Unit 2
Equations and Their Solutions
Linear Equations, Inequalities, and Systems
Lesson 4
HSA-REI.A: Understand solving equations as a process of reasoning and explain the reasoning.
HSA-REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Expressions and Equations
Granola bites
Unit 2 ● Lesson 4
A value for the variable that makes the equation a true statement.
Page 157
The calories from other ingredients
No, because…
C=5.5
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 2 ● Lesson 4
Let’s recall what we know about solutions to equations.
We will be able to explain what it means for a value or pair of values to be a solution to an equation so that we can interpret solutions to equations in one variable and in two variables.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Where were we? Where are we? Where are we going?
Unit 2 ● Lesson 4
Agenda Review
You are successful today when...,
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 2 ● Lesson 4
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
4.2 Activity: Weekend Earnings
You can find solutions to equations by reasoning about a situation or by using algebra
15 mins Total
4 min individual - 3 min team share - 3 mins WB -5 mins class share
It tells us the number of hours that Jada worked that allowed her to take home $90.45 after paying for her bus fare.
pg 157-8
wall whiteboards
C = 8
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Try this! Are your Ready For More?
You can find solutions to equations by reasoning about a situation or by using algebra
Jada should work at the bookstore because she would earn more there. Her pay would be $109.80, and after subtracting $7.15 for the bus pass, she would still earn $102.65. She would only earn $99 from the other option.
Jada should help her neighbors. Working 9 hours at the bookstore would mean a few extra dollars than working 9 hours helping her neighbors, but it would also mean losing some personal time because of the travel involved.
2 min team share -2 mins class share
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
4.3 Activity: Calories from Protein and Fat
You can find solutions to equations by reasoning about a situation or by using algebra
11 mins Total
4 min individual - 2 min team share - 5 mins class share
No
No
Yes
It means a pair of grams of protein and fat in the snack that add up to 60 calories. An example: 6 grams of protein and 4 grams of fat.
pg 159
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
4.3 Activity: Calories from Protein and Fat
You can find solutions to equations by reasoning about a situation or by using algebra
They are not a combination of protein and fat that would produce 60 calories.
Substituting them for the variables in the equation leads to a false equation
Substitute 6 for f and solve the equation.
An example: 6 grams of protein and 4 grams of fat.
MANY
MANY
Multiple variable equations
What constraints are there on the amount of protein? On the amount of fat?
p≤15
f≤6.7
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Outliers
You can find solutions to equations by reasoning about a situation or by using algebra
It has 110 calories from some grams of protein and some grams of fat.
To find the combination of grams of protein and fat that produce 110 calories.
No, they don't add up to 110 calories. Substituting 11 for p and 5 for f into the equation doesn't lead to a true equation.
The snack has 5 grams of protein and a total of 110 calories.
To find the grams of fat that, when combined with 5 grams of protein calories, give a total of 110 calories. Find the value of f that would make the equation true.
f = _______
10
Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Expecting Outlier
You can find solutions to equations by reasoning about a situation or by using algebra
(2, 515), (10, 1,575)
Each solution tells us the number of T-shirts in the box and the corresponding total weight in grams.
It tells us the number of T-shirts in the box that result in a total weight of 2,900 grams.
(T, W)
8
Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 2 ● Lesson 4
● I can explain what it means for a value or pair of values to be a solution to an equation.
● I can find solutions to equations by reasoning about a situation or by using algebra.
Learning
Targets
Unit 2 ● Lesson 1
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.