This Lesson Plan is based on the Standard MAFS.4.NF.1.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions
This lesson focuses on creating equivalent fractions using the numbers 2, 3, and 4. Students will practice multiplying the numerator and the denominator by 2, 3, or 4 to create equivalent fractions.
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LESSON CONTENT

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
 Students will create an equivalent fraction when given a benchmark fraction.
 Students will be able to multiply the numerator and denominator of a fraction by 2, 3, or 4 to find equivalent fractions.
 Students will be able to explain why the created equivalent fractions are equivalent using visual examples or written/verbal explanations.

Prior Knowledge: What prior knowledge should students have for this lesson?
 Students should be able to multiply numbers 110.
 Students should be able to determine if two benchmark fractions are equivalent by creating fraction bar visual examples of them.

Guiding Questions: What are the guiding questions for this lesson?
 What are equivalent fractions? (Fractions that have the same relationship to one.)
 Why do both the numerator and the denominator need to be multiplied by the same number to create an equivalent fraction? (The numerator and the denominator must both continue to represent an equivalent part of the whole when changing to an equivalent fraction.)

Teaching Phase: How will the teacher present the concept or skill to students?
*Prior to instruction, have small paper plates (spinner circles), square card stock, fraction strips, whiteboards and whiteboard markers ready. The overhead projector is not necessary for this activity but is recommended.
 Hook: "Today we are going to make the next part of our game board using fractions. Part of our game requires us to know how to create equivalent fractions out of any fraction that we are given. We are going to start learning how to do that with the numbers 2, 3 and 4."
 "We are going to use our paper plates to make some fractions, similar to what we did yesterday (in Fraction Land lesson) with our fraction strips."
 "Now our classroom assistant is going to pass out scissors and "spinner circles," white boards, and markers. Please hold your scissors and circle up so that I can see that you have them." (Each student will receive one precut circle/paper plate and scissors. Be sure to have extras if students make mistakes.)
 "Now that we all have our spinner circles, please fold the circle once. When you do this, what fraction does one section of our spinner circle represent? (Have the students write down the fraction representing one section of the circle on their white boards. The fraction should be 1/2."
 "What part of the whole does the fraction, 1/2, represent (random student)? (Response can be: half, one of the two parts.) Good."
 "We are going to take our benchmark fraction that we see all the time, 1/2, and we are going to create an equivalent fraction using multiplication. We are going to use the number 2."
 "When we make equivalent fractions using multiplication, we have to remember that anything we do to the top of the fraction, or the numerator, we also have to do to the bottom of the fraction, or the denominator." (Stress this "if we do something to the top, we have to do it to the bottom also")
 "Using the number 2, I'm going to multiply the numerator by two. 2 x 1 = 2. I'm going to multiply the denominator by 2. 2 x 2 = 4. So the equivalent fraction that we created is 2/4. Does anyone remember from yesterday how we were able to find 2/4 using our fraction strips? Good." (Allow a moment for questions. At this point, you may go into explaining why you can multiply by the fraction 2/2 and how it does not change what the benchmark fraction represents, but that is it's own lesson and it is better to leave that for teaching the identity property unless asked by a student.)
 "Now you might be skeptical about whether or not 1/2 really is equivalent to 2/4, even though we proved that yesterday. Let's go to our next step to help us out."
 "Take your circle and fold it along your 1/2 fold again. Now, fold the top point of your half circle down to the bottom point of your half circle."
 "How many sections have we created? (4) Each section should represent what fraction of the circle? (1/4)
 "Two of the sections or 2/4 is the fraction we found to be equivalent with 1/2. Do 1/2 and 2/4 represent the same amount of the circle?" (Yes.)
 "We have found our first equivalent fraction using multiplication. Let's find another. Look at 2/4."
 "Earlier we said that 1/2 represent half or one of the two parts of the whole."
 "If that is true, what does 2/4 represent? We just found out that it is equivalent to 1/2, so what should 2/4 represent? (Half or two of the 4 parts.) Very good."
 "Let's take that 2/4 and multiply the numerator and denominator by 2 again."
 "Each time you use this method to find equivalent fractions, it should look just like this." (Stress to students that you will be looking for this setup on their assessments.)
 "We are going to move into some more examples using numbers other than 2. Do you think we will get equivalent fractions if we use a number other than 2, like 3 or 4?" (Yes, because we are still multiplying the numerator and the denominator by the same number. Use this moment for more formative assessment and to take any questions about the lesson so far.)
*"Please write your name on the back of your spinner circle and cardstock square. When you are done with today's lesson, Ill give you the final pieces to make your spinner.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will use their whiteboards and markers for the next part of this lesson.
 "For the next part of the lesson, I'm going to take suggestions for which number to use."
 "Now would be a good time to get out your multiplication charts if you need them. This is a lesson on equivalent fractions, not multiplying, so please use them if needed."
 "We don't want to make our fractions too complex so you can choose from 2, 3, or 4."
 "What number are we using first?" (2)
 "Ok, if I give you the fraction 3/4, give me an equivalent fraction using the number 2."
 "We created the fraction 6/8 using our multiplication method."
 "Who can tell me what 6/8 represents?" (6/8 shows 6 of the 8 parts which is equivalent to 3/4.) "Great."
 "Now take a 2 fraction circles from your table. Show me one that has 3/4 and one that has 6/8. If you need help folding, raise your hand."
 (When students are done,) "Each of you should now have to fraction circles that show 2 different fractions that represent the same part of the whole."
 "Does anyone have a question about what we just did?"
 "Let's keep the same fraction, 3/4. Let's try another factor to multiply with, 3 this time."
 "We have 3 or 4 left." (random student) "Ok, 3."
 (Random Student), "When you multiply the numerator by 3, what product do you get?" (9) "Very good."
 (Random Student), "What was the product when you multiplied 4 x 3?"(12) "Great."
 "The fraction we should end up with is 9/12. 9/12 is equivalent to 3/4."
 This time take 2 fraction strips. Fold one to show 3/4 and another to show 9/12. Remember, when your are working with higher even numbers like 12, try folding the strip in half until you get 12 parts.
 "Let's try one more fraction before I let you all work on your own. We are going to work with the fraction 1/4 and the number 4."
 "Just to recap, first, I am going to multiply my numerator by 4. When I do this, what should I get?" (random student?) (4) "Very good."
 "Next, I am going to multiply my denominator by the same number, 4. When I do this, what should I get?" (random student?) (16) "Good."
 "If new numerator is 4 and my new denominator is 16, then my equivalent fraction should be 4/16."
 "Now make 2 more visual representations of your fractions, 1/4 and 4/16. You can use the circles or the strips, but you must you 2 of either one." (At this point, you can survey or walk around the room and collect more formative assessment data or offer help.)
 Alright, I think that is enough practice. If you still think you need to work with me please raise your hand. (This can be an opportunity to gather Response to Intervention (RTI) data or work in a small group.)

