A six day fraction unit using TI-73 Graphing Calculator, M&M s, Pattern Blocks, GeoSolids, Microsoft Excel, Money, & Cupcakes for the 6 th Grade.

Transcription

1 A six day fraction unit using TI-73 Graphing Calculator, M&M s, Pattern Blocks, GeoSolids, Microsoft Excel, Money, & Cupcakes for the 6 th Grade. Michael ann I 2 T 2 5

2 Objectives Materials.. 4 Materials..4 Standards.5 Day One Day Two Day Three Day Four Day Five

3 The student will be able to recognize the idea that the whole is made of several parts. The student will be able to create fractions given the whole, broken into parts. The student will be able to recognize fractions in everyday life. The student will be able to interpret a chart in order to create fractions. The students will be able to simplify fractions while playing a modified version of the children s card game Go Fish. The student will be able to analyze two (2) fractions and determine which is larger and which is smaller. The student will be able to communicate why a fraction is larger/smaller than another fraction. The student will be able to use a calculator to communicate relationships between fractions. The student will be able to create at least two (2) situations where smaller GeoSolids are combined to form one (1) bigger GeoSolid. The student will be able to communicate to the rest of the class their group s findings in appropriate mathematical language. The student will be able to determine the fractional value of a specific GeoSolid when it is compared to a larger GeoSolid. Given a handful of pattern blocks the student will be able to compare smaller pieces to larger pieces in terms of a fraction. Given a handful of pattern blocks the students will work together to form various shapes that are comprised of different size and shape pattern blocks. Given a recipe for a double batch the student will be able to create the batter needed to make a single batch of cupcakes. Given various amounts of money, the student will be able to convert that money into fractional statements. Given an excel worksheet with specific directions the student will be able to determine which plot of land would be the pick of the litter. 3

4 Math Journal Pencils M&M s fun size bags (1 per student) M&M s Worksheet Index Cards Markers TI-73 (1 for every 2 students) Fraction Circles Fraction Circles/Number Line Worksheet Overhead Connection for TI-73 Overhead Fraction Circles Overhead 4 Sets of GeoSolids Water (2 cups per station) Paper Towels 4 Bowls Pattern Blocks (6 sets) Pattern Block Worksheet Cupcake Mix (all ingredients/kitchen tools required) Play Money (6 sets) 6 Computers With Microsoft Excel Gardening Worksheet NCTM Standards Addressed: Numbers & Numeration Data Analysis & Probability Problem Solving Communication Geometry Operations Algebra Reasoning & Proof Representation New York State Standards Addressed: Mathematical Reasoning - 1A, 1B, 1C, 1D Number & Numeration - 2A, 2B, 2D Operations - 3A, 3D Modeling/Multiple Representation - 4A, 4B, 4F Measurement - 5D 4

5 Overview Day 1: Re- Introducing Fractions This day will be used to re-introduce the students to the many concepts of fractions and their use in everyday life. This lesson is basically an introductory lesson to make the students comfortable with fractions so that they can apply the many concepts surrounding them. The focus of this lesson is the use of M&M s to find fractions. Day 2: Fraction Go Fish Day two focuses on the idea of different fractions being equivalent to one another. Students will play the game Fraction Go Fish to accomplish objective. Day 3: Number Line This day will incorporate the TI-73 into the classroom to facilitate the student s knowledge of greater than and less than with regards to fractions. The students will be grouped into pairs to play Number Line on the TI-73. Day 4: GeoSolids, Addition, & Fractions Today the students will work with GeoSolids to show the relationship between the part and the whole. This is also being used as an introductory lesson on the addition of fractions. Days 5 & 6: Fraction Stations This two day experience allows the students to apply some concepts we already learned and some new ones that involve real world situations. The stations involve a pattern block activity, a cupcake recipe, a game called Bank Teller, and a Microsoft Excel activity that involves fractions and area in determining potential houses to purchase. 5

