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 Mathematics / Everyday Mathematics / Replaces / Deepens and Extends
Bunk Beds and Apple Boxes
Beads and Shoes, Making Twos* / Kindergarten Teacher’s Guide to Activities / Everyday Math on the Kindergarten level is a compilation of short activities, routines, and games.
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 the math workshop model. Use Bunk Beds and Apple Boxes in the fall and in the spring Beads and Shoes, Making Twos. / Bunk Beds & Apple Boxes introduces the arithmetic rack and focuses on composing and decomposing of number.
It also supports the systematic production of arrangements and the generalization of the relationship between the amount to of the whole and the number of possible arrangements.
Beads and Shoes, Making Twos introduces even and odd numbers, explores doubles, and builds a foundation for patterns in the number system.
Beads and Shoes, Making Twos
The Double Decker Bus
Minilessons for ExtendingAddition and Subtraction (Grade 1)
Organizing and Collecting
Measuring for the Art Show / Teacher’s Lesson (Grade 1) / Volume 1, Unit 3: Lessons 3.1 – 3.4
Volume 1, Units 4, 5 and 6 Lessons 6.1 – 6.5 are focused on the development of basic facts. The Double Decker Bus can replace many of these activities or can be used as a supplement for further work. For added support use the resource guide.
Volume 1 ,Unit 5: Lessons 5.1 and 5.2
Volume 1, Unit 3: Lessons 3.5 -3.6
Volume 2, Unit 9: Lessons 9.1 and 9.2 / The Double Decker Bus strengthens the automatization of basic facts by employing the use of the arithmetic rack, which is based on the five and ten structures. This tool supports the use of doubles plus and minus (e.g., 6 +7 = 6 + 6 +1) and making tens (e.g., 9 + 6 = 10 + 5).
Organizing and Collecting is an important supplement to EDM because it introduces children to 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.
One of EDM’s primary models for addition and subtraction is the number line. This tool is not developed, however, it is simply presented and used 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.
Games for Early Number Sense (Kindergarten and Grade 1) / Resource to deepen all of the above.
Trades, Jumps and Stops / Teacher’s Lesson Guide (Grade 2) / Volume 1, Unit : Lessons 1.10 and 1.12; and Unit 3: Lesson 3.8. / This unit is an important supplement because it emphasizes the algebra strand by focusing on equivalence, exchanging equivalent expressions, solving for unknowns, undoing, and early functional relations.
Ages and Timelines / Teacher’s Lesson Guide (Grade 2) / Volume 1, Unit 2: Lessons 2.6, 2.12, and 2.13
Volume 2, Unit 12: Lesson 12.3 / In EDM the primary algorithm for subtraction is regrouping (called “trade first”). Ages and Timelines deeply explores a variety of strategies and models for subtraction in order to help children develop a repertoire of strategies for mental arithmetic.
The T-Shirt Factory / Teacher’s Lesson Guide (Grade 2)
Teacher’s Lesson Guide (Grade 3) / Volume1, Unit 4: Lessons 4.8 and 4.9
Unit 6: Lessons 6.4 - 6.6
Volume 2: Unit 10: Lessons 10.8 - 10.10
Unit 11: Lessons 11.1, 11.2
Volume 1, Unit 2: Lesson 2.7 -2.9 / The traditional paper/pencil algorithms for addition and subtraction as well as place value to four places are the focus of The T-Shirt Factory. The context used, however, provides a rich opportunity for the algorithms to be constructed with meaning whereas the primary tool in EDM is base-ten blocks.
Minilessons for Extending Addition and Subtraction / These minilessons can be used in place of some of the mental math and reflex minilessons in EDM. / This guide provides an important resource to support the development of efficient computation strategies for double and triple digit addition and subtraction.
