RATIONALE
· The purpose of this lesson is to help students understand equivalent fractions through multiplication. Learning about fractions is important because they are used in measurements across various professions and are essential to the study of algebra and more advanced mathematics. Students need to have a strong foundation in fractions and understand that two equivalent fractions is just two ways of describing the same amount using different sized fractional parts.
STANDARDS
· CCSS.Math.Content.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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.
· CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
· This lesson is important because students need to be able to understand equivalent fractions in order to understand fractions in general.
· Year curriculum: Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions.
OBJECTIVE
· Given brownies, students will be able to partition two brownies two separate ways and show that they are equivalent through checking with peers and group discussion. Students will be able to “prove it” by using multiplication and multiplying the numerator and denominator by the same number.
· Given materials for the student’s interactive notebooks, students will be able to “know, show, and prove” that fractions are equivalent by completing the flipbook and matching the correct circle fraction to the equivalent fraction flap.
LESSON PROGRESSION
· Introduction
o Students will be given a “do now” activity that they will complete independently on the carpet as they come into class.
o Students will talk about “do now” and review information and strategies used to complete the problem.
o Review charts and information they have been working with previously and introduce equivalent fractions using pictures of pizza on the board.
§ Show ½ of a pizza, show that you can divide the pizza again to make it 2/4 and that this is the same amount, show that when you divide the pizza one more time to make 4/8 it still shows the same amount.
§ Draw ¾ of a pizza and ask students to show what other fractions represent the same amount.
§ Show how to use multiplication in order to get equivalent fractions.
· Introduce “know it, show it, prove it”
· Use the two previous problems to demonstrate using multiplication to find equivalent fractions.
o Have students figure out what number they should use to multiply the numerator and denominator by to get the equivalent fraction.
§ http://www.mathsisfun.com/numbers/fraction-number-line.html Show fraction bars and website to provide a different way to see equivalent fractions.
· Students have been working with fraction bars to understand what fractions look like and see equivalent fractions visually. This website is an interactive tool students can use to also use to see equivalent fraction visually.
· Middle
o Set up for using the brownies to show equivalent fractions
o Have one student choose a fraction and cut the brownie to show the fraction.
o Ask another student to take a separate brownie and show a different way to make the same fraction.
o Have the third student complete the “know it, show it, prove it” set up to show how the other two students made equivalent fractions.
o Complete 2 more times until all students have had a chance doing each job.
· Closure
o Have students put together flipbooks in interactive notebook.
§ Glue parts together.
§ Color in pizza.
§ Explain.
o Equivalent Fraction Match
§ Have students shade in fractions on flaps.
§ Have students match the equivalent fractions and glue under flaps.
· Ask students how they know the fractions are equivalent by using the “know it, show it, prove it” system.
· Have students show their work under each flap and record multiplying the numerator and the denominator by the same number to get the equivalent fraction.
o Have students complete tasks independently.
§ It will become homework if they do not finish.
ASSESSMENT
· Students will be assessed when it is their turn to “prove it” on the board. They should be able to multiply the numerator and the denominator by the same number in order to prove that the two fractions are equivalent.
· Students should successfully complete the equivalent fraction matching flaps.
o Students should be able to shade fraction, match the appropriate equivalent fraction, and put it in their notebook.
o Students should be able to “prove it” that the fractions are equivalent by multiplying the numerator and denominator by the same number to get the equivalent fraction.
OTHER CONSIDERATIONS
· Materials: Worksheets, glue, colored pencils, brownies, knife, napkins, pencil, notebook.
· My cooperating teacher gave me the materials for this lesson and helped me develop the lesson progression.
· What are some possible questions you might ask during the lesson that will elicit better mathematical understanding?
o How do you know that the fractions are equivalent?
§ This will allow students to explain verbally and check their understanding of the concept.
o How does using multiplication help find equivalent fractions?
§ This will allow students to explain verbally the importance of using multiplication to find equivalent fractions and check their understanding.
o Can we use division to find equivalent fractions?
§ This will allow us to move into future lessons of finding the greatest common factor to find equivalent fractions.
· I expect students to develop an understanding of equivalent fractions through multiplication. I want students to be able to show equivalent fractions using the “know it, show it, prove it” framework. Potential misconceptions I will look for are that the numerator and denominator are multiplied by the same number in order to create an equivalent fraction. Another misconception is that students over apply whole number concepts. The students in my class have been struggling to see that the larger number denominator is not the larger fraction. Using the brownies and allowing them to see the fractions visually will help straighten out this concept. One last misconception or area that I want to look out for is that the students have a conceptual understanding. The objective of this lesson is very efficient for finding equivalent fractions, but it is important that students are able to create a conceptual understanding as well. Using the brownies as manipulatives, I want students to see that using multiplication is a tool for finding equivalent fractions because it breaks the whole into smaller parts, however the smaller parts are still the same equivalent amount.
DIFFERENTIATION
· The class that I am in is a resource room so the group that I will be working with is only three fifth grade students. Since I am only working with three students, it will be easier for me to make sure that each of them is following along and fully understanding the lesson. All three students struggle with math so giving them a hands on problem that involves food will keep them actively engaged and allow them to learn using manipulatives.
