Unit 12
Algebra 4 (Equations & Substitution)
SUPPORT TEACHING OBJECTIVES
From the Y7 teaching programme (Level 4/5)
 Use letter symbols to represent unknown numbers or variables;
know meanings of term, expression, equation. (and function).
 Construct & solve simple linear equations with integer coefficients
(unknown on one side only), using appropriate methods (e.g. inverse
operations).
Key vocabulary
Date:
KS3 Framework
reference
6 HRS
Targeted activities for the introduction
or plenary part of the lesson
Activity Ref:
Page 113
Pages 123 - 125
algebraic expression, equation, function, variable, evaluate, construct, solve, collect like terms.
Expected outcomes by the end of each lesson:
1. To understand that symbols can replace unknown
numbers, and variables.
1. To be able to construct and solve equations, including:
- unknown on 1 side only:
2x + 8 = 30
- collecting like terms to simplify: 6h +2 = 26 h = 13
- solving by method such as inverse method:
Resources:
Inverse Method
2y + 5 = 23
2y = 23 – 5 = 18 (inv of +5 is -5)
y = 18 ÷ 2 = 9 (inv of x2 is ÷2)
y=9
2. To be able to use letter symbols in different ways in
expressions.
Eg 1: 2x + 10 (expression); 2x + 10 = 30 (equation).
Eg 2: Form an expression to represent:
6 more than a number
4 less than a number
a number plus 3 and then multiplied by 5
a number multiplied by 3
a number multiplied by itself
2 divided by a number
Lesson 5 & 6
Lesson 1 & 2
Eg 1: ∆ +  = 10; find pairs of values for ∆ and  that make
this equation true.
How many possible solutions?
Eg 2: ∆ + 7 = 10: How many possible solutions?
Eg 2: n + 7 = 10: How many possible solutions?
2. To be able to construct simple equations from word
problems and solve, as in:
Class of 30 pupils; 8 more boys than girls. How many girls?
3. Know how to represent x and ÷ in algebraic expressions.
Lessons 3 & 4
Eg: 2f;
d/2;
a(b = c);
(j + k) / 2
To be able to use letter symbols in different ways to
construct a simple linear equation.
Eg 1: I'm thinking of a n umber, multiply it by 2 and add 10.
I get 80. What number was I thinking of?
Eg 2: Solve these equations:
4a = 24; 7 + x = 11; ; 3 = 4h – 5; 5 = 45; 3(t + 6) = 30
x
MATHEMATICS DEPARTMENT
SPRING TERM (SECOND HALF)
YEAR 8 SUPPORT
Resources:
Unit 13
Handling Data 2 (Collecting Data & Averages)
SUPPORT TEACHING OBJECTIVES
From the Y7 teaching programme (Level 4/5)
KS3Framework
reference
 Suggest possible answers to a problem that can be addressed by statistical
methods,; identify possible sources.
 Collect data using a suitable method, such as observation, controlled
experiment using ICT, or questionnaire consider sample size; design and
construct frequency table for discrete data.
 Calculate statistics, recognise appropriate use of range, mean, median and
mode; construct/use stem-and-leaf diagrams.
 Construct, on paper and using ICT: bar-line graphs, bar charts and
frequency diagrams for discrete data.
Pages 249 – 251
 Begin to interpret tables, graphs and diagrams for discrete data.
Pages 269 - 271
Pages 275 - 275
Pages 249 – 251
 Write a short report of a statistical enquiry illustrate with appropriate
diagrams, graphs and charts, using ICT as appropriate; justify the choice of
what is presented.
Key vocabulary
Date:
6 HRS
Targeted activities for the introduction
or plenary part of the lesson
Activity Ref:
Pages 251 – 255
Page 261
Pages 263 - 267
sample, primary source, secondary source, discrete, stem-and-leaf diagram, line graph, bar-line graph, bar chart, frequency diagram.
2. To be able to design a data collection sheet,
questionnaire or 2-way table to suit problem.
B. Collecting & Processing Data
1. To be able to collect discrete data using agreed
method, sample size and table.
2. To be able to calculate the mode, median, mean and
range of data (using calculator for larger sets of data).
