# Teacher Tool of the Month: Decimal Numbers on the Number Line

 The DreamBox interactive white board Teacher Tool for this lesson is on our website under “Resources.” (www.dreambox.com/teachertools) Using this interactive number line, students locate positive and negative decimal numbers by scaling the number line by powers of ten.
 Objective: The purpose of this lesson is for students think critically about the structure of the number line and locate positive and negative decimal numbers using magnification tools. Background: Students should have an understanding of place value to the hundredths place and be able to compare integers to the hundredths place. Instruction: Bring up the DreamBox interactive white board lesson. The teacher begins, “We need to place the pin on the number line as close as possible to the number (1.8).  Who has an idea for how we could begin?”  Possible responses: “We need to see if it falls between the numbers on the number line that we see. I’d like to zoom in between each set of numbers.” “We should move the purple slider to find the number.” “We should use the magnifying glass to zoom and find the number.” “I don’t know what to do.  I’d like to use the hint button.” The teacher invites one student who to approach the board and perform the task she described.  After the first exploration, ask the student if what she did was helpful and why? Possible responses: “Zooming in between 0.6 and 1.1 or 1.1 and 1.6 was not helpful because 1.8 is more than 1.6.  We need to go toward numbers greater than 1.6.” “Scrolling to the right  was a good idea because the section of the number line we need to see was not in the window when the problem started.” “The magnifying glass was helpful because I was able to use patterns on the number line that enabled me to realize that 1.8 is not between any of these numbers.” After students share their responses and have moved to reveal a new portion of the number line (1.6-2.1), the teacher asks the class, “What’s a good next step we could take to find 1.8? “ “I think we need to use the 10x magnifier to look closer at the number line.  But I don’t know exactly where to place the glass.” “We need to figure out about where 1.8 would be and place the magnifying glass there.” “There are about 5 tenths between 1.6 and 2.1.  That means that we should place the glass about 2 tenths greater than 1.6.  That’s a little less than half way between 1.6 and 2.1.” “1.8 is close to 1.6 so I think we should place the glass next to 1.6.” “We could use the 100x magnifying glass, but it will be more challenging.” After students have discussed their options, choose a student to come up to the board to try his or her strategy.  Discuss with students whether this was a good strategy (i.e., place to zoom).  Ask students to defend their explanations as to why or why not.  For those that say it was not a good place to zoom, as them where we should go from there.  Continue to prompt students to explore the number line using the magnifiers and discuss their strategies for finding the accurate range to locate the number and place the pin.  Discuss which strategies are more useful than other, and give students ample opportunity to explore and make sense of the number line with multiple examples.

 Common Core State Standards Grade ID Domain Cluster Standard 5 5.NBT.3 Number & Operations in Base Ten Understand the Place Value System Read, write and compare decimals to thousandths. 6 6.NS.6 The Number System Apply and extend previous understanding of numbers to the system of rational numbers Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 5 5.SMP.2 Standards for Mathematical Practice Reason abstractly and quantitatively. 5 5.SMP.6 Standards for Mathematical Practice Attend to precision. 5 5.SMP.7 Standards for Mathematical Practice Look for and make use of structure.
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