Understanding Rational Numbers and Proportions

In this lesson, students use real-world models to develop an understanding of fractions, decimals, unit rates, proportions, and problem solving. The three activities in this investigation center on situations involving rational numbers and proportions that students encounter at a bakery. These activities involve several important concepts of rational numbers and proportions, including partitioning a unit into equal parts, the quotient interpretation of fractions, the area model of fractions, determining fractional parts of a unit not cut into equal-sized pieces, equivalence, unit prices, and multiplication of fractions.

Standards & Objectives

Learning objectives: 

Learning Objectives:

Students will:

  • Represent parts of a whole using an area interpretation of fractions.
  • Determine the fractional part of a whole when parts are not cut into equal-sized pieces.
  • Develop an understanding of the quotient interpretation of fractions.
  • Find the unit cost of items that are part of a set.
  • Determine the relationship among parts of a whole that are unequal-sized pieces.
  • Express fractional parts of a whole as decimal equivalents.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

Extensions:

  • Students find the cost of various-sized pieces, given that 1/8 of a cake costs $1.59 and a whole cake costs $12.72. The following table is a sample. (Tables may include other fractional parts and need not be limited to eighths, fourths, and halves.) Students may wish to use calculators with fraction capability to help them find the various prices. Using calculators may help students focus on the reasonableness of their solutions rather than on the calculations.
  • How many cookies would each person get if...
  • three people shared twenty cookies? [20/3, or 6 and 2/3 cookies for each person]
  • eight people shared twenty cookies? [20/8, or 2 and 1/2 cookies for each person]
  • x people shared twenty cookies? [20/x cookies for each person]
  • What is a rule for finding the number of cookies each person will get if a people share b cookies? 

Helpful Hints

Materials:

  • Making Four Pieces Overhead 
  • Cakes Cut Into Eighths Activity Sheet 
  • Cakes Cut Into Fourths Activity Sheet 
  • Scissors
  • Calculators (optional)

 

References

Contributors: