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TWO-DIGIT MULTIPLICATION, PART TWO—USING NEGATIVE UNITS

Grades: 4‒5

Students decompose one or both of the factors of two-digit multiplication problems into subtraction expressions with tens and ones. For example, students might decompose 27 × 39 as (30 – 3) × (40 – 1). Students represent this approach geometrically with an array of base-ten blocks. Unlike physical base-ten blocks, which are awkward at best for representing negative areas, the blocks used in the Sketchpad model allow for a clear, intuitive representation of negative area.  

OBJECTIVES 
  • Students will find products of two-digit numbers by decomposing each number into tens and ones, rewriting one or both numbers as subtraction statements.
  • Students will use a rectangular array model composed of base-ten blocks to explore two-digit multiplication problems.
  • Students will understand the relationship between a multiplication problem represented in numerical form and the same problem represented with an array.

COMMON CORE CONNECTIONS 
Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (5) Use appropriate tools strategically; (7) Look for and make use of structure.

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This activity is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: http://creativecommons.org/licenses/by-nc-sa/3.0/. If you adapt and/or share this activity, you must attribute it to "KCP Technologies, a McGraw-Hill Education Company." You may distribute it only non-commercially under the same or similar license.


This material is based upon work supported by the National Science Foundation under KCP Technologies Award ID 0918733, with grant period September 1, 2009 through August 31, 2013. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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