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K–12 teaching and learning · from the UNC School of Education

The Grapes of Math

The book The Grapes of Math is an excellent motivational picture book that models how to use different “thinking” skills to solve word problems by employing a variety of computation strategies. By reading and discussing the possible solutions to the examples provided in the text, students will begin to visualize possible methods to use when trying to solve word problems. Using other word problems to practice the application of these various strategies will enhance the students' abilities to recognize and then apply successful strategies for problem solving.

A lesson plan for grades 3–5 Mathematics

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Learning outcomes

To provide opportunities that allows students to “think” through mathematical problem solving and provide solutions using a variety of strategies. Strategies will include: guess-and-check, find-a-pattern, draw-a-diagram, and other problem-solving strategies which will develop inductive and deductive thinking.

Teacher planning

Time required for lesson

2-3 days

Materials/resources

  • The Grapes of Math by Greg Tang. Published by Scholastic Press in 2001.
  • Grapes.

Technology resources

Computer with internet access hooked to a TV or LCD projection device.

Pre-activities

  • Use some basic repeated addition examples as they relate to multiplication to initiate this lesson. Place these examples on the overhead or board modeling how multiplication is simply a quicker way to solve repeated addition problems.
  • Also, get students to recall ways things/objects can be grouped to aid in quicker ways to problem solve emphasizing the patterns of skip counting.
  • Orally get the children to skip count by 2’s, 5’s, 10’s. Then relate to them they have multiplied by 2, 5, 10 by showing an overhead of these three lines and pointing out the patterns.
  • Remind students of other strategies used to solve word problems that you have covered so far in your classroom studies such as working backwards, rereading the question looking for key words/phrases, restating the question, or estimating.

Activities

Day 1

  1. Show students the book The Grapes of Math by Greg Tang. Explain how it may look like a picture book for younger students, but that the illustrations are used as models for solving word problems.
  2. Read the first poem aloud to the students. Emphasize the “clues” that are in each poem. Reread the clues 2 or 3 times. Next, show students the illustration and let them try to verbalize how to quickly solve the problem. Allow all students the opportunity to discuss how they could solve each problem using which is easiest and quickest way. Talk about possible strategies used as this discourse happens. Reward all those who offer a logical method/strategy a grape. If someone should figure out the “trick” supplied by the author, then they will earn two grapes.
  3. Continue reading the poems and showing the pictures. Also, continue eliciting answers or possible ways to solve each problem from the students. But this time only reward the ones who have a “logical” response supported by the strategy used. Giving hints or an extra clue may help students see the patterns or best strategy for finding each solution. Again, emphasis the repeated pattern of addition as it relates to multiplication.

Day 2 and Day 3

  1. Go to the Webquest site: Searching for Solutions. Talk about the site and how it is designed as a WebQuest. Proceed through each of the six parts of this webquest working with students as they complete each section. This WebQuest may be used as an individual, small group, or total class activity. Depending on the experience of the students will determine the best method for carrying out this activity. (I tend to use whole group initially and then break up into small groups as the WebQuest continues.)
  2. Included in this site is an excellent PowerPoint show that suggests and models strategies for problem solving. Showing this to students will help them to visualize and apply the various problem-solving strategies suggested in this WebQuest.
  3. Time is needed and allowed for each investigation of the real life application exercises in the evaluation part of this WebQuest. Grouping students for this section is recommended since a WebQuest is designed to be a collaborative and cooperative learning experience. Teacher should informally assess the students as they proceed through this section and guide the groups as needed.
  4. Finally as an assessment tool, use the teacher-made worksheet: Word Problems

Assessment

Students will complete the Word Problems worksheet.

Students will work the problems and match them with the strategy they used for solving the problem.

Supplemental information

Related websites

Searching for Solutions. A webquest site that is a wonderful source of word problems. It would work best if modeled by teacher with classroom participation or small groups of experienced computer students with specific strategies to look for and work on cooperatively.

Comments

I did this lesson with small groups so that the students were able to touch the book while explaining their strategy for solving the problems. Using this technique proved to be more effective for my students. The small groups were also easier to work with while modeling the webquest.

North Carolina Curriculum Alignment

Computer Technology Skills (2005)

Grade 3

  • Goal 2: The learner will demonstrate knowledge and skills in the use of computer and other technologies.
    • Objective 2.11: Investigate teacher-selected Internet resources about communities; discuss and compare findings for usefulness as a class. Strand - Telecommunications/Internet

Grade 4

  • Goal 1: The learner will understand important issues of a technology-based society and will exhibit ethical behavior in the use of computer and other technologies.
    • Objective 1.11: Identify and discuss the use of multimedia tools to report content areainformation. Strand - Multimedia/Presentation

Grade 5

  • Goal 1: The learner will understand important issues of a technology-based society and will exhibit ethical behavior in the use of computer and other technologies.
    • Objective 1.12: Recognize and explain the advantages and disadvantages of using multimedia to develop content area projects/products. Strand - Multimedia/Presentation
  • Goal 3: The learner will use a variety of technologies to access, analyze, interpret, synthesize, apply, and communicate information.
    • Objective 3.07: Use evaluation tools to select Internet resources and information for content and usefulness in content area assignments. Strand - Telecommunications/Internet

Mathematics (2004)

Grade 3

  • Goal 1: Number and Operations - The learner will model, identify, and compute with whole numbers through 9,999.
    • Objective 1.03: Develop fluency with multiplication from 1x1 to 12x12 and division up to two-digit by one-digit numbers using:
      • Strategies for multiplying and dividing numbers.
      • Estimation of products and quotients in appropriate situations.
      • Relationships between operations.
  • Goal 5: Algebra - The learner will recognize, determine, and represent patterns and simple mathematical relationships.
    • Objective 5.01: Describe and extend numeric and geometric patterns.
    • Objective 5.02: Extend and find missing terms of repeating and growing patterns.

Grade 4

  • Goal 1: Number and Operations - The learner will read, write, model, and compute with non-negative rational numbers.
    • Objective 1.05: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
  • Goal 5: Algebra - The learner will demonstrate an understanding of mathematical relationships.
    • Objective 5.02: Translate among symbolic, numeric, verbal, and pictorial representations of number relationships.

Grade 5

  • Goal 1: Number and Operations - The learner will understand and compute with non-negative rational numbers.
    • Objective 1.03: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
  • Goal 5: Algebra - The learner will demonstrate an understanding of patterns, relationships, and elementary algebraic representation.
    • Objective 5.01: Describe, extend, and generalize numeric and geometric patterns using tables, graphs, words, and symbols.