6 Day 1 Subject: Re-Introducing Fractions Length: 45 Minutes I. Objective The purpose of this lesson is to re-introduce the idea of fractions to the student. Students will re-visit the idea of parts vs. whole. II. Performance Indicator The student will be able to recognize the idea that the whole is made of several parts. The student will be able to create fractions given the whole, broken into parts. The student will be able to recognize fractions in everyday life The student will be able to interpret a chart in order to create fractions III. Standards NCTM Standards: Numbers & Numeration, Data Analysis, Problem Solving, and Communication NYS Key Ideas: 1A, 1B, 2A, 4F, 5D IV. Materials M&M s Fun Size Bags (1 per student) Pencils Worksheet (see attached) V. Instructional Procedures Opening: Once students are seated ask them how many of them think fractions play a role in our everyday lives? Lead a discussion where examples are given and discuss their relevance to everyday life. i. Examples include: pizza, time, sports (free throws) Discuss how when looking at a pizza if 8 people have one slice each and a whole pizza contains 8 slices, then all of the people constitute a whole pizza. Main Activity: Give each student a worksheet and a package of M&M s (instruct them to open the M&M s, but not to eat them). Ask the students to separate the M&M s by color and to fill in the corresponding blanks in the worksheet. 6

7 Closing: Place the students into pairs and have them compare their findings to one another. Ask the students to discuss with their partner why they feel fractions are important in their lives. VI. Performance Assessment This lesson will be assessed both informally and formally. Informally this lesson will be assessed by the educator walking around the classroom observing the conversations amongst students. Formally this lesson will be assessed by collecting the worksheets. VII. Follow Up Activities Homework Question: Ask your parents how fractions affect their lives on a daily basis. Ask them why fractions are important to them. Be prepared to share with the class the following day. VIII. Teacher Notes Remember that not all students will have the same answers on the worksheet due to each bag of M&M s being different in make-up. 7

8 Name: Directions: Open your bag of M&M s (but don t eat them) and separate them by color. Then fill in the NUMBER column on the following chart and answer the questions below. We will fill in the FRACTION column later. COLOR NUMBER FRACTION Orange Blue Red Green Brown Yellow TOTAL 1) How many Green M&M s do you have? 2) How many M&M s do you have in total? 3) Create a fraction to show the relationship between the number of green M&M s compared to the total number of M&M s. 4) Go back to the chart above and fill in the FRACTION column. 5) If you were to count all of the colors and then create a fraction compared to the total number of M&M s what would it look like? 8

9 Day 2 Subject: Fraction Simplification Length: 45 minutes II. Objective The purpose of this lesson is to facilitate knowledge of simplifying fractions. III. Performance Indicator The students will be able to simplify fractions while playing a modified version of the children s card game Go Fish. IV. Standards NCTM Standards Covered: Reasoning and Proof, Communication, Numbers and Numeration, Operations NYS Key Ideas: 1A, 1B, 1C, 1D, 2A, 2B, 2D, V. Materials Index Cards Markers VI. Instructional Procedures Opening: Ask students who asked their parents the homework question. Ask for examples from the students of answers that their parents gave them. Briefly discuss their responses and their relevance. Main Activity: Review some simple examples of simplifying fractions i. 2/4 = 1/2 ii. 2/8 = 1/4 Begin by asking students, Does anyone remember the game Go Fish? Ask a student who remembers the rules to explain the game to the rest of the class. Explain that this game of Go Fish is going to be slightly different. Explain that instead of looking for cards that have the same number on them the students will be looking for a fraction that is equivalent to the one they are holding. The pairs will be one simplified fraction, and one that is in original form. Group students into groups of four. Each group will receive 30 index cards (15 pairs) with various fractions on them. Determine one dealer for each group (choose the brightest child in the group as he/she will be the decision maker in the case of an argument over equalities). Have this child deal 5 cards to each member of the group and place the rest in a pile face down in the center of the table. 9

