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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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