Mathematics KS3

Unit 1 – place value (1)

• Read and write whole numbers in figures and words
• Multiply, and divide, any whole number by 10, 100, 1000, or 10 000
• Round whole numbers to the nearest 1000, 100 or 10

Unit 2 & 3 – Addition and subtraction (2)

• Use mental strategies
• Add and subtract using formal algorithms
• Calculate and work with perimeters
• Model solve word problems

Unit 4 – Addition and subtraction of decimals (2)

• Understand decimal notation and place value
• Read and write decimals in figures and words
• Convert between decimals and fractions where the denominator is a factor of 10 or 100
• Use the number line to display decimals and round decimals to the nearest whole number, to 1 or 2 decimal places
• Use correctly the symbols <, >, etc. and the associated language to order a set of decimals
• Multiply and divide decimals by 10, 100, 1000, or 10 000
• Solve word problems involving the addition and subtraction of money in decimal notation
• Use  written methods in column format for addition and subtraction of decimals
• Extend existing mental calculation to include decimals
• Calculate the perimeter of rectangles, squares and rectilinear figures

Unit 5, 6, 7 & 8 multiplication and division (5)

• Use multiplication facts to solve mental calculations
• Use the terms ‘product’, ‘multiple’ and ‘LCM’
• Understand and use the column method to multiply integers and decimals
• Divide whole numbers and decimals by whole numbers
• Use the terms ‘quotient’, ‘remainder’, ‘factor’, ‘HCF’
• Represent multiplication word problems using bar models
• Find the area of a rectangle and triangle
• Solve problems involving length, perimeter and area
• Estimate answers in calculations and check that results are reasonable
• Measure time, calculate with time and solve time word problems
• Find the mean average, interpreting average as “total amount ÷ number of items” and solve word problems involving average

Unit 9 – Working with units (1)

• Record and order measurements using decimal notation
• Estimate and/or measure:

Unit 10 – Angles (1)

• Draw and measure  acute and obtuse angles reliably to the nearest degree
• Estimate the size of any given angle
• Recognise acute, right, obtuse and reflex angles
• Know and use the fact that the angles round a point total 360^o, that angles on a straight line total 180^o, and that vertically opposite angles are equal

Unit 11 & 12 – Triangles and quadrilaterals (2)

• Classify triangles and quadrilaterals according to their properties
• Use a ruler and protractor to construct triangles and quadrilaterals from given data
• Know and use the fact that the sum of interior angles of a triangle is 180^o
• know and use the fact that the interior angles of a quadrilateral sum to 360^o
• Solve problems involving coordinates in the first quadrant

Unit 13

Symmetry and tessellation (1)

• Identify lines of symmetry in any shape
• Identify the order of rotational symmetry in any shape
• Create shapes given details of their symmetries
• Investigate and create tessellations

Unit 14 – Understand and use fraction (2)

• Represent fractions using area diagrams, bar models and number lines
• Recognise and name equivalent fractions
• Convert fractions to decimals
• Convert terminating decimals to fractions in their simplest form
• Convert between mixed numbers and improper fractions
• Compare and order numbers
• Convert simple fractions and decimals to percentages
• Express one quantity as a fraction of another

Unit 15 – Fractions of amounts (1)

• Find a fraction of a set of objects or quantity
• Find the whole given a fraction

Unit 16 – Multiplying and dividing decimals (2)

• Multiply a whole number or fraction by a whole number or fraction
• Multiply a mixed number and a whole number
• Divide a whole number or proper fraction by a whole number or proper fraction

Unit 17 – Order of operations (2)

• Carry out calculations involving all four operations
• Understand and use brackets
• Use simple index notation

Unit 18 – Introduction to algebra (2)

• Recognise and continue sequences
• Represent an unknown number using a letter
• Write and understand simple algebraic expressions
• Substitute numerical values into formulae and expressions
• Collect like terms and simplify expressions
• Multiply out brackets, identify and take out common factors to factorise
• Recognise that different-looking expressions may be identical and prove simple algebraic identities

Unit 20 – Percentages (2)

• Understand percentage as a fractional operator with denominator of 100
• Express a part of a whole as a percentage
• Convert between fractions, decimals and percentages
• Find fractions and percentages of given quantities
• Find the whole given a part and the percentage
• Increasing and decreasing by a percentage

Unit 21 – Handling data (2)

• Understand the difference between types of data
• Construct and interpret

• Read and interpret pie charts
• Draw pie charts from raw data
• Explore misleading graphical representations

