In Lesson 3.2.1, you reviewed your equation-solving skills to remember how to
find a solution to an equation. But do all equations have a solution? And how
can you tell if an equation does not have a solution? Learning Target:
Further develop understanding of what
makes a solution to an equation. Work with
equations that have one solution, an infinite
number of solutions, and no solutions. Continue practice with solving equations
while writing down steps, making further
progress toward being able to solve linear
equations without the use of manipulatives.
Focus Questions:
• How can we solve this equation?
• How do you know if your answer is correct?
• How many solutions are possible?
• How do equations with one solution, no solution, and
infinitely many solutions compare?
3-79. GUESS MY NUMBER
Today you will play the “Guess My Number” game. Your teacher will think
of a number and tell you some information about that number. You will try
to figure out what your teacher’s number is, using paper and a pencil if
needed. When you think you know what the mystery number is, sit silently
and do not tell anyone else. This will give others a chance to think about it.
3-80. Use the process your teacher illustrated to analyze Game #3 of “Guess My
Number” algebraically.
a) Start by writing an equation that expresses the information in the game. b) Solve your equation, writing down each step as you go. When you reach
a conclusion, discuss how it agrees with the answer for Game #3 you found
as a class. c) Repeat this process to analyze Game #4 algebraically. Red Light/Green Light
3-81. How many solutions does each equation below have? To answer this
question, solve these equations, recording all of your steps as you go along. Check your solution, if possible.
a) 4x − 5 = x − 5 + 3x
b) − x − 4x − 7 = −2x + 5
c) 3 + 5x − 4 − 7x = 2x − 4x + 1
d) 4x − (− 3x + 2) = 7x − 2
e) x + 3 + x + 3 = −(x + 4) + (3x − 2)
f) x − 5 − (2 − x) = −3
Time Permitting: Pairs Check
3-82. Create your own “Guess My Number” game like the ones you worked with
in class today. Start it with, “I’m thinking of a number that…” Make sure it is a
game for which you actually know the answer! Write the equation and solve it. Learning Log
Explain how to find the number of solutions to an equation. How
do you know when an equation has no solution? How do you know
when an equation has an infinite number of solutions? Give examples of each
kind of equation, as well as an equation with exactly one solution. Title your
entry “How Many Solutions?”
Class Summary Statement:
Circle Vocabulary, Circumference, and Area
The radius of a circle is a line segment from its center to any point on the
circle. The term is also used for the length of these segments. More than
one radius are called radii. A chord of a circle is a line segment joining any two points on a circle.
A diameter of a circle is a chord that goes through its center. The term is
also used for the length of these chords. The length of a diameter is twice
the length of a radius.
The circumference (C) of a circle is its perimeter, or the “distance around”
the circle.
The number π (read “pi”) is the ratio of the circumference of a circle to its diameter. That is
This definition is also used as a way of computing the circumference of a circle if you
know the diameter, as in the formula C = π · d where C is the circumference and d is the diameter. Since the diameter is twice the radius (d = 2r), the formula for the
circumference of a circle using its radius is C = π(2r) or C = 2π · r.
The first few digits of π are 3.141592.
To find the area (A) of a circle when given its radius (r), square the radius and multiply
by π. This formula can be written as A = r2 · π. Another way the area formula is often
written is A = π · r2.
Closure:
3-83 Learning Log
Silent Debate
Using algebra tiles is an easy way to solve equations.
pg 128: 3-84 thru 3-88