Multiplying Fractions Unit...

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Multiplying Fractions Unit Plan EPSY581L-256

Lauren Clarke

12/9/2013

Introduction

This unit plan on multiplying fractions serves as an introduction to multiplying two

fractions. It is designed to meet the Common Core State Standard: Number & Operations –

Fractions Standard 4a and 4b for grade 5. Standard 4 requires students to multiply a fraction or

whole number by a fraction using visual fraction models and by multiplying the numerators and

multiplying the denominators, placing the first product over the second product. This standard

also requires students to apply their knowledge of area and multiplying fractions to find the area

of a rectangle with fractional side lengths.

I chose to focus on multiplying fractions for this unit because the majority of students and

adults when asked how to multiply two fractions, will tell you to multiply the numerators and

write this product over the product of the denominators. Although they are correct, the majority

of these individuals do not understand why the answer is what it is and if asked to show this

problem visually or with concrete manipulatives, will not be able to. The Common Core State

Process Standards require students to conceptually understand the mathematical process rather

than the memorization of rules and the constant procedural practice. As a teacher I value students

understanding the meaning behind mathematical concepts and desire to have my students

understand what is truly occurring when they are multiplying two fractions rather than just being

able to arrive at the correct answer.

However, in “Day 4: Multiplying Two Fractions: Strategy for Checking Your Work” I

decided to introduce students to the procedural strategy used to multiply fractions. I introduce

this procedure towards the end of the unit and would only do so once I am sure students have

gained a full understanding of the process of multiplying two fractions as taking a part of a part

and can visually represent the answer. During this fourth lesson I also emphasize that students

are to use this procedural strategy to check their work and not as an alternate method to

multiplying fractions. I emphasize this to make sure students continue to gain a deeper

understanding of what multiplying two fractions truly means, while also preparing them with a

quicker strategy to use in the future as numbers increase and fractions become more difficult.

Although the Common Core State Standards focus on students gaining a conceptual

understanding of mathematics, teachers need to also make their lessons engaging and

memorable. The fifth grade students participating in my unit will have a difficult time gaining an

understanding of what is occurring when multiplying two fractions unless the lessons capture

their interest. Therefore I strive to teach mathematics conceptually, rather than procedurally

while also making my lessons fun and engaging, to create a learning experience students will

never forget. Each lesson in this unit uses concrete manipulatives including Pattern Blocks,

ingredients, quesadillas, candy, a tablecloth, various food items, literature, and clay. The use of

these items helps students gain a better understanding of the process of multiplying fractions,

while also capturing their attention and interest. The strategic use of these items also provides

students with real life connections to multiplying fractions. By seeing how multiplying fractions

is necessary when doubling recipes, serving food such as quesadillas, and dividing candy bars,

students will value multiplying fractions and be more motivated to learn.

Day 1: Multiplying a Whole Number by a Fraction Title: Let’s Double It! Grade: Fifth NYS Common Core Standards and NCTM Standards: NYS Common Core Standards:

• Number & Operations- Fractions (5.NF): • Apply and extend previous understandings of multiplication and division to

multiply and divide fraction. 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd)

NCTM Standards:

• Number and Operations Standard for Grade 3-5 o develop understanding of fractions as parts of unit wholes, as parts of a collection,

as locations on number lines, and as divisions of whole numbers o use models, benchmarks, and equivalent forms to judge the size of fractions o understand various meanings of multiplication and division

Learning Objectives:

• Students will correctly read a fraction multiplication problem using the word “of”. • Students will understand how to multiply a whole number by a fraction. • Students will multiply a whole number by a fraction using Pattern Blocks. • Students will relate multiplying a whole number by a fraction to recipes. • Students will explain how to multiply a whole number by a fraction.

Materials:

• “Pattern Block Fractions” worksheets • Pattern Blocks • “Dirt Dessert Time!” activity sheets • Chocolate pudding • Oreos • Ziploc bags to crush the Oreos in • Cool Whip • Gummy worms • Mixing bowl • Spoon • Measuring cup

• Plastic cups • Exit Cards: “Oh No!”

