Making Sense of Math: Thinking Rationally. Amy Lewis Math Specialist IU1 Center for STEM Education. Goals for the course. Use a variety of tools to deepen their understanding of rational numbers and explore proportional relationships to connect fractional meanings and representations.
Making Sense of Math:Thinking Rationally
IU1 Center for STEM Education
Students on the 7th grade field trip committee at STEM Middle School are planning a fund raising event. They can’t decide what candy to sell -- Blocko Choco or Choca Latta. Both candies cost the same so it is a matter of which candy will sell more. They use a lunchtime survey to determine the preference of their customers, the students in their school. When the results were tabulated each member of the committee designed an ad to present their results.
Many important mathematical applications involve comparing quantities. In instances where we need to know which quantity is greater or how much greater, we subtract to find a difference. Since addition and subtraction come first in a students’ experience with mathematics, this way of thinking becomes pervasive in any situation requiring comparison.
Beyond subtraction we can compare quantities using ratios, fractions, decimals, percents, unit rates, and scaling. Students must learn different ways to reason proportionally and to recognize when such reasoning is appropriate.
Each year, your class presents its mathematics portfolio to parents and community members. This year, your homeroom is in charge of the refreshments for the reception that follows the presentations.
Four students in class give their recipes for lemon-lime punch. The class decides to analyze the recipes to determine which one will make the Fruitiest-tasting punch. The recipes are shown below.
Adam’s RecipeBobbi’s Recipe
4 cups lemon-lime concentrate 3 cups lemon-lime concentrate
8 cups club soda5 cups club soda
Carlos’ RecipeZeb’s Recipe2 cups lemon-lime concentrate1 cups lemon-lime concentrate3 cups club soda4 cups club soda
In your group, determine:
Record your solutions on poster paper and display it near your table.
Participate in a gallery walk and contrast the methods used by the groups.
Whole group discussion:
In your group examine each team’s solution.
Examining Student Work
Every participant will receive ½ cup of punch. For each recipe, how much concentrate and how much club soda are needed to make punch for 240 people? Explain your answer.
Summarize the work that you have done so far in the table below.
Each person in the group should take one of the recipes and make a table.
Next, each person in the group should make a graph of the cups of concentrate as a function of cups of punch.
The Candy Jar (right) contains Jawbreakers (the circles) and Jolly Ranchers (the rectangles).
Use this Candy Jar to solve the following problems.
Kandies-R-Us sells a super-sized 500-piece Tub-O-Treats. It contains chocolate kisses in addition to Jawbreakers and Jolly Ranchers. If the ratio of Jolly Ranchers to Jawbreakers to kisses is 7:8:10, how many of each candy are in the Tub-O-Treats?
The treat tin containsJawbreakers (circles)and Jolly Ranchers (rectangles).
Ratio, Fraction or Both?
In the world of ratios, can1/2 + 1/3 = 2/5 ?Create an example to support your conclusion.
Jason completed 2/5 of his mathematics homework and 3/7 of his science homework. How much of his mathematics and science homework did he complete?