10 Explain that when asking for the match you must phrase it Does anyone have a fraction that is equivalent to? The blank is the card that child possess. Have the children play Go Fish. When any child has a match they must say to the group, (Original Form Card) is equivalent to (Simplified Fraction Card). If needed model this behavior to the students. The winner of the game is the person who collects the most pairs. Closing: In their math journals students will list five (5) sets of equivalent fractions. VII. Performance Assessment Assessment of this lesson will be both informal and formal. The teacher will circulate the room and view the various groups playing the game and take note of which students excel and which students struggle. Formally this lesson will be assessed through a homework assignment in which the students will create their own index cards with original form fractions and matching simplified fractions. This will be collected and graded for accuracy (additional points may be given for those students who decide to tackle more difficult conversions.) VIII. Follow Up Activities As a follow up students the index cards will be placed in a learning center where when students complete their work they can use the cards in a game of memory. This is where students play in pairs with the cards down and try to turn over similar cards to create matches. This game could be expanded to include different versions such as cards containing fractions and the students need to find pairs that are equivalent decimals. IX. Teacher Notes Remember to not create fractions which will have several equivalent cards this is to avoid confusion while playing the game. Sample Cards

11 Day 3 Subject: Comparing Fractions Length: 30 minutes II. Objective The purpose of this lesson is to further student s ability to compare fractions as to whether they are less than, greater than, or equal to. III. Performance Indicator The student will be able to analyze two (2) fractions and determine which is larger and which is smaller. The student will be able to communicate why a fraction is larger/smaller than another fraction. The student will be able to use a calculator to communicate relationships between fractions. IV. Standards NCTM Standards: Number & Operations, Algebra, Problem Solving, Reasoning & Proof, Communication, and Connections NYS Key Ideas: 1A, 2A, 2D V. Materials TI-73 (1 for every 2 students) Worksheet (see attached) Fraction Circles Overhead Connection for TI-73 Overhead Fraction Circles Overhead VI. Instructional Procedures Opening: Pose the following question to your students I have $96 that I can split between two people. Would you rather have 5/8 of it or 7/12 of it? Students will compose a few sentences to answer this question. Ask your students to explain their reasoning behind their answer. Demonstrate the concept of 5/8 and 7/12 on the overhead using fraction circles to arrive at a final conclusion. Ask your students reasons why they believe that 5/8 is bigger despite the fact that 7 > 5. 11

12 Main Activity: Split the class into groups of two (2). Give each group a TI-73 calculator with the application Number Line already running on it. Explain that we will be playing a game that involves the use of fractions. The object of the game is to place a fraction in-between two previously existing fractions. Explain to students how the draw and b/c buttons function in the playing of this game. To start the game have player 1 enter a fraction. Then player 2 will enter another fraction. Next, player 1 will attempt to enter another fraction between the two existing fractions. The player 2 will enter a fraction between the last two fractions entered. The game continues until someone places a fraction outside of the given maximum and minimum. The winner is the last person to accurately enter a fraction. Play a sample game on your calculator using the overhead connection. Closing: Students will write in their math journals regarding inequalities and fractions. They should discuss what relevance the number in the numerator has. If the number in the first fraction is greater than the numerator in the second fraction does that guarantee that the first fraction is greater than the second fraction? VII. Performance Assessment Informally this lesson will be evaluated by meandering throughout the classroom and overlooking the play among the students and noting any patterns that exist for certain students who may require additional assistance with this concept. Additional informal assessment will take place during the opening activity of the next class period. Formally this lesson will be evaluated through the use of a worksheet that will be assigned for homework. VIII. Follow Up Activities TI-73 s will be located in the Math Learning Center for students to replay this game when in class assignments are completed. IX. Teacher Notes A review of inequality signs may be necessary. 12

13 Name Directions: Place the fraction(s) on the fraction line in an appropriate location 1. 3/4 0 _ /5 _ 3. 1/5 and 3/5 0 _ 1 Directions: Use fraction circles to sketch and determine what sign <, >, or = to place between the circles. 1. 1/2 1/4 4. 7/8 4/5 2. 1/3 1/5 5. 3/9 3/8 3. 2/5 4/ /

