Lesson Plan

# Fractions all Operations

Fractions, decimal and percent revisited for the high school learner
Brenda A.
Classroom teacher
Kearney West High School
Kearney, United States
My Grades 8, 9, 10, 11, 12
My Subjects Math
Objectives

Students will be able to identify the vocabulary associated with fractions, decimals and percent.

Students will add, subtract, multiply and divide fractions.

Subjects
Math
Grades 9 – 12

#### 1 Hook

I will introduce the unit of fractions by having the students watch a video from Math Antics on YouTube.  The video is a little over five minutes long.  This is just a hook to get their attention. After the video I will distribute foam circle fraction manipulatives to each student.  They will look at each piece beginning with the whole and we will investigate how many parts the circle is divided into.  They will practice with a partner saying and writing parts of a whole in fraction form.  They will stay in partners and each group will get a sheet of graph paper.  The groups will choose either color pencils or crayons.  One student will draw a figure and shade its parts and the other student will write it as a fraction.  Both students will verbally express the fraction correctly to each other.

Student Instructions

Students will watch the short video on YouTube from Math Antics that introduces a fraction and its parts.  Students will practice describing parts of a whole with circle foam manipulatives. They will look at each piece beginning with the whole and we will investigate how many parts the circle is divided into.  They will practice with a partner saying and writing parts of a whole in fraction form.  They will stay in partners and each group will get a sheet of graph paper.  The groups will choose either color pencils or crayons.  One student will draw a figure and shade its parts and the other student will write it as a fraction.  Both students will verbally express the fraction correctly to each other.

#### 2 Direct Instruction Day 1

This lesson will revolve around types of fractions. Review the previous lesson of a whole, parts of a whole and reciting and writing a fraction.  Draw or show pictures of fractions and have students identify numerator, denominator and reading the fraction.

The students will watch a video from Math Antics about types of fractions. Students will then play a game in pairs with flashcards to identify what kind of fraction it is (zero, one, proper, inproper, and  mixed number). Use the second link provided in the resources above (Fraction Flash cards) to find the set of cards you would like to use.  I find it necessary to print off multiple sets and mix them together.

Assessment of Mastery: Students will keep track of each other's scores.  They should score a 17 out of 20 cards to reach an 85% mastery level.

Student Instructions

Students will review the previous day's lesson by reading and reciting fractions through pictures.  Students will identify the numerator and denominator of each fraction.  Students will verbally read the fraction.

Students will begin the new lesson by watching the Math Antics YouTube video about types of fractions. Types of fractions discussed on zero, one, proper, improper, and mixed. Students will pair up after the video and are given a set of 20 flash cards with different kinds of fractions on them.  They will take turns identifying what kind of fraction it is as well as reading it correctly to their partner.

Assessment of Mastery: The students will keep track of correct and incorrect identification.  Each student must have 17 out of 20 for an 85% mastery score.

#### 3 Direct Instruction Day 2

Do a quick review of the previous days lesson of identifying types of fractions.  Pick one of each kind and have students orally state what kind of fraction it is.

Today's lesson we will simplify fractions as well as compare fractions.  Watch the first video about simplifying fractions then distribute white boards for the students to practice.  A list of practice fractions is provided at the bottom of this box.  Feel free to make up your own, I'm just including ideas.

After students have practiced simplifying, they will watch the video of comparing.  A good resource to use is the fraction blocks.  Distribute each of the sets to groups of 3 or 4 and have them practice comparing equivalent fractions first, using the list of fractions you just used or you can use your own.  Then use unequivilent fractions to demonstrate greater than and less than.

Assessment of Mastery: Students will complete a worksheet from the Pre-Algebra curriculum.  Must score an 85% to claim mastery.

Simplifying Fractions

Practice Fractions: Use as many as you wish.

5/10 = ½

4/6= 2/3

12/18= 2/3

15/25=3/5

17/19=prime or simplified

0/8= 0

7/7= 1

12/15=4/5

24/36=2/3

Student Instructions

Do a quick review of the previous days lesson of identifying types of fractions.  Pick one of each kind and have students orally state what kind of fraction it is.