Instructional Plan: Introduction:

• The teacher will activate prior knowledge of multiplication of whole numbers emphasizing the language used.

o 2 x 2 is 2 groups of 2 use word “groups” because we have more than 1 whole number

o 2 x ½ is 2 groups of ½ o 1/3 x 2 is 1/3 of 2

just “of” instead of “groups of” because a fraction is a part of a whole and less than 1

Modeling:

• The teacher will use Pattern Blocks to model solving 2 x ½ by reading the problem as “2 groups of ½.”

• He or she will “think aloud” and take 2 parallelogram Pattern Blocks. He or she will show how 2 parallelogram Pattern Blocks equal 1 hexagon, or 1 whole.

Guided Practice:

• As a class, students will solve the problems on their “Pattern Block Fractions” worksheets, using Pattern Blocks.

• The teacher will discuss why when multiplying a whole number by a fraction the product is often less than 1 by asking students:

o “When you multiply two whole numbers what do you notice about the size of the product?”

o “What do you notice about the size of the product when multiplying 2 x ½ ? Why do you think the product is small?” “Do you think this will always be the case? Why?”

Independent Practice:

• In groups of 4, students will complete the “Dirt Dessert Time!” activity. o Students will double a recipe for Dirt Dessert by multiplying the fraction of each

ingredient by 2.

Assessment:

• Students will complete the “Oh No!” exit cards where they have to triple each ingredient in the original dirt dessert recipe in order to have enough dirt dessert for their two hypothetical new classmates.

Name: __________________________________ Date: _____________

Patten Block Fractions

We read 2 x ½ as 2 ____________________ ½. Directions: Solve the following multiplication of a fraction by a whole number problems using Pattern Blocks. Show your work below. 1. 2 x ½

2. 3 x 1/6

3. 3 x 1/6

4. 2 x 1/6

5. 4 x ½

6. 1 x 1/3

7. 3 x 1/2

Name: ___________________________________ Date: _____________

Dirt Dessert Time! Recipe: Dirt Dessert Serves: 2 people Directions: Combine the chocolate pudding, Oreo Cookie crumbs, and Cool Whip in one bowl. Pour the mixture into smaller cups. Add the worms on top. Refrigerate the mixture for 1 hour. Enjoy! • ½ cup of chocolate pudding • 1/3 cup of crushed Oreo Cookie crumbs • ¾ cup of Cool Whip • ¼ cup of gummy worms This recipe only serves 2 people. Since your group has 4 people, what do you need to multiply each ingredient by in order to have enough Dirt Dessert for all 4 people? ___________ Determine how much of each ingredient you need in order to make the recipe for 4 people instead of 2 people. Use Pattern Blocks to help you.

Serves 2 people Serves 4 people

½ cup of chocolate pudding

1/3 cup of crushed Oreo Cookie Crumbs

¾ cup of Cool Whip

¼ cup of gummy worms

Name: __________________________________ Date: _____________

Oh No!

You were just informed that you have 2 new students joining your class…TODAY! You need to make sure you have enough Dirt Dessert for them when they arrive. Since the recipe only serves 2 people and you now need enough for 6 people what do you need to multiply each ingredient (from your original recipe, not your doubled recipe) by in order to have enough Dirt Dessert for all 6 people? ___________ Determine how much of each ingredient you need in order to make the recipe for 6 people instead of 2 people. Use Pattern Blocks to help you.

Serves 2 people Serves 6 people

½ cup of chocolate pudding

1/3 cup of crushed Oreo Cookie Crumbs

¾ cup of Cool Whip

¼ cup of gummy worms

Day 2: Multiplying a Fraction by a Fraction Title: Fraction’dilla Grade: Fifth NYS Common Core Standards and NCTM Standards: NYS Common Core Standards:


multiply and divide fractions. 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd)

NCTM Standards:


as locations on number lines, and as divisions of whole numbers o use models, benchmarks, and equivalent forms to judge the size of fractions o understand various meanings of multiplication and division


• Students will correctly read a fraction multiplication problem using the word “of”. • Students will understand how to multiply two fractions. • Students will multiply two fractions using hands on manipulatives. • Students will represent the multiplication of two fractions visually. • Students will explain how to multiply two fractions.

