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Pattern Block Cookies

|Name: |Jamie Lahey |Section Time: |Wednesday | #: |23 |

| | | |4:30 | | |

|Mathematical Task: Developing familiarity with common equivalent fractions and their relationships |

|Grade Level, approximate number of students, types of students: |

|3rd grade |

|4 students |

|2 with no known disabilities |

|1 student who is color blind |

|1 student who has physical disabilities (this students is in a wheelchair and has trouble doing hands on activities do to limited motion) |

|Materials and Sources: |

|Lesson adapted from Cornelia Tierney and Mary Berle-Carman. Investigations in Number, Data, and Space: Fair Shares. White Plains: Dale Seymour, 1998. |

|Pattern blocks (a number of yellow, red, green, and blue-take out the orange and tan ones) |

|colored pencils, crayons, or markers |

|list of fraction facts (from earlier lesson-I will make them a list) |

|Pencils |

|hexagon cookies worksheet |

|NYS Mathematics Performance Indicator(s): |

|Content Strands: |

| |

|3.N.11-Use manipulatives, visual models, and illustrations to name and represent unit fractions (½, 1/3, ¼, 1/5, 1/6, and 1/10) as part of a whole or a set of |

|objects |

|3.N.13-Recognize fractional numbers as equal parts of a whole |

|3.N.14-Explore equivalent fractions (½, 1/3, ¼) |

| |

|Performance Indicators: |

| |

|3.PS.12-Use physical objects to model problems |

|3.PS.21-Discuss with peers to understand a problem situation |

|3.RP.5-Justify general claims or conjectures, using manipulatives, models, and expressions |

|3.CM.3-Provide reasoning in both written and verbal form |

|.3-Connect and apply mathematical information to solve problems |

|3.R.1-Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations |

|Performance Objectives: |

|The students will demonstrate the ability to use their pattern blocks to help them find all of the ways to make one whole by using combinations of different |

|parts, and then they will draw the picture and write the fraction that each diagram represents on their worksheet. |

|Safety Precautions: |

|Make sure that none of the pattern blocks, worksheets, colored pencils, or pencils fall on the floor, they could cause someone to slip and fall. |

|Part of Lesson |Teacher and Student Actions |Mathematical Questions. These can repeat for different parts|

| | |of the lesson if appropriate. Include both lower order and |

| | |higher order questions for each lesson. |

|Launch/Anticipatory Set/Before |Teacher Actions: |Lower Order Thinking Questions: |

|State prior knowledge needed, then |I will start by reviewing prior concepts that students have |Can different parts make up the same whole? (yes) |

|explain how you will access prior |learned that could help them understand this lesson. They | |

|knowledge and draw the students into |will need a review of their fraction facts from the faction |Are 1, 1/1, 2/2, 3/3, and 6/6 equivalent fractions? (yes) |

|this particular lesson. |facts worksheet they have from an earlier lesson. I will | |

| |review this worksheet and the relationships between the |What is ½ + 2/4? (1) |

|Also explain how you will launch the |fractions on it. | |

|“problem” the students will solve |I will go over the concept with them that different parts can|Higher Order Thinking Questions: |

|during the explore. Some problems |make up the same whole. I will do this by modeling with |Would you solve a similar problem the same way you solved |

|need more extensive launches than |pattern blocks to make sure that they understand the concept.|this one? Why or why not? |

|others. |This concept needs to be understood for students to be able | |

| |to understand this lesson. |Why is there more than 1 way to get 1 whole? |

| |I will model this concept by introducing a similar problem to| |

| |the students. The problem that is used will show students |When we add fractions, we have to get a common denominator |

| |that different parts can make up the same whole. |before we add them together. Can you add ½ + 1/3 + 1/6 to get|

| |The model problem will have students find out how many |1? Can you explain how you would do that? |

| |different parts can make up 1 whole red trapezoid. | |

| |You can make up 1 whole red trapezoid in 2 different ways. | |

| |You could make 1 whole with 3 green triangles. You could also| |

| |make 1 whole with 1 blue diamond and 1 green triangle. | |

| | | |

| |Student Actions: | |

| |Students will have prior knowledge of the basic fraction | |

| |facts. They will have their fraction facts worksheet | |

| |available for a reference. | |

| |Students will understand the concept that different parts can| |

| |make up the same whole. | |

| |Students will use their pattern blocks to model the sample | |

| |problem as I model it. | |

| |Students will understand why these different parts make up | |

| |the same whole (1 trapezoid=3 green triangles=1blue diamond | |

| |and 1 green triangle) | |

|Explore/During |Teacher Actions: |Lower Order Thinking Questions: |

|Describe what the teacher will do and|Give students the directions for the activity. “You will work|Is there only 1 one way to solve this problem? (no) |

|how the students will be engaged in |in pairs (groups of 2). Each pair will be given a set of |Can you use your fraction facts sheets to check your work and|

|the lesson/activity. |pattern blocks to work with. You will also be given a |make sure that you have covered every possible way to make 1 |

| |worksheet. You will need yellow, blue, red, and green |yellow whole? (yes) |

| |crayons, colored pencils, or makers.” |Will each way to make up one whole be all the same color? |

| |Then write the problem on the chalkboard or dry erase board. |(no) |

| |“We are having a math party. For a snack at the party we will|How many ways did you find to make up 1 whole? (8) |

| |have hexagon shaped cookies. Find all of the ways you can | |

| |that we could divide up the cookies and share them.” |Higher Order Thinking Questions: |

