal places after calculations  

• Use the formulae for the circumference, given the circumference,  to calculate the radius or diameter  

• Use the formula for area of a circle, given the radius or diameter  

• Use the formulae for area of a circle, given area, to calculate the radius or diameter 

• Know the formula for Pythagoras' theorem and how to substitute in values from a diagram  

• Use and apply Pythagoras' theorem to solve problems 

• Calculate the surface area and volume of right prisms (including cylinder) 

• Calculate simple error intervals, such as +/– 10%  

• Identify and calculate upper and lower bounds  

• Use inequality notation a < x ≤ b 

Y9 THETA – SUMMER TERM 

Unit 8: Sequences and Graph 

To be able to:  

• Begin to use formal algebra to describe the nth term in an arithmetic sequence   

• Generate terms of a linear sequence using position-to-term rule  

• Generate the next term in a quadratic sequence   

• Recognise geometric sequences and appreciate other sequences that arise  

• Classify sequences as linear, geometric and quadratic 

• Calculate and interpret gradient using y = mx + c   

• Find and interpret the y-intercept from y = mx + c  

• Reduce a given linear equation in two variables to the standard form y = mx + c  

• Use graphs to solve distance-time problems  

• Identify the solution of simultaneous equations on a graph  

• Plot graphs of quadratic functions by hand and using ICT  

• Construct a table of values, including negative values of x for a function such as y = ax3 

Unit 9: Probability 

To be able to:  

• Calculate probabilities from two-way tables with more than two columns / rows each way   

• Use the language of probability to compare the choice of x/a with x/b  

• Use the language of probability to compare the choice of x/a with y/b   

• Calculate the probability of a combination of events or single missing events of a set of mutually exclusive events using sum of outcomes is one 

• Calculate estimates of probability from experiments or survey results   

• Use experimental probabilities to predict outcomes  

• Identify all mutually exclusive outcomes for two successive events    

• Compare experimental and theoretical probabilities  

• Enumerate sets and combinations of sets systematically, using tabular, grid and Venn diagrams   

• Identify conditions for a fair game  

• Use P(A and B) = P(A) × P(B) for two independent events  

• Complete and use tree diagrams to calculate probabilities 

Unit 10: Comparing Shapes 

To be able to:  

• Use congruent shapes to help you solve problems about triangles and quadrilaterals, and explain all your reasoning   

• Know whether two 2D shapes are similar, congruent or neither similar nor congruent  

• Know that enlargements of 2D shapes produce similar shapes  

• Use what you know about the sides and angles of two triangles to decide whether they are similar, congruent or neither similar nor congruent   

• Know and use the criteria for congruence (SSS, SAS, ASA or RHS) 

• Know that if two 2D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio   

• Find points that divide a line in a given ratio, using the properties of similar triangles   

• Know that the scale factor of an enlargement is the ratio of the lengths of any two corresponding line segments   

• Use similarity to solve angle and side problems  

• Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle, using straight-forward algebraic manipulation, e.g. calculate the adjacent (using cosine), or the opposite (using sine or tangent ratios)   

• Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle, using more complex algebraic manipulation, e.g. the hypotenuse (using cosine or sine), or adjacent (using the tangent ratio) 

YEAR 9 PI – AUTUMN TERM 

Unit 1: Number calculations 

To be able to:  

• Be able to add and subtract more than two integers with varying numbers of significant figures   

• Be able to add and subtract more than two decimals with up to two decimal places  

• Convert numbers such as  2 360 000 to 2.36 million  

• Use mental strategies for multiplication - doubling and halving strategies  

• Multiply 4-digit integers and decimals by a single digit integer  

• Multiply 3- or 4-digit integers by a 2-digit integer  

• Divide 3-digit integers by a single digit integer with remainder  

• Divide 3-digit by 2-digit integers – no remainder  

• Divide decimals with one or two places by single-digit integers  

• Divide £.p by a 2-digit number to give £.p  

• Divide an integer or decimal with 1 or 2 dp by a decimal number with 1 d.p. 

