1	Lesson Plans for
Fractions	

CHAPTER LESSON PLANS & OBJECTIVES
Lesson 1.1: Changing a Fraction
1.	Changing an improper fraction to a mixed number
2.	Changing a mixed number to an improper fraction
3.	Changing a fraction to an equivalent fraction with the lowest common denominator
4.	Changing a mixed number to an equivalent fraction with the lowest common denominator

Lesson 1.2: Adding, Subtracting, Multiplying, Dividing, and Reducing a Fraction
5.	Adding fractions having the same denominator, having unlike denominators, or involving whole numbers and unlike denominators
6.	Subtracting fractions having the same denominator, having unlike denominators, or involving whole numbers and unlike denominators
7.	Multiplying fractions and mixed numbers
8.	Dividing fractions and mixed numbers
9.	Reducing a complex fraction
10.	Reducing a complex fraction involving mixed numbers
CHAPTER PRETEST
A 10-question Chapter Pretest is available on the Evolve Instructor Resources. This recall-based assessment may be administered to gauge student understanding and feeds to the instructor gradebook.

CHAPTER BACKGROUND ASSESSMENT
Discuss these questions with your students prior to covering this chapter to understand where they stand in relation to the content.

Question: What part of a fraction is the denominator?

Answer: The denominator is the number below the fraction line in a fraction, and it indicates the number of parts into which the whole has been divided.

Question: What is the lowest common denominator of the following two fractions:  and ?

Answer: The lowest common denominator is 21 because 21 can be evenly divided by 7.

LESSON 1.1
Changing a Fraction	
Instructor Preparation	Textbook Objectives Covered	
	1.	Changing an improper fraction to a mixed number
2.	Changing a mixed number to an improper fraction
3.	Changing a fraction to an equivalent fraction with the lowest common denominator
4.	Changing a mixed number to an equivalent fraction with the lowest common denominator	
	Lesson Preparation Checklist	
	•	Prepare lecture from TEACH lecture slides available on Evolve.
•	Gather problems from the Work Sheet.
•	Assemble materials and supplies needed for each lesson as indicated below.	
	Materials and Supplies	
	•	Computer or overhead projector
•	Whiteboard or blackboard and marker or chalk	•	Internet access	•	Printed handouts of the Work Sheet questions	
	Key Terms	
	•	Common denominator
•	Complex fraction
•	Denominator
•	Dividend
•	Divisor 	•	Fraction
•	Improper fraction
•	Lowest common denominator
•	Mixed number 	•	Numerator
•	Product
•	Proper fraction
•	Quotient 	
Student Preparation	Assignments	10 minutes	
	1	READ – Textbook (pp. 9-11)	
	2	READ – Textbook (p. 11)	
	3	READ – Textbook (pp. 11-12)	
	4	READ – Textbook (pp. 12-13)	

LESSON 1.1
Fractions	
50-Minute Lesson Plan	Lecture Outline	50 minutes	
	1	Slide 4	Fractions (1 of 3) (p. 10)
•	Numerator: the dividend
•	Denominator: the divisor

TALKING POINTS:
•	What is the definition of a fraction?
o	A fraction is a method of expressing the division of a whole into equal parts. Every fraction has a numerator and a denominator.
•	What is the numerator?
o	The numerator indicates the number of parts that you have of a divided whole.
•	What is the denominator?
o	The denominator indicates the number of parts into which the whole has been divided.
•	What is the definition of a complex fraction?
o	A complex fraction is one that has a fraction in its numerator, its denominator, or both.	
		Slide 5	Changing an Improper Fraction to a Mixed Number (p. 11)
•	Divide the numerator by the denominator.
•	Place the remainder over the denominator.
•	Write the proper fraction next to the whole number.
•	Example:

TALKING POINTS:
•	What is the remainder?
o	The remainder is the number left over when dividing two numbers. For example, when dividing 5 by 3, you get 1 with a remainder of 2.
•	Convert: 23/7
o	Dividing 23 by 7, you get 3 with a remainder of 2. Placing the remainder (2) over the denominator (7), you get a proper fraction of 2/7. Combining the proper fraction with the whole number obtained by dividing in the first step, you get a final answer of 3 2/7.	
	2	Slide 6	Changing a Mixed Number to an Improper Fraction (p. 11)
•	Multiply the denominator of the fraction by the whole number in the mixed number.
•	Add the product of the multiplication to the numerator of the fraction.
•	Place the sum over the denominator.
•	Example:

