Description

Through a series of hands-on activities, students develop proportional reasoning and are able to create tables, graphs, and equations.

Levels

• Grades 6 through 8.

Preparation Time

1 - 2 hours

Activity Time

6 lessons

Topics

• ratios
• rates
• unit rates
• measurement conversion
• writing and solving real life equations
• proportions
• tables
• graphing

Goals

• Students will be able to determine a unit rate.
• Students will be able to use proportional reasoning to create tables, graphs, and equations.
• Students will be able to use the d = rt equation to find distances, rates, or times given two of the variables.
• Students will use proportional reasoning to convert measurements.
• Students will be able to analyze graphs for information including rates of change.
• Students will be able to identify proportional and non-proportional relationships through tables, graphs, and/or equations.

Materials

• "If You Hopped Like a Frog" by David M. Schwartz
• 3" x 5" index cards
• pre-measured distance (in hallway, gym, etc.)
• stopwatch
• meter sticks and/or tape measures (with metric and English standard units)
• "T-table and Grid" paper
• graph paper
• Origami Jumping Frog instructions
• large gridded chart paper
• scale (to weigh students)
• student activity sheets - "If you Could..." - "What's My Rate?" - "The Story of Two Frogs" - "More Frog Tales"
• standard calculators
• math journals

Prerequisites

• Students are able to solve one step equations.
• Students are able to graph coordinates on the Cartesian Plane.
• Students can express ratios and verify equivalent ratios.

Related Concepts

• NCTM Illuminations website - Barbie Bungee (linear functions and slope)
• NCTM Illuminations website - Constant Dimensions (ratio of length to width)
• NCTM Illuminations website - Bouncing Tennis Balls (linear relationships between time and bounces)
• NCTM Illuminations website - Pedal Power (slope and rate of change)
• NCTM Illuminations website - Representing Data (create graphs from a table)
• NCTM Illuminations website - Taking Its Toll (exploring toll/distance relationships)
• NCTM Illuminations website - The Line Runner (slope and linear equations with a running model)

Authors

National Common Core Standards

6.RP.1	Understand the concept of a ratio and use appropriate vocabulary to describe a ratio relationship between two quantities.
6.RP.2	Understand the concept of a unit rate a/b associated with a ratio a:b in the context of a ratio relationship.
6.RP.3	Use ratio and rate reasoning to solve real-world and mathematical problems (make tables, solve unit rate problems, work with percents, and convert measurement units).
7.EE.4	Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems.
7.RP.2	Recognize and represent proportional relationships between quantities.
8.EE.5	Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

This work placed into the public domain by the Riverbend Community Math Center.