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BOXED COUNTERS—FIND FACTORS WITH AN ARRAY MODEL

Grades: 3‒4

Students investigate numbers and their factors by manipulating arrays of counters. Students select the number of counters for their array and then observe what happens as they change its dimensions while keeping the total number of counters the same. They pose and explore questions such as, “If I can represent 12 as a 3 × 4 array, can I also show it as a 4 × 3 array? What numbers form square arrays? How many ways can I arrange 23 counters so that every row of my array contains an equal number of counters? Do larger numbers have more factors than smaller factors?” 

OBJECTIVES 
  • Students will use a rectangular array model to find all factors of given numbers.
  • Students will see the relationship between the pictorial representation of multiplication and its symbolic form.
  • Students will make and record observations about relationships and patterns between numbers and their factors. 
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.

Content Standards

3.OA5, 6, 7, 9; 4.OA4, 5

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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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