Lesson: Place Value:Expanded Notation: Lesson 11

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Lesson Objective

Students know how mathematicians locate numbers on a number line?

Lesson Plan

Lessons by Edward Brooke Charter School:

I.                   Curriculum Standards


ü Count by 3 to 30 and 4 to 40, starting at any multiple of 3 or 4.   [M.1.2.a]

ü  Count by 100 and 1000, starting at any number to ten thousand. [M.1.2.b]

ü  Name and write, in numerals and words, whole numbers to 10,000. [M.3.2]

ü  Locate numbers up to (and including) ten-thousand on a number line. [M.5.2]

ü  Order numbers up to 10,000. [M.6.2]





II.                    The Point


                   How do mathematicians locate numbers on a number line?






 III.                Materials Needed


      Copies of 2.5.11 Math Workout

      Large Blank Number Line (on board or bulletin board paper) and sticky notes (or some other method) for labeling points

      Number cards and place value mats for playing 5-digit Number Top It






IV.                 Lesson Outline


     Time:  60 Minutes


     25 min. –   Locating Numbers on Number Lines

     15 min. -    Math Workout

     15 min. –   5-digit Number Top-It (Reading and ordering 5 digit numbers)

       5 min. –   Summary





  V.             Learning Activities


       There is not a math message in this lesson.


       1.  Locating Numbers on Number Lines


         PART I


Display a very long (about 10 feet) blank number line (works well to use adding machine tape or sentence strips) with the point 0 marked.









What do you notice about this number line?


            [0 is labeled, has arrows at the end]


Lead a discussion about the number line.  Be sure to include the following points:


  • Why are there arrows pointing both directions?


The number line has an arrow at both ends because there          is an infinite amount of numbers in both directions.


There are numbers smaller than 0. (as we move to the left, numbers on the number line get smaller.) 


We don’t know the names of these numbers yet.


We also know there are numbers that are greater than 0.        (as we move to the right, numbers on the number line get  larger.) 


The number line goes forever in both directions.


Since it goes forever, we can never draw the whole thing on paper.


When we draw a number line, we are only drawing a piece/section/segment of the number line.  Every single point on a number line represents some amount (even if it is not labeled with a number and even if we don’t know the name of the amount yet!). 




  • Place a finger or pointer on a point in between the 3 and the 4 on the regular class number line. 


      Ask students, “Am I pointing to a number?”  [yes!]


      We don’t know the name of the number, but it is some amount        that is more than 3 and less than 4.




It is a common misconception among older students that only the labeled points on a number line represent numbers.  This is problematic when students learn to locate decimals and fractions on a number line. 


Please repeatedly impress upon your students that EVERY point on the number line is a number.  We just don’t know the names of all of those amounts yet. 

Students should know that a point on the line between 156 and 157 is some amount that is more than 156 but less than 157.





Using a sticky note, label the farthest point on the number line with a 10.


Ask students to approximate where various values are located on the number line.  Label the approximate location of these points with sticky notes.









Where is 10?

Where is 1?

Where is 5?

Where is 100?  (way off to the right)



Remove the sticky notes and replace the 10 and with 100.






Now, where is 10?  50?  1?   5?   100?  200?


Remove the sticky notes and replace the 100 with 1,000.







Now, where is 10?  1?   5?   100?  500?  900?  2000?



            Mathematicians look at the points that are already labeled on a number                       line in order to determine what numbers are represented at various points         on the number line.  Estimate and label the points every 100.  100, 200,                         300, etc.  Why wouldn’t we want to write every number counting by 1s on              this number line? 


            Mathematicians can imagine/draw the numbers pushed very close to each other on the number line or stretched out with a lot of space in between.  When we imagine them pushed very close, we do not write every number because we would need too much space.  Instead we might just label every 10th or hundredth or thousandth number. 







Prepare a variety of additional number line segments in advance and cover certain numerals with sticky notes or leave some written numbers off of the lines.



Students work to label the points on the additional number line segments and explain how they know what number in missing





by 5s









by 1s








Mathematicians look for patterns that can help them locate other numbers.   They have to notice the patterns so that they know which numbers are in between the labeled points.  


 2.  Math Workout (15 min.)


         Students complete 2.5.11 Math Workout




3.  5-digit Number Top-It  (15 min.)


       Students practice reading numbers playing 5-digit number Top-It.  Make sure        that partners are reading their numbers aloud to each other before deciding whose number is greater.




4.    Summary (5 min.)


                 How do mathematicians locate numbers on a number line?





Lesson Resources

3.1.11-place value-exp.doc  


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