Number Operations

By Stacey Carter, July 5, 2009

Grade Level

  • Elementary School


  • Other

Subject Area

  • Mathematics

Lesson Time

120 minutes for classroom activities


Number operations make up most of the mathematic portions of standardized tests. Several school districts across the nation have adopted mathematics initiatives in an effort to increase student achievement in math. This lesson allows students to not only practice basic math facts, but to also gain a deeper conceptual understanding of number relationships through use of the design process. Students will achieve the curriculum standards and other expected outcomes by designing a math game that helps students practice multiplication and division of whole numbers, addition, subtraction, multiplication, and division of decimals, and addition and subtraction of simple fractions. Students will also write clear directions for their game. The design process will aid in the implementation of this lesson because students will be expected to review the challenge given by the teacher, investigate the problem, reframe the problem, generate possible solutions, and self-evaluate. Use of this design process will also include other design strategies like graphic design, “way-finding”, diagrams, illustrations, etc.

National Standards


Students will:
  • practice how to multiply and divide whole numbers
  • practice how to add, subtract, multiply, and divide decimals
  • practice how to add and subtract simple fractions
  • write directions free of grammatical errors through editing and publishing stage of writing



  • markers
  • crayons
  • colored pencils
  • paint
  • paper (construction, notebook, etc.)
  • pencils
  • pens
  • cardboard
  • scissors
  • glue
  • tape
  • pennies or bottlecaps, or other things that can be used as game pieces
  • directions and rubric (see Appendix A)


  • whole numbers: the numbers 0, 1, 2, 3, 4, 5, 6, 7, …….(and so on)


DAY 1:

1. Articulate the goals and standards for this lesson in age appropriate verbiage.

Example: “Students, today we are going to use the design process to review some areas of number operations in math. I’ve noticed that several students are still having trouble in a few areas so you are going to design games that will help us practice those skills.”

(Note: In the case of this lesson the three skills will be multiplication and division of whole number, number operations with decimals, and addition and subtraction of simple fractions. Students will also practice editing in writing when constructing written directions to their game.)

2. Review vocabulary and an example of each area of math that students will review (limit to three skills).

3. Review the directions for the activity with the students.

Example: “Today you will be given a design challenge. You are going to work in cooperative groups of three (six groups total) in order to design a math game that helps students practice a certain skill. Your group will either be assigned to multiplying and dividing whole numbers, number operations with decimals, or addition and subtraction of simple fractions. Your job is to agree on an idea for a game, design the game, and create the game. You will be graded on the appropriateness of the math content (not too hard, not too easy), creativity, work habits, clarity of written directions, and your answer key. All of the art and office supplies are available to you (depending on school and teacher supply inventory) as well as any materials brought from home (with teacher approval). You may design anything from a math board game to a math sports game. Be creative!

Please look at the directions handout as we review the steps to completing this assignment.

First you will brainstorm your ideas independently. Second, you will get into your groups and share your ideas. Next, decide which idea your group will use. Then develop a plan and a list of materials you will need. Check whether the needed materials are available to you. If so, proceed with the final step. If not, consult the teacher. Finally, execute your group’s plan. This should include writing directions and creating the game.”

4. Brainstorm -- Pass out the brainstorm handout (see Appendix B) to the students.  Assign one of the three skills for review to each student (distribute evenly). Guide students through each step of the design process as they brainstorm ideas.

DAY 2:

1. Students sit with their pre-assigned group members to share their ideas, decide on one idea, develop a plan, and check for available materials.

2. Each group executes their plan by designing a review game, making an answer key to the math questions in the game and writing clear directions.


The teacher should informally assess students through observation and listening as he/she walks around the room while students are working. This will give the teacher information about how students are cooperating, following directions, and understanding the objectives of the lesson.

The teacher will further know if students have learned the objectives by using the checklist to evaluate their work.

Moreover, the teacher will collect the brainstorm handout once it’s complete to get a better understanding of how well students are comprehending what they have learned. The brainstorm handout is also a good tool to use to find out where you may have lost a student in the process.

I will use a spiral assessment (to include various skills), a project rubric (See Appendix A), and classroom observation to determine if students have successfully learned the objectives of the lesson.

This lesson has differentiated instruction and assessment throughout. Students can draw on various styles of learning through the lesson’s activities. Students can move, draw, build, write, or use any combination of these.

Enrichment Extension Activities

This lesson is also great because it is easily adaptable to the skill level of any student. Whatever the student needs to work more on can be used to create a game for practice. Not only does the student benefit from making the game, but other students benefit because they can also play. This lesson can be used in various other subjects besides mathematics. This lesson can be enriched by adding a technology component. That is, if the hardware and software are available, students can create computer games. Additionally, students have the opportunity to write about their game, market their game, or simply play their game. Each of these activities makes important connections to other curricular areas (Language Arts, Business and Marketing, Economics).

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