Finding an Original Value

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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.


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.