Groceries, Stamps, and Measuring Strips / Teacher’s Lesson Guide (Grade 2)
Teacher’s Lesson Guide (Grade 3) / Volume 1, Unit 6: Lessons 6.7 – 6.11
Volume 2, Unit 11: LEssons 11.3 – 11.8
Unit 12: Lessons 12.4 and 12.5
Voume 1: Unit 4 / Groceries, Stamps, and Measuring Strips makes use of realistic contexts to introduce big ideas and strategies related to multiplication. This is an important starting place for developing multiplicative thinking.
The Big Dinner / N/A / Volume 2, Insert this unit before EDM unit 7 / The Big Dinner introduces the ratio table model for 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.
Muffles’ Truffles / Teacher’s Lesson Guide (Grade 3) / Volume 2, Unit 9: Lessons 9.2 – 9.9, and 9.11 – 9.12 / Muffles Truffles provides an important addition to 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.
Minilessons for Early Multiplication and Division / Teacher’s Lesson Guide (Grade 4) / Volume 1, Unit 3: Lessons 3.1 – 3.3)
These minilessons can be used in place of some of the mental math and reflex minilessons in EDM. / This is a resource to support the development of all of the above. The minilessons within can also be used develop the automatization of the basic facts.
The Teachers’ Lounge / Teacher’s Lesson Guide (Grade 4)
Teacher’s Lesson Guide (Grade 5) / Volume 1, Unit 5: Lessons 5.5 – 5.7 and Unit 6: Lessons 6.1 – 6.4
Volume 1, Unit 4: Lessons 4.1, 4.2 and 4.5** / The Teachers’ Lounge provides an opportunity for 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 and partial-quotient strategies for multiplication and division. Place value is also emphasized to lay the foundation for the long division algorithm.
The Box Factory / Teacher’s Lesson Guide (Grade 4)
Teacher’s Lesson Guide (Grade 5) / Volume 2, Unit 8: Lessons 8.3 and 8.5)
Unit 11: Lessons 11.4 and 11.5
Volume 1, Unit 1: Lessons 1.2 – 1.4 / Emphasizes the associative property and supports the generalization of the relationship between surface area and volume in rectangular solids.
Minilessons for Extending Multiplication and Division / These minilessons can be used in place of some of the mental math and reflex minilessons in EDM. / This resource makes use of crafted strings of related problems to ensure the development of efficient computation for multiplication and division. The minilessons within this resource emphasize mental arithmetic and the use of the associative and distributive properties.
Field Trips and Fund-Raisers / Teacher’s Lesson Guide (Grade 4) / Volume 2, Unit 7: Lessons 7.1 - 7.3; 7.6, 7.7, and 7.9 / Research shows that it is important to build a connection between fair-sharing whole number 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.
The California Frog-Jumping Context
/Teacher’s Lesson Guide (Grade 5)
/ Volume 2, Unit 10: Lessons 10.1 – 10.3 / Provides an important addition to the algebra strand by focusing on symbolizing with variables and 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.Best Buys, Ratios, and Rates
/Teacher’s Lesson Guide (Grade 4)
Teacher’s Lesson Guide (Grade 5) / Volume 2, Unit 12Volume 1, Unit 6: Lessons 6.8 - 6.10 / Building on some of the ideas that were introducd but not fully developed in Grade 4 (e.g., the clock model 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 extensive work with fraction equivalence, the 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.
The Mystery of the Meter
/ N/A / Insert before Volume 1, Unit 5 in Grade 5 / Provides an important addition to EDM’s treatment of decimals by introducing the analog meter to emphasize place value.Exploring Parks and Playgrounds
/ Teacher’s Lesson Guide (Grade 5) / Volume 2, Unit 8: Lessons 8.5 – 8.12 / This unit provides an opportunity to introduce multiplication and division of fractions within 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.Minilessons for Extending Fractions, Decimals, and Percents
/ These minilesson can be used in place of some of the mental-math and reflex minilessons in EDM. / Year-long resource of minilessons to support the development of efficient computation including a variety of strategies for operations with fractions, decimals, and 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).