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.

Joe's Garden

Question:
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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The Crooked Cop

Question:
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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Dora's Mix Up

Question:
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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Jenny Saves the Day

Question:
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

Question:
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

Question:
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

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