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Grades: 4‒6

Students estimate the location of an unlabeled point on a number line. Students then magnify an interval that contains the point, and view this interval divided into ten smaller equal parts (tenths). Students then explore hundredths (by magnifying twice), thousandths (by magnifying three times), and ten-thousandths (by magnifying four times). Each magnification allows for a more precise view of the point’s location. Finally, students think about place values smaller than ten-thousandths and discuss whether every point on a number line can be represented precisely by a decimal with a finite number of digits. 

  • Students will use a number line model to explore place value from tenths through and beyond ten-thousandths.
  • Students will develop strategies for estimating the location of an unlabeled decimal-valued point (in tenths, hundredths, thousandths, and ten-thousandths) on a number line.
  • Students will develop an understanding of the base-ten number system and place value.
  • Students will develop an understanding that between any two distinct decimal-valued locations on a number line, there are more decimal-valued locations between them.

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

4.NF6, 7; 5.NBT3; 6.NS6

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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.