Answer:
57.35 (dollars / $)
MATH 7: CLUTTER BUSTERS TEACHER KEY Page 1 of 4
MATH 7 • UNIT PROGRESS ASSESSMENT
PAGE 2 OF 4
Case File #2: Measurement & Geometry
Maya is building a raised rectangular wooden garden bed in her backyard. The bed needs to be 8 feet long, 5 feet wide, and 1.5 feet deep. She wants to plant tomatoes, which require 75 days to mature and need to be watered twice a day. The backyard fence is 6 feet tall and is painted green. Maya needs to fill the entire wooden garden bed with organic compost soil. Soil is sold in bags that contain 3 cubic feet of compost and cost $12.50 each. How many bags of soil must Maya purchase to completely fill her garden bed?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Find the total number of soil bags (3 cubic feet each) needed to fill a garden bed of 8 ft × 5 ft × 1.5 ft.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Garden bed dimensions: 8' long, 5' wide, 1.5' deep | ||
| | Soil bag size: 3 cubic feet per bag |
|
| | Tomatoes need 75 days & watering twice/day |
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| | Backyard fence is 6 feet tall and painted green |
|
| | Cost of soil is $12.50 per bag |
|
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3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Write volume formula of rectangular prism
Volume = length × width × depth
STEP 2 Substitute bed dimensions and multiply
Volume = 8 × 5 × 1.5 = 40 × 1.5 = 60 cubic feet
STEP 3 Determine bags needed by division
Bags = Total Volume ÷ Volume per Bag = 60 ÷ 3
STEP 4 State numerical solution & double-check
Bags needed = 20. (Cost of $12.50 was not needed for calculation).
4. FINAL ANSWER:
Key distinction: The cost of soil ($12.50) is indeed extraneous! Highlighting this shows superior mastery of isolating data variables.
Answer:
20 (bags)
MATH 7: CLUTTER BUSTERS TEACHER KEY Page 2 of 4
MATH 7 • UNIT PROGRESS ASSESSMENT
PAGE 3 OF 4
Case File #3: Algebraic Relationships & Rates
A rental company charges a flat base fee of $45.00 plus $18.00 per hour to rent a motorboat. Marcus rents a motorboat starting at 10:30 AM on a sunny 78-degree Saturday. The boat has a maximum passenger capacity of 6 passengers or 900 pounds, and its fuel tank holds 12 gallons of gasoline. Marcus returns the boat at 2:30 PM on the same day. He also purchases a souvenir captain's hat for $15.00. How much is Marcus's total bill from the rental company for the boat rental and the hat?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Calculate Marcus's total bill, combining the flat base fee, the hourly rental cost for the time elapsed, and the cost of the hat.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Flat base fee of $45.00 plus $18.00 / hour | ||
| | Rented boat from 10:30 AM to 2:30 PM |
|
| | Purchased souvenir captain's hat for $15.00 |
|
| | Sunny Saturday, 78-degree weather |
|
| | Capacity: 6 passengers/900 lbs; fuel: 12 gal |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Calculate total rental duration
10:30 AM to 2:30 PM → 4 hours elapsed.
STEP 2 Calculate variable hourly cost
Cost = 4 hours × $18.00 / hour = $72.00
STEP 3 Add base fee & variable cost
Rental subtotal = $72.00 + $45.00 = $117.00
STEP 4 Add captain's hat purchase
Total Bill = $117.00 + $15.00 = $132.00
4. FINAL ANSWER:
Note: Start and end times are critical variables for calculations and must be identified as 'Use It', even though they represent time of day.
