Linear Equations in Real-Life Scenarios
LINEAR EQUATIONS
Eureka Math
8
th
Grade Module 4
Topic B
LESSON 10
Notes, examples(2), workshop
Notes – Distance, speed, time
Average speed is found by dividing the total distance the
total time.
Where
d = distance, t = time, and r = rate or speed
Example 1
Paul walks 2 miles in 25 minutes. How far can he walk in
137.5 minutes?
Example 2
Dave lives 15 miles from town A. He is driving at a constant
speed of 50 miles per hour from his home away from (in the
opposite direction of) the city. How far away is Dave from the
town after 𝑥 hours of driving?
Using your equation, how far from town is he after 1 hour?
Workshop
Must Do
•
Exponents retest
•
Complete Topic A
assessment
•
Lesson 10 cw #1-3
May Do
•
Khan academy
•
Exponents review
If tested out of exponents:
•
Crossing the
River/Carnival Bears
•
Start Homework
LESSON 11
Examples(2), workshop
Example 1
Pauline mows a lawn at a constant rate. Suppose she
mows a 35 sq. ft. lawn in 2.5 minutes. What area can she
mow in 10 minutes?
t
minutes?
Example 2
Water flows at a constant rate out of a faucet. Suppose
the volume of water that comes out in 3 minutes is 10.5
gallons. How many gallons come out in
t
minutes?
Workshop
Must Do
•
Finish lesson 10 cw #1-3
•
Lesson 11 cw #1-3
May Do
•
Khan academy
•
Exponents review
•
Topic A assessment
corrections
If tested out of exponents:
•
Crossing River/Carnival Bears
•
Inky puzzles
•
Integer games
LESSON 12
Warm up, example, notes, workshop
Warm Up
Emily tells you that she scored 32 points in a basketball
game. Write down all the possible ways she could have
scores 32 with only two- and three-point baskets. Use the
table to organize your work.
If x is the number of two-
pointers and y is the
number of three-pointers,
what equation can we
write for the total?
Standard Form of Linear Equations
A linear equation in the form:
Where
A
,
B
, and
C
represent set numbers, and
x
and
y
represent variables or unknowns.
•
A
solution
to this equation is an
ordered pair
(
x, y
), that
makes the equation true.
•
To find solutions, you pick a set number for x or y,
substitute, and then solve for the other value.
Slope-Intercept Form of Linear Equations
A linear equation in the form:
Where
m
and
b
represent set numbers, and
x
and
y
represent variables or unknowns.
•
m
is the constant rate of change (slope)
•
b
is the y-intercept (crosses y-axis)
•
(
x, y
) are
solutions
that make the equation true
Converting Standard to Slope-Intercept
-
Ax
-
Ax
B
B
Example
Choose x-values
•
Let x = 5
•
Substitute:
•
Solve for y:
(5, 265) is a solution
Choose y-values
+250 +250
-10 -10
÷(-50) ÷(-50)
Workshop
Must Do
•
Finish lesson 10&11 cw
•
Exit ticket 10 & 11
•
Lesson 12 cw #1-5
HINTS:
think about why
•
#1-2 small numbers easier!
•
#3 choose y, solve for x
•
#4 choose x that are
multiples of 5
May Do
•
Khan academy
•
Inky puzzles
LESSON 13
Discussion/example, workshop
Example
Workshop
Must Do
•
Finish lesson 12 cw
HINTS:
think about why
•
#1-2 small numbers easier!
•
#3 choose y, solve for x
•
#4 choose x that are
multiples of 5
•
Lesson 13 cw #1-3
May Do
•
Khan academy
•
Folder organize
•
Notes sheet
LESSON 14
Explore, discussion/notes, workshop (part2)
Explore
•
Complete Lesson 14 classwork #1-3 and #7-9
•
SKIP #4-6 and #10-12 FOR NOW
•
Prepare to discuss #3 and #9
Discuss: 1x + 0y = 5
Discuss: 0x + 1y = 2
Notes
When in standard form Ax + By = C:
•
An equation with A=1 and B=0
(in other words: 1x + 0y = C or x = C) will be a
vertical
line
through (C, 0)
•
An equation with A=0 and B=1
(in other words 0x + 1y = C or y = C) will be a
horizontal
line through (0, C)
Workshop
Must Do
•
Finish lesson 12&13 cw
•
Exit ticket 12 & 13
•
Lesson 14 cw #1-12
•
#4-6
•
#10-12
May Do
•
Khan academy
•
Complete all cw & hw
•
Folder organize
•
Notes sheet
Explore the concept of linear equations through real-life examples involving distance, speed, time, and constant rates. Practice solving problems to determine distances covered, areas mowed, and volumes of water coming out of a faucet over specific periods. Engage in workshops and assessments to reinforce learning and apply linear equations in context.
