Fractions

3.2 Number, operation, and quantitative reasoning. //The student uses fraction names and symbols to describe fractional parts of whole objects or sets of objects (with denominators of 12 or less).// 3.2A Construct concrete models of fractions. 3.2B Compare fractional parts of whole objects or sets of objects in a problem situation using concrete models. 3.2C Use fraction names and symbols to describe fractional parts of whole objects or sets of objects.
 * ​TEKS:**


 * Core Components:**


 * Constructs fractions equal to or less than one whole.
 * Understands the relationship of part to whole.
 * Recognizes the meaning of denominator as the number of equal parts in the whole object or set.
 * Recognizes the meaning of numerator as the number of equal parts under discussion.
 * Uses models such as pattern blocks, color tiles, number lines, Cuisenaire rods and Base 10 Blocks.
 * Constructs area models of fractions such as fraction bars, fraction circles or fraction squares.
 * Constructs set models of fractions using groups of objects such as two colors of linking cubes.
 *  Identifies fractions indicated in a problem situation.
 * Identifies fractions that are more than or less than a given fraction.
 * Works with fractions up to twelfths.
 * Uses number lines that show intervals other than "one". (fractions).
 * Uses spinners, coins, dice, drawing a card or choosing an object from a bag to determine the idea of chance through experiments.
 * Records collected data in tables.
 * Analyzes previously recorded data to decide the probability of an event.
 * Day 1:



Introduction to Fractions:**

Have you ever eaten a part of something and not been able to finish it completely? Some foods, like pie and pizza, are already broken into parts which you can eat. Other foods, you may eat until you are full and have something left over. If you have ever wondered how much food was left, then you've probably measured the amount in fractions.

A **fraction** is a math term which means that something is broken into "parts of a whole".

A pie is a circle that is broken into pieces so it can be shared. Any shape or object can be broken into fractions.

One of the main concepts for students to understand is that when talking about fractions you are talking about **equal pieces or equal shares**. This lesson helps to reinforce this:
 * ** DIVIDING SHAPES AND SETS LESSON PLAN **
 * Teacher Materials:**

• Overhead projector • Six paper clips


 * Student Materials:**

• Chalk or white board for each student with accompanying writing utensil, or piece of paper and pencil. ​ • Dividing Shapes Worksheet


 * Lesson Part I:**
 * 1) Draw a large rectangle on the board. Divide it into 5 equal parts. Draw another rectangle and divide it into 5 unequal parts.
 * 2) Ask the students which rectangle has been divided into parts that are the same size and shape. Explain that this means the rectangle has been divided into even parts.
 * 3) Draw a circle and divide it into 4 unequal parts. Draw another circle and divide it into 4 equal parts.
 * 4) Ask the students which circle has been divided evenly.
 * 5) Repeat as many times as the teacher deems necessary.


 * Lesson Part II:**
 * 1) Write the word “set” on the board. Explain that a set is a group of objects that are all the same.
 * 2) Place six paperclips on the overhead projector. Switch it on. Show the students that this is a set of paperclips. Take two of the paperclips and set them apart.
 * 3) Ask the students if the sets are equal.
 * 4) Divide the paperclips into two equal sets.
 * 5) Ask the students if the sets are equal.
 * 6) Repeat as many times as the teacher deems necessary.


 * Assessment:**

Use the worksheet to evaluate whether students understood the concept. || 


 * Day 2 and 3:**

A fraction is made up of two main parts which are separated by a line. The top part (the number on top) is called the **numerator**. This is the part of the fraction you are talking about (the shaded part, the unshaded part, the amount eaten, the amount left). The bottom part (the number on the bottom) is called the **denominator**. This is the number that represents the **whole**.

Have the students copy this graphic organizer into the math journals.




 * Fraction Kit:**

This activity introduces students to fractions as parts of a whole. Organize students into pairs. Each student needs five strips of construction paper in five different colors, a pair of scissors, and a baggie.

Choose one color and discuss the concept of a "whole". Have the students label this strip with the number 1. Additional information you can discuss at this point: The most common fraction is a **whole**. If you have a whole pie then no pieces have been eaten. Let's say you have a pie which is cut into 6 pieces. No one has eaten any of the pie yet so there is: 6 out of 6 pieces of the pie left. Any fraction that is the same on the top and on the bottom is called a **whole**.

