# YEAR 7: SPRING, FIRST HALF TERM

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```							Unit 1 Number/Algebra 1 (Special Numbers & Sequences)                                                Date:                                                                          6 HRS

SUPPORT TEACHING OBJECTIVES                                                     KS3 Framework        Targeted activities for the introduction                  Activity Ref:
From the Y7 teaching programme (Level 4/5)                                        reference          or plenary part of the lesson
          Add and subtract integers.                                           Pages 48 - 51        Use partitioning to multiply, e.g. 13  6.                Number cards at front of room
          Recognise and use multiples, factors (divisors), common factor,      Pages 52 - 55        Order, add, subtract, multiply and divide                 Doubling and halving.
highest common factor, and primes; find the prime factor                                  integers.
decomposition of numbers <100 (e.g. 30 = 2 x 3 x 5).                                                                                                Whiteboards. Loop Cards.
          Use squares, positive square roots, cubes, and index notation for    Pages 56 - 59        Multiply and divide a two-digit number by a one           Badger 7
squares and cubes.                                                                        digit number.
          Generate and describe integer sequences.                             Pages 144 - 147
          Generate terms of a linear sequence using term-to-term and simple    Pages 148 - 151      Know and use squares, positive square roots,              Badger 8, 9
position-to-term definitions (2n +1) of the sequence, on paper and                        cubes of numbers 1 to 5.
using a spreadsheet or graphical calculator.

Key vocabulary                           Special numbers: (integer, negative, positive, sign, square, squared, square root, cube, factors, prime factors, HCF, multiples
Sequences: (sequence, term, nth term, consecutive, predict, rule, generate, continue, ascending, descending, symbol, algebra, index)
Expected outcomes by the end of each lesson:
To be able to add and subtract negative numbers.                       Resources:                  To be able to generate and describe integer sequences              Resources:
given a simple term-to-term rule, or sequence:

Lesson 4
Lesson 1

Eg 1: Order integers position on a number line.
Eg 2: Use number line leading to +/- patterns.                                                     Eg 1: The first term is 4 and each term is 7 more than before
Eg 3: Number pyramids.                                                                             Eg 2: Describe this sequence: 7, 13, 19, 25, …
Eg 4: The answer is –8; what was the question?                                                     Eg 3: Use simple flow diagram to generate sequences.
(Use context, eg: Temperature, Sea level).
1. To be able to find factors and prime factors of                                                 To be able to generate a sequence given a rule for finding
numbers.                                                                                        each term from its position in the sequence:
Lesson 2

Eg 1: Find all the pairs of factors of non-prime numbers.                                          Eg: The nth term of a sequence is 2n + 4. Write the first

Lesson 5
Eg 2: Use prime factor trees to find all prime factors                                                 five terms.
as in 24 = 2 x 2 x 2 x 3.

2. To be able to find HCF of two numbers (< 60)
(Extend to use of prime factors for this).
To be able to find squares, square roots and cubes, and use                                        To be able to generate sequences from simple practical
Lesson 6

appropriate notation.                                                                              contexts.
Lesson 3

Eg 1: Number square with squares up to 144.                                                       Eg: Find the first few terms of the sequence.
Eg 2: Practise estimating square roots from whole number                                              Describe how it continues with reference to the context.
squares. Repeat with cubes.                                                                     Begin to describe the general term using words, then
Eg 3: Use calculator to experiment with squares and cubes.                                            using symbols, justify the generalisation by referring to
the context.

MATHEMATICS DEPARTMENT                 AUTUMN TERM ( FIRST HALF)                   YEAR 8 SUPPORT
Unit 2                 SSM 1 (Angle Rules & Constructions)                                              Date:                                                                            6 HRS

