**Amanda Blagsvedt**

**Unit Plan for Equivalent Fractions.**

Students will learn equivalent fractions with 75% accuracy within the first quarter of her sixth grade school year as measured by the Comprehensive Assessment of Mathematics Strategies or CAMS.

**Objective**

Introduction to Equivalent Fractions

Maria and her classmates love playing games on computers. The students will work on a computer game that helps them explore equivalent fractions. The students will finish three five-minute rounds of the Tony's Fraction Shop Pizza game found at www.mrnussbaum.com/pizza_game/index.html. The game is a good introductory game to equivalent fractions and builds on the previously learned skill of adding fractions.

The students will need help with the directions of the game. Four students from the high school have agreed to play the games with the students in class for fifteen minutes or three games (each game is a timed five minute game). This means there are approximately 20 minutest to work on the dimes and nickles activities. The high school students said they will come early in case the students are able to play the game earlier.

The small group will go down to the cooking room that was previously used for consumer sciences to use the kitchens for cooking with equivalent fractions. The students are familiar with the kitchen because we cook often (becoming familiar with fractions, adding and subtracting fractions), and they love it so behaviors are minimal.

Time for cooking!

Maria and the small group of students will play fractions Go Fish.

Reinforce the Skills

**References**

Artley, A. (n.d.). Here is an idea called equivalent fraction go fish. Retrieved August 13, 2012 from http://www.lessonplanspage.com/mathequivalentfractiongofishidea56-htm/

Dart, L. (2000). Chocolate Zucchini Cake I. Retrieved August 4, 2012 from http://allrecipes.com/recipe/chocolate-zucchini-cake-i/

Google. (2012). Google images. Retrieved August 4, 2012 from images.google.com

MrNussbaum. (n.d.). Tony fraction's pizza shop. Retrieved August 7, 2012 from http://mrnussbaum.com/tonyfraction/.

Watch, Know, Learn (2009). Fundamental interactions of equivalent fractions retrieved August 6, 2012 from

http://watchknowlearn.org/Category.aspx?CategoryID=1966

VPGDEMO. (2010). Math songs equivalent fractions. Retrieved August 13, 2012 from

Frosting

2/6 C. butter

3/9 C. cocoa powder

24/12 C. powdered sugar

9/3 tbs. milk

1 and 8/16 tsp vanilla extract

Preparation

Directions

Ingredients

1st Step:

The dry ingredients are already out on the counter. Please leave them where they are. There are labels in front of every item. There are some labels without items. You need to match the items to the labels for easier organization. You will need to get these items from the refrigerator. The items you need are: a stick of butter, 2 eggs, small container of milk, and container of shredded zucchini (freezer bag). Go to the next card for a picture list of items you need.

Picture list:

Stick of of butter

2 eggs

Small container of milk

Zucchini- freezer bag

Lemon juice

Next:

Wash your hands.

Preheat the oven to 325 degrees

Measure out the ingredients using chart on the next card.

3/3 stick butter

2/4 cup vegetable oil

3/6 cup of milk

8/4 teaspoon lemon juice

5/5 teaspoon vanilla extract

4/2 cup sifted flour

7/7 teaspoon baking soda

4/8 teaspoon ground cinnamon

5/10 teaspoon ground cloves

6/12 teaspoon salt

8/2 tbs cocoa powder

1 cup and 6/8 cup sugar

2 cups plus 8/16 cups grated zucchini

2/8 cup chocolate chips

1. Pour the milk and the lemon juice in a small bowl. Set aside.

2. Mix the following ingredients into the large green bowl: sifted flour, baking soda, cocoa powder, ground cinnamon, ground cloves, and salt.

3. Cream the butter, vegetable oil, and sugar into the blue medium bowl.

4. put the eggs, sour milk (milk and lemon juice), and vanilla in with the butter mixture.

5. Put the ingredients from the medium blue bowl into the large green bowl. Stir the ingredients together in the green bowl. Put the blue bowl in the sink.