Answer:
132.00 (dollars / $)
MATH 7: CLUTTER BUSTERS TEACHER KEY Page 3 of 4
MATH 7 • UNIT PROGRESS ASSESSMENT
PAGE 4 OF 4
Case File #4: Proportional Relationships & Mixtures
An art teacher, Ms. Ramirez, is mixing paint for a large school mural. She needs to create a specific shade of green by mixing 3 parts of yellow paint with 2 parts of blue paint. She wants to make a total of 15 gallons of this green paint. Ms. Ramirez has an art teaching budget of $120.00, and she has been teaching at the school for 8 years. Yellow paint costs $18.50 per gallon and blue paint costs $22.00 per gallon. The art classroom has 28 student desks. How many gallons of yellow paint does Ms. Ramirez need to mix to get her desired total of 15 gallons of green paint?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Find the number of gallons of yellow paint needed to make a 15-gallon green mixture with a yellow-to-blue ratio of 3:2.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Mix ratio is 3 parts yellow to 2 parts blue | ||
| | Target green paint volume is 15 gallons |
|
| | Teaching budget is $120.00; teacher has taught 8 yrs |
|
| | Yellow cost is $18.50 / blue cost is $22.00 |
|
| | Classroom has 28 student desks |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Sum ratio parts to find total parts
Total Parts = 3 (yellow) + 2 (blue) = 5 parts
STEP 2 Find gallon value per ratio part
1 part = 15 gallons ÷ 5 parts = 3 gallons per part
STEP 3 Multiply yellow parts by part value
Yellow Paint = 3 parts × 3 gallons/part = 9 gallons
STEP 4 Verify total mixture volume
Blue: 2 × 3 = 6 gal | Mix: 9 yellow + 6 blue = 15 gal (Correct)
4. FINAL ANSWER:
Note: Costs of individual paints ($18.50 and $22.00) are extraneous. Students often make the mistake of multiplying quantities by costs first.
Answer:
9 (gallons)
MATH 7: CLUTTER BUSTERS TEACHER KEY Page 4 of 4
| Information / Fact | Use It | Extra |
|---|
| | |
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| | |
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3. PLAN & SOLVE: Write and calculate your steps.
STEP 1
STEP 2
STEP 3
STEP 4
4. FINAL ANSWER:
Ensure your answer reflects all calculated steps and includes the appropriate units of measurement.
Answer:
________________________ (UNITS)
MATH 7: CLUTTER BUSTERS PRACTICE Page 2 of 4
MATH 7 • SKILL BUILDER
PAGE 3 OF 4
Case File #3: Algebraic Relationships & Rates
Leo is renting a bicycle. The shop charges a flat base fee of $10.00 plus an hourly rate of $5.00. Leo rents the bicycle for 3 hours. It is a sunny 72-degree day, and the bicycle has 21 gears and is painted bright red. Leo also rents a helmet for a flat, one-time charge of $4.00. How much is Leo's total bill from the shop for renting the bicycle and the helmet?
DATA FILTER & PLAN BOARD
1. UNDERSTAND: What is the primary question you are trying to solve?
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| | |
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| | |
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| | |
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3. PLAN & SOLVE: Write and calculate your steps.
STEP 1
STEP 2
STEP 3
STEP 4
4. FINAL ANSWER:
Ensure your answer reflects all calculated steps and includes the appropriate units of measurement.
Answer:
________________________ (UNITS)
MATH 7: CLUTTER BUSTERS PRACTICE Page 3 of 4
MATH 7 • SKILL BUILDER
PAGE 4 OF 4
Case File #4: Proportional Relationships & Mixtures
An art teacher, Mr. Chen, is mixing paint. He mixes 2 parts of red paint with 1 part of blue paint to create a specific shade of purple. He wants to make a total of 12 gallons of purple paint. Mr. Chen is 35 years old, and he has 25 students in his art class. Red paint costs $15.00 per gallon. How many gallons of red paint does Mr. Chen need to mix to get his desired 12 gallons of purple paint?
DATA FILTER & PLAN BOARD
1. UNDERSTAND: What is the primary question you are trying to solve?
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| | |
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| | |
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| | |
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3. PLAN & SOLVE: Write and calculate your steps.
STEP 1
STEP 2
STEP 3
STEP 4
4. FINAL ANSWER:
Ensure your answer reflects all calculated steps and includes the appropriate units of measurement.
Answer:
________________________ (UNITS)
MATH 7: CLUTTER BUSTERS PRACTICE Page 4 of 4
MATH 7 • SKILL BUILDER KEY
PAGE 2 OF 4
Case File #2: Measurement & Geometry
Sophia is filling a rectangular wooden sandbox in her backyard. The sandbox needs to be 6 feet long, 4 feet wide, and 1 foot deep. She wants to paint the sandbox blue, and she has a friendly dog named Buster who is 3 years old. The sandbox sand is sold in bags that contain 2 cubic feet of sand. How many bags of sand must Sophia purchase to completely fill her sandbox?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Find the total number of sand bags (2 cubic feet each) Sophia must buy to fill a 6 ft × 4 ft × 1 ft sandbox.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Sandbox size: 6' long, 4' wide, 1' deep | ||
| | Sand bag size: 2 cubic feet per bag |
|
| | She wants to paint the sandbox blue |
|
| | Dog named Buster is 3 years old |
|
| | Sandbox is located in her backyard |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Write rectangular prism volume formula
Volume = length × width × depth
STEP 2 Substitute sandbox size & multiply
Volume = 6 × 4 × 1 = 24 cubic feet
STEP 3 Divide sandbox volume by bag volume
Bags = Total Volume ÷ Bag Size = 24 ÷ 2
STEP 4 State numerical solution & units
Bags needed = 12.
