CURRICULUM SUMMARY – September to December 2014
SUBJECT: Mathematics
Week Learning objectives
SEQUENCES
1
YEAR GROUP: Year 8
Activities (in brief)
TEACHER:
Agata Piskorz
Students will:
 Know what is a sequence.
 Understand sequence notation
 Generate sequence using term – to-term rule
 Generate sequence using position-to-term
rule
 Find the general formula for an arithmetic
sequence.
 Know and understand quadratic sequences.
(9-p.2) Revising sequences.
3
ALGEBRA AND EQUATIONS
Students will:
 distinguish the different roles played by letter
symbols in expressions and equations
 use index notation for integer powers.
 Simplify algebraic expressions by collecting
like terms; multiply a single term over a
bracket
 Factorise by taking out single term
(9-p.38) Evaluating algebraic expressions.
Finding algebraic expressions
Simplifying expressions.
(9-p.40) Constructing and solving linear equations
(9-178) Using brackets – expanding and factorizing simple expressions.
4
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(9-p.180) Solving equations with brackets.
(9-P.42) Solving non-linear equations.
(9-p.182) Solving equations with simple algebraic fractions.
2
5
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Construct and solve linear equations.
Check results.
use trial and improvement method to find
approximate solution to an equation.
Add simple algebraic fractions.
Denote a formula and change its subject
(9-p.4) Generating sequences from practical contexts. Writing an expression to describe the n-th
term of an arithmetic sequence.
(9-p.6) Investigating quadratic sequences – generating terms of a quadratic sequences. Finding
the n-th term formula for some simple quadratic sequences.
(9-p.184) Transforming formulae.
FUNCTIONS
Students will:
 Understand functions
Using Venn diagrams and function machines (9-p.10)
Drawing graphs of some simple functions.
Sequence as a function where the input is a set of positive integers.
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6
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7
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Express simple functions in words, then using
symbols; represent them in mappings.
Draw and interpret graphs.
(9-p.12, p.14) Constructing functions arising from real-life problems and plotting their
corresponding graphs; interpreting graphs arising from real situations, e.g. time series graphs.
Know linear function and its graph.
Generate points in all four quadrants and plot
the graphs of linear functions, where y is
given explicitly or implicitly in terms of x
(9-p.126) Completing tables of values and plotting linear graphs.
Checking whether a given point lies an a given line.
(9-p.128) Finding the gradient.
(9-p.130) Generating points and plotting graphs of linear functions, where y is given implicitly in
terms of x (e.g. ay + bx = 0, y + bx + c = 0)
Know the gradient formula.
Write equation of a line through two given
points
FRACTIONS, DECIMALS, PERCENTEGES
Students will:
 Use efficient methods to add and subtract
fractions.
 Multiply and divide fractions.
 Cancel common factors before multiplying or
dividing.
 Understand the effect of multiplying or
dividing by number between 0 and 1
Finding gradient given two point.
Finding equation of a given line.
9
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Multiply and divide decimals.
Calculate part of a given number (fraction,
decimal, percentage)
10
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Express one given number as a percentage of
another.
Understand and use percentage increase and
decrease.
Understand and use simple and compound
interest.
(9-p.110) Multiplying decimals, rounding to make estimations.
(9-p.112) Dividing by decimal by transforming to division by an integer.
(9-p.114) Using calculator methods.
(9-p.24)Finding percentage or fraction of a given number. Solving problems involving percentage
change.
(9-p.26, p.28)Finding the outcome of a given percentage increase or decrease. Using decimals to
find outcome of a given percentage increase or decrease.
Given the outcome and the initial number, finding the percentage increase or decrease.
Introducing simple and compound interest.
8
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11
RATIOS AND PROPORTIONS
Revising fractions.
(9-p.18) Adding and subtracting fractions.
Using the prime factor decomposition to find the common denominator of given fractions.
(9-p.20, p.22) Multiplying and dividing fractions. Interpreting division as a multiplicative inverse.
Dividing objects in given ratio.
12
Students will:
 Interpret and use ratio in a range of contexts.
 Apply understanding of the relationship
between ratio and proportion.
(9-p.30) Simplifying ratios. Given ratio, finding appropriate amounts. Expressing ratio in the form
1:m or m:1.
(9-p.32, p.44) Using directly proportional quantities to solve problems.
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(9-p.158, p.210) Knowing the real distance finding the distance on the map. Knowing the distance
on a map finding the real distance. Finding scale.
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Use and interpret maps and scale
drawing.
Use proportional reasoning to solve
problems.
13
GEOMETRICAL REASONING AND
CONSTRUCTIONS
Students will;
 Explain how to find, calculate and use: the
sums of the interior and exterior angles of
triangles, quadrilaterals, pentagons and
hexagon
 Calculate the interior and exterior angles of
regular polygons.
(9-p.54) Working with angles in polygons.
(9-p.56) Working with angles in regular polygons.
(9- p.58)Identifying and using vertically opposite angles, alternate angles, corresponding angles.
Solving problems using properties of angles, parallel and intersecting lines, and of triangles and
other polygons.
14
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Using a ruler and a compass to construct bisectors of lines and angles.
Investigating and using properties of the perpendicular bisector of a line and the bisector of an
angle.
Constructing the circle inscribed in a triangle and subscribed on a triangle.
(9-p.64)Using a ruler and a compass to construct right-angled triangles.
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15
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Construct midpoint and perpendicular
bisector of a line.
Construct bisector of an angle.
The perpendicular from a point to a line.
The perpendicular from a point on a line
Using a ruler and a compass to construct a triangle given three sides (SSS). Understanding the
Know definition of a circle and names of its
triangle inequality.
parts.
explain why inscribed regular polygons can be
(9-p.62) Using circle properties.
constructed by equal divisions of a circle.