# Show what you know + Equivalency

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## Objective

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.

## Quiz

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.

## Equivalency

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%.

## Percents

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.
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