Below are challenge problems related to our units.
There are also challenge problems you can complete from this shared Google Folder.
Feel free to complete challenge problems at any time. Turn into Mrs. Beihoff or ask questions during CT!
These are not assignments but are fun challenges! Take chances! Make mistakes! Get messy! 😊
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Diego is packing gift boxes shaped like rectangular prisms. Each box has a length of 10 inches, a width of 6 inches, and a height of 4 inches.
What is the volume of one box?
Diego wants to stack several of these boxes together to make a larger rectangular prism that measures 20 inches long, 12 inches wide, and 8 inches tall. How many of the smaller boxes will fit exactly inside the larger prism, with no gaps or overlaps?
If Diego paints the outside of the large prism, how many square inches of surface area will he need to cover?
Extension: Design your own box dimensions (length, width, and height) for a smaller rectangular prism that could also fit perfectly inside the 20 × 12 × 8 prism. Show how many of your new boxes would fit inside.
Challenge Problem 1:
The volume of a new chemical is measured to be 9.? ?5 liters.
Use the clues below to determine the exact volume:
The value of the digit 5 in the thousandths place is 1/10 the value of the digit ? in the number.
The value of the digit ? is 10 times the value of the digit ? in the number.
A.) What is the exact volume in standard form?
B.) What is the exact volume in expanded form?
C.) What is the exact volume in word form?
D.) Round the exact volume to the nearest hundredth.
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Challenge Problem 2:
Three athletes are competing in a long jump competition. Their results are given in three different formats:
Athlete A: Two and eight hundred thirty-one thousandths meters.
Athlete B: 2 + 8/10 + 5/100 meters.
Athlete C: 2.84 meters.
List the athletes in order from the shortest jump to the longest jump.
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Challenge Problem 3:
A student is asked to round the number 4.981 to the nearest tenth. The student provides the answer: 4.9
A.) Identify the student's error.
B.) Explain the correct rounding procedure for this number.
C.) State the correct answer.
Challenge Problem 1:
Error Analysis Challenge: Subtracting Decimals
A fifth grade student named Jill was asked to solve 15.2 - 6.875.
Jill solves the problem and arrives at the answer 8.655. She is incorrect. The correct answer is 8.325. What did she do incorrectly? Guide her to come to the correct answer.
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Challenge Problem 2:
Sarah bought three bags of beads for a project.
The first bag weighed 0.455 kilograms, the second weighed 1.028 kilograms, and the third weighed 0.867 kilograms.
If her project requires a total of 2.5 kilograms of beads, how many more kilograms of beads does Sarah need to buy?
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Challenge Problem 3:
Mr. Dunning is building a shelving unit. He needs three pieces of wood:
A long shelf that measures 1.75 meters
Two identical side supports, each measuring 0.825 meters.
He starts with a single plank of wood that is 4 meters long.
How much wood, in meters, will Mr. Dunning have left over after he cuts the three necessary pieces?
Challenge Problem 1:
The Library Shipment
A school library receives 124 boxes of books. Each box contains 24 hardcover books and 12 paperback books. How many total books did the library receive?
(Hint: Find the total books per box first!)
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Challenge Problem 2:
The Marathon Trainer
Carla's cousin, Miguel, walks 9,450 steps every day. If he maintains this pace for exactly one year (52 weeks), how many steps will he walk in total?
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Challenge Problem 3:
The Craft Show Profits
Wanda sells her bracelets for $15 each. If she sold 351 bracelets this year, how much money did she make? If it cost her $4 in materials to make each bracelet, what was her total profit?
Challenge Problem 1:
You are designing a high-tech microscopic chip that is shaped like a rectangle. The length of the chip is 8.47 mm and the width is 5.63 mm.
The Goal: Calculate the total area of the chip in square millimeters (mm2).
The Twist: Once you have your answer, round it to the nearest tenth.
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Challenge Problem 2:
An experimental hybrid vehicle travels 14.36 miles for every liter of fuel. The fuel tank currently holds 12.75 liters.
The Goal: Determine exactly how many miles the vehicle can travel before the tank is completely empty.
The Twist: If the car's odometer only shows two decimal places, what distance will it display? (Do not round until the final step).
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Challenge Problem 3:
A gourmet coffee shop sells premium beans for $18.65 per kilogram. A customer places a large order for a local event and buys 24.50 kilograms.
The Goal: Calculate the total cost of the beans.
The Twist: The shop offers a "Decimal Discount." If the product of your multiplication has a 5 in the thousandths place or smaller, the customer gets $5.00 off the total. Does this customer qualify for the discount?
Challenge Problem 1:
The Mystery of the Missing Digits
A famous mathematician was working on a long division problem, but a few drops of ink fell on the page, covering up some of the numbers!
Your Mission: Use your long division skills to figure out what the missing numbers (marked with an X) are.
4X8 ➗ 1X
Here are your clues:
The divisor is a 2-digit number starting with 1 (e.g., 10 through 19).
The quotient (the answer on top) is exactly 32.
There is no remainder.
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Challenge Problem 2:
The local bakery has 534 cookies.
They put them into boxes that hold 12 cookies each.
The baker says they need 44 boxes to fit all the cookies.
Is the baker right?
If not, how many cookies will be left over, and how many boxes do they actually need to make sure every cookie is in a box?