Substituting into Expressions 2
Key words: Substitute, expression, statement, expression,
equivalent
Objectives
• Substitute positive integers into simple linear expressions.
• Simplify or transform algebraic expressions
• Explore general algebraic relationships
Instructions for the teacher:
In this activity students will use substitution to explore the
meaning of algebraic expressions and begin to explore
equivalent expressions.
The aim of the discussion is to hear students thoughts on what
the algebraic symbolism means – then using the calculator to
confirm the meaning of the symbolism which has been agreed
(see a good history of maths to look into the history –
comparatively recent – of algebraic symbolism!).
Question: “What is the meaning of 2A?”
Write suggestions on the board asking students to explain why
they think what they do (do not validate them).
Ask the class for a possible value for A. Write it up.
Question: “What is the value of the expression 2A?”
Write up answers taking explanations only. (e.g. if A=3 then
the answer 23 is interesting).
KS3 Framework
page ref: 138
Suppose the class suggested A = 6.
Type 6
Press STO→
Press ALPHA
Press MATH (to type A)
Press ENTER
Now check the value of 2A
Type 2
Press ALPHA
Press MATH (to type A)
Press ENTER
You can now confirm with the student who gave the
explanation yielding the answer 12, what is the meaning of
writing 2A. Check it by entering different values for A and
repeating the steps above.
Question: “How else could I write this”
Again take all answers, validate them all by checking. The two
most interesting that students are likely to give are A2 and
A+A.
We can check A2
Press ALPHA
Press MATH (to type A)
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Type 2
Press ENTER
Fortunately the calculator reports this as correct syntax – so we
can have a discussion with the class about being strictly correct
(but nonetheless not conventional)
Also, we can check A+A (remembering that it will operate on
the last value you entered for A):
Press ALPHA
Press MATH (to type A)
Type +
Press ALPHA
Press MATH (to type A)
Press ENTER
We can suggest that these two expressions are equivalent and
can be written: 2A ≡ A+A
Use other values of A to improve the strength of this statement
(the lesson called Algebraic Identities develops this further).
Repeat this process to develop other algebraic symbolism in the
same way. (For further examples, see the worksheet for
students). Depending on the class you will need to decide how
many to do with the full class and how many to leave for them
to work on in pairs or small groups.
The best example which unpicks a common error and
misconception is: 2(A+B).
Students should offer values for A and B and suggest the value.
The value of 2(A + B) can be checked after the values of A and
B are entered.
Then alternative expressions can be offered – they all need
checking but the clearest common error is 2A + B which can be
checked just before the correct expansion. This will give a
value which is B less than the correct value (known because we
have checked the answer numerically already).
Also, checking the possible interpretations of 2C² generates a
lot of debate!
Note: it must be emphasised to students to fill in the value
column before they use the calculator to check!
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Substituting into Expressions 2
First: Reset your TI 83-Plus
• Press 2nd + to get MEM
• Choose 7 (Reset…)
• Choose 1 (All Ram…)
• Choose 2 (Reset)
We have chosen:
A =
B =
C =
Expression
Value
Guess
Alternative
Expression
Check
Value
Check
2A
A²
2A + B
A+B
A+C
A + 2B
2(A + B)
2(2A + B)
3(A – 2C)
A(A + B)
2C²
(2C)²
Write some of your identities here:
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