Lesson 10
Hart Interactive – Algebra 1
M1
ALGEBRA I
Lesson 10: True and False Equations
Exploratory Exercise
1. Read over Rita’s answers to the six statements below. Was she correct every time? Circle any incorrect
answers given by Rita.
Name:
Rita
Answer True or False for each statement below.
A. The president of the United States is a United States citizen.
True
B. The president of France is a United States citizen.
False
C. 2 + 3 = 4 + 1
True
D. 6 • 2 = 2 • 6
True
E.
2 4
=
4 2
True
False
F. 3 • 6 = 2 • 5
2. What makes a statement true? How can you prove that a statement is false?
A statement is true if the left side equals the right. Or if there's values
make it true. To prove it false, prove both sides are not equal, or give a
counter example.
3. For each statement below, determine if the statement is True or False. Be prepared to support your
answer.
A. (5 + 2)2 = 52 + 22
B. 32 + 42 = 52
C. 6 + 3 = 5 + 4
D. 680 • (520 • 12) = 12 • (520 • 680)
E. 3x + 6 = 9
F. 2x + 7 = 2x
Lesson 10:
True and False Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from ALG I-M1-TE-1.3.0-07.2015
S.89
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 10
Hart Interactive – Algebra 1
M1
ALGEBRA I
4. An open sentence is one in which there might be one or more values that will make the sentence true but
all others will make it false. Open sentences are also called algebraic equations. Which sentences in
Exercise 3 are algebraic equations?
You will need a set of Algebraic Equations Cards.
5. Sort the cards and determine in which category the algebraic equation belongs. One example of each has
been done for you. You will not have enough algebraic equations to fill in this entire table.
One Solution
5x + 3 = 2x + 12
True when x = 3
No Solutions
An Infinite Number of Solutions
This statement is NEVER true!
This statement is ALWAYS true!
2x + 12 = 2x + 3
2x + 12 = 2(x + 6)
6. Write your own equations – one for every category. Then check your answers with your partner.
Lesson 10:
True and False Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from ALG I-M1-TE-1.3.0-07.2015
S.90
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 10
Hart Interactive – Algebra 1
M1
ALGEBRA I
Lesson Summary
•
A number sentence is a statement of equality between two numerical expressions.
•
A number sentence is said to be true if both numerical expressions are equivalent (that
is, both evaluate to the same number). It is said to be false otherwise.
•
True and false are called truth values.
•
An algebraic equation is a statement of equality between two expressions.
•
Algebraic equations can be number sentences (when both expressions are numerical),
but often they contain symbols (variables) whose values have not been determined.
•
When algebraic equations contain a symbol whose value has not yet been determined, we
use analysis to determine whether:
a.
The equation is true for all the possible values of the variable(s), or
b. The equation is true for a certain set of the possible value(s) of the variable(s), or
c.
The equation is never true for any of the possible values of the variable(s).
Lesson 10:
True and False Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from ALG I-M1-TE-1.3.0-07.2015
S.91
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.