· The purpose of this lesson is to help students understand equivalent fractions through multiplication. Learning about fractions is important because they are used in measurements across various professions and are essential to the study of algebra and more advanced mathematics. Students need to have a strong foundation in fractions and understand that two equivalent fractions is just two ways of describing the same amount using different sized fractional parts.
STANDARDS
· CCSS.Math.Content.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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.
· CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
· This lesson is important because students need to be able to understand equivalent fractions in order to understand fractions in general.
· Year curriculum: Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions.
OBJECTIVE
· Given brownies, students will be able to partition two brownies two separate ways and show that they are equivalent through checking with peers and group discussion. Students will be able to “prove it” by using multiplication and multiplying the numerator and denominator by the same number.
· Given materials for the student’s interactive notebooks, students will be able to “know, show, and prove” that fractions are equivalent by completing the flipbook and matching the correct circle fraction to the equivalent fraction flap.
LESSON PROGRESSION
· Introduction
o Students will be given a “do now” activity that they will complete independently on the carpet as they come into class.
o Students will talk about “do now” and review information and strategies used to complete the problem.
o Review charts and information they have been working with previously and introduce equivalent fractions using pictures of pizza on the board.
§ Show ½ of a pizza, show that you can divide the pizza again to make it 2/4 and that this is the same amount, show that when you divide the pizza one more time to make 4/8 it still shows the same amount.
§ Draw ¾ of a pizza and ask students to show what other fractions represent the same amount.
§ Show how to use multiplication in order to get equivalent fractions.
· Introduce “know it, show it, prove it”
· Use the two previous problems to demonstrate using multiplication to find equivalent fractions.
o Have students figure out what number they should use to multiply the numerator and denominator by to get the equivalent fraction.
§ http://www.mathsisfun.com/numbers/fraction-number-line.html Show fraction bars and website to provide a different way to see equivalent fractions.
· Students have been working with fraction bars to understand what fractions look like and see equivalent fractions visually. This website is an interactive tool students can use to also use to see equivalent fraction visually.
· Middle
o Set up for using the brownies to show equivalent fractions
o Have one student choose a fraction and cut the brownie to show the fraction.
o Ask another student to take a separate brownie and show a different way to make the same fraction.
o Have the third student complete the “know it, show it, prove it” set up to show how the other two students made equivalent fractions.
o Complete 2 more times until all students have had a chance doing each job.
· Closure
o Have students put together flipbooks in interactive notebook.
§ Glue parts together.
§ Color in pizza.
§ Explain.
o Equivalent Fraction Match
§ Have students shade in fractions on flaps.
§ Have students match the equivalent fractions and glue under flaps.
· Ask students how they know the fractions are equivalent by using the “know it, show it, prove it” system.
· Have students show their work under each flap and record multiplying the numerator and the denominator by the same number to get the equivalent fraction.
o Have students complete tasks independently.
§ It will become homework if they do not finish.
ASSESSMENT
· Students will be assessed when it is their turn to “prove it” on the board. They should be able to multiply the numerator and the denominator by the same number in order to prove that the two fractions are equivalent.
· Students should successfully complete the equivalent fraction matching flaps.
o Students should be able to shade fraction, match the appropriate equivalent fraction, and put it in their notebook.
o Students should be able to “prove it” that the fractions are equivalent by multiplying the numerator and denominator by the same number to get the equivalent fraction.
OTHER CONSIDERATIONS
· Materials: Worksheets, glue, colored pencils, brownies, knife, napkins, pencil, notebook.
· My cooperating teacher gave me the materials for this lesson and helped me develop the lesson progression.
· What are some possible questions you might ask during the lesson that will elicit better mathematical understanding?
o How do you know that the fractions are equivalent?
§ This will allow students to explain verbally and check their understanding of the concept.
o How does using multiplication help find equivalent fractions?
§ This will allow students to explain verbally the importance of using multiplication to find equivalent fractions and check their understanding.
o Can we use division to find equivalent fractions?
§ This will allow us to move into future lessons of finding the greatest common factor to find equivalent fractions.
· I expect students to develop an understanding of equivalent fractions through multiplication. I want students to be able to show equivalent fractions using the “know it, show it, prove it” framework. Potential misconceptions I will look for are that the numerator and denominator are multiplied by the same number in order to create an equivalent fraction. Another misconception is that students over apply whole number concepts. The students in my class have been struggling to see that the larger number denominator is not the larger fraction. Using the brownies and allowing them to see the fractions visually will help straighten out this concept. One last misconception or area that I want to look out for is that the students have a conceptual understanding. The objective of this lesson is very efficient for finding equivalent fractions, but it is important that students are able to create a conceptual understanding as well. Using the brownies as manipulatives, I want students to see that using multiplication is a tool for finding equivalent fractions because it breaks the whole into smaller parts, however the smaller parts are still the same equivalent amount.
DIFFERENTIATION
· The class that I am in is a resource room so the group that I will be working with is only three fifth grade students. Since I am only working with three students, it will be easier for me to make sure that each of them is following along and fully understanding the lesson. All three students struggle with math so giving them a hands on problem that involves food will keep them actively engaged and allow them to learn using manipulatives.