TALKING POINT:
•	Alert: If fractions are to be added or subtracted, their denominators must be the same.
•	Convert: 3 1/7
•	Multiplying the denominator (7) by the whole number (3), you get 21. Adding 21 to the numerator of the fraction (1), you get 22. Therefore, the final answer is 22/7.	
	3	Slide 7	Changing a Fraction to an Equivalent Fraction with the Lowest Common Denominator (p. 11)
•	Lowest common denominator (LCD)
•	Divide the LCD by the denominator of the fraction to be converted.
•	Multiply the quotient by the numerator of the fraction to be converted.
•	Place the product of the multiplication over the LCD.
•	Example: 

TALKING POINTS:
•	What is the definition of LCD?
o	It is the smallest number that can be divided evenly by all denominators in a problem.	
		Slide 8	Changing a Mixed Number to an Equivalent Fraction with the Lowest Common Denominator (p. 12)
•	Convert the mixed number to an improper fraction.
•	Divide the LCD by the denominator of the fraction to be converted.
•	Multiply the quotient by the numerator of the fraction to be converted.
•	Place the product of the multiplication over the LCD.
•	Example:

TALKING POINTS:
•	The mixed number when converted to an improper fraction will have a numerator that is equal to or larger than the denominator.
•	The LCD is the lowest number that each denominator can be divided into evenly.
•	Convert: 10 2/3 and 1/9
o	Converting 10 2/3 to an improper fraction, you get 32/3. Dividing the LCD (9) by the denominator (3) of the fraction to be converted (32/3), you get 3. Multiplying 3 by the numerator of 32/3, you get 96. Therefore, the final answer is 96/9.	

LESSON 1.1
Changing a Fraction	
	Activities	
	Classroom Choose from below to make 50 minutes	Online	
	1	ASSESS BASELINE
•	Have the class complete the Pretest. Collect their work and use the results to guide how you teach the class.	ASSESS BASELINE
•	Post the Pretest and the Background Assessment online and have your class complete them. Use the results to guide how you teach the class.	
	2	PRACTICE
•	Have students work together in groups of three or four on the handout of the Fractions Work Sheet, the first two sets of 12 questions. For all Class Activities, periodically rotate through the groups to check on progress and answer questions. Present the answers later to the class as a whole.	PRACTICE
•	Post the handout of the Fractions Work Sheet, the first two sets of 12 questions. Have students submit their work for review.	
	3	PRACTICE
•	Have two teams of students race at the blackboard to convert mixed numbers to equivalent fractions with the LCD. The rest of the class should suggest mixed numbers. The team that converts the mixed number correctly gets 1 point. The team with the most points wins.	PRACTICE
•	Post mixed numbers for students to convert to equivalent fractions with the LCD. Have students submit their work for review.	
	4	DISCUSS
•	Have students discuss why they might want to have fractions in terms of their LCDs. One example might be to make adding fractions easier (e.g.,  cup plus  cup is equal to 1 cup).	POST & COMMENT
•	Ask students why they might want to have fractions in terms of their LCDs. One example might be to make adding fractions easier (e.g.,  cup plus  cup is equal to 1 cup). Have students post their comments.	
	Critical Thinking Question	
	When are mixed numbers more useful than improper fractions?

Discussion Guidelines: Often, mixed numbers are more useful than improper fractions when you just want a feel for roughly how much of something you have. For example, do you have more or less than 1? Improper fractions are easier to add, subtract, multiply, and divide.	

LESSON 1.1
Changing a Fraction	
Instructor Notes/Student Feedback	

	

LESSON 1.2
Adding, Subtracting, Multiplying, Dividing, and Reducing a Fraction	
Instructor Preparation	Textbook Objectives Covered	
	5.	Adding fractions having the same denominator, having unlike denominators, or involving whole numbers and unlike denominators
6.	Subtracting fractions having the same denominator, having unlike denominators, or involving whole numbers and unlike denominators
7.	Multiplying fractions and mixed numbers
8.	Dividing fractions and mixed numbers
9.	Reducing a complex fraction
10.	Reducing a complex fraction involving mixed numbers	
	Lesson Preparation Checklist	
	•	Prepare lecture from TEACH lecture slides available on Evolve.
•	Gather problems from the Work Sheet.
•	Assemble materials and supplies needed for each lesson as indicated below.	
	Materials and Supplies	
	•	Computer or overhead projector
•	Whiteboard or blackboard and marker or chalk	•	Internet access	•	Printed handouts of the Work Sheet questions	
	Key Terms	
	•	Canceling
•	Minuend 	•	Mixed number
•	Simple fraction 	•	Subtrahend 	
Student Preparation	Assignments	30 minutes	
	5	READ – Textbook (pp. 13-15)
SOLVE – PRETEST – Part 1, Review of Mathematics Pretest, questions 1-7
	
