Show what you know + Equivalency

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SWBAT: • Show what they know about decimal operations. • Demonstrate equivalence between fractions, decimals, and percents.

Big Idea

What do students understand? What gaps do they have in their understanding? How are fractions, decimals, and percents connected?

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 do a brief review about working with decimals before the quiz.  As students are working, I walk around and observe connections and questions.  I have students come and show and explain their strategies.  I emphasize the importance of using estimation and number sense skills to predict and check answers.

I do my best to keep the review brief.  It is easy for this review to stretch and take over the period.  I set a timer and hold myself to this.


30 minutes

I give students the Unit 2 Quiz 1.  If students do not finish in the allotted time, they set up a time (preferably that day) to come in and complete it.  I use this data to inform my instruction.   If students struggle with a concept, I will spiral it into do nows and homework assignments.  I may also add a few problems on that topic to the next quiz.


5 minutes

I have students work on this independently.  After a couple minutes we share out answers.  I am interested to here the equivalent fractions that students create.  I ask what percent of the grid is shaded for #3-5.  A common mistake that students make is they forget that percent means out of 100 and say that 1/10 is 1%.  


10 minutes

I introduce percent as meaning “out of 100”.  We work on the first three examples in the table together.  I declare that 2/10 must be equal to 2% and I shade 2 squares. I want students to recognize that 2/10 is out of 10, not 100, so the percent is not 2.  Instead we have to figure out what fraction out of 100 is equivalent to 2/10.  Another common mistake is students quickly glance at 0.7 and think that it is 7%.  I have students read the decimal as 7/10.  We then work on creating an equivalent fraction that is out of 100.  I also show students that 0.7 and 0.70 are equivalent in the picture.

I have students work on the next page independently.  I look for the same mistakes that I addressed in the first practice problems.  If students struggle, I will ask them what they know and what they are trying to figure out.  I ask them to describe a percent and how it connects to a decimal and a percent.  Some students may struggle with the last problem, since it represents 12.5% or 12.5/100.  I declare that it shows 125/1000 and ask students if they agree or disagree with me.  I want students to see the connection of these forms to 0.125. 

I ask students to share what they think a one-thousandth block would look like.  I am looking for students to realize that 10% is 1/10 of the whole, 1% is 1/100 of the whole and that one-thousandth should be 1/1000 of the whole.  You would have to split the one-hundredth block into 10 equal pieces.

Percent Ruler

5 minutes

I have students participate in a Think Write Pair Share with this page.  This is a great way to connect all three representations. 

Closure and Homework

5 minutes

 For ClosureI am interested to see where students put (c) 0.29 on their percent ruler.  Some students may make the mistake of putting it where 0.31 actually is.  I ask a couple volunteers to come up and display their work.  I ask students if they agree or disagree and why.  Students are engaging with MP3: Construct viable arguments and critique the reasoning of others

Instead of a ticket to go, I collect students’ work to look at.  I pass out the HW Equivalency at the end of class.