Materials:

• SMART Board • tortilla shells • plastic knives • “Quesadilla Place Mats” glued on plates • “Welcome to Fraction’dilla” activity sheets • “Fraction Riddle” sheets • “Fun Fraction Frenzy” riddles • fraction problem sheets • candy • envelopes • roll of tape

Instructional Plan: Before the lesson:

• The teacher will hide the following envelopes with their corresponding problem sheet and candy.

o Envelope A: Hershey’s bar (water fountain) o Envelope B: Kit-Kat (bulletin board) o Envelope C: Twizzlers (under newspaper)

Introduction:

• The teacher will activate prior knowledge of multiplication of a whole numbers by a fraction emphasizing the language used.

o 2 x ¼ is 2 groups of ¼ use word “groups” because we have more than 1 group

• The teacher will introduce the multiplication of a fraction by a fraction emphasizing the language used.

o 2/3 x ½ is 2/3 of ½ just “of” instead of “groups of” because a fraction is a part of a whole and

less than 1

Guided Practice:

• The teacher will give each student a “Quesadilla Place Mat” and “Welcome to Fraction’dilla” activity sheet.

• The teacher will have students sit in pairs and give each pair 4 tortilla shells. • The teacher will welcome the students to her restaurant Fraction’dilla and tell them they

will be fulfilling quesadilla orders by multiplying fractions. • The teacher will refer back to the previous example of 2 x 2 and ask students to represent

2 x 2 using the tortilla shells. • The teacher will ask the students to explain their thought process when representing 2 x

2. (started with 2, made 2 groups of 2) • Model:

o The teacher will announce that the first order to the restaurant is in and the customer wants ½ x ¼ quesadilla.

o The teacher will think aloud while completing the problem with a tortilla shell. I must start with a whole quesadilla. I need ½ of a ¼, so let me take ¼ of a whole. Now let me take ½ of a ¼ so ½ of this ¼ . Let me compare this piece to the original on my “Quesadilla Place Mat.” I have ⅛ of a whole quesadilla so that means ½ x ¼ is ⅛!

o Students will follow along, showing their work on their “Welcome to Fraction’dilla” activity sheets and writing the answer on the line provided.

• As a class:

o Students will complete orders 2 and 3 on their “Welcome to Fraction’dilla” activity sheets using the tortillas and showing all work on their activity sheet.

⅔ x ½ ¼ x ¼

• In pairs: o Students will complete order 4 on their “Welcome to Fraction’dilla” activity

sheets. ⅓ x ½ The teacher will ask one pair to explain their work to the class.


• The teacher will give each student a “Fraction Riddle” sheet and as a class they will complete the riddle.

• The teacher will then divide students into 3 groups and explain that in their groups they will have to solve a riddle which will reveal the location of a multiplication fraction problem they must solve.

• The teacher will give each group a different “Fun Fraction Frenzy” riddle and allow the students to go find their problem once the riddle is complete.

• Groups will return to the classroom with their problem and solve their problem. • Groups will present their problem and explain/show how they solved it to the class. • The students will discuss what they learned about the multiplication of fractions and ask

any questions they may have.

Assessment:

• The teacher will complete a checklist during the presentations of the Fun Fraction Frenzy activity.

• Each student will individually complete the formative assessment, “How do you feel about multiplying fractions?”

Quesadilla Place Mat

Name: ________________________________________ Date: ______________

Welcome to Fraction’dilla!

Hello chef! You will be helping us make quesadillas for our customers by solving multiplication fraction problems. Cut the actual quesadilla and then draw your answer on the quesadillas images below.

Remember: when multiplying fractions, read “x” as “of.” Good luck!