C. Displaying Data
1. To be able to construct & use bar-line graphs.
2. To be able to construct bar charts or frequency
diagrams appropriate to data.
MATHEMATICS DEPARTMENT
D. Interpreting & Analysing Data
1. To be able to interpret data displays;
Resources:
Lesson 4
A. Making decisions
1. To be able to suggest possible answers, and make
decisions on suitable collection method and sources to
answer a statistical enquiry
Eg: Consider range of prepared problems on whiteboard.
2. - and relate summarised data to initial question
3. To be able to present results and methods used in a
short written report, justifying choices.
To be able to explore a different statistical problem by
going through stages A – D.
Lessons 5 & 6
Lesson 3
Lesson 2
Lesson 1
Expected outcomes by the end of each lesson:
SPRING TERM (SECOND HALF)
YEAR 8 SUPPORT
Resources:
Unit 14
Number 4 (FDP, Estimation & Approximation)
Date:
SUPPORT TEACHING OBJECTIVES
From the Y7 teaching programme (Level 4/5)
KS3 Framework
reference
 Understand addition and subtraction of decimals and integers, and
multiplication and division of integers; use the laws of arithmetic and
inverse operations. Begin to use the order of operations, including
brackets, with more complex calculations.
 Consolidate and extend mental methods of calculation, working with
decimals, fractions and percentages; solve word problems mentally.
 Make & justify estimates & approximations. Convert one metric unit
to another.
Pages 82 - 87
 Consolidate standard column procedures for addition and subtraction
of integers and decimals with up to two places.
 Use standard column procedures for multiplication and division of
2-digit whole numbers; extend to multiplying and dividing
decimals with one or two places by single-digit whole numbers.
 Check a result by considering whether it is of the right order of
magnitude and by working the problem backwards.
6 HRS
Targeted activities for the introduction
or plenary part of the lesson
Activity Ref:
Pages 89 – 101
Page 91,
Pages 103 - 105
Page 104
Pages 105 – 107
Page 111
Key vocabulary
1. To be able to make and justify estimates.
Resources:
To consolidate and extend mental methods in problems:
- from known facts.
Eg: Start at 110, use rule 'add 4'
- using complements.
Eg: 50 = x + 7
- doubles & halves.
Eg: 8 X 2.5 = 4 X 5 =20
- using X and ÷ facts with place value.
Eg: 0.4 X 5 = 4 X 5 ÷ 10
MATHEMATICS DEPARTMENT
Eg 1: No. of weeds in garden  estimate no. in 1m²  scale up.
Lesson 4
To understand and use the laws of arithmetic, including:
- mental, informal written, & calculator methods;
- addition and subtraction of decimals & integers;
- x and ÷ of integers: 840 ÷ 7 = how many 7's in 840?
- inverse operations:
a) n ÷ 4 = 16;  to check 4 x 4 = 16
- order of operations, BIDMAS.
2. To be able to make and justify approximations.
Eg: 527 X 24 ≈ 500 X 30
3. To be able to convert one metric unit to another.
Eg: 1000 m = 1 km. Hpw many metres in 2.5 km.
To be able to x and ÷ integers & decimals using standard
column methods.
Lessons 5 & 6
Lessons 2 & 3
Lesson 1
addition, subtraction, multiplication, division, operation, inverse, commutative, product, quotient, divisor, remainder, brackets,
BIDMAS, complement.
Expected outcomes by the end of each lesson:
Eg: 48.2 X 6
Eg: 42.8 ÷ 4
Estimate: 50 X 6 ≈ 300
48.2
48.2 X 6 = 482 X 6 ÷ 10
X
6
2892
Ans: 2892 ÷ 10 = 289.2
SPRING TERM (SECOND HALF)
Estimate: 40 ÷ 4 ≈ 10
= 428 ÷ 4 ÷ 10
107
4 428 (÷ by chunking)
Ans: 107 ÷ 10 = 10.7
YEAR 8 SUPPORT
Resources:
MATHEMATICS DEPARTMENT
SPRING TERM (SECOND HALF)
YEAR 8 SUPPORT