4. FINAL ANSWER:
Key concept: Sandboxes are rectangular prisms. Simple whole numbers are used to establish mastery of multi-step division modeling.
Answer:
12 (bags)
MATH 7: CLUTTER BUSTERS PRACTICE KEY Page 2 of 4
MATH 7 • SKILL BUILDER KEY
PAGE 3 OF 4
Case File #3: Algebraic Relationships & Rates
Leo is renting a bicycle. The shop charges a flat base fee of $10.00 plus an hourly rate of $5.00. Leo rents the bicycle for 3 hours. It is a sunny 72-degree day, and the bicycle has 21 gears and is painted bright red. Leo also rents a helmet for a flat, one-time charge of $4.00. How much is Leo's total bill from the shop for renting the bicycle and the helmet?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Calculate Leo's total bill from the bicycle shop, including the base fee, 3 hours of rental time, and the helmet rental fee.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Flat base fee of $10.00 plus $5.00 / hour | ||
| | Rented bicycle for 3 hours |
|
| | Flat helmet charge of $4.00 |
|
| | Sunny 72-degree day |
|
| | Bicycle has 21 gears and is painted bright red |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Calculate variable hourly cost
Hourly Cost = 3 hours × $5.00 / hour = $15.00
STEP 2 Add base bicycle flat fee
Bicycle Cost = $15.00 + $10.00 = $25.00
STEP 3 Add helmet rental flat fee
Total Bill = $25.00 + $4.00 = $29.00
STEP 4 State the final numerical total
Total Bill is $29.00.
4. FINAL ANSWER:
Concept breakdown: The bicycle has 21 gears and is painted red; these are physical attributes of the object that do not affect pricing.
Answer:
29.00 (dollars / $)
MATH 7: CLUTTER BUSTERS PRACTICE KEY Page 3 of 4
MATH 7 • SKILL BUILDER KEY
PAGE 4 OF 4
Case File #4: Proportional Relationships & Mixtures
An art teacher, Mr. Chen, is mixing paint. He mixes 2 parts of red paint with 1 part of blue paint to create a specific shade of purple. He wants to make a total of 12 gallons of purple paint. Mr. Chen is 35 years old, and he has 25 students in his art class. Red paint costs $15.00 per gallon. How many gallons of red paint does Mr. Chen need to mix to get his desired 12 gallons of purple paint?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Find the number of gallons of red paint needed to make a 12-gallon purple mixture with a red-to-blue ratio of 2:1.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Mix ratio is 2 parts red to 1 part blue | ||
| | Target purple paint is 12 gallons |
|
| | Mr. Chen is 35 years old |
|
| | He has 25 students in his art class |
|
| | Red paint costs $15.00 per gallon |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Sum ratio parts to find total parts
Total Parts = 2 (red) + 1 (blue) = 3 parts
STEP 2 Find gallon value per ratio part
1 part = 12 gallons ÷ 3 parts = 4 gallons per part
STEP 3 Multiply red parts by part value
Red Paint = 2 parts × 4 gallons/part = 8 gallons
STEP 4 Verify total mixture volume
Blue: 1 × 4 = 4 gal | Mix: 8 red + 4 blue = 12 gal (Correct)
4. FINAL ANSWER:
Note: Cost of red paint ($15.00/gallon) is extraneous since the problem does not ask for financial calculations. This is a common point of confusion for students.
Answer:
8 (gallons)
MATH 7: CLUTTER BUSTERS PRACTICE KEY Page 4 of 4
DATA FILTER & PLAN BOARD
1. UNDERSTAND: What is the primary question you are trying to solve?
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| | |
|
| | |
|
| | |
|
| | |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1
STEP 2
STEP 3
STEP 4
4. FINAL ANSWER:
Ensure your answer reflects all calculated steps and includes the appropriate units of measurement.
