Fostering Estimation Strategies Using The Best Mouse Cookie by Laura Numeroff
Many students are familiar with If I Gave a Mouse a Cookie by Laura Numeroff. This is a great book to teach cause and effect. However, her sequel The Best Mouse Cookie is even better as it can be used as a great tool to encourage estimation. Specifically, we will use the book to launch a Fermi Problem.
Note: This lesson spans 1st grade through Algebra 1. Younger grades can use it as a cross-curricular lesson for math and ELA. You can use the book with older students as an attention grabber to launch a math lesson. When I was teaching even my high schoolers loved when we read picture books in math class.
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Fermi Problems
What is a Fermi Problem?
Have you ever heard of a Fermi Problem? A Fermi Problem is a problem that requires students to estimate and make assumptions for a nearly impossible problem—one that you can never know the exact answer to. Or perhaps a problem where the exact answer is difficult to practically find. For example, how many chair legs are in your school? Or how many blades of grass are in your yard?
Note: This does not necessarily mean that students have to do mental math. Although they could if you require it; it depends on your math goals. If students are dealing with big numbers, you could consider letting them use calculators as long as it aligns with your math goal for the day.
Who is Fermi?
Fermi problems are based on estimation strategies used by Enrico Fermi, a Nobel Prize winning physicist. He worked on developing nuclear weapons for the United States. He was able to estimate the strength of an atomic bomb by dropping pieces of paper.
Why Should You Use Fermi Problems?
Fermi problems are interesting and engaging. They require students to make reasonable assumptions and accurate estimations. They promote problem solving, critical thinking, decision making, numeracy, proper use of units and of course estimation. Students may not get an exact answer, but they should get a reasonable answer based on their assumptions.
Fermi Problems and Mathematical Modeling
Fermi problems are a great introduction to mathematical modeling which is addressed in the Math Practice Standard: SMP.4 Model with Mathematics. They introduce several steps of the modeling process such as making assumptions, but they are short and manageable, so they can be used for a class period or part of a class period unlike more complex modeling problems which may take days or weeks to complete.
What Grade Levels Should Use Fermi Problems?
Fermi problems can be used across grade levels. However, the type of assumptions, the accuracy of estimation, and level of precision would vary based on grade level.
Resources on Fermi Problems
Here are some resources on Fermi Problems:
- An excellent collection of Fermi problems for your class – Innovative Teaching Ideas
- Fermi Problems: Estimation
- Fermi Problem: Fermi Problems: Breaking Down Complex Questions – FasterCapital
- fermi_questions_handouts_and_lesson_plan.pdf (Great resource that breaks Fermi problems down based on grade level)
- fermi problems oapt 2018.pptx is a Powerpoint that you could use in class or to coach teachers.
The Book: The Best Mouse Cookie by Laura Numeroff
Pre-Reading
Making Connections: Ask students if they read If I Gave a Mouse a Cookie by Laura Numeroff. Ask them what they liked and didn’t like about the book. (It may be helpful to read this to the class as a review.)
Making Predictions: Explain to students that The Best Mouse Cookie is the sequel to that book. Have students make predictions about what they think it will be about.
Reading
- Spread 2: The text says that “Mouse has everything he needs to make cookies.” Based on the picture what do you think he needs?
- Spreads 3-4: Inference: Do you think mouse is good at making cookies? Why or why not? Use the pictures to help you justify your conclusion.
- Spread 5: Have you ever heard a cookie plop? Why do you think the author choose to the word “plop” to the story. (Depending on the grade level, discuss onomatopoeia.)
- Spreads 5-6: Making Connections: Who is tired in this book? Who is tired in the original If You Give a Mouse a Cookie? What makes the characters tired?
- Spread 6: Making Predictions: What do you think will happen next? Are there any clues in the pictures?
- Spread 7: Making Inference/Drawing Conclusions: What happened?
- Spread 8: Character Development: What do you learn about Mouse when the book states “Oh well, Mouse doesn’t mind starting over.”
- Spread 9: Do you agree or disagree with Mouse: “There is no such thing as too many cookies…” How many cookies do you think mouse ate? Have students write their guesses on a piece of paper and collect student guesses.