Order 3:

¼ x ¼ = _______

Order 2:

⅔ x ½ = _______

Order 4:

⅓ x ½ = _______

Order 1:

½ x ¼ = _______

Fraction Riddle

Use the clues to solve the riddle! Write the answers to each clue in order

on the blank lines below.

What goes up and never goes down?

Clue 1: First ⅓ of YOGURT

Clue 2: First ½ of UP

Clue 3: First ¼ of READ

Clue 4: second ⅕ of TABLE

Clue 5: Last ⅓ of ORANGE

Answer: ______ ______ ______ ______ ______ ______ ______ (Clue 1) (Clue 2) (Clue 3) (Clue 4) (Clue 5)

Names: _____________________________________________________________ Date: _______________

Group A: Fun Fraction Frenzy!

Use the clues to solve the mystery word(s) that will tell you where your problem is hidden! Write the answers to each clue in order on the blank lines below. Then go find your problem!

Remember: You may have to leave the classroom…

Clue 1: First ½ of WAIT

Clue 2: Last ⅗ of LATER

Clue 3: First ⅔ of FOX

Clue 4: Last ¾ of HUNT

Clue 5: Last ½ of REMAIN

Answer: ______ ______ ______ ______ ______

______ ______ ______ ______ ______ ______ ______ ______

(Clue 1) (Clue 2)

(Clue 3) (Clue 4) (Clue 5)

Names: _____________________________________________________________ Date: _______________

Group B: Fun Fraction Frenzy!



Clue 1: First ½ of BULLFROG

Clue 2: Last ⅔ of WET

Clue 3: First ⅓ of INDOOR

Clue 4: First ⅖ of BOATS

Clue 5: Last ¾ of CARD

Answer: ______ ______ ______ ______ ______ ______ ______ ______

______ ______ ______ ______ ______

(Clue 1) (Clue 2)

(Clue 4) (Clue 5)

(Clue 3)

Names: _____________________________________________________________ Date: _______________

Group C: Fun Fraction Frenzy!



Clue 1: Last ⅓ of ANYONE

Clue 2: Last ½ of JAWS

Clue 3: Second ⅓ of APE

Clue 4: First ⅖ of APPLE

Clue 5: Last ⅖ of DRIVER

Answer: ______ ______ ______ ______ ______ ______ ______ ______ ______

(Clue 1) (Clue 2)

6

(Clue 3) (Clue 4) (Clue 5)

Names: _____________________________________________________________ Date: _______________

Group A: Fun Fraction Frenzy!

Congratulations! You found your problem! Solve the fraction multiplication problem below using the candy provided.

Create a drawing to show your work and write your answer on the line. Prepare to present your problem and how you solved it to the class.

⅔ x ½ Drawing: Answer: ___________

Names: _____________________________________________________________ Date: _______________

Group B: Fun Fraction Frenzy!



⅔ x ¾ Drawing: Answer: ___________

Names: _____________________________________________________________ Date: _______________

Group C: Fun Fraction Frenzy!



½ x ⅘ Drawing: Answer: ___________

6 10

Name: ___________________________ Date: _________ How do you feel about multiplying fractions?

Directions: Circle the thumb up if you understand, thumb in the middle if you somewhat understand, and thumb down if you do not understand yet. If you circled the • thumb up: explain how to multiply fractions. • thumb in the middle: explain what you do and do not understand. • thumb down: explain what you do not understand and ask at least one question.

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

Name: ___________________________ Date: _________ How do you feel about multiplying fractions?

Directions: Circle the thumb up if you understand, thumb in the middle if you somewhat understand, and thumb down if you do not understand yet. If you circled the • thumb up: explain how to multiply fractions. • thumb in the middle: explain what you do and do not understand. • thumb down: explain what you do not understand and ask at least one question.

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

“Fun Fraction Frenzy!” Teacher Checklist

Student Demonstrates understanding of

multiplying two fractions

Comments

Each student will receive a check plus if he or she has mastered the topic, a check if he or she understands the topic, and a check minus if he or she is still learning the topic.