Ask students to take a strip of a particular color, fold it in half, and cut it into two pieces. Have them label each piece 1/2. Review the rationale of the notation by explaining that the whole has been divided into two equal pieces of the same size, that each piece is one of the two pieces, and that the 1/2 notation means one of two equal pieces.

Then choose a color for the next strip and have the students fold it into four equal pieces. Talk about each piece being one of four, or one-fourth, and ask students to label each piece 1/4.

Do the same with eighths and sixteenths.

You can attempt thirds, fifths, or any other fraction you choose, just keep in mind that they are much harder to fold so you may need to break out the rulers and do some measuring.

Each student now has a fraction kit to use. Here are some activities to use with the kits:


 * Cover Up**:

This is a game for two or more players. Each player starts with a whole strip. The goal is to be first to cover the whole strip completely with other pieces of the fraction kit. No overlapping pieces are allowed. Following are the rules for play. 1. Children take turns rolling the fraction die. (Sandy has some in her room.) 2. The fraction rolled tells what size piece to place on the whole strip. 3. When the game nears the end and a student needs a small piece, such as 1/8 or 1/16, rolling a 1/2 or 1/4 won't work. The student must roll exactly what is needed.


 * Uncover:**

This game gives children experience with equivalent fractions. Each student starts with the whole strip covered with the two 1/2 pieces. The goal is to be the first to uncover the strip completely. Following are the rules for play.

1. Children take turns rolling the die. 2. A child has three options on each turn: to remove a piece(only if he or she has a piece the size indicated by the die), to exchange any pieces left on the strip with equivalent pieces, or to do nothing and pass the die to the next player. A player may not remove a piece AND trade on the same turn. It is important for children to check to see that each other trades correctly.


 * Recording Cover-Ups:**

Ask the students to cover their whole pieces with whatever smaller pieces they choose. Recordseveral of their examples on the board. For example, if a child used three 1/4 pieces and two 1/8 pieces, record: 1/4 + 1/4 + 1/4 + 1/8 + 1/8 = 1. Then explain how to shorten the equation by counting the fourths and writing 3/4, and counting the eighths and writing 2/8. Therefore 3/4 + 2/8 = 1. Have the children help you shorten the other recordings on the board. Then have each cover up their strip with at least five different combinations and record on a piece of paper in the journal.


 * Fraction Sentences:**

Give the students incomplete fraction sentences and have them use their fraction kits to decide how to complete them. This is fairly standard fraction practice, but in this case it is related to the students' concrete experience with the fraction kits. In all cases, have students explain, orally and in writing, why their answers make sense. Examples:

1. Give pairs of fractions and have the students write >,<, or = to make a true sentence. 2. Ask the stduents to supply the missing number to make the fractions equivalent. 3. Have students write other fractions that are equivalent to the one you give. 4. Have students find a way to write one fraction to complete a sentence. They can use their fraction kits for this by covering the pieces with all pieces of the same size so the length can be represented with one fraction. 1/2 + 1/4 + 1/8 = 7/8


 * Day 4:**


 * Sharing Brownies:**

Begin by giving each student a 4 x 4 sheet of brown construction paper. Explain that this is a "brownie". They need to be able to share this brownie with a friend. BEFORE CUTTING have the students brainstorm the different ways the brownie can be cut into two equal parts. It would be a good idea for you to have several brownies yourself and make the cuts the class suggests (horizonatally, vertically, diagonally, etc.) When you have explored all of the various combinations as a class, have each student cut their brownie. These can be glued into their journals and labeled 1/2 on each piece.

Do the same with thirds, fourths, sixths, etc. Create a class poster with the brownie pieces you cut and have them glue theirs into their journals.