Answer:
________________________ (UNITS)
MATH 7: CLUTTER BUSTERS ALTERNATE ASSESSMENT Page 2 of 4
MATH 7 • UNIT ALTERNATE ASSESSMENT
PAGE 3 OF 4
Case File #3: Algebraic Relationships & Rates
A tech workspace charges a flat entry fee of $20.00 plus $10.00 per hour to rent a private high-speed computer station. Elena rents a station starting at 1:00 PM on a cool 62-degree Friday. The desk has an ergonomic chair with a weight limit of 250 pounds, and her monitor is 27 inches wide. Elena finishes her work and logs out at 5:00 PM on the same day. She also purchases a gourmet espresso at the tech bar for $5.00. How much is Elena's total bill from the tech workspace for the computer rental and the espresso?
DATA FILTER & PLAN BOARD
1. UNDERSTAND: What is the primary question you are trying to solve?
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| | |
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| | |
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| | |
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3. PLAN & SOLVE: Write and calculate your steps.
STEP 1
STEP 2
STEP 3
STEP 4
4. FINAL ANSWER:
Ensure your answer reflects all calculated steps and includes the appropriate units of measurement.
Answer:
________________________ (UNITS)
MATH 7: CLUTTER BUSTERS ALTERNATE ASSESSMENT Page 3 of 4
MATH 7 • UNIT ALTERNATE ASSESSMENT
PAGE 4 OF 4
Case File #4: Proportional Relationships & Mixtures
A bakery chef, Chef Pierre, is mixing a custom juice blend for a catering event. He needs to create a specific tropical punch by mixing 3 parts of pineapple juice with 1 part of cranberry juice. He wants to make a total of 20 gallons of this punch. Chef Pierre has an ingredient budget of $250.00, and he has worked at the bistro for 12 years. Pineapple juice costs $10.00 per gallon. The banquet hall has 10 round tables. How many gallons of pineapple juice does Chef Pierre need to mix to get his desired total of 20 gallons of punch?
DATA FILTER & PLAN BOARD
1. UNDERSTAND: What is the primary question you are trying to solve?
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| | |
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| | |
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| | |
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3. PLAN & SOLVE: Write and calculate your steps.
STEP 1
STEP 2
STEP 3
STEP 4
4. FINAL ANSWER:
Ensure your answer reflects all calculated steps and includes the appropriate units of measurement.
Answer:
________________________ (UNITS)
MATH 7: CLUTTER BUSTERS ALTERNATE ASSESSMENT Page 4 of 4
Answer:
75.05 (dollars / $)
MATH 7: CLUTTER BUSTERS ALTERNATE KEY Page 1 of 4
MATH 7 • UNIT ALTERNATE ASSESSMENT
PAGE 2 OF 4
Case File #2: Measurement & Geometry
Jackson is building a raised rectangular wooden sandbox for a local community park. The sandbox needs to be 8 feet long, 6 feet wide, and 1.5 feet deep. He wants the children to play safely, so he chooses play sand that requires 14 days to ship and is certified hypoallergenic. The park's main slide is 8 feet tall and is colored blue. Sand is sold in bags that contain 4 cubic feet of sand and cost $14.99 each. How many bags of sand must Jackson purchase to completely fill his sandbox?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Find the total number of sand bags (4 cubic feet each) needed to fill a sandbox of 8 ft × 6 ft × 1.5 ft.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Sandbox size: 8' long, 6' wide, 1.5' deep | ||
| | Sand bag size: 4 cubic feet per bag |
|
| | Play sand hypoallergenic & 14 days shipping |
|
| | Park's main slide is 8 feet tall and blue |
|
| | Bags of sand cost $14.99 each |
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3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Write volume formula of rectangular prism
Volume = length × width × depth
STEP 2 Substitute sandbox size and multiply
Volume = 8 × 6 × 1.5 = 48 × 1.5 = 72 cubic feet
STEP 3 Divide sandbox volume by bag volume
Bags = Total Volume ÷ Volume per Bag = 72 ÷ 4
STEP 4 State numerical solution & double-check
Bags needed = 18. (The cost per bag of $14.99 is extraneous).
4. FINAL ANSWER:
Key distinction: Calculating volume with decimals (1.5 feet) provides an optimal 7th-grade multi-step challenge, while cost values remain extraneous.