Day 3: Area of a Rectangle with Fractional Side Lengths

Title: Let’s Go on a Picnic! Grade: Fifth NYS Common Core Standards and NCTM Standards: NYS Common Core Standards:



b. find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

NCTM Standards:


as locations on number lines, and as divisions of whole numbers o use models, benchmarks, and equivalent forms to judge the size of fractions o understand various meanings of multiplication and division o develop and use strategies to estimate computations involving fractions and

decimals in situations relevant to students' experience


• Students will understand how to find the area of a rectangle with fractional side lengths. • Students will multiply two fractions to find the area of a rectangle. • Students will represent the multiplication of two fractions visually. • Students will explain how to multiply two fractions to find the area of a rectangle by

through a presentation.

Materials:

• Paper • Transparencies • Markers for the transparencies • Rulers • “Multiplication Madness” worksheets • Markers • Color pencils

• Tablecloth • Rectangular shaped cornbread • Rectangular shaped cake • Rectangular shaped whole brownie • Plastic knives • Plates • “Let’s Go on a Picnic” worksheets • Teacher checklist

Instructional Plan:

Introduction:

• The teacher will activate prior knowledge by asking students to recall the formula for finding the area of a rectangle.

• As a class students will use the formula A = lw to find the area of a rectangle drawn on the board with a length of 8in and width of 9in.

• The teacher will ask students, “Do you think we could use this formula to find the area of a rectangle if the side lengths are fractions? Why?”

Modeling:

• The teacher will model finding the area of a rectangle with sides of length ½ and 1/3. • He or she will solve the problem ½ x 1/3 by dividing a rectangle on a piece of paper into

thirds and labeling the thirds on one of the corresponding sides of the rectangle. • He or she will shade 1 of these thirds using one color. • He or she will then divide a rectangle on a transparency of the same size as the paper one,

into halves, and label the halves on one of the corresponding sides of the rectangle. • He or she will shade 1 of these halves using a different color. • The teacher will then overlap the transparency onto the paper and point out where the

shadings overlap and the new total number of equal parts the rectangle is divided into. • The teacher will model counting the boxes and realizing the answer is 1/6 of the whole

rectangle.

Guided Practice:

• As a class, students will repeat the steps the teacher took while modeling for the problems on the worksheet “Multiplication Madness.”

• The teacher will then present a table cloth representing a picnic blanket and tell students the class is going on a picnic but only needs 2/3 of 3/4 of the tablecloth.

• The teacher will ask students, “Estimate how much tablecloth the product will be? Do you think the product be larger than 1 or smaller than 1? Why?”

• As a class, students will draw lines using a yard stick and marker on the tablecloth to divide it into quarters first, shading 3 of the quarters with lines using one color marker.

• Students will then divide the tablecloth into thirds and shade 2 of the thirds using a different color marker. Students will see that 6/12 of the tablecloth is shaded by both colors.


• The teacher will ask students, “Now that we have our picnic blanket ready, what is missing?”

• The teacher will divide students into groups of 3-4 students. • Each group will receive one of the following rectangular foods:

o Cornbread o Cake o Whole brownie

• Each group will also receive a multiplication of two fractions problem on their “Let’s Go on a Picnic” activity sheets.

• The teacher will ask groups, “Before solving your problem, estimate the size of the food you will bring on the picnic by looking at the fractions in your multiplication problem.”

• Students will share their thoughts and reasoning. • Groups will solve their problem by creating and shading visual models on their “Let’s Go

on a Picnic” activity sheets and using a transparency if necessary. • Once a group’s work is approved they will cut their food item by dividing it into

fractional side lengths to represent the portion of their rectangular shaped food they will be bringing on the picnic.

Assessment:

• Each group will present their portion of the food item resulting from their multiplication of two fractions problem explaining how they arrived at their answer using visual supports.

• The teacher will complete a checklist as a method of formative assessment.