Level

Descriptors

3

3.2 Understand prime numbers and their definition as having exactly 2 factors

3.3 Know the prime numbers up to 31 and understand how to determine whether a number is prime

3.4 Use special patterns to find simple factors (e.g. 2, 3, 4, 5, 10 etc.)

3.5 Understand place value up to1000 and down to 1000ths and identify the place value of a given digit.

3.6 Use a ruler for measurement.

3.7 Order negative numbers (including in context – temperature and money)

3.8 Use decimals with money

3.9 Know addition and subtraction facts up to 20

3.10 Simple addition and subtraction of 2-digit and 3-digit numbers (number lines in your head)

3.11 Understand that a fraction is a part of a whole

3.12 Recognise when two fractions are equivalent (pictures)

3.13 Understand the language relating to angles – right, acute, obtuse, reflex

3.14 Naming basic two-dimensional polygons and different quadrilaterals

3.15 Understand ‘regular’ shapes

3.16 Know which type of metric unit to use in a given situation (length, mass or capacity)

3.17 Choose a suitable unit of measure (mili, centi etc.) for a given measurement.

4

4.2 Use place value understanding to multiply/divide numbers by 10,100,1000

4.3 Read and interpret other scales including liquid capacity, speedometers, thermometers, weighing scales etc.)

4.4 Order negative and positive numbers with the use of inequality signs (including ≠)

4.5 Order decimal numbers to 3 decimal places

4.6 Round numbers to the nearest whole, 10, 100, 1000

4.7 Add and subtract with negative numbers (using a number line)

4.8 Add and subtract 2-digit and 3-digit using the column method.

4.9 Add and subtract decimal numbers (up to 2dp) using the column method.

4.10 Use fractions to identify a part of a whole (shading questions) – include basic percentages

4.11 Identify and write equivalent fractions

4.12 Find the perimeter of simple shapes (whole numbers)

4.13 Know the angle sum on a straight line, at a point and vertically opposite

4.14 Know the angle sum of a triangle and the properties of different types of triangle

4.15 Identify the lines of symmetry of a two dimensional shape

4.16 Classify triangles by their properties.

4.17 Know and use all the times tables up to 12×12

4.18 Know and use the related division facts

4.19 Estimate everyday measurements using appropriate units

4.20 Converting between metric units for length

4.21 Converting between metric units for capacity

4.22 Converting between metric units for mass

4.23 Find the area of regular and irregular (curves) shapes by counting squares

4.24 Recognise the simple conversions from memory (list…)

4.25 Understand simple ratio and how it links to proportion

4.26 Know the definition of a square number and recall the square numbers and their associated square roots up to 152

4.27 Use vocabulary and ideas of probability, drawing on experience

5

5.2 Round numbers to decimal places

5.3 Harder addition and subtraction of 2-digit and 3-digit numbers in your head.

5.4 Use addition/subtraction methods in the context of personal finance (must use debit, credit, balance vocab) – electricity bill style questions

5.5 Simplify fractions to their lowest terms

5.6 Convert between mixed numbers and improper fractions and understand the process used

5.7 Add and subtract fractions with the same denominator (including mixed/improper)

5.8 Find the perimeter of compound shapes given all lengths (whole numbers)

5.9 Find missing lengths, given a perimeter

5.10 Find the perimeter of shapes with decimal lengths

5.11 Measure and draw angles to the nearest degree

5.12 Use the angle sum on a straight line, at a point and vertically opposite

5.13 Identify the order of rotational symmetry of a two dimensional shape

5.14 Multiply negative numbers

5.15 Divide negative numbers

5.16 Multiply up to 3-digit x 2-digit numbers using column method

5.17 Mental multiplication of decimal numbers between 0 and 1

5.18 Use bus-stop method to divide by 1-digit numbers including those with decimal answers (remainders not be used)

5.19 Calculate fractions of an amount (including the link to multiplying whole numbers by fractions

5.20 Multiplying fractions which do not require cross-cancelling (including how the method can be used for fractions of amounts)

5.21 Convert between equivalent units of capacity and volume

5.22 Understand and use the formula for area of a rectangle

5.23 Express one a quantity as a percentage of another

5.24 Find percentages of amounts

5.25 Convert decimals in to fractions and percentages

5.26 Convert percentages in to fractions and decimals

5.27 Simplify ratios and proportions

5.28 Express comparisons of quantities as a ratio in its simplest form

5.29 Use the order of operations (BIDMAS) to make accurate calculations

5.30 Know the definition of a cubic number and recall the cube numbers and their associated cube roots up to 53

5.31Understand and use the probability scale from 0 to 1 including use of FDP

5.32 Find and justify probabilities based on equally likely outcomes in basic contexts

6

6.2 Know the best addition/subtraction methods to solve worded problems and apply them.

6.3 Add and subtract fractions with different denominators, using lowest common denominator (not x-factor) (including mixed/improper)

