Open-Ended Math Activities

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Open-ended math problems require students to think critically and come up with creative solutions. Students must come up with their own methods for solving the problem, follow through, and then determine whether the results are reasonable. Students must apply math concepts, analyze data and evaluate their conclusions. Open-ended means the problem has more than one possible answer, as opposed to closed-ended questions that have only one correct answer.

Card Corralling (Grades 3 to 5, Algebra)

  • Number patterns and sorting are the basis for this activity. Each pair of students needs a deck of playing cards. Students work cooperatively to generate as many methods for sorting their decks as possible. Groups create lists of ways to sort the cards. As a follow-up activity, students generate patterns with the cards. Each group must construct five different patterns and present them to the class.

Luncheon Planning (Grades 6 to 8, Number and Operations)

  • Creative thinking and event planning are combined in this middle school activity. Students are challenged to plan a luncheon for the entire class. They work in small groups of three to four to complete the luncheon. Students must plan a menu, figure the cost per student, project the amount of food needed and create a supply list. Each plan must include decorations, party supplies and invitations. This activity is a great precursor to an actual luncheon that students can plan, prepare and serve to their classmates.

Slice of Life (Grades 3 to 8, Data Analysis)

  • In this activity, students analyze how they spend their time. Each student creates a list of his daily activities and how much time he spends on each. Students then construct a pie chart to represent how much of their time is spent on each activity. When their pies are complete, the students form groups of four and discuss how their “life pies” compare to those of others in the group. Each group creates a bar graph to show the differences between their personal data.

Attribute Sort (K-2, Data Analysis and Probability)

  • Young children use their problem solving abilities to classify objects in the classroom. Students work with partners to list as many things as possible that can be sorted by color, shape and size. Students start with objects in the room, and then list things that are not present. Teachers give each pair of students a bag of buttons of various shapes, sizes and colors. Each group has cups to use for sorting the buttons. The object is to see how many different ways the buttons can be sorted. As a follow-up activity, students can form patterns with their buttons and explain the patterns to the rest of the class.

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