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. More pages coming soon.

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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The Walking Woman

Question:
Mrs. Jones takes the same train home everyday, which arrives at her home station at 5:30 PM. At this time, her chauffer always just arrives, picks her up, and takes her straight home. Two weeks ago, Mrs. Jones decided to go home early and arrived at her home station at 4:30 PM. Instead of waiting for her chauffeur, she started to walk home. On the way home she met the chauffeur who took her the rest of the way home. They arrived 27 minutes earlier than usual. Last Friday, Mrs. Jones took another earlier train and arrived at her home station at 4:50 PM. Again instead of waiting for her chauffeur, she started walking home. On her way she was picked up by the chauffeur and taken home. If the walking and driving speed were constant, how many minutes earlier than usual did she arrive home this time?

Key concept: ratios and proportions.

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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.