# Finding an Original Value

3 teachers like this lesson
Print Lesson

## Objective

SWBAT find an original (or whole) value given a part and percent by scaling values in a table

#### Big Idea

Scale a given value down to 1% and then multiply by 100 to find the original value.

## Introduction

5 minutes

I will begin with the essential question:  How can you find an original value (or whole) when given the part and the percent?

Then I'll ask a simple question:  "The donor gave \$20.  This was 10% of their total pledge.  How much did the donor pledge in all?"  The common error will be for a student to say \$2.  When this happens (yes, I said "when") I'll ask:  Do we want 10% of \$20 or 10% of their total pledge?  Or  I may ask: if \$20 represents 10% of their total pledge will the total pledge be less than or greater than \$20?.  A quick bar model drawing will help students see that the total pledge is \$200.

All problem can be solved as easily mentally or using a bar model, so today we will use a table.

This is a direct instruction lesson.  At the beginning I have given 3 steps to solve any of the problems.  Students will be expected to use this method throughout the lesson.

We will work through the 3 examples by filling in any missing values in the table.  Calculators will be on hand to speed up compuations.

## Guided Problem Solving

15 minutes

Before students begin the problems on this page, we will discuss how you can find an original value.  I will cold call a student to tell me each step.  If a student draws a blank, I will ask them or where this information can be found.  Answer: the first page of notes.

Students will then work on the 5 problems with their partners.  I anticipate students having problems with GP2 and GP3.  Students will need to recall that a 40% discount means the sale price is 60% of the original cost or that the total with tax is 109% of the original cost.  Drawing a simple bar model should help remind students of this.

GP5 gives the value 0.3%.  Some students may mistakenly think of this as 30%.  Others may be confused as to how to scale this "down" to 1%.  I will ask them to look at how they scaled other values to 1%.  They'll notice that they divided by that percent amount, so the same should work with 0.3%.  I may even say any number divided by itself equals...?

## Independent Problem Solving

20 minutes

Students will work on this set of problems independently.  The first 5 problems are similar to the first 5 of the previous section.

Problem 6 requires students to find an original amount given a total with tax based on a discount.  It is somewhat scaffolded in two parts.

The last problem presents data in a circle graph.  Students are given the value and percent of 1 section and then must find the values of all other sections.

## Exit Ticket

5 minutes

Before beginning the exit ticket, we will review the 3 steps to find an original value.  Students then have 5 problems to solve.  These are similar to the first 5 guided practice problems and the first 5 independent practice problems.

A successful exit ticket will have at least 4 correct answers.