SUPPORT TEACHING OBJECTIVES                                                     KS3 Framework           Targeted activities for the introduction                   Activity Ref:
From the Y7 teaching programme (Level 4/5)                                        reference             or plenary part of the lesson
 Know the sum of angles at a point, on a straight line and in a                Pages 178 - 83          Estimate and order acute, obtuse and reflex
triangle & quadrilateral. Recognise vertically opposite angles.                                       angles.
 Solve geometrical problems using side and angle properties of                 Pages 184 - 189         Discuss and interpret graphs.
equilateral, isosceles and right-angled triangles and special
quadrilaterals, explaining reasoning with diagrams & text; classify
 Use straight edge and angles measurer to construct: triangles, given          Pages 220 - 223         Know or derive complements of 0.1, 1, 10, 50,
(ASA) or (SAS). Use a straight edge and a compass to construct an                                     100, 1000.
equilateral and isosceles triangle.
 Investigate in a range of contexts: shape and space.                                                  Visualise, describe and sketch 2-D shapes.

Key vocabulary                       Angles: (angles at a point, angles on a straight line, base angles, interior); triangles: (equilateral, isosceles, right-angled, scalene);
Constructions: (construct, draw, measure, protractor, compasses, ruler).
Expected outcomes by the end of each lesson:
To be able to identify angles on a straight line, angles at              Resources:                      To be able to solve angle problems in special                     Resources:
point and vertically opposite angles.                                                                    quadrilaterals.

Lesson 4
OHP,                                                                                              Board
Lesson 1

protractors.                                                                                      compasses,
Eg: Given sufficient information, calculate angles in a                                                 Eg: Introduce special quadrilaterals (parallelogram, kite,
straight line, and at a point. Use protractor to measure                                                rhombus, trapezium, arrowhead); classify, and solve
board
angles accurately.                                                                                      related angle problems.                                    protractor.
1. To be able to show that sum of angles in a ∆ is 180°:                Cut-out                         1. To be able to construct a Δ (ASA and SAS).                     Compasses,
2. … and that the sum of angles in a quadrilateral is 360°:             triangles.                                                                                        Protractors.
Eg: Use compasses and protractor to show construction on
Lesson 2

Lesson 5
Eg: - Paste Δ samples into books, measure angles; cut angles                                                board, and ask students to carry out similar
to show they fit on a straight line                                                                   constructions.
congruent Δs.
- measure angles & compare results.
To be able to solve problems about Δs & quadrilaterals, as                                              To be able to construct Δs to solve problems.                     Compasses,
in:                                                                                                                                                                       protractors.
Eg 1: How many different triangles can you construct where
Lesson 3

Lesson 6

a) Explain angle & side properties of equilateral, isosceles, &                                               2 sides are of length 4 cm and 7 cm & one angle equal
scalene Δs. Use in problems.                                                                               to 25°

MATHEMATICS DEPARTMENT                        AUTUMN TERM ( FIRST HALF)                   YEAR 8 SUPPORT
Unit 3                   Number 2a (Fractions, Decimals, Percentages)                                      Date:                                                                3 HRS

SUPPORT TEACHING OBJECTIVES                                                            KS3 Framework       Targeted activities for the introduction          Activity Ref:
From the Y7 teaching programme (Level 4/5)                                               reference         or plenary part of the lesson
 Use fraction notation to express a smaller whole number as a fraction                Pages 60 - 64       Convert between fractions, decimals and
of a larger one; simplify fractions by cancelling all common factors                                     percentages.
and identify equivalent fractions; convert terminating decimals to
fractions, and fractions to decimals.
 Add and subtract fractions with common denominators; calculate                       Pages 66 - 69        Multiply and divide decimals by 10, 100, 1000.
fractions of quantities (whole-number answers); multiply a fraction by
an integer.
Calculate using knowledge of multiplication and
division facts and place value,
e.g. 432  0.01.

Key vocabulary                           Fraction, numerator, denominator, proper fraction, improper fraction, mixed fraction, equivalent, cancel, cancellation, convert, simplest form.

Expected outcomes by the end of each lesson:
1.    To be able to describe one number as a fraction of a larger number and simplify fractions in easy cases.                                                     Resources:
OHP shapes.
Eg 1: What fraction is shaded in this shape?
Lesson 1

Eg 2: What fraction of 1 metre is 40 cm? of 1 hr is 20 mins?
Eg 3: 42/56 = 6/8 = 2/3.

