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Contexts for Learning Mathematics

By Yolanda Sims,2014-04-08 07:29
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Contexts for Learning Mathematics units can be used as a supplement to introduce children to more in-depth, long-term investigations as an introduction to

    Crosswalk between the Everyday Mathematics curriculum and Context for Learning Mathematics:

    Number Sense, Addition and Subtraction (Grades K-3)

For further details for each of the units described below, please see the Overview for Number Sense, Addition and Subtraction, pages, 18-

    22.

    Contexts for Learning Everyday Replaces Deepens and Extends Mathematics Mathematics

    Everyday Math on the Bunk Beds & Apple Boxes introduces the arithmetic Bunk Beds and Apple Kindergarten

    Kindergarten level is a rack and focuses on composing and decomposing of Boxes Teacher’s Guide to

     compilation of short activities, number. Activities

     routines, and games.

     It also supports the systematic production of Contexts for Learning

     Mathematics units can be used arrangements and the generalization of the

     as a supplement to introduce relationship between the amount to of the whole and

     children to more in-depth, long-the number of possible arrangements.

     term investigations as an

     introduction to the math Beads and Shoes, Making Twos introduces even and

    workshop model. Use Bunk odd numbers, explores doubles, and builds a Beads and Shoes,

    Making Twos* Beds and Apple Boxes in the fall foundation for patterns in the number system.

    and in the spring Beads and

    Shoes, Making Twos.

    Volume 1, Unit 3: Lessons 3.1 Beads and Shoes, Teacher’s Lesson

    (Grade 1) 3.4 Making Twos

    Volume 1, Units 4, 5 and 6 The Double Decker

    Lessons 6.1 6.5 are focused on The Double Decker Bus strengthens the Bus

     the development of basic facts. automatization of basic facts by employing the use of

     The Double Decker Bus can the arithmetic rack, which is based on the five and ten

    replace many of these activities structures. This tool supports the use of doubles plus

    or can be used as a supplement and minus (e.g., 6 +7 = 6 + 6 +1) and making tens

    for further work. For added (e.g., 9 + 6 = 10 + 5).

    support use the resource guide.

     Minilessons for

     ExtendingAddition and

     Subtraction (Grade 1)

    Volume 1 ,Unit 5: Lessons 5.1 Organizing and Collecting is an important Organizing and

    and 5.2 supplement to EDM because it introduces children to Collecting

     place value by providing them with ample opportunity

     to bundle and explore groups of fives and tens. In

     contrast EDM uses base-ten blocks, which research

     has shown do not support the development of place

     value.

    Volume 1, Unit 3: Lessons 3.5 -One of EDM’s primary models for addition and Measuring for the Art

    3.6 subtraction is the number line. This tool is not Show

    Volume 2, Unit 9: Lessons 9.1 developed, however, it is simply presented and used

    and 9.2 for counting. Measuring for the Art Show, on the

     other hand, provides a rich context for the emergence

    of the open number line as a model. Research shows

    that over time this is a powerful tool to support

    children’s reasoning and helps them move beyond

    counting to efficient computation strategies.

    It is suggested that Measuring for the Art Show be

    used in the spring. This unit can be followed by EDM

    lessons 4.1 - 4.6 that focus on developing standard

    units of measure.

     Resource to deepen all of the above. Games for Early

    Number Sense

    (Kindergarten and

    Grade 1)

    Volume 1, Unit : Lessons 1.10 This unit is an important supplement because it Trades, Jumps and Teacher’s Lesson

    Guide (Grade 2) and 1.12; and Unit 3: Lesson 3.8. emphasizes the algebra strand by focusing on Stops

     equivalence, exchanging equivalent expressions,

    solving for unknowns, undoing, and early functional

    relations.

    Volume 1, Unit 2: Lessons 2.6, In EDM the primary algorithm for subtraction is Ages and Timelines Teacher’s Lesson

    Guide (Grade 2) 2.12, and 2.13 regrouping (called “trade first”). Ages and Timelines

     Volume 2, Unit 12: Lesson 12.3 deeply explores a variety of strategies and models for

    subtraction in order to help children develop a

    repertoire of strategies for mental arithmetic.

    Volume1, Unit 4: Lessons 4.8 The traditional paper/pencil algorithms for addition The T-Shirt Factory Teacher’s Lesson

    Guide (Grade 2) and 4.9 and subtraction as well as place value to four places

     Unit 6: Lessons 6.4 - 6.6 are the focus of The T-Shirt Factory. The context

     Volume 2: Unit 10: Lessons 10.8 used, however, provides a rich opportunity for the

     - 10.10 algorithms to be constructed with meaning whereas

     Unit 11: Lessons 11.1, 11.2 the primary tool in EDM is base-ten blocks.

    Volume 1, Unit 2: Lesson 2.7 -Teacher’s Lesson

    Guide (Grade 3) 2.9

     These minilessons can be used in This guide provides an important resource to support Minilessons for

    place of some of the mental math the development of efficient computation strategies Extending Addition

    and reflex minilessons in EDM. for double and triple digit addition and subtraction. and Subtraction

    Volume 1, Unit 6: Lessons 6.7 Groceries, Stamps, and Measuring Strips makes use Groceries, Stamps, and Teacher’s Lesson

    Guide (Grade 2) 6.11 of realistic contexts to introduce big ideas and Measuring Strips

     Volume 2, Unit 11: LEssons strategies related to multiplication. This is an

     11.3 11.8 important starting place for developing multiplicative

     Unit 12: Lessons 12.4 and 12.5 thinking.

