Increasing and Decreasing Quantities by a Percent (Day 1 of 2)

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SWBAT interpret equivalent representations of increases and decreases of quantities

Big Idea

In the formative assessment lesson students grapple with increasing and decreasing quantities as percents, then decimals, then fractions.

Pre-Assessment Task

15 minutes

This task can be done in class or for homework.  It should be completed before the actual formative assessment lesson.  Ideally, it should be done early enough so that you have time to assess students understanding.  This will allow you to be more strategic in the help you give during the lesson.  

You will note that the teacher guide suggests that you do not score students' work.  Instead make notes on what it reveals about their current level of understanding.  If you have time you might write questions on each student's work.  Or if you do not have time, select a few questions that pertain to the misunderstandings of most students.  These question can be posted at the end of the lesson.

More details are given on page T-2 of the teacher's guide.  

Page T-3 offers suggested questions and prompts based on common student issues.  I have attached the page in the resources below.  

See: PercentChanges_PreAssessment_QuestionsPrompts.docx

Collaborative Activity 1 - Percent Increases and Decreases

30 minutes

In this activity students work in pairs or trios.  Students get cards sets A and B.  Card Set A should be arranged on the desk with $100 in the top left corner, $150 in the top right corner, $160 in the bottom left corner, and $200 in the bottom right corner.

Students are to work to place cards from Set B between the quantities showing percents of increase and decrease.  Look out for some common misconceptions here.  Students may correctly place an arrow card saying "Up by 50%" from $100 to $150 but they may want to use the "down by 50%" card back from $150 to $100.  When this happens ask:  "What does it mean for a value to go down by 50%? How much is 50% of $150?"  The questions could go further if necessary but you may want students to struggle with what the appropriate percent decrease is for $150 to $100.

For struggling students, you may suggest that they find the percent of change between each value or use guess and check.

The teacher resource offers these suggestions and more on page T-4 and T-5.

When groups are mostly done, a classroom discussion can take place.  Common errors that have been noted by the teacher can be addressed.  For example, the case of students thinking that increasing and then decreasing quantities by the same percent results in no change in value.  Also, it is a great time to share how different groups were able to solve the problems.  

Collaborative Activity 2 - Decimal Multipliers

15 minutes

Now students place the decimal multiplier cards between the values.  Leave out the previous cards so that students can make the connection between the percents and the decimal multipliers.  

As the teacher guide says on page T-5, students may need help using their calculators for values like 1.33333333.....  I suggest you have students repeat the threes to the calculators limit or perhaps 7-10 times.  Depending on the values and the calculator, this may require students to round to the nearest dollar or so.  

This part of the activity will go more quickly as calculators may be used to figure out where to place the decimal arrow cards.  Ask students to look for patterns in the multipliers used to increase and decrease the same two values.  For example, an increase of 50% requires multiplying by 1.5, yet to return the increased value back a multiple of 0.6666666.... is required.

Some particularly astute students may notice that these values (though in decimal format) are reciprocals of each other.  

Day 1 of 2 - Conclusion

10 minutes

Since we will be using the cards in tomorrow's lesson, students should record their progress so far.  It could be as simple as making a sketch of the setup.  A template is also given if you prefer students use this.

The Complete Resource

This is the complete resource for the lesson.  The lesson was created by the Mathematics Assessment Project.  It can be found here.