This lesson was designed to review operations with fractions. The activities provide ample
practice opportunities to reinforce the information from the discussions.

Objectives

Upon completion of this lesson, students will:

understand addition and subtraction of fractions

understand multiplication and division of fractions

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

Numeration

The student demonstrates conceptual understanding of simple fractions with denominators 2, 3, 4, or 10.

Grade 4

Numeration

The student demonstrates conceptual understanding of fractions with denominators 2 through 12.

Grade 5

Numeration

The student demonstrates conceptual understanding of positive fractions with denominators 1 through 12 and 100 with proper and mixed numbers and benchmark percents (10%, 25%, 50%, 75%, 100%).

Grade 6

Numeration

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

The student demonstrates conceptual understanding of fractions, mixed numbers, or percents.

Grade 7

Numeration

The student demonstrates conceptual understanding of rational numbers (fractions, decimals, percents, or integers).

The student demonstrates conceptual understanding of positive fractions, decimals, or percents.

Grade 8

Numeration

The student demonstrates conceptual understanding of real numbers.

The student demonstrates conceptual understanding of rational numbers (fractions, decimals, or percents including integers).

Grade 9

Estimation and Computation

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

Numeration

The student demonstrates conceptual understanding of real numbers.

Fifth Grade

Number and Operations-Fractions

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Fourth Grade

Number and Operations-Fractions

Extend understanding of fraction equivalence and ordering.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Sixth Grade

The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Third Grade

Number and Operations-Fractions

Develop understanding of fractions as numbers.

Grades 3-5

Numbers and Operations

Compute fluently and make reasonable estimates

Grades 6-8

Numbers and Operations

Compute fluently and make reasonable estimates

Understand meanings of operations and how they relate to one another

Grade 6

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

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

Grade 7

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

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

3rd Grade

Computation and Estimation

3.11 The student will add and subtract with proper fractions having like denominators of 10 or less, using concrete materials and pictorial models representing areas/regions, lengths/measurements, and sets.

Number and Number Sense

3.05a The student will divide regions and sets to represent a fraction;

3.05b The student will name and write the fractions represented by a given model (area/region, length/measurement, and set). Fractions (including mixed numbers) will include halves, thirds, fourths, eighths, and tenths.

3.06 The student will compare the numerical value of two fractions having like and unlike denominators, using concrete or pictorial models involving areas/regions, lengths/measurements, and sets.

3.5a The student will divide regions and sets to represent a fraction;

3.5b The student will name and write the fractions represented by a given model (area/region, length/measurement, and set). Fractions (including mixed numbers) will include halves, thirds, fourths, eighths, and tenths.

3.6 The student will compare the numerical value of two fractions having like and unlike denominators, using concrete or pictorial models involving areas/regions, lengths/measurements, and sets.

4th Grade

Computation and Estimation

4.8 The student will estimate and find the quotient of two whole numbers, given a one-digit
divisor.

4.9.a The student will add and subtract with fractions having like and unlike denominators of 12 or less,
using concrete materials, pictorial representations, and paper and pencil;

4.9.c The student will solve problems involving addition and subtraction with fractions having like and
unlike denominators of 12 or less and with decimals expressed through
thousandths, using various computational methods, including calculators, paper
and pencil, mental computation, and estimation.

4.8

4.9.a

4.9.c

Number and Number Sense

4.2.b The student will represent equivalent fractions;

4.2.c The student will relate fractions to decimals, using concrete objects.

4.3 The student will compare the numerical value of fractions (with like and unlike denominators) having denominators of 12 or less, using concrete materials.

4.2.b

4.2.c

4.3

5th Grade

Computation and Estimation

5.4 The student will find the sum, difference, and product of two numbers expressed as decimals through thousandths, using an appropriate method of calculation, including paper and pencil, estimation, mental computation, and calculators.

5.5 The student, given a dividend of four digits or fewer and a divisor of two digits or fewer, will find the quotient and remainder.

5.6 The student, given a dividend expressed as a decimal through thousandths and a single-digit divisor, will find the quotient.

5.7 The student will add and subtract with fractions and mixed numbers, with and without regrouping, and express answers in simplest form. Problems will include like and unlike denominators limited to 12 or less.

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

6.6b The student will find the quotient, given a dividend expressed as a decimal through thousandths and a divisor expressed as a decimal to thousandths with exactly one non-zero digit.

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 s

Number and Number Sense

6.1 The student will identify representations of a given percent and describe orally and in writing the equivalence relationships among fractions, decimals, and percents.

6.4 The student will compare and order whole numbers, fractions, and decimals, using concrete materials, drawings or pictures, and mathematical symbols.

7th Grade

Computation and Estimation

7.4a The student will solve practical problems using rational numbers (whole numbers, fractions,
decimals) and percents

7.4 The student will

Number and Number Sense

7.1 The student will compare, order, and determine equivalent relationships between fractions, decimals, and percents, including use of scientific notation for numbers greater than 10.

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.

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,

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

Key Terms

denominator

In a rational number, the number below the fraction bar that indicates how many parts the whole is divided into.

fraction

A rational number of the form a/b where a is called the numerator and b is called the denominator

numerator

The number above the fraction bar that indicates the number of parts of the whole there are in a rational number

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 key terms:

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

Today, class, we will be talking more about fractions, and how to do basic math operations
with them such as addition, subtraction, multiplication and division.

We are going to use the computers to learn about fractions, but please do not turn your
computers on or go to this page until I ask you to. I want to show you a little about this
activity first.

Open your browser to
Fraction Four in order to demonstrate this activity to the students.

Make sure the students are comfortable with how the game works before letting students work on
their own.

You may want to have students take turns giving answers to the problems and work through one
or two games as a class until students are ready to try it on their own.

Make sure that students select addition/subtraction and multiplication/division problems only
when they set up the game.

Independent Practice

Allow the students to work in groups of two to play the Fraction Four game. Monitor the room for
questions and to be sure that the students are on the correct web site.

You may want to pair the students according to ability level so that students don't consistently
win or lose their games.

You also may want to monitor the time limit student set for the game. You can either assign
students a time limit according to their ability level or instruct students to use no time
limit.

Closure

You may wish to bring the class back together to discuss any problems that were especially hard
for students to solve. You can also use this as a time to have students share different methods
they used to solve the problems. Potentially, the class could create pro/con lists for the
different methods of solving these problems. Once the students have been allowed to share what
they found, summarize once more the main points of the lesson.

Alternate Outline

This lesson can be rearranged in several ways if there is only one available computer:

Have students complete paper worksheets of problems with fractions and use
Fraction Four as a reward for two students at a time who have showed proficiency in solving the problems on
paper.

Alternatively, select students who need additional practice to use the game. Teams of one
strong student and one who needs help work well with this activity so that the more advanced
student can help the other student with difficult problems.

Suggested Follow-Up

After completing this lesson, several lessons could be tackled. For example: