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 Addressed:

Grade 10

Estimation and Computation

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of real numbers.

Grade 3

Estimation and Computation

The student determines reasonable answers to real-life situations, paper/pencil computations, or calculator results.

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of whole numbers up to one thousand.

Grade 4

Estimation and Computation

The student determines reasonable answers to real-life situations, paper/pencil computations, or calculator results.

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of whole numbers to ten thousands.

Grade 5

Estimation and Computation

The student determines reasonable answers to real-life situations, paper/pencil computations, or calculator results.

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of whole numbers to millions.

Grade 6

Estimation and Computation

The student accurately solves problems (including real-world situations).

Measurement

The student demonstrates understanding of measurable attributes.

Numeration

The student demonstrates conceptual understanding of fractions (proper or mixed numbers), decimals, percents (whole number), or integers.

Grade 7

Estimation and Computation

The student accurately solves problems (including real-world situations).

Grade 8

Estimation and Computation

The student accurately solves problems (including real-world situations).

Grade 9

Estimation and Computation

The student accurately solves problems (including real-world situations).

Numeration

The student demonstrates conceptual understanding of real numbers.

Grade 6

Number Sense

2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division

Grade 7

Algebra and Functions

1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs

Number Sense

1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms

Fourth Grade

Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

Third Grade

Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

Understand properties of multiplication and the relationship between multiplication and division.

Multiply and divide within 100.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Grades 6-8

Algebra

Use mathematical models to represent and understand quantitative relationships

Numbers and Operations

Compute fluently and make reasonable estimates

Grades 9-12

Numbers and Operations

Compute fluently and make reasonable estimates

Grade 6

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.

COMPETENCY GOAL 5: The learner will demonstrate an understanding of simple algebraic expressions.

Grade 7

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.

Grade 8

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 1: The learner will understand and compute with real numbers.

Technical Mathematics I

Number and Operations

Competency Goal 1: The learner will apply various strategies to solve problems.

6th Grade

Algebra

The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

Numbers and Operations

The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers.

8th grade

Algebra

The student will demonstrate through the mathematical processes an understanding of equations, inequalities, and linear functions.

Numbers and Operations

The student will demonstrate through the mathematical processes an understanding of operations with integers, the effects of multiplying and dividing with rational numbers, the comparative magnitude of rational and irrational numbers, the approximation of cube and square roots, and the application of proportional reasoning.

6th Grade

Algebra

Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Number and Operation

Content Standard 1.0 The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

7th Grade

Algebra

The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Number and Operation

The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

8th Grade

Algebra

The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Grade 6

Number, Operation, and Quantitative Reasoning

2. The student adds, subtracts, multiplies, and
divides to solve problems and justify solutions.

Grade 7

Number, Operation, and Quantitative Reasoning

2. The student adds, subtracts, multiplies, or divides
to solve problems and justify solutions.

6th Grade

Computation and Estimation

6.6a The student will solve problems that involve addition, subtraction, multiplication, and/or division with fractions and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less, and express their answers in simplest form; and

7th Grade

Computation and Estimation

7.5 The student will formulate rules for and solve practical problems involving basic operations (addition, subtraction, multiplication, and division) with integers.

8th Grade

Computation and Estimation

8.3 The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data, such as finding a discount and discount prices and balancing a checkbook.

Reason for Alignment: The Practicing Arithmetic lesson provides students with the chance to practice a variety of types of problems, and then check with the Graph It activity. This is a different method than usual, and should be good for students this late in the year. This lesson helps take skills to higher level with a tie to algebra. This lesson could be made into a challenge if integers and decimal problems are included. A skills practice worksheet is provided with the lesson, if the teacher chooses to use it.

Reason for Alignment: Practicing Arithmetic does just that, with single operation problems. The teacher will need to come up with some practice problems for addition/subtraction of integers, as in the text. Graphit is the chosen activity withing the lesson, which will probably need some teacher guidance this early in the year. This one may not be for everyone just yet, but has application for some.

Reason for Alignment: This lesson gives students the opportunity to practice these operations in a different way. This lesson allows students to first work out a set of problems either chosen beforehand by the teacher, or selected from the lesson. Students can then use the Graphit activity to input their data sets and rules. In this way they can check for any solutions which are incorrect. The teacher will need to help get students started on this lesson, but it is worthwhile, especially for the students as this level. This tool ties algebra with skills practice.

Student Prerequisites

Technological: Student must be able to:

perform basic mouse manipulations such as point, click and drag

use a browser for experimenting with the activities.

Teacher Preparation

Access to a browser

Pencil and paper

Lesson Outline

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.

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.

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

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."

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.

Closure

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

Alternate Outline

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.