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Paper bag fractions:
 For each student prepare one bag with 2 groups of items in them.
 On each back, tape an index card that is broken into 2 columns (3 if there is room on the card).
 Write "results" at the top of each column on the index card. Inside of each back should be 3 groups of items.
 Items can be pencils, colored blocks, dice, straws, or coins.
 Items should clearly represent a fractional amount such as 2 red pencils and 1 blue pencil. The fraction can be 1/2. Remind students that for right now, the smaller number should be the numerator.
Directions are as follows:
 "Each student has a bag." (You can play up the suspense of what's in the bag if you choose.) "At this time, please remove the contents of your bag put them on your desk. Take a look at them and make sure you know what they are and how they are different." (Allow a minute or two for students to examine the items.)
 "Please put all the similar items together. Pencils with pencils, bears with bears, etc."
 (Use a students items as an example.) "(Random Student) has 3 pencils. 2 are blue and 1 is red. What fraction can he make with those items? (1/3 or 2/3) That's right, 2 of the 3 pencils are red."
 "Your job is to write the fraction you found in the bag and then 2 equivalent fractions. You get to choose which number you multiply by. Use your white board to do your calculations. Record your equivalent fractions on the card attached in the format that I showed at the beginning of this lesson."
 "(On the board,) So if my fraction is 2/3, I'll write 2/3 and then I'll choose the number 2. I'll multiply the numerator and the denominator by 2 and I get the equivalent fraction 4/6. I write my name and my whole answer on the card attached to the bag."
 "When another student is done with their bag, raise your hand and you can switch bags with them."
"When all the columns on a card are full, bring me the bag and Ill give you the other pieces to build you board game spinner."

