034. Substituting into Algebraic Expressions
Learning Intentions
- To understand that variables/pronumerals can be replaced with numbers
- Substitute numbers for variables/pronumerals
- Evaluate an expression Use order of operations once all variable/pronumeral values are known
Pre-requisite Summary
- Understand that a variable or pronumeral is a symbol that represents a number
- Know that substitution means replacing a variable with its given value
- Recognise that multiplication can be written without a sign, for example
- Recall the order of operations for expressions involving more than one operation
- Be able to Use brackets correctly when substituting negative or multi-step values if needed
- Be able to perform basic arithmetic accurately after substitution
Worked Examples
Worked Example 1
Substitute the given value and evaluate:
a) Solve the value of
b) Find the value of
c) Explain what substitution means
Worked Example 2
Substitute and evaluate:
a) Find the value of
b) Find the value of
Worked Example 3
Substitute and evaluate using order of operations:
a) Find the value of
b) Find the value of
Worked Example 4
Substitute and evaluate using order of operations:
a) Find the value of
b) Find the value of
Worked Example 5
Substitute and evaluate expressions with brackets:
a) Find the value of
b) Find the value of
Worked Example 6
Substitute and evaluate:
a) Find the value of
b) Find the value of
Problems
Problem 1
Substitute the given value and evaluate:
a) Find the value of
b) Find the value of
c) Explain what substitution means
Problem 2
Substitute and evaluate:
a) Find the value of
b) Find the value of
Problem 3
Substitute and evaluate using order of operations:
a) Find the value of
b) Find the value of
Problem 4
Substitute and evaluate using order of operations:
a) Find the value of
b) Find the value of
Problem 5
Substitute and evaluate expressions with brackets:
a) Find the value of
b) Find the value of
Problem 6
Substitute and evaluate:
a) Find the value of
b) Find the value of
Problems
Problem 1
a) Evaluate
b) Evaluate
Problem 2
a) Evaluate
b) Evaluate
Problem 3
a) Evaluate
b) Evaluate
Problem 4
a) Evaluate
b) Evaluate
Problem 5
a) Evaluate
b) Evaluate
Problem 6
a) Evaluate
b) Evaluate
Exercises
Understanding and Fluency
Exercise 1.
Substitute and evaluate:
a)
b)
c)
Exercise 2.
Substitute and evaluate:
a)
b)
c)
Exercise 3.
Substitute and evaluate:
a)
b)
c)
Exercise 4.
Substitute and evaluate:
a)
b)
c)
Exercise 5.
Substitute and evaluate using two variables:
a)
b)
c)
Exercise 6.
Substitute and evaluate using two variables:
a)
b)
c)
Exercise 7.
Substitute and evaluate using order of operations:
a)
b)
c)
Exercise 8.
Substitute and evaluate using brackets:
a)
b)
c)
Exercise 9.
Substitute and evaluate powers:
a)
b)
c)
Exercise 10.
Mixed substitution:
a)
b)
c)
Reasoning
Exercise 11.
Explain why
Exercise 12.
A student says that if
Exercise 13.
Explain why order of operations is still needed after substituting values into an expression.
Exercise 14.
A student substitutes
Problem-solving
Exercise 15.
A taxi fare is given by the expression
Exercise 16.
The total cost of buying
Exercise 17.
The perimeter of a rectangle with length
Exercise 18.
A phone plan costs $10 plus $2 for each gigabyte
Potential Misunderstandings
- Students may think substitution means adding the variable value to the expression without replacing the variable first
- Students may not recognise that
means - Students may forget to replace every occurrence of the variable in an expression
- Students may ignore brackets when substituting and evaluating
- Students may not Apply order of operations after substitution
- Students may confuse
with - Students may treat adjacent numbers as separate digits, for example reading
with as instead of - Students may substitute correctly but make arithmetic errors in the evaluation step
Next: 035. Equivalent Expressions and Algebraic Generalisation