MATHS DEPARTMENT
YEAR 8
SCHEME OF WORK
SET 4: IMPACT 2G
2G PLAN
AUTUMN TERM – FIRST HALF
Topic 1 / Understanding Number / 2G Ch. 1Topic 2 / Symmetry & Angles / 2G Ch. 2
Topic 3 / Multiplication & Division / 2G Ch. 3
Topic 4 / Working with Algebra / 2G Ch. 4
AUTUMN TERM – SECOND HALF
Topic 5 / Fractions / 2G Ch. 6Topic 6 / Probability / 2G Ch. 7
Topic 7 / Decimals & Percentages / 2G Ch. 8
SPRING TERM – FIRST HALF
Topic 10 / Number Patterns / 2G Ch. 5Topic 11 / Multiplicative Relationships / Additional Unit
Topic 12 / Shape & Measure / 2G Ch. 9
SPRING TERM – SECOND HALF
Topic 13 / Handling Data + unit / 2G Ch. 12 + Additional UnitTopic 14 / Formulae & Equations / 2G Ch. 13
Topic 16 / Positive & Negative Numbers / 2G Ch. 10
SUMMER TERM – FIRST HALF
Topic 17 / Graphs / 2G Ch. 11Topic 18 / Problem Solving / Additional Unit
Topic 19 / Perimeter, Area & Volume / 2G Ch. 14
SUMMER TERM – SECOND HALF
Topic 20 / Averages / 2G Ch. 15Topic 21 / Calculation & Problem Solving / Additional lessons (8N4.1 & 8N4.2)
Topic 22 / Fractions, Decimals & Percentages / Additional Lessons (8N5.1 & 8N5.2)
“OPTIONAL TESTS”
Topic 21 / InvestigationAUTUMN TERM A TOPIC 1
Topic: Understanding Number
/ NC Level: 3 & 4NC Programme of Study:
Ref2a: use previous understanding of integers and place value to deal with arbitrarily large positive numbers and round them to a given power of 10; order integers.
Ref3agij: add, subtract integers and then any number. Recall all positive complements to 100 (e.g. 37+62=100). Develop a range of strategies for mental calculation. Use standard column methods for addition and subtraction of integers.
Ref4c: use a variety of checking procedures, including working through the problem backwards, and considering whether the result is of the right order of magnitude.
Learning Objectives:
· understand place value, recognising HTU etc.
· add and subtract integers
· extend mental methods of computation for addition and subtraction
· consolidate standard column procedures for addition and subtraction
· mentally estimate and approximate solutions to numerical calculations; justify such estimates
· use the laws of arithmetic and inverse operations
· use checking procedures, including working through the problem backwards and considering whether the answer is sensible
· round positive numbers to any given power of 10.
Key Vocabulary:
PLACE VALUE ORDER MENTAL ROUND NEAREST CHECK ESTIMATE
Impact Reference:
Book 2G – ch. 1
/ Other references:L4 to L5 Lesson 8N1.1
V3 – ch. 1 – 5 V4 – ch. 2 – 4 V5 – ch. 2 KM81 – ch. 1 - 2
Mental & Oral Starters:2G folder: pg. 4 – 6
101 Starters: pg. 14-18, 22, 47, 58
Discussion opportunities:Perhaps do some place value work verbally as a class / whiteboards?
Spend time allowing pupils to explain their methods for addition / subtraction.
Discuss whether an answer is ‘sensible’.
Discuss how to use the number line to help mental calculations.
Pair / Group Work:
Students can show each other their methods or check each other’s answers; compare estimations.
ICT Links:
SMILE.. Outware: “Balloon” , “Coin It”
Spiritual/Moral/Citizenship Links:We should all respect each other’s different methods and views
Investigation:
Activity 2G pg.10 – using activity sheet 1
Time: 6 lessonsAUTUMN TERM A TOPIC 2
Topic: Symmetry & Angles / NC Level: 4 & 5NC Programme of Study:
Ref2abc: recall and use properties of angles at a point, angles on a straight line, perpendicular lines and opposite angles at a vertex. Distinguish between acute, obtuse, reflex and right angles; estimate the size of an angle in degrees. Use parallel lines; the angle sum of a triangle is 180 degrees.
Ref3b: recognise and visualise rotations, reflections, including the reflection and rotation symmetry of 2D shapes; transform 2D shapes by rotation and reflection, recognising that these transformations preserve length and angle.
Ref4bd: understand angle measure, using the associated language. Measure and draw lines to the nearest millimetre and angles to the nearest degree; draw triangles and other 2D shapes using a ruler and protractor, given information about their side lengths and angles.
Learning Objectives:
· Identify all symmetries of 2D shapes – reflective and rotational
· Transform 2D shapes by simple rotations about a given point and reflections in a given mirror line
· Use correct vocabulary, notation and labelling for lines, angles and shapes.
· Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles.
· Use a ruler and protractor to measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree
· Identify parallel and perpendicular lines; know the sum of right angles, angles at a point, on a straight line and in a triangle. Recognise vertically opposite angles
Key Vocabulary:
SYMMETRY MEASURE TURN ANGLE DEGREE PROTRACTOR ACUTE OBTUSE REFLEX CONSTRUCT ESTIMATE LINE AT A POINT SHAPE SUM
Impact Reference:
Book 2G – ch. 2
/ Other references:V3 – ch. 9 V4 – ch. 13, 18 V5 – ch. 15 KM81 – ch. 5, 7
Mental & Oral Starters:2G folder: pg. 24 – 26
101 Starters: pg. 73, 79, 80
Discussion opportunities:
Categorise shapes: no. of lines of symmetry and order of rotational symmetry – poster?
Pair / Group Work:
Discuss how to categorise shapes
ICT Links:SMILE – Angle 360, Snooker. LOGO can be used to construct shapes, experiment with angles. Maths Mansion programme 35, 38 & 39
Spiritual/Moral/Citizenship Links:
Reflection on own character
Investigation:
Find a shape with 4, 5, 6 lines of symmetry etc.
Time: 5 lessons
AUTUMN TERM A TOPIC 3
Topic: Multiplication & Division
/ NC Level: 3 - 5NC Programme of Study:
Ref2ab: Use concepts and vocabulary of factor, multiple, common factor, highest common factor, least common multiple, prime number and prime number decomposition. Use the terms square, positive square root.
Ref3agk: multiply and divide integers; multiply or divide any number by powers of 10; find the prime factor decomposition of positive integers. Recall all multiplication facts to 10 x 10, and use them to derive quickly the corresponding division facts. Use standard column procedures for multiplication of integers.
Ref4b: Select appropriate operations, methods and strategies to solve number problems.
Learning Objectives:
· multiply and divide integers
· use standard column procedures for multiplication and division of integers
· mentally estimate and approximate solutions to numerical calculations
· recognise and use multiples, factors and primes
· use squares and square roots
Key Vocabulary:
MULTIPLY DIVIDE TIMES TABLES REMAINDER MULTIPLE FACTOR SQUARE SQUARE ROOT ODD EVEN
Impact Reference:
Book 2G – ch. 3
/ Other references:L4 to L5 lesson 8N2.1
V3 – ch. 2 - 3 V4 – ch. 3, 4, 8 V5 – ch. 2 - 3 KM81 – ch. 2
Mental & Oral Starters:2G folder: pg. 50-52
101 Starters: pg. 7, 24-31, 39, 48-51
Discussion opportunities:Pupils can explain their methods of computation.
Using a counting stick encourages discussion.
Pair / Group Work:
Check each others’ methods/ answers.
Dice Bingo – multiply the 2 scores on 12 sided dice together.
ICT Links:
SMILE. “Balloon” (Outware)
Maths Mansion programmes 23 & 24Spiritual/Moral/Citizenship Links:
Sharing equally – we are all entitled to the same. Does it always happen?
Investigation:
Find all numbers that sum to 13 – which give the largest product? Etc.
Time: 7 – 8 lessonsAUTUMN TERM A TOPIC 4
Topic: Working With Algebra
/ NC Level: 5NC Programme of Study:
Ref5ab: distinguish the different roles played by letter symbols in algebra, knowing that letter symbols represent definite unknown numbers in equations. Understand that the transformation of algebraic expressions obeys and generalises the rules of arithmetic; simplify or transform algebraic expressions by collecting like terms; distinguish in meaning between the words ‘equation’, ‘formula’, ‘identity’ and ‘expression.’
Learning Objectives:
· use letter symbols to represent unknown numbers or variables
· distinguish the different roles played by letter symbols in equations, formulae and functions
· know the meaning of the words ‘formula’ and ‘function’
· know that algebraic operations follow the same conventions and order as arithmetic operations
· simplify linear expressions by collecting like terms and by multiplying terms together
Key Vocabulary:
LETTER COLLECT TERM SIMPLIFY EXPRESSION MULTIPLY
Impact Reference:
Book 2G – ch. 4
/ Other references:L4 to L5 lesson 8A2.1
V4 – ch. 9 V5 – ch. 8, 9 KM81 – ch. 4
Mental & Oral Starters:2G folder: pg. 66-67
101 Starters: pg. 65
Discussion opportunities:Discuss what the expressions can represent. Verbally substitute in values.
Pair / Group Work:
Pupils can make up their own word / algebraic equations and test each other.
Match up expressions when simplified – card-like game.
ICT Links:
EXCEL – inputting formulae to get the desired output, rather than typing in numbers.
