Abstract

This lesson allows students to practice their arithmetic skills and check their answers using the Graphit activity.

This lesson utilizes the mathematical fact that the graph of a linear function can be developed from the equation y = bx or y = x + b. Students are given a list of arithmetic problems where all of the problems are of the same operation and the same operand (represented in the equations as b) while the second operand varies (represented in the equations as x). The second operand and the result (represented in the equations as y) are then graphed as ordered pairs. If the student answers the problems correctly, all ordered pairs will fall in a straight line.

Objectives

Upon completion of this lesson, students will:

• have practiced single operation arithmetic. The type of arithmetic, ranging from single digit addition to long division of decimals or arithmetic with real numbers, is determined by the instructor.

Standards

The activities and discussions in this lesson address the following NCTM standards:

Number and Operations
Understands meanings of operations and how they relate to one another

• understand the meaning and effects of arithmetic operations with fractions, decimals, and integers

• develop and analyze algorithms for computing with fractions, decimals, and integers, and develop fluency in their use

• relate and compare different forms of representation for a relationship

• use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;

Links to other standards.

Student Prerequisites

• Technological: Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

• Access to a browser
• Pencil and Paper

Lesson Outline

1. Focus and Review

   Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   • Review any algorithms they have learned to complete the specific type of arithmetic problems you would like them to practice.
   • Students should complete the practice problems prior to this lesson.

2. Objectives

   Let the students know what they will be doing and learning today. Say something like this:

   • Today, class, we are going to use the computers to help practice our arithmetic skills.

3. Teacher Input
   • Using the Graphit! activity, demonstrate how to use the activity to check their answers to their practice problems. Use the following set of problems or your own set:
     • 3 + 2 = 5
     • 3 + 5 = 8
     • 3 + 7 = 10
     • 3 + 9 = 12
     The input from this problem set should be:
     • 2,5
     • 5,8
     • 7,10
     • 9,12
   • After these ordered pairs are graphed show the students what an incorrect answer will look like. Use your own problem or 3 + 1 = 3 and the data point 1,3. Note that this data point will not fall on the line.
   • You can then enter in "the rule" 3 + x in the y(x)= text box. This line will be the line all graphed points should fall on. If a point does not fall on this line then the student has an incorrect answer and should go back and double check his/her work.

4. Guided Practice
   • Using the first set of practice problems, call on the students in the class to tell you what should be the input. Call on a different student for each data point then graph the result.
   • Call on a student to tell you what you should enter as "the rule."

5. Independent Practice
   • Students should complete other problem sets (this can be done either in class or prior to this lesson).
   • Students should input their data sets and rules. If a point does not lie on the line, they should go back and determine which answer in their problem set was incorrect.

6. Closure
   • You may wish to bring the class back together for a discussion of the findings.

Alternate Outlines

This lesson can be rearranged in several ways.

• Problem sets can be done prior to class or during class.
• Students can work in groups of two.

Suggested Follow-Up

• This lesson can be reused as the difficulty level of types of arithmetic problems increase throughout the school year.