6. Mix the zucchini in the green bowl.

7. Mix the chocolate chips in the green bowl.

8. Spray the baking sheet with cooking spray.

9. Pour the batter from the green bowl into the silver pan, scrape the bowl out with the white rubber spatula to get all the batter in the pan, even out the batter in the pan. Put the pan in the oven. Set the timer for 35 minutes. I will take your cake out for you and we will make frosting after the cake is cooled during seventh period.

The students have index cards of the information presented below. Each separate section is a different numbered index card that is held together with a ring at the corner so it is easy for the students to navigate and keep organized.

The original recipe taken from allrecipes.com. There are a few minor modifications to the recipe.

Money Sense

The teacher will be prepared to teach equivalent fractions using money. She will need four quarters, 20 dimes, and 32 nickles. She will also have index cards cut in half with fractions written on each. As students come into the classroom the teacher will ask the students to pick one index card out of her hand (there are four quarter index cards). There are four students. The options for quarters are: 1/4, 2/8, 3/12, or 4/16 of a dollar. The following is an example of the quarter index cards.

The students will be directed to look at the fraction card they picked and discuss who they believe will have the most quarters. The teacher will ask them to explain their reasoning. After sufficient discussion has taken place (they are at a stopping point) the teacher will lay out four quarters on the table, ask the students how much money is on the table, and ask the students if there is enough money for each of the students to receive the amount indicated on the fraction card they chose. If the students grasp the concept right away, the teacher will ask how they knew all of the fractions were equal. If the students are struggling, the teacher will bring out pictures of 1/4, 2/8, 3/12, and 4/16 and ask the students if they see any similarities. The fraction picture index cards can be folded in quarters so students can visualize that all shaded portions are equal. The teacher can also help the students visualize the fractions by pairing the fraction picture cards with the fraction card. The following provides a visual of what the picture fractions look like for quarters.

The students will be guided through questioning until they find similarities. If they become frustrated, the teacher will show them the similarities. The students will then be asked if they can figure out how many quarters each student will receive now that they know everyone has an equal amount. The students may need a hint. Tell them one of the denominators (the bottom number) is the same as the total number of quarters. Ask them how many quarters the person with the denominator of four gets. If they struggle tell them the numerator or top number will help them figure out the answer. If one student knows the answer without the hint, have that student explain how he came to the answer. After they each receive their quarter, tell them they can keep the quarter. Ask the students to explain how each fraction card is the same or equivalent. Tell them equivalent means equal, which is what all of their quarter fraction cards are. Ask them if they can see any patterns in the numerators and then ask if they can see any patterns in the denominators. Are the patterns the same for the numerators and denominators? What is the pattern? What would be the next number in the pattern? Work out the problem on the white board.

When the students enter the classroom they will be given the same introductory activity as in the first lesson. Today they will work with fractions using dimes. The fraction cards for today's activity are: 2/4, 3/6, 4/8, and 5/10. Each student gets one fraction card.

Put 10 dimes on the table and ask them how much money is on the table. After their response tell them they will be finding a fraction or part of the whole dollar. Ask the students if they can all get the number of coins they need to fill their fraction card. If they do not come up with this on their own, see if they notice any classmate's fraction card that has the same denominator as the number of dimes that are on the table. They can help that person get the right amount of dimes to find out how many dimes all the other students get (all the cards are equal).

It will not take long for them to realize they do not have enough money for all of them to get the amount on their cards. After they fill two fraction cards, ask them how much more money they need to ensure all students have an equal amount. When they come up with the right answer the teacher will put the other ten dimes on the table.

Next, have the students find the pattern and ask them what comes next and what goes first in the pattern. Have them tell you how much money they have all together so far (a quarter from day one plus five dimes). The teacher will write these numbers on the board to help them add their money. Tell them they can keep the dimes.

The students will work on their assessments in the consumer science room at the small tables while they are waiting for their cakes to cook or the bell to ring (whichever comes first). When the cake is cooled and frosted have each student cut his or her cake into 32 pieces and tell the them they can each have 1/16 of the cake. Day four and the intensive stretch of teaching equivalent fractions is done. Equivalent fractions will be revisited throughout the school year as needed using various activities.