	6	READ – Textbook (pp. 15-17)
SOLVE – PRETEST – Part 1, Review of Mathematics Pretest, questions 8-14	
	7	READ – Textbook (pp. 17-18)
SOLVE – PRETEST – Part 1, Review of Mathematics Pretest, questions 15-22	
	8	READ – Textbook (p. 18-19)
SOLVE – PRETEST – Part 1, Review of Mathematics Pretest, questions 23-30	
	9	READ – Textbook (p. 19)
	
	10	READ – Textbook (p. 20)
	
50-Minute Lesson Plan	Lecture Outline	50 minutes	
	5	Slide 10	Adding Fractions Having the Same Denominator (p. 13)
•	Add the numerators.
•	Place the sum of the numerators over the common denominator.
•	Reduce the resulting fraction to lowest terms.
•	Example:
Add:

TALKING POINTS:
•	The numerator is the number above the line in a fraction.
•	The denominator is the number below the line in a fraction.
•	If the numbers below the line are the same, that is their common denominator.	
		Slide 11	Adding Fractions Having Unlike Denominators (p. 13)
•	Convert fractions to equivalent fractions with the LCD.
•	Add the numerators.
•	Place the sum of the numerators over the LCD.
•	Reduce the resulting fraction to lowest terms.
•	Example:
Add:

TALKING POINTS:
•	Remember that LCD is the LCD.
•	The numerators being added are the numerators of the equivalent fractions.
•	Add: 2/3 + 1/9
o	Converting the fractions to equivalent fractions with the LCD (9), you get 6/9 and 1/9. Adding the numerators, 6 and 1, you get 7. Placing the sum (7) over the common denominator, you get 7/9. Reducing 7/9 to lowest terms, you get the final answer, 7/9.	
		Slide 12	Adding Fractions Involving Whole Numbers and Unlike Denominators (1 of 2) (p. 14)
•	Convert the fractions to equivalent fractions with the LCD.
•	Add the numerators of the equivalent fractions.
•	Place the sum of the numerators over the LCD.

TALKING POINT:
•	This method works for fractions of all kinds. If there are mixed numbers, add the whole number portions of the mixed numbers separately, then add the fractions, and finally recombine the added whole numbers with the added fractions.	
		Slide 13	Adding Fractions Involving Whole Numbers and Unlike Denominators (2 of 2) (p. 14)
•	Reduce the resulting fraction to lowest terms.
•	Write the reduced fraction next to the sum of the whole numbers.
•	Example:
Add:

TALKING POINTS:
•	Add: 5 2/3 + 1 1/9
o	In this case, you have already added the fractions in the last exercise, getting 7/9 for the sum of 2/3 and 1/9. Therefore, the next step is to write the reduced fraction next to the sum of the whole numbers (5 + 1 = 6). The final answer is 6 7/9.	
	6	Slide 14	Subtracting Fractions Having the Same Denominator (p. 15)
•	Subtract the numerator of the subtrahend from the numerator of the minuend.
•	Place the difference between the numerators over the common denominator.
•	Reduce the resulting fraction to lowest terms.
•	Example:
Subtract:

TALKING POINTS:
•	What is the subtrahend?
o	The subtrahend is the fraction that is being subtracted from the other fraction (minuend). It typically appears to the right of the minus sign (or below it).
•	What is the minuend?
o	The minuend is the fraction from which the other fraction (subtrahend) is being subtracted. It typically appears to the left of the minus sign (or above it).	
		Slide 15	Subtracting Fractions with Unlike Denominators (p. 15)
•	Convert fractions to equivalent fractions with the LCD.
•	Subtract the numerators.
•	Place the difference between the numerators over the common denominator.
•	Reduce the resulting fraction to lowest terms.
•	Example:
Subtract:

TALKING POINTS:
•	Remember that LCD is the lowest common denominator.
•	The numerators being subtracted are the numerators of the equivalent fractions.	
		Slide 16	Subtracting Fractions Involving Whole Numbers and Unlike Denominators
(1 of 2) (p. 16)
•	Convert fractions to equivalent fractions with the LCD.
•	Subtract the numerators of the equivalent fractions.
•	Place the difference between the numerators over the common denominator.