- Spread 11: What do you learn about mouse on this page? What do you learn about the boy from this book? What kind of relationship do you think the boy and mouse had? Who would you like to share cookies with?
- Spread 12: What happened to Mouse? What can you learn from Mouse?
Post-Reading
This is where the math comes in! Flip back to spread 9 where it shows Mouse with his pile of cookies.
Step 1: Understanding the Problem and Initial Estimation
Make sure that students understand the question being asked. Ask student the following questions to the whole class:
- How many cookies do you think Mouse made? Before we begin what are some guesses that are too high? What are some guessed that are too low?
Record those answers on the board. Then explain that a correct answer should be between those two numbers. Depending on the age of the students, you could write that as a compound equality on the board.
Note: For 1st and 2nd graders you could ask them how high the pile of cookies is to hit a measurement standard?
Allow students in middle and upper grades to take ownership of their learning. Have them choose the questions to explore. If you want students to practice fraction and proportions, you can ask questions such as how much flour did mouse use to make his cookies?
Step 2: Making Assumptions
Explain to students what an assumption is. A Mathematical Assumption is something that the problem solver accepts to be true (without actually knowing for sure). Making a Mathematical Assumption allows people to solve the problem. They can also help simplify problems to make them more manageable.
For example, in The Best Mouse Cookie an assumption could be that Mouse only ate the one cookie that we see in the picture or that he only burned the 8 cookies we see him throwing out the window. However, that may not actually be the case as the picture may not show all the information.
When solving Fermi problems, it’s important that students actually write down their assumptions because the assumptions impact the answer to the problem. Having them in written form allows you as a teacher to check reasonableness of their answers. Assumptions also allow for students to make decisions in the problem-solving process.
Step 3: Finding a Solution
Grades 1-2
- Students need to understand that there are cookies behind what can be seen in the picture. Break down the problem into a simpler problem. Buy a package of cookies and arrange them in a pile. Ask students how many cookies are in your pile. Let them discover that there are cookies they can’t see from the front.
- Ask students if your pile of cookies is smaller, bigger, or the same size as Mouse’s cookies and then have them make their estimates from there.
- Instead of asking “How many cookies?”, you may ask “How tall is Mouse’s pile of cookies?” You could have them estimate using either standard or nonstandard (e.g., paperclips, sticky notes etc.) units of measure.
Grades 3-5
Have students model the picture of cookies using Legos, number cubes, integer chips, or play money. Encourage them to build their own pile of cookies. Show students that they can break down the problem into a simpler problem. Illustrate the concept by bringing in a package of cookies and make a small pile of cookies. Ask students how they can use that information to help them solve the problem.
Grades 6-8 and Algebra 1
Ask students what questions they want to explore. You might start with the number of cookies Mouse made and then explore how much flour or sugar it took to make them thereby emphasizing proportional reasoning. Students may even wonder how much it would cost to make the cookies.
Step 4: Determining Reasonableness of the Results
Revisit your original inequality. Are your results reasonable? This would be a good time to do peer feedback. Have students decide if a neighboring group’s results are reasonable and then write a paragraph explaining why or why not.
This would also be a good time to have discussion of the importance of units.
Step 6: Refining the Results If Needed
If students results are not reasonable, have them go back and refine their results.
Grading
I would use a rubric to grade the problem with an emphasis on process and problem solving. Here is one example of a rubric that you could use in your classroom:
You could also modify a rubric based on the modeling math practice standard:
Conclusion
Pull out the carpet squares and read a book! Using picture books in math class makes math fun and engaging. Fermi problems and other modeling problems are a great way to improve numeracy and problem solving in a way that is an enticing to students. These types of problems are also accessible to most students as there are multiple entry points.
Visit my Math Lessons webpage to download the lesson in MS Word or PDF.
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Another very insightful lesson from Annie Cannelongo. She makes learning math fun and interesting. Plus her ideas work on numerous levels at the same time. Keep up the good work Annie.
I’m a retired teacher now, but if I were still teaching first grade, I would definitely have used this lesson in my classroom! It’s so engaging and another wonderful example of how we use math in our everyday lives. I’m a Nana, so I can relate to using these with my grandchildren who span 3 to 12 years old. Well done! 👍
Thank you! 🙂