Today's lesson we will simplify fractions as well as compare fractions.  Watch the first video about simplifying fractions then distribute white boards for the students to practice.   A list of practice fractions is provided at the bottom of this box. Feel free to make up your own, I'm just including ideas.

After students have practiced simplifying, they will watch the video of comparing.  A good resource to use is the fraction blocks.  Distribute each of the sets to groups of 3 or 4 and have them practice comparing equivalent fractions first, using the list of fractions you just used or you can use your own.  Then use unequivilent fractions to demonstrate greater than and less than.

Assessment of Mastery: Students will complete a worksheet from the Pre-Algebra curriculum.  Must score an 85% to claim mastery.

#### 4 Direct Instruction Day 3 Finding a Common Denominator

Do a short review of the previous lesson of simplifying and comparing fractions.

Today's lesson will focus on adding/subtracting fractions with unlike denominators.  Begin by giving examples of adding fractions with like denominators.  Students should grasp prior knowledge of this.  If they are having a hard time, use the fraction cubes to demonstrate how adding with like denominators work.

The next step is to watch the videos from Math Antics about ECD and LCD.  They are very similar but we want to focus mostly on LCD.  After watching the videos, students will practice finding the LCD.  They will practice by being given two factors and finding the multiples of each factor.  They will then identify the smallest/least common multiple for each factor. That is the LCD.  They should practice this on white boards until you see mastery.

Then you put the two concepts together.  Begin with easy ones like 1/2 + 1/4.  Reminding them that you can only add fractions with like denominators. Gradually move to more complex numbers. Remind them to simplify their answers (Day 2 skill) at the end.

Assessment of Mastery: Students will complete Day 4 of the Pre-Algebra curriculum.

Student Instructions

Do a short review of the previous lesson of simplifying and comparing fractions.

Today's lesson will focus on adding fractions with unlike denominators.  Begin by giving examples of adding fractions with like denominators.  Students should grasp prior knowledge of this.  If they are having a hard time, use the fraction cubes to demonstrate how adding with like denominators work.

The next step is to watch the videos from Math Antics about ECD and LCD.  They are very similar but we want to focus mostly on LCD.  After watching the videos, students will practice finding the LCD.  They will practice by being given two factors and finding the multiples of each factor.  They will then identify the smallest/least common multiple for each factor. That is the LCD.  They should practice this on white boards until you see mastery.

Then you put the two concepts together.  Begin with easy ones like 1/2 + 1/4.  Reminding them that you can only add fractions with like denominators. Gradually move to more complex numbers. Remind them to simplify their answers (Day 2 skill) at the end.

Assessment of Mastery: Students will complete Day 4 of the Pre-Algebra curriculum.

#### 5 Day 4 Adding/ Subtracting Fractions (Mixed Numbers)

Review the previous lesson of adding fractions with common denominators.

Today's lesson will coincide very closely to yesterday's only we are adding subtracting fractions to the mix.  Yesterday we focused on finding the common denominator.  When we subtract fractions we also have to find the common denominator.  When we add or subtract mixed numbers we have to also find a common denominator but we also have to add the step of changing that mixed number to an improper fraction.  We will watch the YouTube video from Math Antics about mixed numbers.

After watching the video, we will practice making mixed numbers to improper and then improper to mixed.  Plan on spending about 15 minutes doing this. Divide the class in half.  Have half the group practice mixed to improper and have the other half practice improper to mixed, then switch.

We are now ready to apply that concept to adding/subtracting fractions.

1.  Turn all mixed numbers into improper fractions.

2. Find the common denominator for the equation.  Make sure you are finding the LCD.

3. Add or subtract.  Pay attention for positive/negative signs.

4. Simplify your fraction.  Reduce then make a mixed number.

5. Does your answer make sense?  If not, what should you do? What are some things you can check?

Assessment: Complete Day 5 of Pre-Algebra Curriculum. Must have an 85% for mastery.