| |Explain to students that they will use their pattern blocks |Before we break into pairs can someone explain to me what we |

| |to solve the problem. They will find out how many different |are going to do? |

| |parts can make up 1 yellow whole. They will draw each way |Can you solve this problem without using pattern blocks? |

| |they find using the appropriate colors on their hexagon |Explain how you would do so. |

| |cookies worksheet. In each section of each picture they will |How did you go about solving the problem and making sure you |

| |write the corresponding fraction. |had all the ways to make 1 whole? Does everyone have to solve|

| |Let students know that you will be walking around the |the problem this way/in this order? Why or why not? |

| |classroom monitoring the groups' progress and that you will |How did you know when you were finished? How did you know you|

| |be available for questions and to assist those who need help.|had all of the answers? |

| | | |

| |Student Actions: | |

| |Students will break into pairs (groups of 2) | |

| |Each group will get a set of pattern blocks. Each person will| |

| |need their fraction facts worksheet, hexagon cookie | |

| |worksheet, and the appropriate colors to work with (red, | |

| |yellow, blue, and green colored pencils, markers, or crayons)| |

| |Each pair will work together to solve the problem, “We are | |

| |having a math party. For a snack at the party we will have | |

| |hexagon shaped cookies. Find all of the ways you can that we | |

| |could divide up the cookies and share them.” | |

| |Each person will draw the different ways that they have found| |

| |to make up a yellow hexagon with different parts on their | |

| |worksheet and color the pictures accordingly. | |

| |Each person will then write the fractions that correspond to | |

| |each part in that section of their picture. | |

|Summary/Closure/After |Teacher Actions: |Lower Order Thinking Questions: |

|Describe how you will summarize the |Ask students to share the answers they got and how they got |Did everyone go about solving the problem the right way? (no)|

|lesson. This is a most important |their answers. |Will every word problem that has different parts adding up to|

|part of a problem solving lesson |Write all of the different ways that students got to come up |a whole have the same answer? (no) |

|where the students share their |with 1 whole on the board. |Can you use addition to check your answers? (yes) |

|strategies. The teacher should |Check and make sure that all of the “parts” added up to | |

|facilitate the discussion and the |exactly 1 “whole.” |Higher Order Thinking Questions: |

|students should be actively engaged. |Generate a discussion among the students about how they went |Can you explain how someone else solved the problem in your |

| |about tackling the problem. |own words? |

| |Collect each student's work to make sure that they thoroughly|What other strategies could you use to solve this problem. |

| |understood the problem. |Explain. |

| |Have students see if they can come up with word problems |Are there any problem solving strategies that we have |

| |where different parts can add up to 1 whole. |discussed in other lessons that you do not think would work |

| | |to solve this problem? Why or why not? |

| |Student Actions: |Is everyone's word problem going to have the same answer? Why|

| |Will share how they went about solving the problem with the |or why not? |

| |rest of the class. | |

| |Will give the teacher the different parts that they added | |

| |together to get 1 whole. | |

| |Will help teacher check and make sure all of the different | |

| |“parts” added up to exactly 1 “whole.” | |

| |Hand in their hexagon cookie worksheets to be looked over by | |

| |the teacher. | |

| |In their pairs, make up word problems similar to the one that| |

| |they solved. (adding different parts up to get 1 whole). | |

|Assessment |The teacher will know if the students met the objective by collecting each student's worksheet to check and see that they |

|Clearly describe how the teacher will|really understood the problem. You will check this by checking for the right answers and making sure that the answers made |

|know if the students met the |sense. (no one wrote ½, or 1/8, etc. on any parts of their worksheet). Students do not have to have ALL of the ways to make|

|objective. Assessment should be |up 1 whole, but should have at least half of the possible ways with the fractions labeled properly. Assessment will also be|

|embedded within the activities. The |based on how the students explained what they did to get their answer to the rest of the class. Understanding will also be |

|assessment may include a separate |measured by checking to make sure that students' word problems make sense and are similar to the one that they completed |

|independent component. |(you are finding different parts that make up a whole). |

|Modification for Advanced Learners |Advanced learners will complete the same problem as the rest of the class. When they have finished this problem, challenge |

| |them to try and solve a similar but more complicated problem. Have them solve a problem broken down into 12ths and not |

| |6ths. See if they can get each of the ways to make up 1 whole this way. They can do so using and strategy they want to. |

| |They do not have to solve the problem using objects. |

|Modifications for two types of |Color blind: In this activity students are using colored pattern blocks and colored pencils, crayons or markers to solve a |

|disabilities-state the name of the |problem and complete a worksheet. This student does not have to use colors to complete this activity. Make sure the child |

|disability here. You may include a |knows that the shapes are hexagons, diamonds, trapezoids, and triangles. This student can work on the activity using shapes|

|modification for ELL. |instead of color. When doing the worksheet, allow the child to color the pictures in using different shading or designs |

| |instead of using the different colors. |

| | |

| |Physical Disability (in a wheelchair and limited motion): In this activity students are moving the pattern blocks around |

| |and finding out which parts can make up a whole. Make sure this student has a buddy that is willing to help them with the |

| |problem. Allow the student to tell his/her buddy which pieces he/she thinks will make up 1 whole and the buddy can check |

| |and see if it is correct. This student can tell his/her buddy how to draw the pictures on the worksheet, and how to color |

| |and label them. Allow these 2 students to have more time to complete the activity if needed. It will not be fair to either |

| |one of them if they do not have sufficient time to finish. |

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