Classwork Guided Packet 8th Grade Math • Lesson 38
Classwork: Real-World Standard Form
Name:
Date: Class:
Big Question How do we write real-world math stories in standard form?
1
Warm-Up: Find the Intercepts
Put in 0 to find where the line hits the axis
a. 4x − 8y = 2 Equation 1
1. Find x-intercept (set y = 0):
4x − 8(0) = 2 → 4x = 2
x =
Pair: ( , 0 )
2. Find y-intercept (set x = 0):
4(0) − 8y = 2 → −8y = 2
y =
Pair: ( 0, )
b. y = 3x − 5 Equation 2
1. Find x-intercept (set y = 0):
0 = 3x − 5 → 5 = 3x
x =
Pair: ( , 0 )
2. Find y-intercept (set x = 0):
y = 3(0) − 5
y =
Pair: ( 0, )
Key Takeaway: The Standard Form Rule
Ax + By = C
Ax Rate A times item x
By Rate B times item y
C Total amount
Remember: A, B, and C are numbers. They do not have fractions or decimals in strict form. Page 1 of 2
Part 2: Guided Practice
Classwork: Real-World Scenarios
Name:
Page 2 of 2
Example 1: Elena Runs and Walks
Total = 8 miles
Elena runs and walks. Her total goal is 8 miles .0.2 miles each minute (x). | • Walk: 0.1 miles each minute (y).
a. Write equation:
x +
y =
b. Elena runs for 30 minutes (x = 30). How long did she walk?
0.2(30) + 0.1y = 8 → 6 + 0.1y = 8
y =
min
c. Her watch says: 25 min run and 20 min walk = 8 miles. Is that right?
0.2(25) + 0.1(20) = 5 + 2 = 7 miles
YES
NO
Example 2: Christian at the Gas Station
Shift = 120 minutes
Christian works for 2 hours (120 minutes ).2 minutes to fill (x). | • A truck takes 4 minutes to fill (y).
a. Write equation (in minutes):
x +
y =
b. If Christian fills 20 cars (x = 20), how many trucks can he fill?
2(20) + 4y = 120 → 40 + 4y = 120
y =
trucks
Teacher Check / Stamp:
Independent Practice Worksheet Part 3: Priority Practice
Independent Practice
Name:
Date: Class:
Standard Form: Ax + By = C Page 1 of 3
1
Find the Standard Form Equation
Which equation looks like Ax + By = C? (Both letters on the left side)
a. y = 2x − 3
b. 3x + 2y = 7
c. y − 3 = 4(x − 1)
d. 4y = 3x − 6
Problem 2: Silverware for the Kitchen
Budget = $36
You shop for forks and knives for a new kitchen.
You have $36 in all to spend.
• Each fork costs $5 (x).$4 (y).
a Write the equation:
x +
y =
b Can you buy 5 forks and 5 knives? Test the math:
5(5) + 4(5) = 25 + 20 = $45
Equal to $36?
YES
NO
c Find a set of forks and knives that totals exactly $36:
forks ($5 each)
knives ($4 each)
= $36
Part 3 & 4: Practice
Independent Practice (Continued)
Name:
Page 2 of 3
Problem 3: Toys and Treats for Pluto
Total = $25
Michael has $25 in all to spend on his dog Pluto.$4 each (x). | • Dog toy = $3 each (y).
a. Write equation:
x +
y =
b. Can he get 3 snacks & 4 toys?
4(3) + 3(4) = 12 + 12 = $24
Equal to $25?
YES
NO
c. Can he get 1 snack & 7 toys?
4(1) + 3(7) = 4 + 21 = $25
Equal to $25?
YES
NO
Problem 4: Kayla's Cash Wallet
Total Cash = $36
Kayla has $36 in cash in her wallet.$5 bills (x) and $1 bills (y).
a. Write equation:
x +
y =
b. Which bill combinations equal $36? (Select all that work)
3 fives and 10 ones 3(5) + 10(1) = $25
4 fives and 16 ones 4(5) + 16(1) = $36
6 fives and 6 ones 6(5) + 6(1) = $36
5 fives and 9 ones 5(5) + 9(1) = $34
Part 4: Extra Practice
George at the Craft Store
Name:
Page 3 of 3
Problem 5: Blue Squares and Red Circles
Total = $21
George buys beads for a craft project. He has $21 in all .
• Blue square beads cost $3.50 per pound (x).$1.75 per pound (y).
a Write the equation:
x +
y =
b George buys 0 red beads (y = 0). How many pounds of blue beads (x) can he buy?
3.50x + 1.75(0) = 21 → 3.50x = 21
x =
pounds
c George buys 0 blue beads (x = 0). How many pounds of red beads (y) can he buy?
3.50(0) + 1.75y = 21 → 1.75y = 21
y =
pounds
d Can George buy 4 pounds of blue beads and 4 pounds of red beads?
3.50(4) + 1.75(4) = 14 + 7 = $21
Does it equal $21?
YES
NO
How did I do on these problems?
😄 Easy 🙂 Good 🤔 Need Help
Standard Form Exit Ticket Quick Check • Lesson 38
Standard Form Exit Ticket
Name:
Date: Class:
1
The Standard Form Rule
A Write the formula for standard form:
x +
y =
B What kind of numbers are A, B, and C in standard form? (Check the true sentence):
A, B, and C are whole numbers (integers with no fractions).
A, B, and C must always be decimals.
Question 2: Study Time for the Big Test
Total = 60 minutes
You study for a big math test tonight.
You have 60 minutes in all before bed.
• Each graph question takes 2 minutes (x).4 minutes (y).
A Write an equation in standard form to show your 60 minutes:
x +
y =
B Can you do 8 graph questions (x = 8) and 12 word problems (y = 12)?
Check the minutes:
2(8) + 4(12) = 16 + 48 =
total minutes
Can you finish in 60 minutes?
YES
NO
Tell why:
Exit Ticket Score:
_______ / 4 points
Standard Form Homework Sheet Homework 12.1 • Lesson 38
Homework: Real-World Standard Form
Name:
Date: Class:
Standard Form Rule: Ax + By = C Page 1 of 2
1. Seafood Dinner (Fish and Shrimp)
Budget = $40
You buy salmon and shrimp for dinner. Your total budget is $40 .$6 per pound (x). | • Shrimp is $4 per pound (y).
Write the equation:
x +
y =
2. Football Game Tickets
Total = $6,300
The school sells tickets to a big football game. Total sales are $6,300 .$7 each (x). | • Student ticket = $4 each (y).
Write the equation:
x +
y =
3. Community Care Packages
Total Weight = 30 lbs
You pack bottles into care boxes. The box can hold 30 pounds in all .2 pounds each (x). | • Conditioner bottle = 1.5 pounds each (y).
Write the equation:
x +
y =
4. Rate of Change (More Women in Senate)
• Year 1985: 22 women .68 women . (20 years later)
Find the rate: How many women were added per year?
Change: 68 − 22 = 46 women in 20 years
46 ÷ 20 =
per year
Homework 12.1 • Part B
Graphing and Slope Review
Name:
Page 2 of 2
5. Graph: y = −x + 1
• y-intercept = (0, 1) (start here)
• slope = −1 (go down 1, right 1)
x y
6. Graph: m = 1/3, b = −4
• y-intercept = (0, −4) (start here)
• slope = 1/3 (go up 1, right 3)
x y
7
Find Slope Between Two Points
Find the slope of the line through (3, −5) and (−3, 1).
Use the slope formula: m = (y₂ − y₁) / (x₂ − x₁)
m = 1 − (−5) / −3 − 3 = 6 / −6
Slope m =
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