Where Does That Fall On The Number Line?

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Objective

SWBAT: • Compare decimals and fractions • Place decimals and fractions on a number line

Big Idea

Where does five-thirds belong on a number line? What about 1.61? Students apply their knowledge of fractions and decimals in order to compare and order fractions and decimals.

Do Now

10 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Here, I want students to work on converting fractions to decimals, which they will work on later in the lesson.  The first two examples should be familiar to students, but they may struggle with 1/6 and 5/6 and this is okay!  I am curious to see what strategies they will use.  If students are completely stuck, I’ll ask questions like, “Is it bigger or smaller than 0.5?  How do know?  Is it bigger or smaller than 0.75? How do you know?”

I ask a couple students to share out their strategies for 1/6 and 5/6.  If students do not mention it, I remind them that fractions can be interpreted as division.  One sixth is equivalent to 1 divided by 6.  I divide 1 by 6.  After a few repeating decimal places, I ask students what they think will happen if I continue to divide.  I want students to recognize that the 6 will continue to be repeated in the quotient.  

Number Categories

5 minutes

I introduce students to the graphic by explaining that in unit 3 we will be working with integers and rational numbers.  I have volunteers read the descriptions from the table.  I ask students what ¾ would be considered.  What about -10? Why are the natural numbers inside of the whole numbers, integers, and rational numbers ovals?  It is likely that students have interesting questions, but after five minutes I move on to the next activity.

How do they compare?

15 minutes

I have students work with a partner on this activity.  I walk around and ask students to explain why they have chosen a particular sign.  I am looking to see what strategies students are using to compare decimals with decimals and fractions with decimals.

After about 3-5 minutes, we come back together as a class.  I declare that for #4 I believe they are equal.  I ask for a show of hands, to see whether people agree or disagree with me.  I have students share out their ideas.  Students are engaging with MP3: Construct viable arguments and critique the reasoning of others.  I ask for volunteers to explain their thinking about problems 5, 7, and 8.  These are questions that are sometimes a struggle with students. 

Next I ask a few questions about the number line.  An easy way to make this a movement break is to set up three labels along a classroom wall: 0, ½, and 1.  I ask a question and students have to go and stand by the number that they believe is closest. 

I ask:

  • Is 0.4 closer to 0, ½, or 1?
  • Is 0.08 closer to 0, ½, or 1?
  • Is ¾ closer to 0, ½, or 1?

After each question I briefly ask students why they are standing in a particular place.  I am interested to see where students stand for ¾, since it is exactly in between ½ and 1.  

Where does it fall on the number line?

25 minutes

Note:

I have students move to their groups.  I explain that students will be working on a similar activity creating equivalent fractions and decimals, comparing them, and then placing them on a number line.   I pass out a Group Work Rubric for each group.  Students are engaging in MP6: Attend to precision and MP8: Look for and express regularity in repeated reasoning.

As students are working, I walk around and monitor student progress and behavior.  I am looking to see how students convert 5/3 and what fractions they say it will fall between on a number line. 

If students are struggling, I may ask the following questions:

  • What do you know?  What are you trying to figure out?
  • A fraction also represents division.  How could you use this connection to help you?
  • Is it bigger or smaller than ½?  How do you know?  1? 1 ½?
  • How do you read that decimal?  How could we represent it with a fraction? 
  • How can we represent a fraction that is larger than 1?

If students are successfully completing the table, I briefly check it over.  Students then move on to place the numbers on the number line.  If students complete this task successfully, I give students butcher paper and have them recreate the number line and label the same numbers.  I will display these number lines in the room.

Closure and Homework

5 minutes

 For Closure I ask about five-thirds.  Is it between 0 and ½, ½ and 1, 1 and 1 ½, or 1 ½ and 2?  How do you know?  I want students to recognize that it is an improper fraction, so it must be larger than 1.  Six-thirds is equivalent to 2, so five-thirds must be between 1 and 2.  I ask students to share the strategies they used for creating an equivalent decimal for five-thirds.   I ask, “Is 5/3 equivalent to 0.66?”  I want students to explain the difference between these two numbers.

Instead of a ticket to go, I have students put their name on their number lines and turn them in.  I pass out the Unit 3.1 HW  at the end of class.