TALKING POINTS:
•	This method works for fractions of all kinds. If there are mixed numbers, subtract the whole number portions of the mixed numbers separately, then subtract the fractions, and finally recombine the subtracted whole numbers with the subtracted fractions.
•	See the example on the next slide.	
		Slide 17	Subtracting Fractions Involving Whole Numbers and Unlike Denominators
(2 of 2) (p. 16-17)
•	Reduce the resulting fraction to lowest terms.
•	Write the reduced fraction next to the difference between the whole numbers.
Example:
Subtract:

TALKING POINTS:
•	Subtract: 5 2/7 – 1/14
o	Changing the fractions to equivalent fractions gives 4/14 for 2/7 and 1/14 for 1/14. The difference between the two fractions is 3/14, which is already in lowest terms. The difference between the whole numbers is 5. Therefore, the final answer is 5 3/14.	
	7	Slide 18	Multiplying Fractions and Mixed Numbers (p. 17)
•	Convert any mixed numbers to improper fractions.
•	Multiply the numerators.
•	Multiply the denominators.
•	Place the product of the numerators over the product of the denominators.
•	Reduce the resulting fraction to lowest terms.

TALKING POINT:
•	The numerators and denominators being multiplied are those of the improper fractions.	
	8	Slide 19	Dividing Fractions and Mixed Numbers (p. 18)
•	Convert any mixed numbers to improper fractions.
•	Invert the divisor.
•	Multiply the two fractions.
•	Reduce the resulting fraction to lowest terms.

TALKING POINTS:
•	The divisor, in this case, is the fraction by which the other fraction is being divided. The divisor typically appears to the right of the division sign (or below it).
•	The dividend, in this case, is the fraction that is being divided by the other fraction. The dividend typically appears to the left of the division sign (or above it).
•	The two fractions being multiplied are the dividend and the inverted divisor. They should have been converted to improper fractions (if they were mixed numbers) before being multiplied.	
	9	Slide 20	Reducing a Complex Fraction (p. 19)
•	Rewrite the complex fraction as a division problem.
•	Invert the divisor.
•	Multiply the two fractions.
•	Reduce to lowest terms.

TALKING POINTS:
•	Rewriting the complex fraction as a division problem helps to visually simplify the question.
•	The divisor follows the division sign.
•	Multiply the numerators and place them over the answer when you multiply the denominators.
•	If the result is an improper fraction, reduce to lowest terms.	
	1 0	Slide 21	Reducing a Complex Fraction with Mixed Numbers (p. 20)
•	Rewrite the complex fraction as a division problem.
•	Change the mixed numbers to improper fractions.
•	Invert the divisor.
•	Multiply the two fractions.
•	Reduce to lowest terms.

TALKING POINTS:
•	Reduce: (5 3/7) / (1 1/5)
o	Converting the mixed numbers to improper fractions gives 38/7 for 5 3/7 and 6/5 for 1 1/5. Rewriting this as a division problem, you have 38/7 ÷ 6/5. The inverted divisor is 5/6, and the product of the fractions is 190/42. Therefore, reducing to lowest terms, the final answer is 4 11/21.	

LESSON 1.2
Adding, Subtracting, Multiplying, Dividing, and Reducing a Fraction	
	Activities	
	Classroom Choose from below to make 50 minutes	Online	
	5	PRACTICE
•	Have students work together in groups of three or four on questions 1-12 from the Fractions Work Sheet section “Add and reduce fractions to the lowest terms.”	PRACTICE
•	Post questions 1-12 from the Fractions Work Sheet section “Add and reduce fractions to the lowest terms.” Have students submit their answers for review.	
	6	PRACTICE
•	Have students work together in groups of three or four on questions 1-12 from the Fractions Work Sheet section “Subtract and reduce fractions to the lowest terms.”	PRACTICE
•	Post questions 1-12 from the Fractions Work Sheet section “Subtract and reduce fractions to the lowest terms.” Have students submit their answers for review.	
	7	PRACTICE
•	Have two groups of students compete at the board to solve questions 1-12 from the Fractions Work Sheet section “Multiply and reduce fractions to the lowest terms.” The first group to correctly answer the question gets 1 point, and the group with the most points at the end wins.	PRACTICE
•	Post questions 1-12 from the Fractions Work Sheet section “Multiply and reduce fractions to the lowest terms.” Have students submit their answers for review.
	