HINT: Have several extra brownies for mistakes. **Day 5: Fractions of a Set ** Bring a six-pack of soft drinks to class. Remove one can from the pack and tell the children: "If I drink this soft drink, I can write a fraction that shows what part of the six-pack I drank." On the board, write 1/6. Tell the children that this is read "one-sixth" and means one of six parts. Then pose the following questions: What do you think the six refers to?What do you think the one stands for?Why does this mathematical notation make sense?What could I write to show the fractional part of the rest of the six-pack, the part I didn't drink? Have students explain their thinking. Correct any erroneous notions. Remove another can and ask the same sorts of questions. Continue, introducing three-sixths, four-sixths, five-sixths, and six-sixths. Be sure to point out that six-sixths equals one whole six-pack. Follow the same procedure for other sets of objects: ex. a pack of five sticks of gum, a bunch of seven bananas, a box of crackers with three separately wrapped packages. Also, have similar discussions about sets that contain different things. The following are examples:
 * Ask a group of 8 students to come to the front of the room. Ask: "What fraction of the group are boys? Girls? Are wearing blue? Are wearing long sleeves?"
 * Show a box of colored birthday candles. Ask: "What fraction of the candles in the box are pink? Blue? Green?"
 * Show a set of pencils, some sharpened and some unsharpened. Ask: "What fraction of the set are sharpened? Unsharpened? Have good points? Have erasers?"
 * Stack about a dozen textbooks on the table. Ask: "What fraction of the set are math books? Science books? Social Studies books?"
 * Have nine children take off one shoe. Set them on a table at the front of the room, or have students gather so all can see them. Ask: "What fraction of the set are tennis shoes? Have alces? Don't have laces? Have bumpy soles?"
 * Bring to class a bag of apples, some red and some green. Ask: "What fraction of the set are red? Green?"
 * Take a handful of color tiles, with some of red, yellow, blue, and green. Ask: "What fraction fo the set are red? Yellow? Blue? Green?


 * Day 6: Fractions with Two-Color Counters**

Distribute twelve two-colored counters to each student. Give students the directions and questions that follow. Have them discuss the questions in small groups and then present their answers to the entire class, explaining their reasoning for each.

1. Divide the 12 counters into 3 equal groups with all yellow sides showing. What fractional part of the whole set is represented by each group? How many counters are in 1/3? 2. Flip the counters in one group. What fractional part of the whole set is red? Yellow? How many are in 1/3? In 2/3? 3. Rearrange the counters into six equal groups with all yellow sides up. Flip the counters in one group. What fractional part of the whole set is red? Yellow? Flip another group.What fractional part of the whole set is red? Yellow? Continue until all groups have been flipped. 4. Arrange the counters so 1/4 of them have red sides showing. What fractional part of the whole set is yellow? Show another set with fewer than 12 counters that also has 1/4 of the set with red sides showing. See how many different solutions you can find. 5. Show a set of counters that has 2/6 of them with their yellow sides showing. Find as many different solutions as you can that use 12 or fewer counters. Continue with other fractions: 2/8, 5/6, 3/5, and so on.)


 * Day 7: Exploring Fractions Through Sharing Problems**

This is similar to the Sharing Brownies activity. You can use the "cookies" from the division lessons earlier in the year (Sandy has some) or you can cut circles from construction paper.

In this investigation, children share different numbers of cookies among members of a group. Introduce this task by presenting the following problem: If I gave each of a group of four children four cookies to share, how much would each person get? This will most likely be obvious to them "1", but it will give you the chance to discuss what is meant by "sharing equally", and to lead them to discover that each child received 1/4 of the total cookies. Then have children solve the same problem but this time have 8 cookies. Lead students to make the connection that, although they still each have 1/4 of the cookies, they each now hove two cookies. Draw a visual of this on the board. have students solve for 12 cookies, 16 cookies.

See what students would do if there were 18 cookies (They will need to cut the cookies in half).

Extend the investigation by changing the number of cookies they are sharing, by changing the size of the group to six or eight people.

This game is PERFECT for playing after you have done this lesson:




 * Day 8 and 9:**

Use any of the games, worksheets, links, books, etc. to explore fractions. Test on the last day.


 * Links: After looking closely at these sites, I recommend that you do these WITH your class before just letting the go to do these on their own.**

EXCELLENT SOURCE!! Scroll down to the Fractions section of this website. They have tons of questions you can do with your students. This would be a great review practice during the week or at the end of the unit. @http://www.ixl.com/math/grade/third/ (after playing a few rounds this one will stop and try to make you join the website)

@http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/fractions/introduction/activity.shtml


 * Literature Connections: The titles with an asterisk are in Sandy's room, please feel free to come borrow them anytime.**

//The Doorbell Rang,// //Gator Pie// //Hershey’s Fraction Book// //Clean-Sweep Campers// //Skittles Riddles Math// //No Fair!,// //Dad’s Diet,// //Eating Fractions,// //Fraction Action// //Fraction Fun// //The Half-Birthday Party,// //Little House in the Big Woods// //*Apple Fractions// //*Piece, Part, Portion// //*Working with Fractions// //*Adding Fractions// //*Give Me Half//

We have the game, **Pizza Fraction Fun,** in the 3rd grade printer closet. Sandy has **Fraction Bingo!**
 * Additional Resources:**

These are some fun activities I found to introduce fractions to your class. Since we are unable to use food in our classes, these can be done with paper cutouts instead.