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15 Day Four Subject: GeoSolids, Addition, & Fractions Length: 45 minutes II. Objective The purpose of this lesson is to further student s knowledge of fractions with regards to the sum of the parts equaling the whole. III. Performance Indicator The student will be able to create at least two (2) situations where smaller GeoSolids are combined to form one (1) bigger GeoSolid. The student will be able to communicate to the rest of the class their group s findings in appropriate mathematical language. The student will be able to determine the fractional value of a specific GeoSolid when it compared to a larger GeoSolid. IV. Standards NCTM Standards: Number & Operations, Geometry, Data Analysis & Probability, Problem Solving, Reasoning & Proof, and Communication NYS Key Ideas: 1A, 1B, 1C, 2A, 2B, 4A V. Materials Overhead 4 Sets of GeoSolids Water (2 cups per station) Paper Towels 4 Bowls VI. Instructional Procedures Opening: Pose the following situation. You are making brownies and you need 1 cup of water. The problem is that you lost your 1 cup measuring cup. All you have is measuring cups of the following capacities 1/2, 1/3, 1/4, and 1/6. How can I make 1 cup by using any combination of the above measuring cups? Place any answers on the board and as a class determine their validity. Main Activity: Guide groups to their respective stations Inform them that GeoSolids A, B, & C (note: the GeoSolids will be labeled A, B, C, & D from smallest to largest) can be filled with water in combinations that will fill GeoSolid D. Ask the students to experiment with the smaller solids and determine what fraction of the largest GeoSolid each is. Show students an example using the triangle shaped GeoSolids. Instruct students to begin using the smaller GeoSolids to completely fill GeoSolid D. 15

16 Remind students to keep track of their trials using this format B + B + C = D Instruct students to replace the letters A, B, C, & D with their fractional equivalent. Have each group select a reporter. Have the reporter share with the class one way in which his/her group determined that the A, B, & C could be combined to form D. Ask if they used all of one GeoSolid to fill in the larger shape or if they used a combination of all/some of the GeoSolid. Closing: In their journals have the students contemplate the following What did this experiment tell us about parts and wholes? How is it possible that 1/8 + 1/8 +1/4 + 1/2 = 1 VII. Performance Assessment Informally this lesson will be evaluated by witnessing the groups working. The teacher must continually circulate to determine multiple things. First the teacher needs to make sure that all students are given the chance to contribute to the group. Second the teacher must be available to answer any confusion that arises from the use of the GeoSolids. VIII. Follow Up Activities GeoSolids will be placed in the learning center and students may use them to explore other relationships between 3-D models. IX. Teacher Notes There are numerous solutions to the problem using the cube. There is no homework assignment for this lesson This problem can be done in reverse in order to show subtraction of fractions. 16

17 Day 5 Subject: Fraction Stations Length: 2/45 minutes I. Objective The purpose of this lesson is to facilitate knowledge the students obtained from the previous lessons but in different forms. II. III. IV. Performance Indicator Given a handful of pattern blocks the student will be able to compare smaller pieces to larger pieces in terms of a fraction. Given a handful of pattern blocks the students will work together to form various shapes that are comprised of different size and shape pattern blocks. Given a recipe for a double batch the student will be able to create the batter needed to make a single batch of cupcakes. Given various amounts of money, the student will be able to convert that money in to fractional statements. Given an excel worksheet with specific directions the student will be able to determine which plot of land would be the pick of the litter. Standards NCTM Standards: Number & Operations, Geometry, Data Analysis & Probability, Problem Solving, Reasoning & Proof, and Communication NYS Key Ideas: 1A, 1B, 1C, 2A, 2B, 2D, 3A, 3D, 4B Materials Pattern Blocks (6 sets) Pattern Block Worksheet Cupcake Mix (all ingredients/kitchen tools required) Play Money (6 sets) 6 Computers With Microsoft Excel Gardening Worksheet Timer V. Instructional Procedures Opening: Students will be instructed that when they come in the room they are to form their teams (these have been pre-assigned). They will go directly to their assigned stations. Main Activity: See attached sheets that are the instructions for each station. 17

