Mathematics (NYS P-12 Common Core)
Elementary, 1st Grade
Learning Context/ Introduction
First-grade students are asked to work with a partner to solve a problem about buying pumpkins. The problem could be made easier or more difficult by changing the total amount of money the pumpkins cost, or by asking each pair or group of students to find as many solutions as possible.
- At least 4 pumpkins—1 large, 1 medium, and 2 small (if real pumpkins are not available, you could use paper cut-outs of pumpkins)
- A variety of mathematic manipulatives and collections for the students to use to “stand for” the pumpkins as they work out their solution(s)
- Paper (white & orange), pencils, crayons/markers
- Large chart paper to record the brainstorming and the multiple solutions during the class discussion
- Present the following problem to the students: I went to the pumpkin farm with $5.00 to spend. Big pumpkins were $2.00. Medium pumpkins were $1.00. Small pumpkins were 2 for $1.00. I spent all of my money. What kind of pumpkins could I buy?
- Place the pumpkins on a table with a sign showing the prices of each kind of pumpkin. Refer to them as you describe the problem.
- Explain that students may use any materials in the room, or draw, to help them solve this problem. Brainstorm a list of mathematic manipulatives that they use to stand for the pumpkins as they work on solving this problem.
- After students have solved the problem, they should write and/or draw to explain how they solved it. Give them an opportunity to share their solution(s) with the class.
- The students then work in pairs or small groups. The teacher should circulate throughout the room to observe them and to conference where needed.
- As students finish, they should share their solutions. The teacher should record the various solutions on chart paper so that they can see the multiple solutions and check to see if their solution has been mentioned.
- Observe and record student participation in class discussion by audio-taping and making written notes during and/or after the lesson regarding:
- ability to explain reasoning
- willingness to take risks
- level of involvement and interest in the assignment
- inventiveness in thinking about how to solve the problem.
- Observe and record information about the student’s work with a partner by taking brief notes during the work session and talking to groups as they work through the problems regarding:
- grasp of numerical relationships
- ability to represent numerical relationships with words and symbols
- process of working with others
- choice of materials and how they were used to solve the problem
- level of involvement in the process.
- Review the written work done by the students, making notes on the information gained and using the process of analyzing the work to plan the next steps in the instructional process, in terms of individual students and of the class as a whole.
Merri Jones Earl
John Harshaw Primary School
Chenango Forks Central School District
Binghamton, NY 13901
Earl, Merri Jones "Harvest Halloween." Mathematics Resource Guide with Core Curriculum. New York State Education Department, 175-176.
Adapted from: Caren, Ann, Beverly J. Martin School, Ithaca City Schools.
- To solve a "real" problem that is connected to
students’ interests (and is integrated with other
curriculum areas, i.e., science, social studies,
- To relate mathematics to things students do outside
of school (with their families) and thus to see
that mathematics is present and useful (both
inside and outside the classroom).
- To see that a problem can have more than one
- To develop students’ ability to communicate
mathematically through writing and/or drawing
and to share their thinking (with others) through
- To foster curiosity about mathematics and to
make connections between mathematics and other