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Delaware Curriculum Unit Template Preface: This unit has been created as a model for teachers in their designing or redesigning of course curricula. It is by no means intended to be inclusive; rather it is meant to be a springboard for a teacher’s thoughts and creativity. The information we have included represents one possibility for developing a unit based on the Delaware content standards and the Backward Design framework and philosophy. Subject/Topic Area: Math Grade Level(s): 6 Searchable Key Words: Comparing Quantities – Section A : Math in Context, Substitution Property, Pre-Algebra Designed By: Amy Brown and Dana Griffith District: Appoquinimink Time Frame: 2-3 Days Brief Summary of Unit: These lessons are based on Section A of the Mathematics In Context Book, Comparing Quantities. Students exchange goods and quantities to solve problems involving bartering, balances, and simple equations. It includes differentiating ideas for each of the lessons and extension activities to be used both in and out of the classroom. Stage 1: Desired Results (Determine What Students Will Know, Do and Understand) Delaware Content Standards Standard 1- Numeric Reasoning: Students solve equations that show how numbers can be related in multiple ways. Standard 2 –Algebraic Reasoning: Students describe, represent, and analyze relationships between variable quantities Delaware Process Standards Standard 5- Problem Solving: Students use developmentally appropriate strategies to solve problems involving variable quantities. Standard 6- Reasoning and Proof Students investigate variable relationships and use multiple strategies to justify their thinking about these relationships. Standard 7- Communication Students use their reading and writing strategies to communicate the link between mathematical symbols and language. They process mathematical reasoning in visual and oral formats. Standard 8- Connections Students use their ideas from real world contexts to promote algebraic reasoning. Big Ideas: Students exchange goods and quantities to solve problems involving bartering, balances, and simple equations. As they do this, they develop informal understandings of variables and symbolic reasoning. They develop a sense that different numeric values can be assigned objects and combinations of objects. Unit Enduring Understandings Students will understand that… Numbers can be represented in multiple ways. Knowing the reasonableness of an answer comes form using good number sense and estimation strategies. Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found. Mathematics can be used to solve problems outside of the mathematics classroom. Mathematics is built on reason and always makes sense. Reasoning allows us to make conjectures and to probe conjectures. Classifying helps us build networks of mathematical ideas. Precise language helps us express mathematical ideas and receive them. Unit Essential Question(s) What makes a strategy both effective and efficient? How can change be described mathematically? How do mathematical models/representations shape our understanding of mathematics? How are solving and proving different? How are showing and explaining different? What does it take to verify a conjecture? How do you develop a convincing argument Knowledge & Skills Students will be able to… Exchange goods and quantities to solve problems involving bartering, balances and simple equations. Use combination charts to organize information about combinations of two items. Explore exchange patterns in the combination charts and use the patterns to solve problems. Use exchange strategies to determine the price of individual items within a single purchase and use combination charts to solve equation-like problems. Write equations to represent combinations. Stage 2: Assessment Evidence (Design Assessments To Guide Instruction) Suggested Performance Task(s) Dinner Menu Assessment (See attached) Students will have the opportunity to choose from the two “appetizer” problems to solve. Differentiation note: Everyone is required to do the “main course” as it emphasizes the important big idea. The “desert” is an optional problem for those students who may need enrichment. Rubrics/checklists for Performance Tasks: See attached Other Evidence : Bartering Poster Challenge Cards Tic-tac-toe Activity Cooperative Group Work Student Self-Assessment and Reflection At the conclusion of each day, student will be given an “exit card” where they will be required to color a stoplight to represent their confidence level with the day’s activity. If the color in the green light, they are feeling confident and are ready to go. Yellow means that they are approaching the task cautiously and still need time. Red means that student needs help from the teacher. This will allow the teacher to assess the daily needs of the students and to adjust accordingly. Stage 3: Learning Plan (Design Learning Activities To Align with Goals and Assessments) Key learning events needed to achieve unit goals ALL HANDOUTS ARE HYPERLINKED BELOW. TO SEE THE HANDOUT, HOLD THE “CONTROL” KEY AND CLICK WITH YOUR MOUSE ON THE APPROPRIATE LINK. Students will be introduced to the MIC Unit, Comparing Quantities – section A: Bartering with a Prior Knowledge Writing Opportunity: Take 5 minutes and write about a personal experience in which you traded or bartered to get something you wanted. What was it? What did you trade to get it? Was it a fair trade? Day 1: Launch Section A: Compare & Exchange (Student Page 1). As a whole class, “Bartering” will be read and the stage set. Students will work in groups of 4 to play the role of Paulo. o The teacher will need to give each group 3 trading cards – two sheep and one goat (what Paulo goes to the market with). In addition, the teacher will need to place baskets or bins in an area of the room for students to access. On each basket, place the name of a person Paulo meets at the market. For example, on one basket you will write the name, Aaron. In Aaron’s basket, the teacher will have a large of number of salt trading cards. Students will work as a group to trade their cards in an effort to acquire only corn. Only one trade can be made at a time so that students come back to their tables to reflect before making another exchange. o Once the group has successfully traded for only corn, their group is to go back and do it again BUT this time record their trades on the group poster. Rubber stamps of the different items will be available for students to use. (see poster template attached). Small Groups Explore: Farmer’s Market & Thirst Quencher (Student Pages 2). Students will receive the teacher made graphic organizers “Apples and Bananas” and “Carrots, Corn, and Peppers”. In addition to the graphic organizer, triple beam balances will be available in the classroom for students to use. o Teacher should have available triple beam balance scales