054e. Substituting Integers into Expressions
Learning Intentions
- To understand that substitution involves replacing a pronumeral (letter) with a number
- Substitute positive or negative integers into an expression and Evaluate
Pre-requisite Summary
- Understand that a pronumeral or variable is a letter that represents a number
- Know that substitution means replacing the letter everywhere it appears with the given value
- Recognise that multiplication can be written without a sign, for example
- Be able to Use brackets when substituting negative numbers, for example if
, then - Recall the order of operations for expressions involving more than one operation
- Be able to add, subtract, multiply and divide positive and negative integers
Worked Examples
Worked Example 1
Substitute and evaluate:
a) Solve the value of
b) Find the value of
Worked Example 2
Substitute and evaluate:
a) Find the value of
b) Find the value of
Worked Example 3
Substitute and evaluate:
a) Find the value of
b) Find the value of
Worked Example 4
Substitute and evaluate:
a) Find the value of
b) Find the value of
Worked Example 5
Substitute and evaluate Use order of operations:
a) Find the value of
b) Find the value of
Worked Example 6
Substitute and evaluate with two pronumerals:
a) Find the value of
b) Find the value of
Problems
Problem 1
Substitute and evaluate:
a) Find the value of
b) Find the value of
Problem 2
Substitute and evaluate:
a) Find the value of
b) Find the value of
Problem 3
Substitute and evaluate:
a) Find the value of
b) Find the value of
Problem 4
Substitute and evaluate:
a) Find the value of
b) Find the value of
Problem 5
Substitute and evaluate using order of operations:
a) Find the value of
b) Find the value of
Problem 6
Substitute and evaluate with two pronumerals:
a) Find the value of
b) Find the value of
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:
a)
b)
c)
Exercise 6.
Substitute and evaluate using two pronumerals:
a)
b)
c)
Exercise 7.
Substitute and evaluate using two pronumerals:
a)
b)
c)
Exercise 8.
Substitute and evaluate using order of operations:
a)
b)
c)
Reasoning
Exercise 9.
Explain why
Exercise 10.
A student says that if
Exercise 11.
Explain why using brackets helps when substituting a negative number into an expression.
Exercise 12.
A student substitutes
Problem-solving
Exercise 13.
The temperature is modelled by
Exercise 14.
A game score is given by
Exercise 15.
The lift position is represented by
Exercise 16.
A bank balance is modelled by
Exercise 17.
A diver’s position is represented by
Exercise 18.
The expression for a point score is
Potential Misunderstandings
- Students may think substitution means adding the given number to the expression instead of replacing the pronumeral
- Students may forget to replace every occurrence of the pronumeral in an expression
- Students may not recognise that
means multiplication - Students may treat a negative substituted value as if the negative sign disappears
- Students may fail to use brackets when substituting a negative number and then make sign errors
- Students may ignore order of operations after substitution
- Students may confuse the operation sign in the expression with the sign of the substituted integer
- Students may make arithmetic errors when evaluating expressions with negative integers
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