Name: __________________________________ Date: _____________

Multiplication Madness

Directions: Use the rectangular papers and transparencies to find the areas of the following problems. Show your work below. 2/3 x ¾ = _____________ (divide into quarters and (divide into thirds and (combine the first 2 shade 3/4) shade 2/3) boxes and shadings)

2/3 x 1/2 = _____________ 1/2 x 5/6 = ______________

Name: __________________________________ Date: _____________

Let’s Go on a Picnic! Group 1

Directions: Show your work for how we determined as a class the area of the picnic blanket we need below. ½ x 1/3 = _____________

Directions: In your group, determine the area of the cornbread you need and show all work below. Once your work is approved by the teacher, cut the correct amount of cornbread. 1/4 x 2/3 = _____________

Name: __________________________________ Date: _____________



Directions: In your group, determine how much brownie you need and show all work below. Once your work is approved by the teacher, cut the correct amount of brownie. 4/5 x 1/2 = _____________

Name: __________________________________ Date: _____________



Directions: In your group, determine how much cornbread you need and show all work below. Once your work is approved by the teacher, cut the correct amount of cornbread. 3/5 x 2/3 = _____________

“Let’s Go on a Picnic” Teacher Checklist

Student

Demonstrates understanding of finding the area of a rectangle

with fractional side lengths.

Comments

Each student will receive a check plus if he or she has mastered the topic, a check if he or she understands the topic, and a check minus if he or she is still learning the topic.

Day 4: Multiplying Two Fractions: Strategy for Checking Your Work

Title: Multiplying Menace Grade: Fifth NYS Common Core Standards and NCTM Standards: NYS Common Core Standards:



a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd). b. find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

NCTM Standards:





• Students will understand the strategy for checking their work when multiplying two fractions.

• Students will use this strategy when solving word problems multiplying two fractions. • Students will create word problems multiplying two fractions based on literature. • Students will solve word problems multiplying two fractions based on literature. • Students will reflect on what they have learned and still have questions about.

Materials:

• Multiplying Menace: The Revenge Of Rumpelstiltskin

• “Multiplying Menace” worksheets • Exit Cards: “3-2-1”

Instructional Plan:

Introduction:

• The teacher will activate prior knowledge by having students solve the following word problem multiplying a fraction by a whole number using visual representation:

o 3 x 1/5 • The teacher will ask students, “Is there another way the number 3 can be written?” • He or she will prompt students by asking if there is another way the number 3 can be

written in fractional form. • The teacher will discuss how 3 can also be written as 3/1. • The teacher will then rewrite 3 x 1/5 as 3/1 x 1/5 and ask students if they see another way

to get the solution 3/5 using multiplication of some combination of the whole numbers in the numerators and denominators.

• The teacher will guide students to the process that the product of the numerators over the product of the denominators also results in the correct answer.

• The teacher will emphasize that students need to understand what is occurring when they are multiplying two fractions and will still be asked to represent this process visually, as in previous lessons. He or she will affirm students that this second method can be used to check their work, and when dealing with larger numbers in the future, but they must also always show their work visually.

• The teacher will then read Multiplying Menace: The Revenge Of Rumpelstiltskin

Guided Practice:

to the class.

• The teacher will create 1 word problem multiplying a fraction by a fraction using the numbers in the book and the storyline. As a class, students will solve this problem using a visual representation first, and then using the rule of multiplying the numerators over multiplying the denominators.

• The teacher will create 1 word problem multiplying a whole number by a fraction using the numbers in the book and the storyline. As a class, students will solve this problem using a visual representation first, and then using the rule of multiplying the numerators over multiplying the denominators.


• In pairs, students will individually create their own word problems based on the book that include multiplying a fraction by a fraction and multiplying a fraction by a whole number.

• Students in the pairs will then switch word problems and solve their peer’s word problem. Students within a pair will help one another. Students will solve their problems with a visual representation, showing all work and then check their answer using the rule of multiplying the numerators over multiplying the denominators.

Assessment:

• Students will complete a “3-2-1” formative assessment, listing 3 things they learned, 2 things they liked, and 1 question they still have about multiplying fractions.