** Fractions With Candy Bars and M&M's

Materials ** **Activity**
 * M & Ms of different colors
 * Hershey Candy Bars
 * Magnetic fraction bars

I start by passing out a paper candy bar to everyone that has 12 parts.

We talk about how a candy bar is the whole and they they cut it in half so they see that 6 pieces=1 half. I model with a real candy bar. We talk about them splitting this with a friend so they would have EQUAL PARTS.

Then I tell them 2 other friends come over so they have to split each half into equal parts again. As we do each split, I draw a picture of the fraction and label it.

Once we have divided the candy bar into twelve pieces and I have shown them how we went from 1/2 to 1/12, I use magnetic fraction bars to show them briefly how 1/12 is much smaller than 1/2.

Once they get this down and have enjoyed a real candy bar, I then take small bags of M & Ms and pass them out to pairs of kids. We divide our candy into groups by color and then figure out which fraction of the different colors everyone has. For example, if they have 24 total candies and 8 of them are red, I show them that 8/24 are red. Those that are ready always seem to tell me that this is 1/3. (I divide candy in advance so there is always an even number in bags, but not always the same number so some groups may get 24, others 30, others 36, etc.).

When we have figured out the fraction of each color (I have them draw it out on paper with crayons and label the pictures), I let them eat their fractions. My kids always love this since it involves food and they always get fractions too!

**Teaching Fractions with Tortillas **  **Mater​ials **

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">**Activity** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">1. Each student gets 2 tortillas and puts one on top of the other.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">10 inch flour tortillas (2 for each student)
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Markers and marker board (one large one for all responses or individual ones for each student)

2. The teacher explains that one tortilla equals one whole.

3. Each student carefully folds the flour tortilla in half (as the teacher models it).

4. The teacher asks students questions about what each has now and asks for math statements about what they have. Students have to concretely show their statement as well as state it.

5. Students reply and teacher writes down their responses - examples 1/2 + 1/2 = 1, 1/2 = 1/2, 1>1/2, 1/2<1

6. The students then carefully fold one half into two pieces and the teacher asks the questions again.

7. This continues until the student has one tortilla in eighths and the whole one stays the same so the students can compare and make many statements.

8. This exercise leads to many statements that can lead to establishing rules about fractions. For example - 2/2 = 1, 4/4 = 1, 8/8 = 1 If the teacher continues to ask questions and does not give the students answers, the students will discover the rules on their own. I believe this is vital for the students to "own" their learning.


 * <span style="color: #ff0000; font-family: Arial,Helvetica,sans-serif;">Spelling Fractions **

**<span style="font-family: Arial,Helvetica,sans-serif;">Materials **
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Paper with three columns
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">pencil
 * <span style="font-family: Arial,Helvetica,sans-serif;">Activity **

Write our spelling words in first column.

Second column is fraction of vowels.

Third column is fraction of consonants.

example: determine 4/9 5/9

<span style="color: #ff0000; font-family: Arial,Helvetica,sans-serif;">**<span style="color: #ff0000; font-family: Arial,Helvetica,sans-serif;">Pizza Fractions **


 * <span style="font-family: Arial,Helvetica,sans-serif;">Materials **


 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Construction paper circles (pizzas)
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Index cards with fractions
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">linking cubes, bingo markers, or any small items in classroom to use as toppings

<span style="font-family: Arial,Helvetica,sans-serif;">**<span style="font-family: Arial,Helvetica,sans-serif;">Activity **

The circles (pizzas) are already divided into halves, thirds, fourths, sixths, and eighths (depending on level of students).

As a whole class the pizzas are displayed where everyone can see them. Each student will take turns and pick an index card with a fraction.

The student must decide which pizza they must put their topping on.

Example. If the student draws 2/3, they must determine that they have to use the pizza that is divided into thirds to put their topping on. The student will then cover 2/3 of the right pizza with (pepperoni, cheese) whatever they choose for their topping.

After this lesson the materials may be placed for center time or free choice play.

A guide for making a quilt. There are two that you would need to color in so the kids can read the fractions.


 * Exemplar:**
 * Envision:**