with a variety of fishing weights to correspond to the proportional weights of the items. These weights could be labeled or painted to represent the given fruits or vegetables. Students could use the weights and the balances to determine equivalent weights if needed. For example: Carrots could weigh 1 gram Peppers could weigh 2 grams Corn could weigh 4 grams Differentiation: Challenge Card Bags will be available for students who finish early or who are in need of an extension activity. (see attached Challenge Card) “Thirst Quencher” – Students will choose to work through this activity as it exists in the text or to use the teacher made graphic organizer for support. Differentiation Process Note: o The graphic organizer includes small magnetic replicas of the objects from the text that can be manually manipulated on small magnetic boards to help them balance trade the items. Day 1: Sharing Out: o For sharing out purposes, a class set of large magnetic replicas will be available. o Teacher highlights a variety of strategies that work and encourage all students to demonstrate their ideas using the manipulatives. Resources & Teaching Tips o What text/print/media/kit/web resources best support this unit? Mathematics in Context “Comparing Quantities”; “Algebra Tools” http://www.mathcats.com/explore/balance/balance.html http://www.mathplayground.com/algebraic_reasoning.html http://illuminations.nctm.org/ActivityDetail.aspx?ID=33 For those who need a challenge: http://www.learner.org/channel/courses/learningmath/algebra/session6/part_c/index.html http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html?open=instructions http://www.mathkangaroo.org Differentiation A variety of differentiated activities have been incorporated into each of the lesson activities described above. Manipulatives in the form of cut outs, magnets, Velcro, and weights have been included. In addition, triple beam balance scales have been used. Student movement, role playing, cooperative group work, and student choice have been utilized. Students are encouraged to personally reflect on their own strengths and needs and to choose appropriate tools to help them gain true understanding of the essential questions. Challenge cards, tic-tac-toe, and web-sites that both remediate and extend are shared and included in class and at home activities. An assessment that allows students to make choices is also provided. Technology Integration http://www.learner.org/channel/courses/learningmath/algebra/session6/part_c/index.html http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html?open=instructions http://www.mathcats.com/explore/balance/balance.html http://www.mathplayground.com/algebraic_reasoning.html http://illuminations.nctm.org/ActivityDetail.aspx?ID=33 Content Connections Comparing Quantities Name_______________ Section A- Homework Date________________ Directions: Use the following Tic-tac-toe board to complete a row of three activities. You may go vertically, horizontally, or diagonally. Make your own fair Complete the Balancing Complete the Cubes and trade puzzle similar to Fruit Activity Sheet Solids Activity Sheet the activities done in class and give to a friend to solve. Solve a friend’s fair Complete Balancing Visit the following interactive trade problem and Cats and Dogs Activity website. Play for 15 minutes attach to this homework Sheet and have a parent sign this sheet. block when you finish. http://www.mathplayground.com/ algebraic_reasoning.html Complete the Puzzle Complete the Balancing Complete Alphabet Soup From The Sea Activity Act Activity Sheet Activity Sheet Sheet Comparing Quantities Name___________________ Section A Summary Date____________________ Delia lives in a community where the people trade goods they produce for other things they need. Delia has some fish that she caught and wants to trade them for other food. Delia hears that she can trade fish for melons. She wants more than just melons, so she decided to see what else is available. This is what she hears: For five fish you can get two melons. For five apples you can get one loaf of bread. For one melon you can get one ear of corn and two apples. For ten apples you can get four melons. Unit Title: Comparing Quantities Section A ______________________________________________ 1. Rewrite the information so that it is easier to use. 2. Use the fair trade statements above and write two other fair statements about the exchange of apples, melons, corn, fish, and bread. 3. Delia has 10 fish and she wants 10 apples. How can she do this? 4. Delia has 15 fish. How many melons can she get? Explain how she can do this. How many apples can she get? Explain how she can do this. Page 20 of 26 Unit Title: Comparing Quantities Section A ______________________________________________ Extension 1: Is it true that Delia can trade three fish for one loaf of bread? Explain why or why not. Extension 2: Delia wants to trade 5 fish while at the market. Explain how she can trade for only corn. Page 21 of 26 Unit Title: Comparing Quantities Section A ______________________________________________ Page 22 of 26 Unit Title: Comparing Quantities Section A ______________________________________________ Comparing Quantities Name ____________________ Section A Date _____________________ Dinner Menu Assessment Appetizer Choose from one of the following delicious starters. Mexican Delight: o One chicken quesadilla weighs 6 kg. Find the weight of one jalapeno pepper Chicken Quesadillas = Chicken Quesadillas Jalapeno Pepper 1 Jalapeno Pepper = _________________kg American Grill: o 3 Breadsticks weigh 12 kg. o 1 Bowl of soup weighs 15 kg. Find the weight of a large salad = 1 Large Salad = _____________________kg Page 23 of 26 Unit Title: Comparing Quantities Section A ______________________________________________ Main Course Everyone will be treated to the same delicious meal. Two Baked Potatoes and one sirloin steak costs $62.00 = $62.00 One baked potato and one sirloin steak costs $40.00 = $40.00 One baked potato and three sirloin steaks cost $76.00 = $76.00 Page 24 of 26 Unit Title: Comparing Quantities Section A ______________________________________________ Find the cost of one baked potato and one sirloin steak. One baked potato = $___________ One sirloin steak = $__________ Desserts For those of you hungry for more, feel free to try our delicious dessert. Chocolate Lovers: One chocolate Cake and One Chocolate Chip Cookie together weigh 100 grams = 100 grams Two chocolate cakes together weigh the same as three Chocolate Chip Cookies = Find the weight of one chocolate cake and one chocolate chip cookie. One chocolate cake = _________grams One chocolate chip cookie = _________ grams Page 25 of 26 Unit Title: Comparing Quantities Section A ______________________________________________ Page 26 of 26

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posted: | 10/28/2012 |

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