Fraction Cards

Quarters

Quarters

2/8

Nickles

4/10

Quarters

3/12

Nickles

8/20

Quarters

4/16

Dimes

6/15

Nickles

5/10

Nickles

2/5

Dimes

4/8

Dimes

3/6

Dimes

2/4

**Picture Cards for Quarters**

Time for a Break!

Hopping Equivalent

Fractions

Four equal lines will be marked out on the classroom floor with masking tape. One line will be marked out in four equal sections, another in eight, the next in 12, and the last in 16 sections. Each student will be instructed to stand by a line that has their name. The students will be given a fraction verbally from the teacher and the fraction will be written on a piece of paper for easier reference in case they forget their fraction. The teacher will explain that the denominator is the bottom number and the number of total markers on their lines. The numerator is the top number and the number of markers they are suppose to hop. The students will each take turns hopping to the appropriate fraction. The teacher tells the students how many sections their line has. The teacher will make sure the students understand the sections the line is broken down into are equal parts of a whole line. The fractions given are: 3/4, 6/8, 9/12, and 12/16. All four students should end up standing next to each other after they are done hopping. They will be asked to repeat the fraction they had to hop and explain how they all ended up the same distance when they had different fractions. Here is an example of what the lines look like.

Lesson Two

Students will start with the dimes and nickels activity (approximately 20 minutes), which is the same thing as the quarter activity from Lesson one. Then the students will play a game involving fractional pizza. The students will be playing this game with some students from the high school. Seven minutes before the end of class the students will end their games and sit at the moon table for their last five minutes of class, which is good news time.

Assessment Choices

Lesson Three

Students will reinforce their skills with a fraction Go Fish game adapted from Abbie Artley. After they play Go Fish they will watch another short video song about fractions as a fun refresher on equivalent fractions and how to find equivalents of fractions. The additional time left in class will be allocated to helping the students choose an assessment. The students will begin working in the assessments in class and the rest will be homework.

Lesson Four

Students will be applying their skills in the art of baking a cake. They will be using their downtime to work on their assessments.

Lesson One

The first day is an introduction to equivalent fractions. The students should make it through the quarter activity, the hopping game, and the song video. If there is time left, the students should start working on their assignment. They will be making ten pairs of equivalent fractions for a game they will be playing later in the week. The last five minutes of class are reserved for good news. The students love this portion of class so do not short them their five minutes. Give them at least five minutes before the good news portion to start putting their things away and to get back into their seats. If the students do not make it to the song video they can watch it in the beginning of day two, but they should be able to watch it.

Make sure every student has their assignment written down in their assignment notebooks. All four of the students' caregivers are wonderful about reading the notebooks and helping them with their schoolwork.

1/4

These are made on the back of index cards by marking out equal sections and shading in the specified area with a marker.

Next it is time to explore equivalent fractions with nickles. The fraction cards for nickles are: 2/5, 4/10, 6/15, and 8/20.

Now the students should understand they all have equivalent fractions, but the fact still needs reiterated. Put 20 nickles (one dollar) on the table and wait to see if the students can find the fraction with the same denominator as the number of nickles. Hopefully, they will figure out that one student gets eight of the twenty nickles. If not, lead them by asking how many nickles are on the table. Ask them why this number may be important to them. Give them a moment. If all their faces are without a clue, ask them if there is a denominator with a 20. Then tell them the numerator is the amount of money they receive out of 20. They will then count out how much money the student with the 8/20 fraction card received. Ask if there is enough money left for another student to receive their equivalent share. Let them figure out that there is enough money. Ask them how much more money they need if every student receives 40 cents and only two student have their money. When they come up with the right answer put 12 more nickles out (there should be four nickles still on the table). Have the students work together to find a pattern and find the next fraction in the pattern.

Ask them to add up how much money they have all together. On the board write that they have 25 cents in a quarter, 50 cents in dimes, and 40 cents in nickles. Help them work out the problem after you give them time to think, write the answer, and share with the group. Ask them to compare the fractions to order the fractions from greatest to least based on the amount of money they have for each fraction set and discuss why.

Nickles

Dimes

Before the students enter the classroom they will read the small whiteboard on the outside window of the classroom door. The whiteboard tells them what they need to be successful in the classroom. Today it says to bring their assignment notebook and a pencil. The teacher will be standing at the door to greet students and to remind students to read the whiteboard if it appears the students have forgotten.

As they come into the room they will sit at the moon-shaped table that is facing the large white board. The large whiteboard explains they are learning a new concept, which is equivalent fractions. It also lists the expected activities for the day, which include an introductory activity using quarters where students will sit in their desks and work cooperatively with the teacher, an active activity where students will be able to hop to equivalent fractions, and a video further introducing them to equivalent fraction. After the bell rings and roll call is sent to the office the teacher will read the information on the board. The following is an example of a graphic organizer to be passed out to each student.

Transition

The teacher will now ring the transition bell. The students already know this means they sit still and quiet and wait for transition instructions. The instructions are written on a small whiteboard that is turned backward on the large whiteboard ledge directly behind where the teacher is sitting.

The teacher puts the whiteboard on the table facing the group of students and reads the directions aloud. The directions tell the students they will each stand on a piece of tape marked start here with their name on it. The students are to wait at the table until the teacher calls the student over to their spot. The students are to remain quiet and await further instructions.

Start here: Maria

Fourths

Start here: Antonio

Eighths

Start here: Anghelika

Sixteenths

Start here: Mark

Twelfths

Assessment

Students will take ten index cards. On one half of the index card the students will write one fraction and on the other half of the card, the student will write an equivalent fraction to the first fraction written.

The teacher will demonstrate what is expected. The students will receive ten points when they turn in their index cards complete and correct. Students will be given as much time as they need to correct the index cards. The ideal timeline to turn in their assignment is in two days. They receive two bonus points if they turn in their assignment on time. The bonus points are accumulated to earn rewards such as being the line leader for a week or being able to listen to music during free time. Here is an example of what the cards should look like.

1

2

2

4

Before the students enter the classroom they will read the small whiteboard on the outside window of the classroom door. The whiteboard tells them what they need to be successful in the classroom. Today it says to bring their assignment notebook and a pencil. The teacher will be standing at the door to greet students and to remind students to read the whiteboard if it appears the students have forgotten.

As they come into the room they will sit at the moon-shaped table that is facing the large white board. The large whiteboard explains they are continuing to learn a new concept, which is equivalent fractions. It also lists the expected activities for the day, which include an introductory activity using dimes and nickles where students will sit in their chairs and work cooperatively with the teacher, and a computer game they will play with a student from the high school. Students are expected to be courteous and polite to the high school students. After the bell rings and roll call is sent to the office the teacher will read the information on the board.

Transition to Computer Time

The teacher will ring the transition bell and read the directions for transition on the transition board. The directions are to go to their assigned computers. The screen will be ready for them to play their game. Their high school partner has already played the game and is familiar with the rules of the game. The high school partner is available to help with directions and will not give answers. The partner will give reminders if a step is forgotten and will act as a guide throughout the game time. Each student will complete three five-minute rounds, which is fifteen minutes.

Class is finished with seven minutes left of class. Two minutes to log out and sit at the moon-shaped table and five minutes to share good news.

Students will use their equivalent fraction cards to play Go Fish. If students did not finish their assignment, the teacher has some Go Fish cards pre-made sitting on her desk. If the students finished their assignment and the equivalent fractions are correct, the student will tear the index cards in half to use in the game. The first round will be played in pairs. Two students on one team and two students on the other team. If a student is absent, the students will play individually and the teacher will coach all students if needed.

Each student receives five cards and the rest of the cards are placed in the middle of the table. The students ask another student for an equivalent of their fraction. If the student has the equivalent fraction, he gives it to the student to keep as a pair and the student continues until she is told Go Fish. Play continues until someone runs out of cards. The person with the most pairs wins (Artley, n.d.). The directions will be written on a white board and read aloud to the students. The teacher will be available to help when needed.

The students can play two to three rounds. If they are really enjoying the game they can play until ten minutes before good news time, which will give them the time they need to watch the song video. If they are enjoying drilling each other on equivalent fractions, they should be allowed to continue. The assessment portion of the day can be pushed back to day four.

Equivalent Fraction Go Fish

Transitions

Transitions from the card game to the movie include putting their cards away in their cubbies. The transition from the video to picking out assessments involves listening to the options that are written in front of them and then returning to their desks to pick out the assessment they most want to complete. They return to their desks without talking. They read through the choices, raise their hand, wait for the teacher, and tell the teacher what assessment they are choosing. They check out appropriate materials. If the teacher is busy with another student for an extended period of time, the student can begin picking out materials for their assessment. The students know where all the materials are located.

Before the students enter the classroom they will read the small whiteboard on the outside window of the classroom door. The whiteboard tells them what they need to be successful in the classroom. Today it says to bring their assignment notebook, their equivalent flash cards, and a pencil. The teacher will be standing at the door to greet students and to remind students to read the whiteboard if it appears the students have forgotten.

As they come into the room they will sit at the moon-shaped table that is facing the large white board. The large whiteboard explains the students are reinforcing their skills for equivalent fractions. It also lists the expected activities for the day, which include a game of equivalent Go Fish, a song video, and possibly a chance to choose an assessment. After the bell rings and roll call is sent to the office the teacher will read the information on the board.

Before the students enter the classroom they will read the small whiteboard on the outside window of the classroom door. The whiteboard tells them what they need to be successful in the classroom. Today it says to bring their assignment notebook, anything they need to work on their assessments, and a pencil. The teacher will be standing at the door to greet students and to remind students to read the whiteboard if it appears the students have forgotten.

As they come into the room they will sit at the moon-shaped table that is facing the large white board. The large whiteboard explains the students are applying their knowledge of equivalent fractions to the real-life situation of cooking. It also lists the expected activities for the day, which include baking a cake with frosting and working on their assessments. After the bell rings and roll call is sent to the office the teacher will read the information on the board.

The students will then walk quietly down the hall to the family and consumer science room where the mini kitchens are located. They will be told to follow directions and have fun. They are all working individually. They will be sharing their cakes with their families after they are finished. While they are waiting for their cakes to cook, they will be working on their assessments.

Musical

Create a song about three ways people use equivalent fractions and use three examples of equivalent fractions.

Intrapersonal

Create ten more pairs of equivalent fractions for the classroom equivalent Go Fish game. Use index cards just as in the previous assignment.

Interpersonal

Persuade people you know into getting into equivalent fractions and take pictures of them. Create a poster board display of the equivalent fraction pictures. An example of an acceptable picture pair is to have one picture of three people standing above a line (yard stick?) and six people standing below the line. The pair to that picture is a picture of one person above a line and two people below the line. On the poster board the pictures will be grouped together. This project requires five pairs of equivalent fractions.

Linguistic

Write a story about five equivalent fraction pairs. Make sure the reader knows which equivalent fractions match with the other equivalent fraction.

Visual-Spatial/Naturalistic

Take pictures of equivalent fractions in real life. Put the equivalent fractions on a poster board. You will need five pairs of equivalent fractions. All the fractions will need to be different items. For example, you cannot only use pizzas cut into different equivalent fractions.

The students who are taking pictures will be supplied with a Polaroid camera and one package of film.

Kinesthetic/Additional ideas

Come see me if you have an idea for how you will show me you know equivalent fractions and we will work out the details of the assessment together.

For assessments to be considered for points (20 points) they must be complete and accurate. To receive bonus points the assignment must be turned in within five days. This means you need to turn your assignment in for me to tell you what corrections to make within four days at the latest.

The assignment expectations and dates will be written in the assignment book to communicate with parents.

The instructional approaches for this paper are whole group, cooperative groups, and individual learning. The lesson plan teaches the students in a manner so all students will have the best chances of achieving the objective. The lesson was also adapted in many ways. Transition directions were provided, lists of materials needed were written and verbally expressed, and material was presented in different modalities (hands-on, visual, auditory, kinesthetic, and musically). The material was also presented to express the real-life applicability of equivalent fractions.

Additionally, the assessments include the students' family members and the students interacted with other students in the school district, which represents the consideration for a multidisciplinary approach. Technology was used when appropriate to enhance students' technical skills and provide tools to better understand the material. Furthermore, the lesson plan is written so any person can pick up the lesson and teach the students. The materials are all ready for convenient use in the classroom.

Summary