Abstract
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 3
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Numeration
- The student demonstrates conceptual understanding of simple fractions with denominators 2, 3, 4, or 10.
Grade 4
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Numeration
- The student demonstrates conceptual understanding of fractions with denominators 2 through 12.
Grade 5
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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
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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
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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
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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
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Estimation and Computation
- The student accurately solves problems (including real-world situations).
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Numeration
- The student demonstrates conceptual understanding of real numbers.
Grade 10
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Estimation and Computation
- The student accurately solves problems (including real-world situations).
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Numeration
- The student demonstrates conceptual understanding of real numbers.
Third Grade
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Number and Operations-Fractions
- Develop understanding of fractions as numbers.
Fourth Grade
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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.
Fifth Grade
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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.
Sixth Grade
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The Number System
- Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Grades 3-5
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Numbers and Operations
- Compute fluently and make reasonable estimates
Grades 6-8
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Numbers and Operations
- Compute fluently and make reasonable estimates
- Understand meanings of operations and how they relate to one another
Grade 6
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Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra
- COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.
Grade 7
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Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra
- COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.
3rd Grade
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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.
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Number and Number Sense
- 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.
- 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.
7th Grade
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Computation and Estimation
- 7.4 The student will
- 7.4a The student will solve practical problems using rational numbers (whole numbers, fractions, decimals) and percents
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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.
4th Grade
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Computation and Estimation
- 4.8
- 4.9.a
- 4.9.c
- 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.
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Number and Number Sense
- 4.2.b
- 4.2.c
- 4.3
- 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.
5th Grade
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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.
8th Grade
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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,
6th Grade
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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
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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.
Textbooks Aligned
Grade Six
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Bits and Pieces I
- Investigation One: Fund-Raising Fractions
- Investigation Four: From Fractions to Decimals
- Investigation Five: Moving Between Fractions and Decimals
- Investigation Six: Out of One Hundred
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Bits and Pieces II
- Investigation Five: Finding Areas and Other Products
Student Prerequisites
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Arithmetic:
Students must be able to:
- add, subtract, and multiply whole numbers
- work with simple fractions in lowest terms
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Technological:
Students 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
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
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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:
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Objectives
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.
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Teacher Input
- Lead students in a discussion about adding and subtracting fractions. Allow students to practice this skill by working through some practice problems as a class.
- Lead students in a discussion about multiplying and dividing fractions. Allow students to practice this skill by working through some practice problems as a class.
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Guided Practice
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.
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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.
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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: