Scrambled Eggs I – Proportions and Equivalent Ratios

This resource was created by Big Ideas in Beta, a Big Ideas Fest project, with acknowledgement to Pat C. Browne

LEARNING OUTCOMES:

• Students will be able to compare two quantities, part-to-part, and represent these two quantities as a ratio. 
• Students will be able to represent equivalent fractions. 
• Students will be able to use proportional reasoning to create a table of equivalent ratios.

COMMON CORE STANDARDS ADDRESSED:

Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

6.RP.3. Use 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.

TIME REQUIRED FOR LESSON:

45 minutes - 50 minutes

TIME REQUIRED FOR TEACHER PREPARATION:

20 minutes - 30 minutes

MATERIALS FOR LESSON:

• Blackboard, whiteboard, or chart paper 
• Markers 
• A class set of 60 large egg signs printed on colored cardstock (30 red and 30 blue); one color of each for all students to wear during activity. Attach egg with yarn around the neck of each student.  (A free egg template is available at http://www.firstpalette.com/tool_box/printables/eastereggs.html.) Paper and pencils (for each student)

OVERVIEW OF LESSON:

1.  Explain to the students that some ratios can express comparisons of a part to a whole (number of girls in the class to the number of students in the class.   Explain that other ratios can relate one part of a whole to another part of a whole, for example the number of boys in a class is compared to the number of girls in the class.

2.  Explain that today the class will demonstrate how to make comparisons using ratios by acting out a people sort where students will play the parts of colored eggs.  Divide the class into two groups. Ask the students in each group to stand together with each student in one group wearing a red egg sign and in the other a blue egg sign.  Write the ratio 3:10 on the board.  Ask the students: “How might you create a human ratio that portrays this part-to-part ratio?”   Discuss what to do with the students who aren’t needed to portray the ratio.  Allow students to act out this ratio by grouping themselves.

3. Bring all the students together again, and draw one red egg and five blue eggs on the board.  Ask, “How would you write this ratio of red to blue eggs?”   Write the students responses on the board. Explain that their task now is to create another ratio that is equivalent.  Start by asking students to assemble themselves into groups where there are two red eggs.  Ask, “How many blue eggs would be needed to create an equivalent ratio?”   Ask the remaining students to group themselves to create a 3:15 ratio of red to blue eggs.

4.  Draw an example of the ratio table that describes how the numbers of eggs (students) are related, asking for volunteers to complete the table.

Ask the class: “What numbers should go in the last column of the table?”

3.  Ask the class to again organize themselves in groups to demonstrate a ratio that is equivalent to the following ratio:  (write on the board or display on chart paper): 12:60.  Discuss that since there aren’t enough students to increase the proportion to an equivalent ratio beyond 60 their groups will need to be smaller.

5.  Ask the students to work with a partner at their seats to create a similar table for the ratio, 12:50.  Discuss how they created their tables, focusing on patterns and the multiplicative reasoning.

6.   As a follow-up, ask students to return to their seats to copy and find missing numbers on their papers in the following ratio table (written on the board), in which 5 students in the class prefer skateboards while 7 students prefer in-line skating:

7.  Assess the student’s understand by writing the following problems on the board and ask each student to complete the problem independently on paper at their seat:

At a community football program, the ratio of coaches to players is 18 to 100.

Which ratio is equivalent to the ratio of coaches to players?

                                                            1.         1 to 18

                                                            2.         9 to 50

                                                            3.         4 to 25

                                                            4.         6 to 20

ADDITIONAL INFORMATION:

            Sousa, D. A. How the Brain Learns Mathematics, Corwin Press, 2008.

            Van de Walle, j. A., K. S. Karp, and J. M. Bay-Williams, Elementary and Middle School      Mathematics – Teaching Developmentally, Allyn & Bacon, 2010.