2.    To be able to convert decimals (up to 2 d.p.) to fractions, and vice versa.
Eg 1: 0.8 = 8/10 = 4/5; 4.45 = 4 45/100 = 4 9/20.
Eg 2: 2/5 = 4/10 = 0.4; 3/20 = 15/100 = 0.15
To be able to add & subtract fractions (same denominator), using diagrams initially.
Lesson 2

Eg 1: Use common fractions – 1/2, 1/3, 1/4, 1/5, 1/8, 1/10.
Eg 2: Know addition facts of simple fractions: 1/2 + 1/4 = 3/4.

To be able to multiply an integer by a fraction, & in context:
Lesson 3

Eg 1: 1/3 of 12 = 1/3 x 12 = 12  3 = 4 (i.e. x 1/3 is same as  3).
Eg 2: one eighth of 40kg = 1/8 x 40 = 40  8 = 5kg.
Eg 3: Also use simple complex fractions, such as ¾ of 20.

MATHEMATICS DEPARTMENT                       AUTUMN TERM ( FIRST HALF)             YEAR 8 SUPPORT
Unit 4                Handling Data 1 (Probability)                                                 Date:                                                                                 6HRS

SUPPORT TEACHING OBJECTIVES                                                   KS3 Framework         Targeted activities for the introduction                     Activity Ref:
From the Y7 teaching programme (Level 4/5)                                      reference           or plenary part of the lesson
 Use the vocabulary of probability when interpreting the results of an       Page 277              Know or derive complements of 0.1, 1, 10, 50,
experiment; appreciate that random processes are unpredictable.                                   100, 1000.
 Understand and use the probability scale from 0 to 1; find and              Page 278              Consolidate and extend mental methods of
justify probabilities based on equally likely outcomes in simple                                  calculation, working with decimals, fractions
contexts.                                                                                         and percentages. Solve word problems
mentally.
 Know that if the probability of an event occurring is P then the            Page 279              Solve word problem mentally.
probability of it not occurring is 1 – P.
 Collect data from a simple experiment and record in a frequency table;      Page 283              Multiply and divide a two-digit number by a
estimate probabilities based on this data.                                                        one-digit number.
 Compare experimental and theoretical probabilities in different             Pages 284 - 285
contexts

Key vocabulary                       Description: (fair, certain, likely, unlikely, impossible, good chance, poor chance, even chance, fifty-fifty chance);
Probability: (chance, likelihood, risk, doubt, probability, Experiments: (experimental probability, theoretical probability, random, outcome).
Expected outcomes by the end of each lesson:
To be able to use the vocabulary of probability (eg: likely).                                           To be able to estimate probability from an experiment,
in the context of a probability scale from 0 – 1.                                                       and compare with theoretical probability:
Lesson 1

Eg 1: On a probability line, what is probability:                                                           10 Different coloured cubes (or counters) in a bag; take
- of doing maths homework,                                                                          one out record and replace; repeat 10 times, and then

Lesson 4 & 5
- that next year there will be less than 52 Fridays,                                                20 times; estimate the probability for each colour and
Eg 2: P(3) on a dice, etc.                                                                                   how many of each in the bag.
To be able to state probability of an event happening as a            Fwk, page 281                            Compare with theoretical probability.
fraction:                                                                                                      Have bags with 2, 3 and 4 colours in.
Lesson 2

Eg: Coloured counters on OHP - 6 red, 4 blue,
What is P( red)? P(blue)? ( check totals = 1);
P(green) = 0; why?
(Use dice and cards for further examples)
To be able to state the probability of an event not                                                      To be able to compare experimental and theoretical                Fwk, page 284
happening:                                                                                              probabilities in other contexts, (see Fwk, page 284).
Lesson 3

Lesson 6

- Develop work on P(events happening) and then consider
the other outcomes,
Eg: P(1 or 2) with a dice, what is P(not 1 or 2)?
Or P(3,4,5,6) etc.

MATHEMATICS DEPARTMENT                    AUTUMN TERM ( FIRST HALF)                      YEAR 8 SUPPORT

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