Interpreting Functions Using Real Life Examples

By Tara Mason on Apr 24, 2017

Students will model a simple linear function such as y = mx to show that these functions increase by equal amounts over equal intervals using tactile graphing paper and a talking calculator.

Understanding of how to find patterns in mathematical functions

Materials

  • Two or more teacher-made tactile graphs displaying two simple linear functions
  • Wikki Stix
  • Braille graph paper (3-6 pieces)
  • Braille ruler
  • Braille dots for plotting points

Procedure

In this lesson, students will relate real life applications such as buying "x" items that cost "m" each to get a total cost = y OR growing "m" inches over "x" years to find total length. Students will break this equation into parts to learn about what is happening when we graph rate of change.

  1. Present an example graph with two trends moving side by side, ask the student to describe what he/she sees. Ensure student is using systematic search patterns to identify the pattern and describes the pattern accurately.
  2. Come up with an example together of patterns that this graph could describe, i.e., a plant growing, a child growing in height of the years, city growth...
  3. Using the tactile graph paper, braille dots, ruler, work with your student to go through an experimental problem comparing two simple linear equations.
  •    "Leandra wanted to experiment with sunlight and growth. She wanted to answer the question, "can different types of sunlight change the speed of a plant's growth?" Plant "A"- is from a seed and gets morning sun & Plant "B" is a 3 inch sprout and gets afternoon sun
  • On the student graph, label X Axis (horizontal) the "weeks" and label Y Axis (vertical) the height in inches.
  • Leandra measured her plants once a week for 8 weeks. The height in inches is listed below.
  • Plot these data points:
    • Plant "A" Morning Sun: 1, 2, 3, 4, 5, 6, 7, 8
    • Plant "B" Afternoon Sun: 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7
  1. After plotting the points, have your student use wiki stix to connect the braille dots to see the growth trend.
  2. In order to find the growth trend which we will plug into our simple linear equation, students must identify the Rise/Run. The Rise is the "vertical change" and the Run is the "horizontal change."
  • First we examine the growth over time which is the "rate of change." Have your student measure the Rise/Run. The Plant A has a faster rate at 1/1 instead of 1/2 (Plant B).
  • Next look at the intersection of the two lines. This is how we can analyze the rate of change. At the intersection, both plants are 6" at 6 weeks (6,6). Plant A is growing faster and Leandra can conclude that the time of day can be a primary indicator of plant growth.
  1. With this example completed, come up with a real world example with your student to graph such as comparing how fast your student grew compared to their sibling. Your student could come up with hypothetical numbers for his/her graph.

Problem set for this lesson was adapted from Learn Zillion's "Comparing relationships between quantities using linear models."

 

 

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