### Mathematics Outside the Math Classroom

By Matt Mcleod

While playing Monopoly with my 5-year-old, I gave him a $100 bill to pay $12 in rent. He wasn’t exactly happy, but he figured out that he owed me $88 and then figured out how to make that amount with the available bills. Several years later, while walking through the forest, my 7-year-old daughter looked down at her feet and said, “I wonder how many steps I’ve taken in my life.” After a few silent shouts of joy upon hearing her curiosity, I replied, “What a great question. How would you figure that out?” Fast forward to a few days ago, my 10-year-old son was grocery shopping with me. “Can we buy this bag of pistachios?” “We don’t need pistachios,” was my reply. “Ple-e-e-ease?” accompanied by puppy dog eyes. “Okay, but get the small bag.” “The big bag is a better buy,” he replied, “because, look, this one is 8 ounces for $6, but the bigger one is twice as big for only $9, which is less than twice the price.” We went home with a big bag of pistachios.

Lots of people will say they are not very good at doing math. Yet we all engage in math in almost every activity we do. There are some (potentially) more obvious examples that involve numbers, such as calculating “better” prices, measuring quantities for a recipe, dosing medicine, or telling time. And these are just a few of the things we do at home. Careers that are labeled “STEM” typically require a great deal of math. In actuality, there are things we do in any job that require mathematics. Building or reading a schedule; comparing sizes or quantities of items; reading a map; giving or getting directions; making or following a set of sequenced instructions; sizing things to fit in a particular space or stacking lighter items on top of heavier (instead of vice-versa) are a few examples.

In addition to the home- and work-based explicit uses of math, we engage in a great deal of mathematical thinking that we might not recognize as mathematics. Throwing a baseball or hitting a tennis ball requires geometry (with an underpinning of numeric calculations that most of us don’t do). We find ways to estimate sizes, distances, and quantities without ever actually counting or measuring. Driving a car and deciding how hard to hit the brakes, how far to turn the steering wheel, or whether there is enough gas in the tank to take you where you need to go. Math is literally everywhere and being done by everyone.

So, if math and mathematical thinking are so predominant, why do so many people claim they aren’t good at it? The catch is to realize when we are doing mathematics and perhaps, rethink what we are calling “doing math.” For many, math consists of doing calculations such as addition, multiplication, and “fractions” quickly with or without paper and pencil. We also (often) believe that calculating an exact answer is the only thing that counts as mathematics, but estimating is just as mathematical. Math should not be limited to the problems presented on a worksheet from the school’s curricular materials.

So, how do we expand our ideas of what “doing mathematics” means? Let’s start by engaging in conversations and activities with students that require all kinds of natural, mathematical thinking. Some ideas for classroom teachers and parents and caregivers are below.

**Ideas for Teachers**

- Open up your students’ recognition of the math they do “without thinking.” Our colleague Karen Rothschild shares examples of everyday activities that naturally leverage mathematical skills and concepts that go well beyond the summer.
- Talk to your students about math that you did over the summer, last night, or over the weekend.
- Ask your students where they have used numbers or what they have noticed or think about shapes. Ask them to share if they built or cooked something or where they used math in a game they played.
- Give them space to share a problem they solved over the summer, last night, or over the weekend and tell how it involved mathematics. This could be through sharing with you, discussing with the class, or even posting on a “Math is Everywhere” wall.
- Present them with a mathematical problem you are genuinely struggling with. Ask them what they would do.
- Play games with them in class. A deck of cards and a set of dice go a long way and are very adaptable to particular levels of complexity and ages.
- Take them for a community walk or a school walk and challenge them to name all the instances of mathematics they see. You could even, in advance, brainstorm possible observations one might be able to make. Encourage students to consider things such as shapes, numbers, calculations, heights, distances, angles, angles at intersections, timing of stop lights, numbers of doors and windows, sale signs, or price advertisements (like a sign that offers something for 99¢).
- Do mental math as you stand in line. For example, give them a number and ask them to name it a different way (24 could be 20+4 or 4*6 or 1*2*3*4 or 48/2 or 100-76 or anything else). Go beyond the flashcard-type facts of just memorization and ask them to think, predict, and try.
- Show the students how
*you*start on a problem you don’t yet know how to do. For example, what would you do if asked how many steps you’ve taken in your life? - Organize a Family Math Night for your class, grade, or school using the guides, handouts, and activity ideas in the Institute of Education Sciences’ Community Math Night Toolkit.

**Ideas for Parents and Caregivers**

- Identify the math in all the things you do and explicitly engage your children when you realize it. This could be during cooking; scheduling your day; counting things such as your steps; sharing food (or other things) equally; estimating the number of books in your house or the number of people at an event; highlighting numbers or calculations done while you are playing games (rolling dice; moving your game piece a number of spaces; keeping score; matching numbers on cards). The list is endless.
- Start young. It is never too early to count things as you are playing or walking with your children, or to read books about numbers and shapes. Even if you are the one doing the counting or naming the shapes, they will hear it and learn. It’s also never too late to start.
- Alternate reading bedtime stories with reading and doing or discussing math. For example, ask them all the ways they can combine numbers to make 20 (or some other number).
- Play games. Almost every game involves mathematics somehow, so, again, find the math and make it explicit with your children. There also are games that are explicitly designed to practice specific number skills and arithmetic operations. As we suggested to teachers, a deck of cards or a set of dice can go a long way towards developing a range of mathematical skills.
- Ask questions and discuss mathematics. Ask your children to identify the math in the games you play and in their daily lives. Ask them how they would calculate the number of steps they’ve taken in their life, and share what you would do. Ask them to name all the ways they can think of to make 24 (or any number).
- Collaborate on problem solving. Rather than say “I’ve never been good at math,” say things like, “I don’t know how to do this, but we can figure it out.” (Then ask them what they would do.)
- Be patient. Let your child do the mathematical thinking. Avoid stepping in too soon.

These short lists of ideas could be used to help students realize how prominent mathematics is in the world around us, and not limited to the handouts they often have to complete in math class.

Math for All is a professional development program that brings general and special education teachers together to enhance their skills in

planning and adapting mathematics lessons to ensure that all students achieve high-quality learning outcomes in mathematics.