Name: __________________________________ Date: _____________

Multiplying Menace

Directions: • Create word problems based on the book Multiplying Menace. • Switch worksheets with your partner and solve your partner’s word problems. • Solve the problems with a visual representation, showing all work and then check your answer using the rule of multiplying the numerators over multiplying the denominators. 1. Word problem multiplying a whole number by a fraction:

2. Word problem multiplying a fraction by a fraction:

Name: __________________________________ Date: _____________

Multiplying Menace: 3-2-1

Three things I learned are…

1.

2. 3.

Two examples of what I learned are…

1.

2.

One question I still have or something I am confused about is…

1.

Day 5: Summative Assessment: Multiplying Two Fractions Three Different Ways

Title: Fraction Story Grade: Fifth NYS Common Core Standards and NCTM Standards: NYS Common Core Standards:



a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd). b. find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

NCTM Standards:





• Students will create and illustrate a story including a word problem multiplying two fractions.

• Students will predict the size of fraction solutions. • Students will solve fraction multiplication word problems. • Students will represent the multiplication of two fractions in three different ways:

concrete, visual, and in writing. • Students will explain and reflect on the process of multiplying two fractions.

Materials:

• “Fraction Story Project” instructional worksheet

• Blank books made from computer paper • Posters • Clay • Colored pencils

Instructional Plan:

• Students will each receive a “Fraction Story Project” instructional worksheet. • The teacher will explain the assignment.

o Students will create a word problem multiplying two fractions. o Students will expand this word problem into a short story. o Students will write and illustrate this story in the form of a short book (5-6 pages). o Once a student’s story is approved by the teacher, he or she will find another

student whose story has also been approved. o These two students will read each other’s stories and record the multiplication of

two fractions problem from their peer’s story. o Students will then individually predict which multiplication problem will result in

a bigger answer (the problem in their story or the problem in their peer’s story) and why in a paragraph.

o Students will solve both multiplication of fractions problems in three different ways. Students will represent their work and writing on a poster. Students will then solve both multiplication of fractions problems using

clay. Students will glue their clay representation onto a poster. Students will draw the steps they used to solve the problem with clay

visually. Students will solve the problem mathematically. Students will write two paragraphs. Paragraph 1: Students will explain their work, thus explaining how to

multiply two fractions. Paragraph 2: Students will explain if their prediction was correct or

incorrect and why.

Assessment:

• The teacher will collect students’ books and posters. • He or she will grade the projects using a rubric and provide additional comments.

Name: __________________________________ Date: _____________

Fraction Story Project

Directions: 1. Create a word problem multiplying 2 fractions. 2. Expand this word problem into a short story.

• Write and illustrate this story in the form of a short book (5-6 pages).

3. Ask the teacher to approve of your story. 4. The teacher will pair you with another student whose story has been

approved. 5. Read your partner’s story and record the multiplication of two fractions

problem found in your partner’s story. 6. By yourself, predict which multiplication problem will result in a bigger

answer (the problem in your story or the problem in your partner’s story).

7. Explain why in a paragraph. 8. By yourself, solve both multiplication of 2 fractions word problems in 3

different ways. • Using clay • Draw the steps taken when using clay. • Solve the problem mathematically when paper, pencil, and

numbers only to check your work. 9. Write 2 paragraphs:

• Paragraph 1: Explain your work, explaining how to multiply two fractions.

• Paragraph 2: Explain if your prediction was correct or incorrect and why.

10. Represent your work and writing on a poster.

Name: __________________________________ Date: _____________

Fraction Story Project

Your book should include: • 5-6 pages • Title • Illustrations and words on every page

Your poster should include: • Paragraph stating your prediction of whether your world problem or your partner’s word problem will result in a larger product and explaining why you predicted this • Your problem

• Solved with clay • Solved with drawings • Solved with just math

•Partner’s problem •Solved with clay • Solved with drawings • Solved with just math

• 2 paragraphs: • Paragraph 1: Explain your work, explaining how to multiply two fractions. • Paragraph 2: Explain if your prediction was correct or incorrect and why.

