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BALANCE—BALANCING WITH POWERS OF TWO

Grades: 4‒7

Students are given a random value between 1 and 63 on one side of a scale and must balance it by selecting variables whose assigned values are powers of 2 (1, 2, 4, 8, 16, and 32). Students write equations to represent their model and then make conjectures about the properties of powers of 2 based on their observations.

OBJECTIVES 
  • Students will use a balance model to explore early algebraic concepts.
  • Given a set of possible addends, students will select numbers whose sum equals a given target value.
  • Students will develop strategies for finding combinations of addends that equal a target sum.
  • Students will pose questions and make observations and conjectures about using the powers of 2 to make sums.

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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