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OHS
A5a/1: Equations
Find the missing numbers in each equation(by inspection,
inverse method …)
(Red herrings: cannot solve expressions, equations
with two variables.) |
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| - Construct and
solve simple linear equations with integer coefficients
(unknown on one side only) using an appropriate
method (e.g. inverse operations). |
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expression
equation
formula
linear
solve
mapping
collecting
simplifying
multiplying out |
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Q: What’s the difference
between an expression and an equation? (See Starter.)
Eg: 2n + 3 (how many solutions?)
2n + 3= 23 (how many solutions?)
Rewrite this equation:
- in words;
- as a mapping’
- using a flow chart;
- as a graph.
Emphasise that all represent the same connection
between two variables. |
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1. Use a variety
of problems to consolidate and extend previous
skills with equations, including:
- collection of like terms;
- multiplying an integer over brackets.
Eg: 
If total of these cards is 22, what is v?
Equation: 3v + v
+ 2 + v = 22
Collect like terms:
5v + 2 = 22
Solve:) 5v + 2 –
2 = 22 – 2
5v = 20
5v ÷ 5 = 20 ÷ 5
v = 4
OR Math
Fighter
(Choose 'Games' > 'Math Fighter')- solve &
shoot down equations!
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1. How
many different equations can you make and solve
from:
1 2 3 5 + x = Eg: equation:
2(n + 6) = 12
n = 0
2. Review methods of simplifying expressions (collecting
like terms, multiplying out).
3. Review solving strategies used so far (eg: inspection,
inverse …). |
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OHS
A5a/2: Mobile Phone Bills
Use to derive word formulas from algebraic formulas.(Use
formulas in £ instead of pence, if appropriate,
i.e.
C = 0.1T + 9
Suggest a word formula and ask pupils for algebraic
formulas.
OR
Tell pupils that all six people get a phone bill
for £14 (1400p). Who talks the most?
(Answer: Narinder with 100 min talk time). |
|
| - Use simple formulae
from mathematics and other subjects, substitute
positive integers in simple linear expressions and
formulae and, in simple cases, derive a formula. |
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expression
equation
formula
linear
solve
substitute |
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1. Discuss answers
to Starter:
- answers form sequence (910, 920, 930…)
- can predict answers (position-to term);
- nth term? (10T + 900)- Which numbers change?
- Which stay the same? - Why?
- Discuss difference between an expression
(10T + 900); an equation
(10T + 900 = 950); a formula
(C = 10T + 900). (where T is time in minutes and
C is total cost of bill in pence.)
2. Rewrite 10T + 900 = C,
- in words;
- as a mapping;
- in a flow chart;
- with coordinates on a graph.
Emphasise that all represent the same connection
between T and C.
3. Discuss and agree how to derive, substitute and
solve formulae from other contexts, such as 6, 8
and 9 times tables. |
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Extend skills with
equations to formulae, by:
1. - substituting values into a formula.
2. - generating sequences from practical contexts,
and deriving formula from nth term. 
Eg:
3, 6, 9, 12, 15, 18
y = 3n
(LINK TO A5B: Sequences.)
3. - deriving formulae for other contexts.
Eg 1: Areas such as A =
lw
Eg 2: Conversions: m = c x 10 (10mm=1cm)
f = i ÷ 12 (12"= 1 ft)
Eg 3: SCIENCE
Using the formula W = FD, What is W when F is 11kg,
d is 5m?
OR
How much work, W, is done, to move a table with
a mass of 11kg a distance of 5m?
OR
Constructing
Formulas
- 4 worked examples. |
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Which
formulas are correct for perimeter of a rectangle:
1) P = 2(l + w)
2) P = 2l + w
3) l + w + l + w
4) P = 2l + 2w
5) P = 2l + 8
6) P = l + w + l + w
7) 20 = 2l + 2w ?
Use to distinguish between expressions (3), equations
(5) and formulae (the rest).
Can also use to verify pupils' understanding that:
a) l + w + l + w = 2l + 2w by collecting like terms;
b) 2(l + w) = 2l + 2w by multiplying out;
c) there are an infinite number of solutions for
P = 2(l +w);
d) and, there is only 1 solution when l = 2cm, w
= 1cm. |
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