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
 Exit Slips: The exit slip is either a premade document or it can be scrap paper or flash card, used as a formative assessment and to transition into the next subject or activity.
 Possible questions for your exit slips:
 Why are 2/4 and 4/10 NOT equivalent fractions? (They do not have the same relationship to one.)
 Explain, in your own words, why multiplying the numerator and denominator of a fraction create an equivalent fraction.
 In 2 or 3 sentences, tell me one thing you learned, or did not understand about today's lesson.
 Were the items that you found in your bag what you expected? What items would you have liked to see? (I like to give at least one question that any student would want to respond to but make sure it give you information that you can use in the future.)

Summative Assessment
 Students will be given 5 groups of 2 fractions. For each problem, using the multiplication method taught during this lesson, students must determine if the fractions are equivalent or not. Students should be able to find the number used to multiply and create the equivalent fraction and they can only use 2, 3, or 4.
 Students will record their responses on notebook paper and turn in to the teacher. Focus on the student's ability to correctly multiply the numerator and the denominator to find each equivalent fraction. After students have done correct calculations, students must show evidence that the fractions are equivalent or not equivalent. They can create 2 fraction strips or circles, demonstrating the relationship between the 2 fractions.
 They will explain the relationship between the 2 fractions (verbally or in written form) and tell what part of the whole they both represent. *Remind students that it is easier to start with the smaller fraction.
 1/2 = 4/8 Yes, equivalent.
 3/4 = 1/4 No.
 1/5 = 4/20 Yes.
 3/6 = 1/2 Yes.
 2/4 = 6/6 No.

Formative Assessment
Recognizing Equivalent fractions:
 The teacher will ask students to prepare for their warm up, which will be posted on the walls of the room.
 The teacher will post fractions around the room on printer paper, large enough to be seen anywhere in the room. The fractions will be: 1/2, 2/3, 2/6, 3/4, 1/4, 1/5
 The teacher will write a fraction on the board and ask students to stand next to the fraction that they think is equivalent to that fraction.
 Students may use their scrap paper to find answers.
 After each student has chosen, the teacher will select a student(s) to explain why their answer is correct. Continue giving fractions until all students have given an explanation or gotten several incorrect. Make sure to ask if students have different explanations for the correct answers. Examples of fractions the teacher can give are: 2/10, 4/8, 3/6, 2/8, 4/6, 5/10
 The teacher will record observations about what each student is able to accomplish on a Role Sheet. (Role Sheets have each students name listed with boxes beside each with room to record student responses. Spaces for dates should be available also).
 Students would score 0 for no understanding or being unable to explain their answer.
 Students would score 1 for correct answers and explanations.

