Family of Problems is dedicated to building a warehouse of creative, interactive, flexible problems for innovative math teachers. All the problems within this site have been successfully used by experienced math teachers in the classroom. Problems are grouped in threes based upon related content and learning concepts.
Each problem is documented with an Anticipatory Set, Lesson Plan, and Black Line Master.
- An apple A Day
An Apple a Day
Grade: 3-8
Have you ever heard someone say, “An apple a day keeps the doctor away”? At a
local grocery store, you can buy a bag of 8 apples for $5.00. If everyone in your
family ate one apple every day, how much money would your family spend in one
year on apples? - Bicycles and Tricycles
Bicycles and Tricycles
Grade: 3-12
Jenny’s Bicycle Shop sells only bicycles and tricycles. They have a total of 24 seats and 61 wheels in the shop.
How many bicycles and how many tricycles are in the shop?
- Birthday Balloon Bash
Birthday Balloon Bash
Grade: 3-8
Mr. Al Gebra’s class wanted to surprise him on his birthday by filling his classroom
with inflated balloons. How many balloons did they need? - Bubble Gum
Bubble Gum
Grade: 3-8
Have you ever wondered why gum loses its sweetness so quickly? Does it seem like the gum gets smaller after you chew it? Well, sugar contributes to gum’s flavor. During chewing, the sugar is lost, which makes the gum get smaller as it loses sweetness.
- Bucket of Trouble
Bucket of Trouble
Grade: 3-8
The ceiling of Betty’s kitchen has a leak. She hears 10 drips of water in 15 seconds. She puts a bucket under the leak and frantically calls the plumber. The plumber can’t be there for 5 hours. Will Betty need to empty the bucket? How much water will she waste?
- Bundle of Books
Bundle of Books
Grade: 3-5
Nate’s grandma bought him 4 new books to read. She spent $38, and each book cost the same amount of money. Nate wants to return one of the books to the store. How much money will he get back?
Nate is a fast reader! He can read 4 books in one hour. If he has 38 books to read, how many hours will it take him to read them all?
- Buying MP3s
Buying MP3s
Grade: 3-12
You have decided to use your allowance to buy an mp3 purchase plan. Your friend Alex is a member of i sound and pays $1 for each download. Another one of your friends, Taylor, belongs to Rhaps and pays $13 a month for an unlimited number of downloads. A third friend, Chris, belongs to e-musical and pays a $4 monthly membership fee and $0.40 a month per download. Each friend is trying to convince you to join their membership plan. Under what circumstances would you choose each of these plans and why?
- Carlos’ Cell Phone
Carlos’ Cell Phone
Grade: 3-12
Carlos is thinking of changing cell phone plans so he is comparing several different plans.
- Plan 1) Pay as you go plan $0.99
- Plan 2) Per minute $30 monthly fee plus $0.45
- Plan 3) Per minute $40 monthly fee plus $0.35
- Plan 4) Per minute $60 monthly fee plus $0.20
- Plan 5) Per minute $100 monthly fee for unlimited minutes
What will Carlos need to consider to make his decision? How can Carlos figure out which plan is best for him?
- Eucalyptus
Eucalyptus
Grade: 3-8
99% of the trees in our neighborhood are eucalyptus trees. The town planning commission wants to get rid of some of these trees because they spread too quickly. However, the people in my neighborhood like the trees. The commission argues that their new eucalyptus tree removal plan will cut down so few eucalyptus trees that 98% of the trees in our neighborhood will be eucalyptus trees. If the plan only involves removing eucalyptus trees, what percent of the existing tress in my neighborhood would the plan remove?
- Fun at the Fair
Fun at the Fair
Grade: 3-5
Mrs. Hoffmann brings her 6 children to the fair. She buys a big box of 45 mini- donuts for the children to share equally. How many mini-donuts will each child get?
The children are ready to go on the fair rides! Mrs. Hoffmann buys a bag of 45 ride tokens for the children to share equally. If each ride costs one token, how many rides can each child enjoy?