Student Instructions

Review the previous lesson of adding fractions with common denominators.

Today's lesson will coincide very closely to yesterday's only we are adding subtracting fractions to the mix.  Yesterday we focused on finding the common denominator.  When we subtract fractions we also have to find the common denominator.  When we add or subtract mixed numbers we have to also find a common denominator but we also have to add the step of changing that mixed number to an improper fraction.  We will watch the YouTube video from Math Antics about mixed numbers.

After watching the video, we will practice making mixed numbers to improper and then improper to mixed.  Plan on spending about 15 minutes doing this. Divide the class in half.  Have half the group practice mixed to improper and have the other half practice improper to mixed, then switch.

We are now ready to apply that concept to adding/subtracting fractions.

1.  Turn all mixed numbers into improper fractions.

2. Find the common denominator for the equation.  Make sure you are finding the LCD.

3. Add or subtract.  Pay attention for positive/negative signs.

4. Simplify your fraction.  Reduce then make a mixed number.

5. Does your answer make sense?  If not, what should you do? What are some things you can check?

Assessment: Complete Day 5 of Pre-Algebra Curriculum. Must have an 85% for mastery.

#### 6 Day 5 Multiplying Fractions

Review adding/subtracting mixed numbers.  Reviewing turning a mixed number to an improper is important as they will use that skill again today.

Multiplying fractions is like a breath of fresh air when it comes to fractions.  It is probably one of the easier concepts of fractions when it comes to operations.  It is important not to over think this concept! We are going to watch a video from Math Antics to begin explaining the process, then we will work some together.

1. Review of basic multiplication facts might be a good thing to start with.

2. Unlike adding/subtracting fractions, we do not need a common denominator.  Yay!!! If it is a mixed number, you must turn it into an improper fraction before you multiply.  Look for opportunities to simplify before you multiply! Then,  multiply straight across and you are almost finished.

3. After multiplying, simplify, either by reducing or making a mixed number or both!

It's that easy!

Assessment of Mastery: Students will play Snow Sprint Fractions on the link provided.  They will choose 8th grade, then they will choose any of the skills already learned.  All results are sent to the teacher for measurement.

Student Instructions

Review adding/subtracting mixed numbers.  Reviewing turning a mixed number to an improper is important as they will use that skill again today.

Multiplying fractions is like a breath of fresh air when it comes to fractions.  It is probably one of the easier concepts of fractions when it comes to operations.  It is important not to over think this concept! We are going to watch a video from Math Antics to begin explaining the process, then we will work some together.

1. Review of basic multiplication facts might be a good thing to start with.

2. Unlike adding/subtracting fractions, we do not need a common denominator.  Yay!!! We can just multiply straight across and we are almost finished.

3. After multiplying, simplify, either by reducing or making a mixed number or both!

It's that easy!

Assessment of Mastery: Students will play Snow Sprint Fractions on the link provided.  They will choose 8th grade, then they will choose any of the skills already learned.  All results are sent to the teacher for measurement.

#### 7 Day 6 Dividing Fractions

Review multiplying fractions, especially mixed numbers.  Turning that mixed number to improper is so important.  Also, re-visit reducing before you operate.  Answer any questions about reducing before your operate.

Today we are discussing division of fractions.  Previous skills we are using are multiplying fractions, simplifying and changing mixed numbers into improper.  Watch the Math Antics YouTube video to introduce the topic of division.  It is a good idea to stop and ask questions about reciprocals after the explanation.  This is an area of division that gets sticky for kids. Continue with the video.

Once the video has finished practice reciprocals.  Make 20 cards, 10 with fractions and 10 with their reciprocals.  Shuffle them well.  Distribute all 20 to the class. At the count of ready, set, go have students find their reciprocal match. Make sure to include some negative numbers in there too!

Send kids back to their seats.  Questions to ask about the video would be:

What is the same about multiplying and dividing fractions?

Answer: No common denominator, mixed fractions have to be turned to improper, and multiply straight across, simplify before operating, simplify when finished.

What is different about multiplying and dividing fractions?