Answer:
18 (bags)
MATH 7: CLUTTER BUSTERS ALTERNATE KEY Page 2 of 4
MATH 7 • UNIT ALTERNATE ASSESSMENT
PAGE 3 OF 4
Case File #3: Algebraic Relationships & Rates
A tech workspace charges a flat entry fee of $35.00 plus $16.00 per hour to rent a private high-speed computer station. Elena rents a station starting at 1:15 PM on a cool 62-degree Friday. The desk has an ergonomic chair with a weight limit of 250 pounds, and her monitor is 27 inches wide. Elena finishes her work and logs out at 5:15 PM on the same day. She also purchases a gourmet espresso at the tech bar for $8.50. How much is Elena's total bill from the tech workspace for the computer rental and the espresso?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Calculate Elena's total bill, combining the flat entry fee, the hourly rental cost for the time elapsed, and the cost of the espresso.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Flat entry fee of $35.00 plus $16.00 / hour | ||
| | Rented computer station from 1:15 PM to 5:15 PM |
|
| | Purchased gourmet espresso for $8.50 |
|
| | Friday, cool 62-degree weather |
|
| | Chair weight limit 250 lbs; 27-inch monitor size |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Calculate total rental duration
1:15 PM to 5:15 PM → 4 hours elapsed.
STEP 2 Calculate variable hourly cost
Cost = 4 hours × $16.00 / hour = $64.00
STEP 3 Add entry base fee & variable cost
Rental subtotal = $64.00 + $35.00 = $99.00
STEP 4 Add gourmet espresso purchase
Total Bill = $99.00 + $8.50 = $107.50
4. FINAL ANSWER:
Note: Converting 12-hour clock times to elapsed duration is an essential 7th-grade rate concept. The chair weight limit is extraneous.
Answer:
107.50 (dollars / $)
MATH 7: CLUTTER BUSTERS ALTERNATE KEY Page 3 of 4
MATH 7 • UNIT ALTERNATE ASSESSMENT
PAGE 4 OF 4
Case File #4: Proportional Relationships & Mixtures
A bakery chef, Chef Pierre, is mixing a custom juice blend for a catering event. He needs to create a specific shade of tropical punch by mixing 4 parts of pineapple juice with 3 parts of cranberry juice. He wants to make a total of 28 gallons of this punch. Chef Pierre has an ingredient budget of $250.00, and he has worked at the bistro for 12 years. Pineapple juice costs $12.40 per gallon, and cranberry juice costs $15.50 per gallon. The banquet hall has 14 round tables. How many gallons of pineapple juice does Chef Pierre need to mix to get his desired total of 28 gallons of punch?
DATA FILTER & PLAN BOARD (IDEAL SOLUTION)
1. UNDERSTAND: What is the primary question you are trying to solve?
Find the number of gallons of pineapple juice needed to make a 28-gallon tropical punch with a pineapple-to-cranberry ratio of 4:3.
2. FILTER: List facts. Mark whether to use or discard.
| Information / Fact | Use It | Extra |
|---|---|---|
| Mix ratio is 4 parts pineapple to 3 parts cranberry | ||
| | Target punch volume is 28 gallons |
|
| | Ingredient budget is $250.00; worked at bistro 12 yrs |
|
| | Pineapple cost is $12.40 / cranberry is $15.50 / gal |
|
| | Banquet hall has 14 round tables |
|
|
3. PLAN & SOLVE: Write and calculate your steps.
STEP 1 Sum ratio parts to find total parts
Total Parts = 4 (pineapple) + 3 (cranberry) = 7 parts
STEP 2 Find gallon value per ratio part
1 part = 28 gallons ÷ 7 parts = 4 gallons per part
STEP 3 Multiply pineapple parts by part value
Pineapple Juice = 4 parts × 4 gallons/part = 16 gallons
STEP 4 Verify total mixture volume
Cranberry: 3 × 4 = 12 gal | Mix: 16 pine + 12 cran = 28 gal (Correct)
4. FINAL ANSWER:
Note: Individual costs ($12.40 and $15.50) are completely extraneous since the question doesn't ask for cost. Correct classification is required.
Answer:
16 (gallons)
MATH 7: CLUTTER BUSTERS ALTERNATE KEY Page 4 of 4