Spiritual/Moral/Citizenship Links:
We tend to be close to people who are similar to ourselves
Investigation:
What happens when we change the value of the variable?
Time: 5 lessons
AUTUMN TERM B TOPIC 5
Topic: Fractions/ NC Level: 3 & 5
NC Programme of Study:
Ref2c: Use fraction notation; understand equivalent fractions, simplifying a fraction by cancelling all common factors; order fractions by rewriting then with a common denominator.
Ref3c: Calculate a given fraction of a given quantity, expressing the answer as a fraction; express a given number as a fraction of another; add and subtract fractions by writing them with a common denominator.
Learning Objectives:
· recognise proportions of a whole and use simple fractions to describe these
· recognise equivalent fractions
· find equivalent fractions by multiplying or dividing
· cancel fractions to their lowest terms
· understand & interpret ‘mixed numbers’ and ‘improper fractions’
· understand addition and subtraction of fractions
· add & subtract fractions by writing them with a common denominator
· calculate fractions of quantities
Key Vocabulary:
MIXED NUMBER IMPROPER FRACTION QUANTITY NUMERATOR DENOMINATOR EQUIVALENT ADD SUBTRACT
Impact Reference:
Book 2G – ch. 6
/ Other references:L4 to L5 lesson 8N3.1
V4 – ch. 6 V5 – ch. 5 KM81 – ch. 9
Mental & Oral Starters:2G folder: pg. 96 - 97
101 Starters: pg. 36-37
Discussion opportunities:Discuss different ways of writing fractions of certain quantities
Pair / Group Work:
Change the quantities of a recipe.
ICT Links:
Maths Mansion programmes 25 & 26
Spiritual/Moral/Citizenship Links:
Everything is significant no matter how small
Investigation:
Time: 5 -6 lessons
AUTUMN TERM B TOPIC 6
Topic: Probability
/ NC Level: 3 – 5NC Programme of Study:
Ref4cd: Understand and use the probability scale. Understand and use estimates or measures of probability from theoretical models, including equally likely outcomes, or from relative frequency.
Learning Objectives:
· understand and use the probability scale from 0 to 1 – in words and numbers.
· find and justify probabilities based on equally likely outcomes in simple contexts.
· calculate probabilities with one or more successful outcomes
· use the vocabulary of probability when interpreting the results of an experiment
· appreciate that random processes are unpredictable
· understand that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p (numerically rather than algebraically at this level)
· find and record all possible outcomes for single events and 2 successive events in a systematic way using diagrams or tables.
Key Vocabulary:
IMPOSSIBLE POSSIBLE CERTAIN SCALE EVENT OUTCOME
Impact Reference:
Book 2G – ch. 7
/ Other references:V4 – ch. 22 V5 – ch. 22 - 24 KM81 – ch. 8
Mental & Oral Starters:2G folder: pg. 114-115
101 Starters: pg. 99 - 101
Discussion opportunities:Discuss the likelihood of things happening in everyday life.
Pair / Group Work:
Probability experiments can be done in pairs to ensure results are recorded carefully.
‘Play your cards right’, human probability scale, Bingo with dice.
ICT Links:
SMILE
Spiritual/Moral/Citizenship Links:Morality of gambling
Investigation:
Investigate the probability of various real events – e.g. rain, red car in car park etc.
Time: 5 lessons – perhaps more, depending on practical work
AUTUMN TERM B TOPIC 7
Topic: Decimals & Percentages/
NC Level: 4 - 6
NC Programme of Study:Ref2de: Use decimal notation and recognise that each terminating decimal is a fraction. Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions; interpret percentage as the operators ‘so many hundredths of’.
Ref3acejk: add, subtract, multiply and divide integers and then by any number; multiply or divide any number by powers of 10, and any positive number between 0 and 1. Perform short division to convert a simple fraction to a decimal. Convert simple fractions of a whole to percentages of the whole and vice versa, then understand the multiplicative nature of percentages as operators. Use standard column procedures for addition and subtraction of integers and decimals. Use standard column procedures for multiplication of integers and decimals, understanding where to position the decimal point by considering what happens if they multiply equivalent fractions; solve a problem involving division by an integer.
Learning Objectives:
· order decimals
· use standard column procedures for addition and subtraction of decimals with up to two places
· multiply and divide decimals by powers of 10
· use standard column procedures for multiplication and division of decimals by single digit whole numbers; understand where to position the decimal point by considering equivalent calculations
· use division to convert a fraction to a decimal
· interpret percentage as the operator ‘so many hundredths of’
· express one given number as a percentage of another
· calculate simple percentages
· use the equivalence of fractions, decimals and percentages to compare proportions
Key Vocabulary:
PLACE VALUE WHOLE NUMBER FRACTION DECIMAL PERCENTAGE ORDER AMOUNT
Impact Reference:
Book 2G – ch. 8