Student’s Name: ___________________ Date: _______ Grade: __________

Fraction Story Project Rubric

3 2 1 0

Word Problem & Story Creation

Created a 5-6 page story with an accurate word problem multiplying 2 fractions.

Created a 1-4 page story with an accurate word problem multiplying 2 fractions.

Created a 5-6 page story with an inaccurate word problem multiplying 2 fractions.

Created a 0-4 page story with an inaccurate word problem multiplying 2 fractions.

Solving Your Word Problem

Correctly solved his or her word problem using all 3 strategies: clay, visually, mathematically.

Correctly solved his or her word problem using 2 strategies: clay, visually, mathematically.

Correctly solved his or her word problem using 1 strategy clay, visually, mathematically.

Did not correctly solve his or her word problem using any of the 3 strategies: clay, visually, mathematically.

Solving Your Partner’s Word Problem

Correctly solved his or her partner’s word problem using all 3 strategies: clay, visually, mathematically.

Correctly solved his or her partner’s word problem using 2 strategies: clay, visually, mathematically.

Correctly solved his or her partner’s word problem using 1 strategy clay, visually, mathematically.

Did not correctly solve his or her partner’s word problem using any of the 3 strategies: clay, visually, mathematically.

Writing: Prediction & Explanation

Wrote a detailed and accurate paragraph for all 3 of the following: prediction, explanation, explanation of prediction accuracy

Wrote a detailed and accurate paragraph for 2 of the following: prediction, explanation, explanation of prediction accuracy

Wrote a detailed and accurate paragraph for 1 of the following: prediction, explanation, explanation of prediction accuracy

Did not write a detailed and accurate paragraph for any of the following: prediction, explanation, explanation of prediction accuracy

Comments:

Conclusion

Assessment is a necessary component to teaching as it provides teachers and students

with information about progress and performance. The observations made and results gained

from assessments help teachers adapt their instruction if necessary in order to assist in students

reaching their learning potential. Assessment also helps students self-regulate their learning,

providing them with the opportunity to reflect on their strengths and weaknesses, and what

changes they can make to improve their own learning. This information is gained through both

formative and summative assessments.

I chose to include a variation of formative assessments, and a summative assessment in

the form of a project in this unit on multiplying fractions. The formative assessments in this unit

include a variety of exit cards, teacher checklists, and presentations. The exit cards ask students

to reflect on what they have learned and what they are still confused about, such as in the “3-2-1”

exit card, as well as apply their knowledge, such as in the “Oh No!” exit card. Throughout the

duration of all lessons the teacher will be making informal observations about students’

understanding.

It is important to provide students with opportunities to demonstrate their knowledge by

including a variety of assessment measures including students’ performance on projects in

addition to paper and pencil tests to accommodate all learners. Therefore I included the “Fraction

Story Project” on day 5 of my unit. This summative assessment asks students to create a story

including a word problem multiplying two fractions. Students then interpret a word problem

from a partner’s story, after the stories have been approved by the teacher. Students are asked to

solve both their own word problem and their partner’s using three different strategies taught in

class: using concrete materials (clay), visual diagrams, and through multiplying the numerators

and denominators. Using the three different strategies provides the teacher with a detailed

understanding of students’ true abilities to multiply fractions and see which areas students have

mastered and which areas students need further instruction.

In addition, students are asked to predict which problem will result in a larger product

and why, and then reflect on their prediction and explain their work throughout the project in

paragraph form at the end of the project. Students will not be graded on the accuracy of their

prediction, but rather their ability to explain how to multiply fractions and explain why their

prediction was correct or incorrect. The written piece included in this assessment incorporates

English language arts and requires higher order thinking as students reflect and think critically

about their learning process. This summative assessment will be graded based on a rubric that

clearly states the teacher’s expectations and criteria for each category. This rubric includes a

“comments” section for the teacher to provide more detailed and specific positive and

constructive feedback individualized for students. Students will receive a copy of the rubric in

addition to the thorough “Fraction Story Project” instruction sheet to help them self-regulate

their learning.

Multiplying Fractions Unit...

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