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Problem of the Week


Welcome to our Problem of the Week page. These free problems we're created by Math Crush or discovered somewhere in the math world. Each page includes the question and a solution. We enjoy these types of open questions and answers because they allow students to use other prior knowledge to solve. Use them as you want, but our recommendation is to put a problem up once a week and call it the Problem of the Week. Students can solve it on their own time for extra credit or a treat.

Scroll down to see all choices.

Joe's Garden

1. Joe wants to separate his garden into 12 congruent individual plots with rope as shown in the figure. How much rope will Joe need?

2. If Joe only divides the garden into 6 congruent rectangles, how much rope will he not need (save)?

3. If the rope cost $1 per foot, how much money will Joe save if he separates the garden into 6 sections?

Key concept: Perimeter.

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Preview of Joe's Garden

The Crooked Cop

Curly, Bart, and Henry are three innocent men being held by a crooked cop. The cop tells each of the men that he has five hats, two black and three white. He positions the three men in line so that Henry can see both Bart and Curly, Bart can only see Curly, and Curly cannot see anyone. He places one hat on each person and tells them that if one of them guesses the correct color of their hat, they will all be freed. Within a minute, Curly shouts out the color of his hat and they are all set free!

What was the color of Curly's hat and how did he know?

Key concept: Probability.

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Preview of The Crooked Cop

Dora's Mix Up

Dora was studying her family tree and found out that her grandparents are mixed with French and Japanese. Her grandmother on her father's side is 1/4 French and 3/4 Japanese, and the grandfather is 3/4 French and 1/4 Japanese. Dora's grandmother on her mother's side is 1/8 French and 7/8 Japanese, and the grandfather is 3/8 French and 5/8 Japanese.

What is Dora's exact percentage of each ethnicity (French and Japanese)?

Key concept: Average and Percents.

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Preview of Dora's Mix Up

Jenny Saves the Day

Jenny walked up her driveway to the sound of grinding and roaring coming from her backyard. She opened the gate and saw her father cutting into the old dead willow tree. Her father saw her and shut off the chainsaw. Jenny looked at her father and then at the tree. "Dad, how do you know the tree won't hit the house when it falls?"
Her dad smiled and said, "Well, the shadow is not touching the house, so I think that means the tree won't hit the house either."
Jenny was about 4 feet tall and her shadow was about 2 and 1/2 feet long. Jenny walked over to the tree. "Dad, let me check something out."
She measured the tree's shadow, which was approximately 60 feet long. She already knew the tree was 80 feet from the house. Before her dad could start the chainsaw again, Jenny yelled, "Mom, dad is about to crush the house!"

1. How did Jenny know that her father was about to make a big mistake?

2. How much of the tree would have hit the house?

Key concept: Ratios and Proportions.

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Mathman is flying 720 miles per hour (mph) towards a storm. He is 8 miles away from it when he sees a bolt of lightning. Assuming that sound takes 5 seconds to travel one mile, how long will it take him to hear the thunder from the lightning bolt?

Key concept: Distance and Time.

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A Really Big Secret

Blister goes to a really, really big school. On Monday during first period, she told three friends a secret. During second period, each of her three friends told another three students and each one of those students told another three people during third period. Assuming there are six periods a day, each person only tells three people, and this pattern continues, how many students will know about the secret by the end of the week?

Key concept: Exponential Growth.

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The Widgets

Roxanne needed to purchase a specific number of widgets to complete a job for a customer. She visited two hardware stores. The first one sold widgets for $3.00 each. Roxanne realized that the number she needed would cost $9.00 more than she had.
She went to the second store which sold the widgets for $2.50 each. Roxanne purchased the number of widgets she needed and left the store with $3.00 in her pocket.

How many widgets did she buy?

How much money did Roxanne have before purchasing the widgets?

Key concept: Solving Variables.

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Beep Beep

A cargo train made up of an engine car and 5 cargo cars is being followed by a high speed passenger train and needs to let it pass. They both arrive at a station that has a side track that can only hold 3 cars.

How does the cargo train let the passenger train pass?

Key concept: Critical Thinking and Problem Solving.

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Shorten Version of Question:
The Sticks challenged the Line Segments to a snowball fight. They each built a fort out of snow to defend. The Sticks decided to be defensive and placed all 40 teammates around their fort. They were arranged in the shape of a square and had 11 guards defending each side of the fort. The Line Segments decided to be a little more offensive and everyone just attacked.
During the first four assaults by the Line Segments, the Sticks lost 4 soldiers each time and sustained heavy damage to their fort, and after the fifth assault they only had 22 people left. Even though they lost soldiers, they always had 11 people defending each side of the fort. How was this possible?

Key concept: Algebraic Equations.

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Question: Four injured military men are stuck in enemy territory on one side of a bridge and have issued an airstrike which will destroy everything in the area in 17 minutes. They need to cross the bridge to safety, but it is heavily mined and they only have one mine detector. The mines are constantly moving which makes them impossible to mark. This means the mine detector needs to be taken back and forth so no one blows up. Of course it cannot be thrown either. In addition, the bridge is old and can only hold two people at a time. Each man has different injuries and can walk at different speeds. When a pair crosses they must walk together at the rate of the slower man. Clark has only scratches and bruises and will take one minute to cross. Hershel lost an arm and is very tired and will take two minute to cross. Tank lost a foot and will take five minutes to cross. Skippy has many injuries and will take ten minutes to cross.
   How can all four men make it across before the air strike comes?

Key concept: Critical Thinking.

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Table Art

Every week certain classes come together to do an art project with Miss Delly. Today Mrs. Ling and Mr. Hollerís class are working together. Before the students arrived, Miss Delly realized she does not have enough art supplies for each student. Each classroom table can sit 6 students together. She has enough crayons for each student, but every two students will have to share a box of color pencils, and every three students will have to share a paint set.

Miss Delly knows she needs 132 art supplies total, but how many tables will she need?

Key concept: Algebra.

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Cakes and More Cakes

Griddle is planning to surprise her grandmother for her birthday with some cakes. Her grandmotherís home is located in the land of Trollypolly and she must cross ten bridges to get to her house. All the bridge guards love cake and require a payment before she can cross each bridge. In order to cross a bridge she has to give the guard half of the cakes she is carrying but since she is so kind and sweet they each give one cake back.

How many cakes will she have to make to be able to have 2 cakes left when she arrives at her Grandmotherís house?

Key concept: Critical Thinking and Patterns.

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Preview of Cakes and More Cales - Critical Thinking and Patterns

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Note: Math Crush is supplying these free Problems of the Week as a courtesy to the math community. Please enjoy and let us know if they work in your classroom.