18 Closing: As a class discuss the findings we made at each station and why they are important. VI. VII. Performance Assessment This lesson will be evaluated both formally and informally. Informally the students will be observed through all activities and the educator will take notes whenever possible. Station 3 (Bank Teller) will only be able to be assessed on an informal basis. At the end of each rotation the teacher will go to this station and determine which students correctly administered the transactions. Formally stations 1 and 4 (pattern blocks and excel) can all be evaluated through the use of the worksheet that will accompany those stations activities. Station 2 (cupcakes) will be evaluated based on whether or not the students cupcakes taste correct. If they taste normally it will be obvious that the directions were followed. On the other hand if the cupcakes taste a little funny then we will know that a mistake was made somewhere in the division of the fractions. Follow Up Activities Microsoft Excel will be left set up for students to explore when they have finished their work on future days. The Bank Teller Game will be available for students in the future for an activity once their work is completed. Pattern Blocks will be made available in the future to students who have completed assigned work. Order pizza for the day after the stations are completed and have a fraction party with the pizza and cupcakes the students made. VIII. Teacher Notes To save time the Excel worksheets can be made prior to the class and students can merely explore them rather than create them. Pay attention to the bank Teller game it is the only station that has no formal assessment. This works best if there is a Teacher s Aide available to help. Have timer set up to ring after 18 minutes. Then inform students that that was the 2 minute warning and they will need to finish what they are doing so we can move onto the next station. 18

19 Station 1: Pattern Blocks Directions: In part one of this station you will need to compare the size of smaller blocks to the size of the larger blocks in terms of fractions. Complete the following questions. 1. The red trapezoid is exactly the size of the yellow hexagon. 2. The green triangle is exactly the size of the red trapezoid. 3. The green triangle is exactly the size of the yellow hexagon. 4. The blue parallelogram is exactly the size of the yellow hexagon. 5. You can create the red trapezoid can be created by using blue parallelogram and green triangle(s). Directions: Create the following figures by using the fractions to determine how many of each shape constitutes the figures. Use the crayons to color in the appropriate shapes. 1. This shape is composed of _ red trapezoids and _ blue parallelograms. 2. This shape is composed of 6 pieces. _ are green triangles, 1/3 are blue parallelograms, and 1/6 are red trapezoids. 19

20 3. This shape is composed of 14 pieces. 3/7 are green triangles, 7/14 are orange squares, and 1/7 are red trapezoids. 20

21 Station 1: Pattern Blocks (Answer Key) Directions: In part one of this station you will need to compare the size of smaller blocks to the size of the larger blocks in terms of fractions. Complete the following questions. 1. The red trapezoid is exactly 1/2_ the size of the yellow hexagon. 2. The green triangle is exactly _1/3_ the size of the red trapezoid. 3. The green triangle is exactly _1/6_ the size of the yellow hexagon. 4. The blue parallelogram is exactly _1/3_ the size of the yellow hexagon. 5. You can create the red trapezoid by using _1_ blue parallelogram and _1_ green triangle(s). Directions: Create the following figures by using the fractions to determine how many of each shape constitute the figures. Use the crayons to color in the appropriate shapes. 1. This shape is composed of _ red trapezoids and _ blue parallelograms. 2. This shape is composed of 6 pieces. _ are green triangles, 1/3 are blue parallelograms, and 1/6 are red trapezoids. 21

22 3. This shape is composed of 14 pieces. 3/7 are green triangles, 7/14 are orange squares, and 1/7 are red trapezoids. 22

23 Station #2: Cupcakes Directions: Follow the recipe below to make cupcakes. BE CAREFUL!!! The recipe is written to make a double batch. Make sure to divide each ingredient in half so that your cupcakes will taste right. Ingredients: 1. 8/12 cup sweetened condensed milk 2. 1_ cup semisweet chocolate chips 3. 2 packages of cake mix 4. 1 cup vegetable oil 5. 2 cups of applesauce 6. 4 eggs 7. 4/6 cup of chopped pecans Recipe Microwave milk and chocolate chips for one minute or until chocolate is melted. Beat cake mix and oil in a large bowl by hand for 1 minute. Remove 1 cup of this mixture. Beat applesauce and eggs into remaining cake mixture by hand for 3 minutes. Spread in pan. Drip melted chocolate over the cake batter. Stir pecans into the remaining 1 cup of reserved cake mixture; sprinkle over batter. Place this mixture in the refrigerator and I will take care of the rest this evening. I hope you remembered to cut everything in half!!!! If not we will definitely know tomorrow when we all eat the cake!!!! 23

