150r. Review Equations, Solutions and Inspection
Learning Intentions
- To understand that an equation is a mathematical statement that can be true or false
- To understand that a solution is a value for the unknown that makes an equation true
- Solve a solution to simple equations by inspection
- write equations from worded descriptions
Pre-requisite Summary
- Know that an expression represents a quantity, while an equation compares two quantities
- Understand that the equals sign means the values on both sides are the same
- Be able to Substitute a value into an expression
- Know that a pronumeral or variable stands for an unknown number
- Be able to Use basic number facts for addition, subtraction, multiplication and division
- Understand that checking means substituting a value back into the equation
- Be able to translate simple word phrases into algebraic expressions
Worked Examples
Worked Example 1
State whether each equation is true or false:
a)
b)
c)
Worked Example 2
State the solution of each equation by inspection:
a)
b)
c)
Worked Example 3
State the solution of each equation by inspection:
a)
b)
c)
Worked Example 4
Check whether the given value is a solution:
a) Is
b) Is
c) Is
Worked Example 5
Write an equation for each description:
a) A number
b) Three times a number
c) A number
Worked Example 6
Write an equation from each worded situation, then Solve by inspection:
a) Sam has
b) A packet has
c) A chair costs $
Problems
Problem 1
State whether each equation is true or false:
a)
b)
c)
Problem 2
State the solution of each equation by inspection:
a)
b)
c)
Problem 3
State the solution of each equation by inspection:
a)
b)
c)
Problem 4
Check whether the given value is a solution:
a) Is
b) Is
c) Is
Problem 5
Write an equation for each description:
a) A number
b) Four times a number
c) A number
Problem 6
Write an equation from each worded situation, then solve by inspection:
a) Mia has
b) A jar has
c) A pen costs $
Exercises
Understanding and Fluency
Exercise 1.
State whether each statement is an equation or not:
a)
b)
c)
d)
Exercise 2.
State whether each equation is true or false:
a)
b)
c)
d)
Exercise 3.
Find the solution by inspection:
a)
b)
c)
d)
Exercise 4.
Find the solution by inspection:
a)
b)
c)
d)
Exercise 5.
Check whether the given value is a solution:
a) Is
b) Is
c) Is
d) Is
Exercise 6.
Write an equation for each description:
a) A number
b) A number
c) Twice a number
d) A number
Exercise 7.
Write an equation from each situation:
a) A bag has
b) A score is
c) Five equal boxes hold
d) A ribbon of length
Exercise 8.
Write the equation, then solve by inspection:
a) A number increased by
b) Three times a number is
c) A number divided by
d) A number decreased by
Reasoning
Exercise 9.
Explain why an equation can be true or false.
Exercise 10.
A student says that
Exercise 11.
Noah says that if
Exercise 12.
Explain why a solution must make both sides of an equation equal.
Exercise 13.
A student says that the solution to
Problem-solving
Exercise 14.
A game score starts at
Exercise 15.
A pack contains
Exercise 16.
Four equal bags contain
Exercise 17.
A movie ticket costs $
Exercise 18.
A rope of length
Exercise 19.
A student has
Potential Misunderstandings
- Students may think any algebraic expression is an equation
- Students may forget that an equation must include an equals sign
- Students may think a solution is any number that can be substituted, rather than one that makes the equation true
- Students may check only one side of the equation instead of both sides
- Students may confuse solving by inspection with using a random guess without checking
- Students may reverse word phrases such as “a number increased by
equals ” - Students may write an expression instead of an equation from a worded description
- Students may use the wrong operation when finding a solution by inspection
Next: 151r. Reviewing Equivalent Equations and Solving Algebraically