	8	PRACTICE
•	Have students work together in groups of three or four on the handout of the Fractions Work Sheet.	PRACTICE
•	Post questions 1-12 from the Fractions Work Sheet section “Divide and reduce fractions to the lowest terms.” Have students submit their answers for review.	
	9	DISCUSS
•	Ask students to discuss the relationship among multiplying fractions, dividing fractions, and reducing complex fractions. Then have a volunteer explain how the three processes are related to one another. Get the class involved and make certain that they understand the relationship before moving on.	POST & COMMENT
•	Post the statement, “Discuss the relationship between multiplying fractions, dividing fractions, and reducing complex fractions.” Ask students how the three processes are related to one another. Make certain that students understand the relationship before moving on.	
	10	PRACTICE
•	Have pairs of students go to the board and compete to reduce complex fractions and to reduce complex fractions containing mixed numbers.	PRACTICE
•	Assign students to create two complex fractions containing mixed numbers and apply the five steps needed to reduce the fractions to the lowest terms.	

LESSON 1.2
Adding, Subtracting, Multiplying, Dividing, and Reducing a Fraction	
	Critical Thinking Question	
	When are mixed numbers more useful than improper fractions?

Discussion Guidelines: Mixed numbers often are more useful than improper fractions when you just want a feel for roughly how much of something you have. For example, do you have more or less than 1? Improper fractions are easier to add, subtract, multiply, and divide.	
Instructor Notes/Student Feedback	

	

1	Assessments for
Fractions	

CHAPTER OBJECTIVES
Lesson 1.1: Changing a Fraction
1.	Changing an improper fraction to a mixed number
2.	Changing a mixed number to an improper fraction
3.	Changing a fraction to an equivalent fraction with the lowest common denominator
4.	Changing a mixed number to an equivalent fraction with the lowest common denominator

Lesson 1.2: Adding, Subtracting, Multiplying, Dividing, and Reducing a Fraction
5.	Adding fractions having the same denominator, having unlike denominators, or involving whole numbers and unlike denominators
6.	Subtracting fractions having the same denominator, having unlike denominators, or involving whole numbers and unlike denominators
7.	Multiplying fractions and mixed numbers
8.	Dividing fractions and mixed numbers
9.	Reducing a complex fraction
10.	Reducing a complex fraction involving mixed numbers

Assessments by Lesson & Objective	
Lesson 1.1	1	Text
•	Posttest 1: questions 1-30
 Posttest 2: questions 1-30 	
	2	•	Posttest 1: questions 1-30
Posttest 2: questions 1-30 	
	3	•	Posttest 1: questions 1-30
Posttest 2: questions 1-30 	
	4	•	Posttest 1: questions 1-30
 Posttest 2: questions 1-30 	

Assessments by Lesson & Objective	
Lesson 1.2	5	Text
•	Posttest 1: questions 1-7
•	Posttest 2: questions 1-7

Evolve
•	Drug Calculations Comprehensive Test Bank 01A
o	Create a quiz using ExamView; sort by objective	
	6	Text
•	Posttest 1: questions 8-14
•	Posttest 2: questions 8-14

Evolve
•	Drug Calculations Comprehensive Test Bank 01A
o	Create a quiz using ExamView; sort by objective	
	7	Text
•	Posttest 1: questions 15-22
•	Posttest 2: questions 15-22

Evolve
•	Drug Calculations Comprehensive Test Bank 01A
o	Create a quiz using ExamView; sort by objective	
	8	Text
•	Posttest 1: questions 23-30
•	Posttest 2: questions 23-30

Evolve
•	Drug Calculations Comprehensive Test Bank 01A
o	Create a quiz using ExamView; sort by objective	
	9	Text
•	Posttest 1: questions 1-30
•	Posttest 2: questions 1-30 	
	10	Text
•	Posttest 1: questions 1-30
•	Posttest 2: questions 1-30 	
Instructor’s Notes/Student Feedback