24 Station 3: Bank Teller Directions: Each person will start off with the game with $2.00 worth of random coins. No two people will have the same combination of coins. The goal is to trade your money evenly with the other bank tellers. THE TWIST you can not say, I will give you 5 pennies for a nickel. You have to say, I will give you 1/20 of a dollar in pennies for 1/20 of a dollar in nickels. If the player you ask does not have that combination you are looking for they may substitute another coin value, but must be able to communicate the fractional value of a dollar it equals. The object of the game is to complete 20 transactions and end up with the each player still having $2.00 at the conclusion of time. If somebody does not have $2.00 at the end then a mistake was made. Pay close attention to the transactions, you don t want to end up with less or more money than anyone else. The winner is the person(s) who end up at exactly $

25 Station 4: My Garden Directions: Sit down at one of the computers and open the file entitled my garden. Each square on this grid is equal in size. Now we need to follow the next few steps to create our homes and gardens 1. Hit ctrl+a. 2. Use the grid function to place the grid on the worksheet. 3. Click on A1 hold the click and drag it all the way to G6. 4. Use the paint bucket to color this section red. 5. Click on B2 and drag until E4. 6. Color this section green. 7. Label this Plot A by placing an A in C3. 8. Click on A9 hold the click and drag until P Use the paint bucket to color this section blue. 10. Click on B10 and drag until M Use the paint bucket to color this section purple. 12. Label this Plot B by placing a B in G Click on A20 hold the click and drag until Y Use the paint bucket to color this section orange. 15. Click on B21 hold the click and drag until R Use the paint bucket to color this section white. 17. Click on S27 hold the click and drag until W Use the paint bucket to color this section white as well. 19. Label this Plot C by placing a C in K27. You now have three plots of land with three houses on those plots. The outside color is the entire plot of land. Within that color we built houses that are represented by a different color. It is your job to order these three houses in terms of what fraction of the land is available to plant a garden. You will accomplish this by determining the area of the entire plot and placing that in the denominator. Then you will determine the area of the garden. This number will go in the numerator. Lastly you will rank these three plots by looking at each fraction and telling which on has the biggest fraction of garden land. NOTE: 1 BLOCK = 1 SQUARE INCH 1. Plot A has a fractional representation of. 2. Plot B has a fractional representation of. 3. Plot C has a fractional representation of. 4. Rank the plots based on the fraction of land that is available to plant a garden. 1 is the biggest fraction and 3 is the smallest fraction. Plot A Plot B Plot C 25

26 Station 4: My Garden (Answer Guide & Excel Worksheet) Directions: Sit down at one of the computers and open the file entitled my garden. Each square on this grid is equal in size. Now we need to follow the next few steps to create our homes and gardens 1. Hit ctrl+a. 2. Use the grid function to place the grid on the worksheet. 3. Click on A1 hold the click and drag it all the way to G6. 4. Use the paint bucket to color this section red. 5. Click on B2 and drag until E4. 6. Color this section green. 7. Label this Plot A by placing an A in C3. 8. Click on A9 hold the click and drag until P Use the paint bucket to color this section blue. 10. Click on B10 and drag until M Use the paint bucket to color this section purple. 12. Label this Plot B by placing a B in G Click on A20 hold the click and drag until Y Use the paint bucket to color this section orange. 15. Click on B21 hold the click and drag until R Use the paint bucket to color this section white. 17. Click on S27 hold the click and drag until W Use the paint bucket to color this section white as well. 19. Label this Plot C by placing a C in K27. You now have three plots of land with three houses on those plots. The outside color is the entire plot of land. Within that color we built houses that are represented by a different color. It is your job to order these three houses in terms of what fraction of the land is available to plant a garden. You will accomplish this by determining the area of the entire plot and placing that in the denominator. Then you will determine the area of the garden. This number will go in the numerator. Lastly you will rank these three plots by looking at each fraction and telling which on has the biggest fraction of garden land. NOTE: 1 BLOCK = 1 SQUARE INCH 1. Plot A has a fractional representation of 5/7. 2. Plot B has a fractional representation of 2/3. 3. Plot C has a fractional representation of 3/5. 4. Rank the plots based on the fraction of land that is available to plant a garden. 1 is the biggest fraction and 3 is the smallest fraction. Plot A 1 Plot B 2 Plot C 3 26

27 Microsoft Excel Worksheet and Answers A B C 27