• Multiply negative integers by a negative number  

• Divide negative integers by a positive or negative numbers 

• Understand the infinite nature of the set of real numbers (whole numbers and decimals here)  

• Know all the squares of numbers less than 12 and give the positive and negative square root of a square number  

• Work out cubes and cube roots mentally or with a calculator 

• Use index notation for small integer powers, eg up to 5  

• Establish index laws for positive powers where the answer is a positive power  

• Find the prime factor decomposition of a number >100  

• Find the HCF or LCM of 2 numbers less than 100 using prime factor decomposition  

• Combine laws of arithmetic for brackets with mental calculations of squares, cubes and square roots  

• Be able to work with decimals and a calculator with expressions that contain brackets, squares and square roots as well as the four operations  

• Be able to estimate answers to calculations involving 2 or more operations  

Unit 2: Sequence and equations 

To be able to:  

• Construct expressions from worded description, using all 4 basic operations, e.g. 30/x, x – y, m/2, 3m + 4, a + a + 3, a²  

• Know that multiplication and division are carried out before addition and subtraction, e.g. ab + cd, a × b and c × d must be calculated before adding  

• Simplify simple expressions in more than one variable, including positives and negatives, by collecting like terms 

• Generate terms of a linear sequence using position-to term-with positive integers.  

• Generate terms from a complex practical context (e.g. maximum crossings for a given number of lines)  

• Generate terms of a linear sequence using position-to-term with negative integers.  

• Begin to use linear expressions to describe the nth term in a two-step arithmetic sequence. (e.g. nth term is 3n + 1 or n/2 – 5)  

• Find outputs of more complex functions expressed in words (e.g. add 6 then multiply by 3) 

• Solve simple two-step linear equations with integer coefficients, of the form ax + b = c, e.g. 3x + 7 = 25  

Unit 3: Statistics 

To be able to:  

• Select and identify the data related to a problem  

• Select the range of possible methods that could be used to collect this data as primary or secondary data  

• Discuss the range of possible methods that could be used to investigate a problem, e.g. questionnaire, survey, modelling, data logging, etc.  

• Select appropriate level of accuracy of data from limited choices  

• From a range of sample sizes identify the most sensible answer  

• Discuss factors that may possibly affect the collection of data, e.g. time, place, type of people asked, phrasing of questions  

• Find the mode and range from a frequency table  

• Calculate the mean from a simple frequency table  

• Draw conclusions from simple statistics for a single distribution 

• Compare two simple distributions using the range and the median  

• Compare two simple distributions using the range and the mean or range and mode  

• Compare two distributions given summary statistics  

• Recognise when it is appropriate to use mean, median, or mode in more complex cases 

• Use two-way tables  

• Construct a simple (no boundary data) frequency table with given equal class intervals for continuous data  

• Identify discrete and continuous data  

• Design tables recording discrete and continuous data  

• Find the modal class of a set of continuous data  

• Construct on paper and using ICT simple pie charts using categorical data, e.g. two or three categories  

• Draw pie charts from data presented in a table.  

• Interpret and plot scatter graphs and recognise anomalies 

• Interpret and / or compare bar graphs (with crumple zones, different scales) and frequency diagrams where data is incomplete / scales are incorrect.  

• Interpret and / or compare bar graphs and frequency diagrams which are misleading (with false origins, different scales etc.)  

• Choose and justify appropriate diagrams, graphs and charts, using ICT as appropriate, to illustrate a short report of a statistical enquiry  

• Identify further lines of enquiry from information provided for an initial enquiry  

Unit 4: Fractions, decimals and percentages 

To be able to:  

• Recall known facts including fraction to decimal conversions  

• Convert terminating decimals to fractions  

• Learn fractional equivalents to key recurring decimals, e.g. 0.333333..., 0.66666666..., 0.11111…  

• Interpret rounded off recurring decimals displayed on a calculator as fractions – 2/3, 1/6, 1 2/3, 1 1/6  

• Know the denominators of simple fractions that produce recurring decimals, and those that do not  

• Use division to convert a fraction to a decimal  

• Add and subtract simple fractions with denominators of any size  

• Check addition or subtraction of fractions with an inverse calculation  

• Add and subtract mixed number fractions without common denominators  

• Add and subtract up to 3 fractions mixing both addition and subtraction in the calculation  

• Interpret division as a multiplicative inverse; know that 1 divided by 1/4 is the same as 1 × 4  

• Understand the effect of multiplying a positive number by a fraction less than 1  

• Multiply a fraction by a fraction 

• Divide an integer by a fraction 

• Use the equivalence of fractions, decimals and percentages to compare proportions (i.e. compare a fraction and a percentage)  

• Find the outcome of given percentage increase or decrease 

Y9 PI – SPRING TERM 

Unit 5: Geometry in 2D and 3D 

 To be able to:  

• Identify alternate angles  

• Identify corresponding angles  

• Explain how to find the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons  

• Use scales in maps and plans 

• Make simple drawings, demonstrating accurate measurement of length and angle (draw accurately from a plan).  