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Presentation Transcript
LINEAR EQUATIONS Eureka Math 8thGrade Module 4 Topic B
LESSON 10 Notes, examples(2), workshop
Notes Distance, speed, time Average speed is found by dividing the total distance the total time. d =rt r =d t =d t r Where d = distance, t = time, and r = rate or speed
Example 1 Paul walks 2 miles in 25 minutes. How far can he walk in 137.5 minutes?
Example 2 Dave lives 15 miles from town A. He is driving at a constant speed of 50 miles per hour from his home away from (in the opposite direction of) the city. How far away is Dave from the town after ? hours of driving? Using your equation, how far from town is he after 1 hour?
Workshop Must Do May Do Exponents retest Complete Topic A assessment Lesson 10 cw #1-3 Khan academy Exponents review If tested out of exponents: Crossing the River/Carnival Bears Start Homework
LESSON 11 Examples(2), workshop
Example 1 Pauline mows a lawn at a constant rate. Suppose she mows a 35 sq. ft. lawn in 2.5 minutes. What area can she mow in 10 minutes? t minutes? (time in minutes) Linear Equation: (area in square feet)
Example 2 Water flows at a constant rate out of a faucet. Suppose the volume of water that comes out in 3 minutes is 10.5 gallons. How many gallons come out in t minutes? (time in minutes) Linear Equation: (in gallons)
Workshop Must Do May Do Finish lesson 10 cw #1-3 Lesson 11 cw #1-3 Khan academy Exponents review Topic A assessment corrections If tested out of exponents: Crossing River/Carnival Bears Inky puzzles Integer games
LESSON 12 Warm up, example, notes, workshop
Warm Up Emily tells you that she scored 32 points in a basketball game. Write down all the possible ways she could have scores 32 with only two- and three-point baskets. Use the table to organize your work. If x is the number of two- pointers and y is the number of three-pointers, what equation can we write for the total?
Standard Form of Linear Equations A linear equation in the form: Where A, B, and C represent set numbers, and x and y represent variables or unknowns. + = Ax By C A solution to this equation is an ordered pair (x, y), that makes the equation true. To find solutions, you pick a set number for x or y, substitute, and then solve for the other value.
Slope-Intercept Form of Linear Equations A linear equation in the form: Where m and b represent set numbers, and x and y represent variables or unknowns. = + y mx b m is the constant rate of change (slope) b is the y-intercept (crosses y-axis) (x, y) are solutions that make the equation true
Converting Standard to Slope-Intercept + = -Ax Ax Ax -Ax By BB By C = C + C Ax Ax C = = y B B A C = + y x B B
+ = Example 50 15 x y Choose x-values Let x = 5 Substitute: Solve for y: Choose y-values Let y = 10 Substitute: Solve for x: + = 50 ) 5 ( 15 y + = 50 10 15 x + = 50 10 -10 -10 50 = x (-50) (-50) 5 = 15 x + = 50 ) 5 ( 250 +250 +250 15 15 y + = y 5 = 265 y 1 = x (5, 265) is a solution 50 10 1 10, 10) is a solution (
Workshop Must Do May Do Finish lesson 10&11 cw Exit ticket 10 & 11 Lesson 12 cw #1-5 HINTS: think about why #1-2 small numbers easier! #3 choose y, solve for x #4 choose x that are multiples of 5 Khan academy Inky puzzles
LESSON 13 Discussion/example, workshop
Example 5 1 1 4 2 2 3 -1 -2 7 8
Workshop Must Do May Do Finish lesson 12 cw HINTS: think about why #1-2 small numbers easier! #3 choose y, solve for x #4 choose x that are multiples of 5 Lesson 13 cw #1-3 Khan academy Folder organize Notes sheet
LESSON 14 Explore, discussion/notes, workshop (part2)
Explore Complete Lesson 14 classwork #1-3 and #7-9 SKIP #4-6 and #10-12 FOR NOW Prepare to discuss #3 and #9
Notes When in standard form Ax + By = C: An equation with A=1 and B=0 (in other words: 1x + 0y = C or x = C) will be a vertical line through (C, 0) An equation with A=0 and B=1 (in other words 0x + 1y = C or y = C) will be a horizontal line through (0, C)
Workshop Must Do May Do Finish lesson 12&13 cw Exit ticket 12 & 13 Lesson 14 cw #1-12 #4-6 #10-12 Khan academy Complete all cw & hw Folder organize Notes sheet