Feedback to Students
 During the formative assessment, students are required to explain their thinking or reasoning for the answers they chose.
 There are multiple times during teaching phase and guided practice for students to ask questions and the teacher to provide feedback.
 During guided practice, there are stopping points to allow for questions.
ASSESSMENT
 Feedback to Students:
 During the formative assessment, students are required to explain their thinking or reasoning for the answers they chose.
 There are multiple times during teaching phase and guided practice for students to ask questions and the teacher to provide feedback.
 During guided practice, there are stopping points to allow for questions.
 Summative Assessment:
 Students will be given 5 groups of 2 fractions. For each problem, using the multiplication method taught during this lesson, students must determine if the fractions are equivalent or not. Students should be able to find the number used to multiply and create the equivalent fraction and they can only use 2, 3, or 4.
 Students will record their responses on notebook paper and turn in to the teacher. Focus on the student's ability to correctly multiply the numerator and the denominator to find each equivalent fraction. After students have done correct calculations, students must show evidence that the fractions are equivalent or not equivalent. They can create 2 fraction strips or circles, demonstrating the relationship between the 2 fractions.
 They will explain the relationship between the 2 fractions (verbally or in written form) and tell what part of the whole they both represent. *Remind students that it is easier to start with the smaller fraction.
 1/2 = 4/8 Yes, equivalent.
 3/4 = 1/4 No.
 1/5 = 4/20 Yes.
 3/6 = 1/2 Yes.
 2/4 = 6/6 No.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
 Students are allowed to use premade fraction strips to assist them in finding equivalent fractions.
 Students may use multiplication charts to aid in their calculations.
 Students are able to copy equivalent fractions that they have discovered on the board or desk for easy reference, if necessary.
 Modified Summative assessment will include fewer questions. Students will be able to use their fraction strips created earlier in the previous lesson and any notes taken in order to keep the student's thinking on track with the lesson.
Extensions:
 Allow students who complete the activities early to create ratios comparing the numbers of items in the room to the number of students in the room. For example, students could create a ratio that shows the number of computers in the classroom compared to the number of students (3/16, for example) and then create equivalent ratios using the method taught in this lesson. Stress that although ratios and fractions may look the same, that fractions compare part to a whole, while ratio compares to things directly with each other.
 Students may also offer ideas for creating their own fractions.

Suggested Technology: Document Camera, Computer for Presenter, Interactive Whiteboard, LCD Projector
Special Materials Needed:
 Construction Paper
 Scissors
 Square Cardstock
 Spinner pin (brad)
 Spinner pointer
 paper bags
 groups of 2, 3, or 4 common items
 flash cards
 Premade Fraction Pie(s): 2/2 3/3 4/4 5/5 6/6 8/8
 Premade Fraction bar(s): 2/2 3/3 4/4 5/5 6/6 8/8
 1 Paper cutter
 Pencils
 Board game example
Further Recommendations:
 If you are following the Fraction Land series, you should have enough spaces for a large monopoly sized game board and a spinner for each student that have been divided into 8ths by the end of this lesson. Below are instructions for the board game.
 The Fraction Land board game is played in two phases, but it can be modified in anyway you choose.
 Phase 1:
 There are 5 different benchmark fractions displayed at the top of the game board:
 1/2
 1/3
 3/4
 1/4
 2/3
 1 "Equivalent Star
 Each student rolls a die. If the student rolls 15 the student moves their game piece to the next space on the game board that displays an equivalent fraction to the one that matches their die roll, respectively. A roll of 1 would be for 1/2, 2 would be for 1/3, etc.
 The rolling player picks another player to judge and explain why their answer is correct or incorrect. A correct explanation allows that player to move forward, 1 space. If the rolling player student is incorrect, they do not move forward.
 The student must move the very next space on the board and no farther. (there are multiple strategies involved in this game that students may become aware of, such as teaming up with other students.)
 Phase 2:
 Phase 2 only occurs when a student rolls a six. That student picks up an "Equivalency Star" card. When the card is flipped, students must solve the card on their scrap paper and then put their answer face down. Students with correct answers move forward 3 spaces. The cards have 3 levels of difficulty. All cards use the "cross multiplication" format.
 The first level uses only benchmark fractions such as 1/2 and 1/3.
 The second level uses both benchmark and lesser known fractions such as 1/2 and 4/6.
 The third level uses only lesser known fractions such as 3/7 and 5/9.
 Students repeat Phase 1 (and 2 if necessary) until a student has reached the end.
 Another added wrinkle could be the "Make a Space" card. If a student gets this card from the "Equivalency Star" stack, they can skip their next turn to create their own fraction strip and add it to the board. They may also travel to the end of it, possibly creating a short cut to the finish.
Additional Information/Instructions
By Author/Submitter
 This resource is likely to support student engagement in the following the Mathematical Practice:
 MAFS.K12.MP.2.1 Reason Abstractly and quantitatively. Students must explain the importance of each digit in the fractions and how they relate to the fractions being equivalent or not equivalent.
SOURCE AND ACCESS INFORMATION
Contributed by:
Eric Peebles II
Name of Author/Source: Eric Peebles II
District/Organization of Contributor(s): Brevard
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.
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