• Use straight edge and compasses to construct the midpoint and perpendicular bisector of a line segment 

• Use straight edge and compasses to construct the bisector of an angle  

• Recognise and use the perpendicular distance from a point to a line as the shortest distance to the line  

• Visualise and use a wide range of 2D representations of 3D objects  

• Analyse 3D shapes through informal 2D representations  

• Begin to use plans and elevations.  

• Find volumes of shapes made from cuboids  

• Be able to correctly identify the hypotenuse  

• Carry out an investigation leading to understanding of Pythagoras' theorem 

Unit 6: Algebraic and real-life graphs 

 To be able to:  

• Draw conclusions based on the shape of line graphs   

• Interpret information from a real-life graph  

• Plot a graph of a simple linear function in the first quadrant  

• Recognise straight-line graphs parallel to x- or y-axes   

• Express simple functions in symbols, e.g. y = x + 3 to draw graph   

• Generate four quadrant coordinate pairs of simple linear functions 

• Plot a simple straight-line graph (distance–time graphs)   

• Discuss and interpret line graphs and graphs of functions from a range of sources  

• Know how to find the midpoint of a line segment   

• Find the midpoint of a horizontal (or vertical) line AB, using the coordinates of these points  

• Interpret intercept of real-life graphs   

• Plot the graphs of simple linear functions in the form y = mx + c in four quadrants  

Unit 7: Multiplicative reasoning 

 To be able to:  

• Divide a quantity into two parts in a given ratio, where ratio given in ratio notation  

• Divide a quantity into two parts in a given ratio (whole numbers), where the answer is a decimal  

• Divide a quantity into more than 2 parts in a given ratio  

• Reduce a ratio to its simplest form, where a ratio is expressed in different units 

• Understand the relationship between ratio and proportion 

• Recognise when values are in direct proportion by reference to the graph form  

• Solve problems involving direct and inverse proportion, including graphical and algebraic representations 

• Use units of measurement to calculate and solve problems in everyday contexts involving length, area, volume, mass, time and angle  

• Convert between area measures (e.g. mm² to cm², cm² to m², and vice versa)  

• Know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons)  

 Y9 PI – SUMMER TERM 

Unit 8: Algebraic and geometric formulae 

To be able to:  

• Substitute integers into formulae expressed in letter symbols   

• Derive formulae expressed in letter symbols   

• Substitute integers into formulae to give equations and solve  

• Substitute integers into formulae (involving brackets and more than one operation) expressed in letter symbols  

• Substitute positive and negative integers into simple formulae  

• Understand the different role of letter symbols in formulae and functions 

• Use a formula to calculate the area of triangles  

• Change the subject of a one-step formula 

• Find the measurement of a side given the perimeter of squares and rectangles, where one or more lengths are decimals  

• Calculate the perimeter and area of shapes made from rectangles  

• Calculate areas of compound shapes made from rectangles and triangles   

• Use a formula to calculate the area of parallelograms 

• Know the names of parts of a circle   

• Use a formula to calculate the circumference of a circle   

• Use a formula to calculate the area of a circle 

Unit 9: Probability 

To be able to:  

• Apply probabilities from experimental data to a different experiment in simple situations 

• Apply probabilities from experimental data to a different experiment in applying to two step outcomes  

• Identify all mutually exclusive outcomes for two successive events – with three outcomes in each event.  

• Identify conditions for a fair game – from a small set of simple options  

• Use two-way tables for discrete data. Complete and collect probabilities  

• Use the language of probability to compare the choice of x/a with x/b  

• Find the probability from two-way tables 

• Identify dependent and independent events  

• Work out the probability of two independent events  

• Draw and use tree diagrams to represent outcomes of two independent events and calculate probabilities 

Unit 10: Polygons and Transformations 

To be able to:  

• Classify quadrilaterals by their geometric properties  

• Plot points on a grid an identify resulting geometric shapes across all four quadrants 

• Solve simple geometrical problems using properties of triangles  

• Solve simple geometrical problems showing reasoning  

• Solve geometric problems using side and angle properties of equilateral and isosceles triangles   

• Solve geometric problems using side and angle properties of equilateral, isosceles and right-angled triangles  

• Understand and use the language associated with rotations  

• Translate a shape on a coordinate grid   

• Rotate a shape on a coordinate grid   

• Reflect a shape on a coordinate grid  

• Transform 2D shapes by simple combinations of rotations, reflections and rotations 

• Use the language and notation associated with enlargement  

• Enlarge 2D shapes, given a centre of enlargement and a positive whole-number scale factor  

• Know that in congruent shapes, corresponding sides and angles are equal  

• Know that translations, rotations and reflections preserve length and angle