Summer can be a time for students and teachers alike to take a break from the intense lockstep schedule and pressures of the school year and take a breath. We might be outdoors more often, engage in sports or the arts, and generally do things we don’t have time for during the school year. It can also be a time to find joy in the life of the mind, without the usual structures, stresses, and constraints that come with days divided into time slots, subjects, and pacing charts. There may be time to discover what thoughts and theories one is curious about, what one likes to learn about, and what ideas are fun to play with. When children play with math, without expectations of demonstrating achievement or competence, they too may find the fun and the beauty in math, as well as a sense of empowerment in doing so. Developing a positive disposition toward math is likely to lead to learning, both in the summer and in the school year to come.

That said, there are particular skills and concepts that we would like students to keep fresh over the summer. Equally, if not more important, we want students to enhance their use of the mathematical practices—to reason about ideas, to make sense of mathematical situations, to create and test conjectures, and to persevere when answers don’t come easily. We want children to see the utility of the math they know in their real world, and hopefully come to see the beauty of the ideas themselves.

Whether living in cities, suburbs, or rural areas, children’s worlds are filled with opportunities to engage in mathematical processes and practices in fun, practical, and challenging ways. Might some of the examples below be “summer math” for your students?

Games—As Matt McLeod discusses in his blog post, Do you Want to Play a Game?, many games are designed to reinforce specific mathematical ideas. The links and resources he offers in that blog post are plentiful. However, there is no need to limit children to games that are designed with specific compentencies in mind. Many commercial games provide a way to practice mathematics skills and thinking processes like counting, deductive reasoning, and one-to-one correspondence. As elementary mathematics researcher Dr. Janelle McFeetors discusses in her video, popular commercial games offer engaging and accessible opportunities to immerse oneself in valuable mathematics. What games do you remember from your childhood that were fun and also made you a more proficient mathematician?

Sports—Math is deeply embedded in all sports. Baseball has batting averages, team rankings, RBIs, and home run statistics. Other sports have scores, time, and distances embedded in them. Children’s own games, perhaps made up in the street, the park, or the yard, also engage them in practical mathematics. Plotting out an obstacle course or a race, keeping score and keeping time, all provide opportunities to think mathematically. There’s lots to talk about and understand, whether you’re playing or watching any kind of game. What math might the children in your grade be doing as they play their favorite sport?

Family Life—There is math in the daily activities of running a household. Feeding a family demands mathematical thinking and processes: What items, and how many of each, go onto a grocery list? How do we determine which brand and package size is a better deal? How can we predict which checkout line will be fastest? How do we count money and check change? Older children may earn money by babysitting or working after school, and so have context for managing money or contributing to family finances. Is a lemonade stand a possibility in your students’ lives? What mathematical opportunities may arise in your students’ families lives?

Cooking and Baking—Many children love to cook and bake. Using kid-friendly recipes offers lots of opportunities to measure, keep track of time, divide food into portions, and decide on utensils and tools. What size pot will be needed? Which container is just the right size for the leftovers? What if a recipe is for two people, but four will be eating? When there is a limited amount of something, how do we figure out how much everyone gets? Should all shares be equal, or should older children get more?

Books—Many stories have mathematical situations in them, with opportunities to think about the problems that the characters encounter. Some stories are explicitly about math, and others have the math embedded in tales about children, fantasy tales, and books about the world in general. There are many math-related stories to choose from. What could you suggest your students read over the summer?

Gardening—Gardening offers multiple opportunities for children to engage in mathematical thinking. Whether in a pot indoors or a plot of land outside, growing plants requires us to think about how much area, water, and food a plant needs to grow. Children can measure the height of their plants over time and plot the time it takes to reach maturity. What might the children in your classes like to grow next year?

Summer offers myriad opportunities to engage children in mathematics in ways that are engaging, challenging, motivating and, in many cases, part of day-to-day life. Developing a positive disposition toward mathematical activities through routine experiences can have a productive effect on more formal learning in school. How can you support families to engage in activities that help children deepen and expand their mathematical thinking in age-appropriate and enjoyable ways?