K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

Students will:

  • calculate fractions from a set of objects.
  • convert fractions to decimals and percents.
  • develop a circle graph based on their individual information and compare/contrast it with others in their cooperative groups.

Teacher planning

Time required for lesson

2 hours

Materials/resources

  • M&M Madness reproducible (PDF document)
  • Magnetic bingo chips
  • Large paper for chart making
  • 9″ x 12″ drawing paper
  • 2 party bags of M&M’s, measure out 2 Tbsp. M&M’s for each student.
  • Compasses
  • Pencils
  • Colored pencils, markers, or crayons

Technology resources

  • Calculator for each student
  • Overhead calculator

Pre-activities

Students should be familiar with what a fraction, a decimal, and a percent are and why and how we use them. They have had prior experience composing fractions from sets of data.

Activities

Hour One

  1. Teacher uses magnetic bingo chips (5 blue, 3 red, 4 purple) to illustrate how to find a fraction. Example: 3/12 are red.
  2. Then, using a chart similar to the M&M Madness reproducible, the teacher leads the students through the process of finding the equivalent decimal and percent for each color. (See #3 & #4)
  3. To find the equivalent decimal the student is shown (on the overhead calculator) how to divide the numerator by the denominator. If a more advanced calculator is available, the teacher could show how to use the fraction to decimal function key.
  4. Then, the students are reminded of a previous lesson on percents and once again shown how to move the decimal point of the decimal over two spots to the right to create a percent.
  5. Teacher states that it is time for the students to show their knowledge of this process. Teacher states that the M&M’s are needed for the whole activity. So, students are not to enjoy them until they are told to do so. Pass out M&M’s and M&M Madness handout.
  6. Students will sort their M&M’s by color, tally them, and total them on the handout.
  7. Students will then write the number of orange M&M’s (numerator) over the number of total M&M’s (denominator) to produce the fraction of orange M&M’s. They will then calculate the decimal and percent of each (see #3 and #4 above).
  8. The students will repeat the procedure with their red, brown, blue, green, and yellow M&M’s.
  9. While the students are working on their individual sets of M&M’s, they may ask a group member for help if needed, and the teacher is circulating and checking for understanding.
  10. When students have completed their tables, the teacher once again calls their attention to the earlier presentation with the bingo chips. The teacher shows them that the decimals found with all the colors should add up to near 1. Students add their decimals and write down the sum. Have students brainstorm why they might not have gotten 1 exactly. (ex: Did they round any of their decimals?)
  11. Again, call the class’ attention to the percent line of the bingo chip table. Add the percents up on the overhead calculator. The sum should be 100%. Have students calculate their total percentages. What did they get? Discuss why/why not they might have gotten 98% or 101%. Discuss how it is related to their answer with the decimals.

Hour Two

  1. Now students are ready to proceed with the circle graph. Teacher asks that they make a circle with their M&M’s on a large sheet of drawing paper. Make sure that all the oranges are next to each other, all the blues are next to each other, and so forth.
  2. Next, students will carefully position their compasses in the middle of their circles and draw a circle just inside the M&M’s.
  3. Now that their circles are complete, the students will use rulers to draw straight lines from the middle of their circles to the beginning of each color in the circles. For example, one might draw a line up to where the red starts. Then, draw a straight line to where the red would end in the circle. Keep doing this until the circle is sectioned off for all of the colors.
  4. The student has now drawn a circle graph. Have each student label the sections with the color and the percentage (found on the M&M Madness reproducible completed in Hour One).
  5. Students may now add a title and color in their graphs. They may also eat their M&M’s at this stage "to give them energy."
  6. When completed, have students in cooperative groups discuss their graphs and come up with a list of ten statements comparing their graphs. (Ex: Tony has over 50% red M&M’s and Sam only has 10% red). They write these on a piece of chart paper and then share with the class in a short presentation.
  7. Hang the charts and graphs for all to see.

Assessment

By the end of this lesson, students should be able to calculate fractions, decimals, and percents correctly on the M&M Madness activity. A common error is that the student will not calculate the decimal correctly and will simply write the numerator of the fraction with a decimal. Show these students again how to calculate the decimal with the calculator.
Students will have labeled their graphs correctly and included all requested components. The teacher is looking for a title, the percentage, and color noted in each section of the circle graph. The percentages should add up to close to 100%.

Written assessment #1:

The student explains how to convert fractions to decimals and percents. The student also gives an example.

Student Prompt. Please explain how you would find the fraction of a set. Then explain how you would convert this fraction to a decimal and a percent. Use appropriate terminology and specific examples.

Assessment. On a scale of 1 to 4, the 1 is low and the 4 is high.

4:

  • The student uses the terms fraction, decimal, percent, numerator, and denominator correctly.
  • The student explains how to find the fraction of a set of objects by noting the number of objects specified over the total number of objects. ("7 out of 10" or 7/10)
  • The student demonstrates an understanding of the fact that fractions, decimals, and percents are related.
  • The student has given a clear and concise example of converting the fraction to a decimal and of converting the decimal to a percent.

3:

  • The student uses the terms fraction, decimal, percent, numerator, and denominator correctly.
  • The student explains how to find the fraction of a set of objects by noting the number of objects specified over the total number of objects. ("7 out of 10" or 7/10)
  • The student demonstrates an understanding of the fact that at least two of the terms (fractions, decimals, and percents) are related.
  • The student has given a clear and concise example of either converting the fraction to a decimal or of converting the decimal to a percent.

2:

  • The student uses at least two following terms (fraction, decimal, percent, numerator, and denominator) correctly.
  • The student shows knowledge of, but does not explain, how to find the fraction of a set of objects.
  • The student does not demonstrate an understanding of the fact that fractions, decimals, and percents are related.
  • The student has not given a clear and concise example of either converting the fraction to a decimal or converting the decimal to a percent.

1:

  • The student may not be able to use the terminology correctly or give appropriate examples.
  • The student does not exhibit an understanding of this content.

Written assessment #2:

The student is able to sketch a sample circle graph and give five facts about it.
Student Prompt: Please sketch a circle graph illustrating the amount of dogs, fish, cats, and iguanas our class has as pets. Write five fact statements about your graph.

Assessment: The students percentages should add up to 100% and the pieces of the circle should be approximately correct. The student may make statements of fact such as:

  • Over half of the animals are dogs.
  • The least popular animal is the iguana.
  • There are more fish than cats.
  • If I added the fish, cats, and iguanas, the percentage would almost equal the total percentage of dogs.

Supplemental information

Challenge Activity: For students who need a challenge with the circle graph, allow them to draw a large circle and explore splitting it up into appropriate percentages without the circle of M&M’s.

Comments

Snack-sized M&M’s require less preparation. If you use the party bag, it saves class instructional time if they are measured out in advance (2 Tbsp = about 50 M&M’s). Snack sized baggies work well.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 5

        • 5.NOF.3Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations...
        • Number & Operations in Base Ten
          • 5.NO.4Use place value understanding to round decimals to any place.
      • Grade 6

        • Ratios & Proportional Relationships
          • 6.RPR.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number...

North Carolina curriculum alignment

Mathematics (2004)

Grade 5

  • Goal 1: Number and Operations - The learner will understand and compute with non-negative rational numbers.
    • Objective 1.02: Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).
      • Develop and analyze strategies for adding and subtracting numbers.
      • Estimate sums and differences.
      • Judge the reasonableness of solutions.
  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems.
    • Objective 4.02: Compare and contrast different representations of the same data; discuss the effectiveness of each representation.