- Ichiro Problem
Ichiro Problem
Grade: 3-12
It has been one month since Ichiro’s mother has entered the hospital. Ichiro decided to pray with his younger brother at a local temple every morning so that she will get better soon. There are 18 ten-yen coins in Ichiro’s wallet and just 22 five-yen coins in the younger brother’s wallet. They decided to take one coin from each wallet every day, put them in the offertory box, and continue to pray until either wallet becomes empty. One day when they were done with their prayer, they looked into each other’s wallets. The amount of money in the younger brother’s wallet was greater than Ichiro’s amount of money. When this happened, how many days had it been since they started their prayers?
- Magic Bag
Magic Bag
Grade: 3-8
You’re cleaning out your closet and find a velvet bag in the corner. When you pick up the bag it feels heavy, and you find 24 pennies inside it. Before you go to sleep, you pull out the pennies and count them up again.
Now there are 27 pennies in the bag! When you check the bag at the end of the second day, you count 30 pennies.
At the end of Day 3, you count 33 pennies.
How many pennies will be in the bag after 10 days? 25 days? 100 days? Can you come up with a rule to find the number of pennies in the bag on any day?
- Magic Box
Magic Box
Grade: 3-8
Your Grandma gives you a wooden box for your birthday. When you unwrapped the gift and opened the box, you were expecting some cash inside but found the box was empty.
You felt bad for not appreciating the box, and decided you could use it to store important things. Just before you go to bed, you open the box to put a photo inside, and see 2 pennies.
When you check the box at the end of the second day, you count 4 pennies.
At the end of Day 3, you count 8 pennies.
How many pennies will be in the box after 10 days? 15 days? 20 days? Can you come up with a rule to find the number of pennies in the box on any day?
- Magic Vase
Magic Vase
Grade: 3-8
You’re planting in the garden and uncover a vase buried in the soil. After cleaning the vase, you place it on your bedside table.
You notice something shiny in the vase before you go to sleep. You pull out a handful of pennies and count them up. There are 6 pennies in the vase.
When you check the vase at the end of the second day, you count 12 pennies.
At the end of Day 3, you count 18 pennies.
How many pennies will be in the vase after 10 days? 25 days? 100 days? Can you come up with a rule to find the number of pennies in the vase on any day?
- Million Dollar Question
Million Dollar Question
Grade: 3-8
Your friend has sent you a text saying you can become a millionaire! He tells you that he won $2 million in a contest. The money was sent to him in two suitcases, each containing $1 million in one-dollar bills. He will give you one suitcase of money if you can go to the airport and pick up both suitcases. Is it possible that you could get the suitcases at the airport and get them home?
- Party Time
Party Time
Grade: 3-5
Andrew is planning a surprise birthday party for his dad. Sixty people will be at the party, and each table will seat 8 people. How many tables does Andrew need?
Andrew has 60 balloons to use for decorating the tables. If he wants every table to look exactly the same, how many balloons will be at each table?
- Solar Power City
Solar Power City
Grade: 3-8
Solar panels collect energy from the sun so people can use that energy to power things in their homes.
Is it possible to power an entire city by using only solar energy?
New York City uses about 164,380 kilowatt hours of electricity each day. Usually, it takes 25 solar panels to produce about 5 kilowatt hours of electricity. How many solar panels would it take to power all of New York City for one day?
- Spiders and Ants
Spiders And Ants
Grade: 3-8
A spider’s web contains a certain number of spiders, which have eight legs, and their six-legged meal: ants. There are 64 legs in all, and four times as many ants than spiders. How many of each bug is there?
- Touchdowns & Field Goals
Touchdowns & Field Goals
Grade:3-8
Emma plays in a flag football league where the only two ways to score are via touchdowns, which are worth 7 points, and field goals, which are worth 3 points. In yesterday’s game, her team scored eight times. How many points did her team score?
Find all possible solutions.
- Watermelon
Watermelon
Grade: 3-8
A giant watermelon weighed 100 pounds and was 99 percent water. While sitting in the sun, some of the water evaporated. Now, the watermelon is only 98 percent water. How much does the watermelon weigh now?
- World’s Largest Cookie
World’s Largest Cookie
Grade: 3-8
The world’s largest chocolate chip cookie was created using 40,000 pounds of cookie dough! (The recipe is listed below.)
A school wants to make a smaller version of this cookie to feed all 800 students in their school. They decide that each pound of dough will feed 4 students.
How many pounds of chocolate chips will they need?