Lesson 2Truth and Equations
Learning Goal
Let’s use equations to represent stories and see what it means to solve equations.
Learning Targets
I can match equations to real life situations they could represent.
I can replace a variable in an equation with a number that makes the equation true, and know that this number is called a solution to the equation.
Lesson Terms
- coefficient
- constant term
- difference
- factor
- product
- quotient
- solution to an equation
- sum
- term
- variable
Warm Up: Three Letters
Problem 1
The equation
If
is 3, is 4, and is 5, is the equation true or false? Find new values of
, , and that make the equation true. Find new values of
, , and that make the equation false.
Problem 2
The equation
If
is 3, is 4, and is 12, is the equation true or false? Find new values of
, , and that make the equation true. Find new values of
, , and that make the equation false.
Activity 1: Storytime
Problem 1
Here are three situations and six equations. Which equation best represents each situation? If you get stuck, consider drawing a diagram.
After Elena ran 5 miles on Friday, she had run a total of 20 miles for the week. She ran
miles before Friday. Andre’s school has 20 clubs, which is five times as many as his cousin’s school. His cousin’s school has
clubs. Jada volunteers at the animal shelter. She divided 5 cups of cat food equally to feed 20 cats. Each cat received
cups of food.
Activity 2: Using Structure to Find Solutions
Problem 1
Here is a list of values followed by equations that each contain a variable. Think about what each equation means and find a solution in the list of values. If you get stuck, consider drawing a diagram. Be prepared to explain why your solution is correct.
List:
Are you ready for more?
Problem 1
One solution to the equation
How many different whole-number solutions are there to the equation
Activity 3: Card Sort: What’s in an Expression?
Problem 1
Find cards that match each mathematical term. Some cards may match more than one mathematical term. Parts of the expressions may be underlined to clarify what part of the expression should be matched to the mathematical term. Explain or show your reasoning to your partner with each match you make.
When you and your partner are in agreement about all the card matches, create three parts of an expression on the three blank cards for the mathematical terms of your choosing.
Lesson Summary
An equation can be true or false. An example of a true equation is
An equation can have a letter in it, for example,
A letter in an equation is called a variable. In
When a number is written next to a variable, the number and the variable are being multiplied. For example,