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

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## Objective

SWBAT interpret equivalent representations of increases and decreases of quantities

#### Big Idea

In the day 1 we worked with percents and decimals, today we work with fractions.

## 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.

## Day 1 - Recap

10 minutes

We will start part 2 of the lesson by review the work from the previous day.  Students will set that cards up as they left them in the previous day.

An opening question suggested in the resource on page T-6 is "A mobile phone is reduced by 60% in a sale.  Give an example of what the phone originally cost and what is costs now." Then follow with "When the sale is over, the phone will be returned to its original price.  What is the percent increase?"

## Sharing Work

10 minutes

At this point, groups share their work.  The resource suggests picking one student from each group to visit another group's work.  Students remaining at the desk should be prepared to explain their thinking.  Students visiting other groups should compare their own groups work with the work of the group they are visiting.

I will most likely have groups come to the front and share their work with the class.  It will allow me to make sure conversations are focused on the work at hand.  The group presenting will need to be prepared to explain their thinking.  The students sitting will take the place of the visiting student.  They will compare their own work to the work of the presenting group.  If there are differences in work, students should ask for an explanation and be prepared to explain their own reasoning.

Once each group, or at least a few, have presented, groups may consider changing the arrangement of the cards.

## Collaborative Activity 2 - Fraction Multipliers

30 minutes

Now students use card set D with the fraction multipliers.  These are to be placed between quantities as the percents and decimals were the previous day.  Again students may use calculators.

This activity may go quickly for some groups as they may recognize the fraction equivalences to the decimal multipliers that have already been placed.

As students work with these fractions the reciprocal relationships will become more apparent - if a quantity is scaled by 2/3, the new quantity will need to be scaled by 3/2 to return to its original value.

Once students have their cards placed where they want them, they may glue their final card arrangement onto a large sheet of paper.  Or they may sketch, the placement if you would prefer.

## Whole Class Discussion

10 minutes

Now we'll summarize what we learn.  The resource suggests giving students a mini white board and markers to record their answers during the discussion.

Suppose prices increase by 10%.  How can I write this as a decimal multiplication?

How can I write this as a fraction multiplication?

What is the fraction multiplication to get back to the original price?

How can you write that as a decimal multiplication?  How can you write that as a percentage?

I will try other values and follow a similar line of questioning.  Perhaps an increase of 20% and a decrease of 75%.

Of course, between each question pause to give students time to work out their answers on the what boards.

## Post Lesson Assessment

10 minutes

Students will receive back their pre-lesson assessment.  It will either have comments written on it from the teacher or general comments for each question will be posted in the room.  Students are to make improvements to their original answers.  A new blank copy of the assessment will be given.

If time is short, you may consider giving this as a homework assignment or even as an activity for the next class period.