Answer: The division sign is changed to multiplication, the second fraction is flipped or becomes the reciprocal.

If you have a mixed number, does it have to be changed before or after you flip?

Answer: Before! A mixed number must be improper before it is made the reciprocal.

What about the fraction we do not make a reciprocal? If it is a mixed number can I leave it that way?

Answer: No! It also should be changed at the same time you change the other.

For additional practice, students are given a fraction card. Make sure to make some with mixed numbers. Also make a double sided card with a multiplication sign on one side and a division side on the other.  Give each student a fraction.  Give one student the operation sign.  Students will make human equations then act out the change in problem.  For example:

Student 1 has 1/2, student 2 is the operation, student 3 has 4 3/4. The class solves the problem, but the students have to change their sign or fraction before the class can solve. So, student 1 stays the same, student 2 turns the card to multiply and student 3 has to make an improper fraction then a reciprocal.  They let the class know when they should be ready to solve.  Even if this takes a little time, let the problem solving come from the group. Plan on spending 20-30 minutes on this so each student has a chance to change and flip.

Assessment of Mastery: Day 5 of Pre-Algebra curriculum.

Student Instructions

Review multiplying fractions, especially mixed numbers.  Turning that mixed number to improper is so important.  Also, re-visit reducing before you operate.  Answer any questions about reducing before your operate.

Today we are discussing division of fractions.  Previous skills we are using are multiplying fractions, simplifying and changing mixed numbers into improper.  Watch the Math Antics YouTube video to introduce the topic of division.  It is a good idea to stop and ask questions about reciprocals after the explanation.  This is an area of division that gets sticky for kids. Continue with the video.

Once the video has finished practice reciprocals.  Make 20 cards, 10 with fractions and 10 with their reciprocals.  Shuffle them well.  Distribute all 20 to the class. At the count of ready, set, go have students find their reciprocal match. Make sure to include some negative numbers in there too!

Send kids back to their seats.  Questions to ask about the video would be:

What is the same about multiplying and dividing fractions?

Answer: No common denominator, mixed fractions have to be turned to improper, and multiply straight across, simplify before operating, simplify when finished.

What is different about multiplying and dividing fractions?

Answer: The division sign is changed to multiplication, the second fraction is flipped or becomes the reciprocal.

If you have a mixed number, does it have to be changed before or after you flip?

Answer: Before! A mixed number must be improper before it is made the reciprocal.

What about the fraction we do not make a reciprocal? If it is a mixed number can I leave it that way?

Answer: No! It also should be changed at the same time you change the other.

For additional practice, students are given a fraction card. Make sure to make some with mixed numbers. Also make a double sided card with a multiplication sign on one side and a division side on the other.  Give each student a fraction.  Give one student the operation sign.  Students will make human equations then act out the change in problem.  For example:

Student 1 has 1/2, student 2 is the operation, student 3 has 4 3/4. The class solves the problem, but the students have to change their sign or fraction before the class can solve. So, student 1 stays the same, student 2 turns the card to multiply and student 3 has to make an improper fraction then a reciprocal.  They let the class know when they should be ready to solve.  Even if this takes a little time, let the problem solving come from the group. Plan on spending 20-30 minutes on this so each student has a chance to change and flip.

Assessment of Mastery: Day 5 of Pre-Algebra curriculum.

#### 8 Fraction Wrap up

Review concepts of dividing.

Today is a review day before our written assessment on fractions tomorrow.

The class will play Fraction Jeopardy on Math Play.  We will play at the 8th grade level and we will include all concepts.

Student Instructions

Review concepts of dividing.

Today is a review day before our written assessment on fractions tomorrow.

The class will play Fraction Jeopardy on Math Play.  We will play at the 8th grade level and we will include all concepts.

#### 9 Fraction Assessment

Students will complete the attached assessment.  Students will also complete a self-assessment of skills at the end of the written assessment.

85% mastery is required.

Student Instructions

Students will complete the attached assessment.  Students will also complete a self-assessment of skills at the end of the written assessment.

85% mastery is required.