    Voume 1: Unit 4 Teacher’s Lesson

    Guide (Grade 3)

    N/A Volume 2, Insert this unit before The Big Dinner introduces the ratio table model for The Big Dinner

    EDM unit 7 multiplication. This model is missing in EDM. The

    ratio table is an important model that supports the

    development of multiplicative thinking and leads to

    proportional reasoning.

    Volume 2, Unit 9: Lessons 9.2 Muffles Truffles provides an important addition to Muffles’ Truffles Teacher’s Lesson

    Guide (Grade 3) 9.9, and 9.11 9.12 EDM by developing the open array as a model that

    can be used as a powerful tool to support the

    development of partial products, and the distributive,

    commutative, and associative properties.

    Volume 1, Unit 3: Lessons 3.1 This is a resource to support the development of all of Minilessons for Early Teacher’s Lesson

    Guide (Grade 4) 3.3) the above. The minilessons within can also be used Multiplication and

     develop the automatization of the basic facts. Division

    These minilessons can be used

    in place of some of the mental

    math and reflex minilessons in

    EDM.

    Volume 1, Unit 5: Lessons 5.5 The Teachers’ Lounge provides an opportunity for The Teachers’ Lounge Teacher’s Lesson

    Guide (Grade 4) 5.7 and Unit 6: Lessons 6.1 6.4 children to deepen their understanding of the

     connection between partitive and quotative division.

     It also emphasizes the distributive property within real

     life contexts for the development of partial-products

    Volume 1, Unit 4: Lessons 4.1, and partial-quotient strategies for multiplication and Teacher’s Lesson

    Guide (Grade 5) 4.2 and 4.5** division. Place value is also emphasized to lay the

    foundation for the long division algorithm.

    Volume 2, Unit 8: Lessons 8.3 Emphasizes the associative property and supports the The Box Factory Teacher’s Lesson

    Guide (Grade 4) and 8.5) generalization of the relationship between surface area

     Unit 11: Lessons 11.4 and 11.5 and volume in rectangular solids.

    Volume 1, Unit 1: Lessons 1.2 Teacher’s Lesson

    Guide (Grade 5) 1.4

     These minilessons can be used in This resource makes use of crafted strings of related Minilessons for

    place of some of the mental math problems to ensure the development of efficient Extending

    and reflex minilessons in EDM. computation for multiplication and division. The Multiplication and

    minilessons within this resource emphasize mental Division

    arithmetic and the use of the associative and

    distributive properties.

    Volume 2, Unit 7: Lessons 7.1 - Research shows that it is important to build a Field Trips and Fund-Teacher’s Lesson

    Guide (Grade 4) 7.3; 7.6, 7.7, and 7.9 connection between fair-sharing whole number Raisers

    division situations and fractions.

    This unit supports the generalization between various

    fraction models such as fair-sharing, the bar model,

    part/whole. It also introduces the use of the open

    number line, which supports addition and subtraction

    fraction work to come.

    Volume 2, Unit 10: Lessons 10.1 Provides an important addition to the algebra strand The California Frog-Teacher’s Lesson

    Guide (Grade 5) 10.3 by focusing on symbolizing with variables and Jumping Context

     emphasizing that an algebraic expression can be

    treated as an object (not only as a procedure). The

    double open number line is used throughout as a tool

    to support the development of strategies for solving

    for unknowns in simultaneous equations, in contrast to

    EDM where the pan balance is the primary model.

     Volume 2, Unit 12 Building on some of the ideas that were introducd but Best Buys, Ratios, and Teacher’s Lesson

    Guide (Grade 4) not fully developed in Grade 4 (e.g., the clock model Rates

     and the ratio table), Best Buys, Ratios, and Rates can

     be used as a beginning unit in Grade 5. This is an

     important supplementary unit because it provides

    Teacher’s Lesson Volume 1, Unit 6: Lessons 6.8 - extensive work with fraction equivalence, the

    Guide (Grade 5) 6.10 changing whole, and addition and subtraction of

    fractions. It also makes use of the double open

    number line model for addition and subtraction of

    fractions.

    EDM uses a fraction slide rule as a tool for addition

    and subtraction of fractions. On the surface, this

    model may seem similar to a double open number

    line, but there is significant difference. The double

    open number line helps children think about and pick

    a common denominator of their choice while the

    fraction slide rule only promotes an action in the

    reading off of an answer.

    Insert before Volume 1, Unit 5 Provides an important addition to EDM’s treatment of The Mystery of the N/A

     in Grade 5 decimals by introducing the analog meter to Meter

     emphasize place value.

    Volume 2, Unit 8: Lessons 8.5 This unit provides an opportunity to introduce Exploring Parks and Teacher’s Lesson

    Guide (Grade 5) 8.12 multiplication and division of fractions within Playgrounds

    meaningful contexts. We recommend that it actually

    be used in Grade 6. However, this content is dealt

    with in EDM in Grade 5. If you need to teach this

    content in Grade 5, we recommend that you replace

    Lessons 8.5 8.12 in Unit 8 (Volume 2) with

    Exploring Parks and Playgrounds.

     These minilesson can be used in Year-long resource of minilessons to support the Minilessons for

    place of some of the mental-development of efficient computation including a Extending Fractions,

    math and reflex minilessons in variety of strategies for operations with fractions, Decimals, and

    EDM. decimals, and percents. Percents

    * This unit can be used either at the end of Kindergarten or at the beginning of first grade. That’s why the unit is listed twice.

    ** Volume 1, Unit 4 in Grade 5 reexamines many of the ideas developed in Grade 4 when division was the focus. If The Teacher’s Lounge was not

    done then, it might be beneficial to replace Unit 4 with this context unit (excluding Lesson 4.4).

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