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Grades: 3‒6

Students investigate the concepts of multiples, common multiples, and least common multiples by using a “dynamic” interactive grid. The grid displays multiples of any two numbers simultaneously, showing multiples of one number in orange, multiples of the other number in blue, and their common multiples in an orange-blue combination. By experimenting with a variety of number pairs and different grid dimensions, students are able to identify least common multiples and analyze visual and numerical patterns associated with common multiples. 

  • Students examine patterns relating to multiples, common multiples, and least common multiples in a interactive number grid.
  • Students make and test conjectures about multiples, common multiples, and least common multiples.
  • Students shade cells in an interactive number grid to display multiples of any number.
  • Students shade multiples of any two numbers to determine their common multiples and least common multiple.

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; 6.NS4

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This activity is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: 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.