6.4 Solving worded problems involving fraction skills used.

6.5 Find the perimeter of shapes with fractional lengths

6.6 Find the perimeter of compound shapes where some lengths are missing

6.7 Measure and draw reflex angles to the nearest degree

6.8 Use angle facts for parallel line with one transversal (do not use z/c/f angle vocab)

6.9 Classify quadrilaterals by their properties (sides and angles) – use standard notation

6.10 Multiply decimal numbers using column method (up to 2dp)

6.11 Divide a 3-digit number by a 2-digit number using bus-stop method (short division)

6.12 Divide a decimal number by a whole number using bus-stop method

6.13 Multiplying fractions by cross-cancelling first

6.14 Divide a whole number by a fraction

6.15 Understand how dividing a whole number by a fraction works using circles/pizzas/cakes etc.

6.16 Divide a fraction by a fraction using switch and flip method

6.17 Multiply and divide mixed numbers by converting to improper fractions first

6.18 Use the area formula for a parallelogram and understand it’s derivation from a rectangle

6.19 Use the area formula for a triangle and understand it’s derivation from a rectangle

6.20 Use the area formula for a trapezium and understand it’s derivation from a parallelogram

6.21 Find the area of compound shapes

6.22 Find the area of shapes with fractional and decimal lengths

6.23 Increase/decrease quantities by a given percentage)

6.24 Increase/decrease by a percentage in real life contexts (vocab – discount, depreciate, profit, loss, VAT, cost price, selling price, interest rate)

6.25 Convert fractions in to percentages and decimals

6.26 Divide a quantity in to two or more parts in a given ratio

6.27 Use the unitary method to solve problems involving ratio and direct proportion

6.28 Use order of operations including fractions, decimals and negative numbers

6.29 Understand and calculate (mental or written methods) higher powers of numbers e.g. 56

6.30 Understand prime factor composition

6.31 Find the prime factor decomposition of any positive number using factor trees

6.32 List the prime factors using index notation

6.33 Place prime factors correctly in to a Venn diagram for two numbers

6.34 Use a Venn diagram to find the HCF and LCM of two numbers

6.35 Use systematic listing strategies to list possible outcomes of an event

6.36 Use sample space diagrams to clearly display all possible outcomes and use them to calculate associated probabilities

7

7.2 Add and subtract three or more fractions.

7.3 Use angle facts for parallel lines with more than one transversal and forming triangles within the parallel lines.

7.4 Use angle properties of straight lines, points and parallel lines to solve problems involving quadrilaterals

7.5 Divide a whole number by a decimal number

7.6 Divide a decimal number by a decimal number

7.7 Understand the effects of multiplying and dividing a number between 0 and 1

7.8 Problem solving involving use of multiplication/division of fractions

7.9 Find the area of shapes when the length units require converting first

7.10 Find percentages and fractions of shapes which are shaded in. (Compound)

7.11 Use the unitary method to solve problems with given non-standard conversions

7.12 Find equivalent ratios when expressed with non-integer parts and use them to solve problems

7.13 Understand what makes a perfect square

7.14 Use prime factor decomposition to decide if a number is a perfect square

7.15 Find the necessary multiplier to make a number a perfect square

7.16 Make predictions based on expected outcomes from probabilities calculated in previous lessons i.e. calculate expectation

7.17 Conduct basic experiments to ‘test’ predictions by calculating relative frequencies.

7.18 Understand the reasons for differences between expectation and relative frequencies and how to improve results

8

8.2 Sustains a critical evaluation of secondary sources relating to the set text

8.3 Offers a sustained analysis of language and structural features

8.4 Uses punctuation judiciously, with flair and skills (no mistakes)

8.5 Rare loss of control within sentence structures

8.6 Skilfully manages paragraphs to achieve overall effect

8.7 Uses impressive vocabulary skilfully and with precision

8.8 Correct spelling throughout

8.9 Use the OR (addition) rule to calculate probabilities of mutually exclusive events

8.10 Understand why two events are mutually exclusive, including events in real life contexts

8.11 Use the AND (multiplication) rule to calculate the probabilities of independent events

8.12 Understand why two events are independent including events in real life contexts