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YEAR 9: AUTUMN TERM
Algebra 3 (6 hours)
Equations, formulae and identities (112–113, 122–125, 132–137)
Teaching objectives for the main activities
CORE
From the Y9 teaching programme
A. Distinguish the different roles played by letter symbols in equations, identities, formulae and functions.
B. Construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere
in the equation, positive or negative solution) using an appropriate method.
C. Use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as
x3 + x = 20.
D. Solve problems involving direct proportion using algebraic methods, relating algebraic solutions to graphical
representations of the equations; use ICT as appropriate.
Unit:
Number of 1 Hour Lessons:
Algebra 3
6
Oral and Mental
Objective q and a
+
= 46
What could the missing numbers be?
How could we write an algebraic
equation?
What about = - 46?
What about x – 12 = - 46?
How does this differ?
What does n – 1 mean?
What does n(n – 1) mean?
Solve
n(n – 1) = 56
Answer 8 x 7 = 56 n = 8
Is this the only solution?
n = -7 ?
Pupils produce their own puzzle
equations.
Teacher selects some, class discuss
and solve.
Questions on directed numbers.
Question on equivalent expression.
3(x + 2) = 3x + 6
Year Group:
Class/Set:
Y9
Core
Main Teaching (2 lessons - possibly 3)
Objective A
In equation 5x + 4 = 2x + 31 x is a particular
single value. What is it? Discuss method of
solution.
In the formula v = u + at v, u, a and t are variable
values. If we know 3 values we can work out the
fourth value. (What if we know 2 values).
In the function y = 8x + 11 for any chosen value
of x a value of y can be calculated.
(Discuss other functions and methods of writing
them).
Objective B
Assessment of were to begin with groups on
solving equations will be needed but some
practical starting points may be:
-x- -x-
-62x + 6 = 30
30
x
3x – 1
(3x-1) + (3x-1) + x + x = 30
or
Perim = 30 x
2(3x-1) + 2x = 30
3x - 1
4(3 x - 4) = 44
Do we expand
3x-4
perim = 44
brackets or teach
3x – 4 = 11?
Graded question needed appropriate to pupils’
level (see page 123 and 125 of framework)
Notes
Key Vocabulary
Equation
Expression
Variable
Solve
Equivalent
equivalence
Plenary
 Ask for examples of equations, functions
and formulas. Discuss solutions.
 Revisit key language.
 Explore misconceptions.
 Model some questions from the lesson.
 Explore extension activity
 (x + 2)(x + 1) = 42
What does it mean?
A number + 2 times same number + 1 = 42
How much bigger is x + 2 than x + 1?
Try 9 x 8, 8 x 7, 7 x 6 etc.
7 x 6 = 42
(x + 2) = 7 and (x + 1) = 6, x = 5.
 What about –7 x –6 = 42, can x be –8?
Oral and Mental
Objective e
Count up in square numbers.
Main Teaching 2 lessons
Objective C
Solve simple non-linear equations.
Count up in cube numbers up to 10
cubed.
x2 = 81 x2 + 24 = 60 x3 – 2 = 25
Notes
Key Vocabulary
Non-linear
Trial and
improvement
Substitute
Demonstrate solution to equations like:
Square and cube roots of square and
cube numbers.
Revisit/model using a calculator.
x2 + x = 49
x2 – x + 7 = 50
3 x2 – 2x – 4 = 270
Estimate square roots and cube roots
by trial and improvement.
√110 is between 10 and 11 etc.
Questions needed for practice.
If facilities available
spreadsheets or
graphical calculators
could be used.
Plenary

9 =x+2
x+2
looks hard but can you reason why the
answer is (x + 2) = 3 so x = 1?
Does x = -5 work? Why?
 Model solutions and substitutions from
questions set in lesson on trial and
improvement.
x+7
Area =
182cm2
x+2
Model how this becomes:
x
x2
7
7x
x
2x
14
2
x2 + 11x + 14 = 182 and now solve.
Oral and Mental
Objective a, g, h, o, p, i
What is half of …….?
What is quarter of……..? etc.
Main Teaching 1 lesson
Objective D
10 = 17.5
3
5.25
Notes
Key Vocabulary
Direct proportion
Ratio
Decimal and percentage equivalents.
How does this link to 10 : 17.5 = 3 : 5.25
10 : 3
=17.5 : 5.25
What is 4 ÷ 3, 3 ÷ 4? Etc.
Revisit ideas of ratio and direct proportion.
What is 50 ÷ 3 approx.?
51.2 ÷ 3.1 approx.?
How would we tackle these without a
calculator?
Why is
50 = 500 = 0.5
3
30
0.03
is
10 the same as 17.5 ?
3
5.25
How do we check?
x
y
1
3.5
2
7
3
10.5
4
14
5
17.5
6
21
7
?
If the x and y values are from a science experiment
what might x and y be?
Are the ratios of x and y equal?
Re-establish the direct proportion is an equality of
ratios.
Plot graph, note the gradient – establish
y = 3.5x
relate to earlier work on sequences.
How could we use the graph or table or function to
predict future values?
Questions needed
See resource sheet 9Alg3a. (ideal for group work and
students feeding back with reasoning). This asks
students to compare 5 variables. Note that variable C
has partial variation to the others. Variable E appears
to have one rouge measurement.
Plenary
 How do we check for
direct proportion?
 “Direct proportion is an
equality of ratios.” What
does this mean?
 If a function gives a
straight line graph, does it
guarantee direct
proportion?
 Relate to sequences
T(n) = 2n
T(n) = 2n + 3
 Generate sequences and
model proportionality.
 In a science experiment
why might direct
proportion not appear very
often or does it?