Building Block Percents

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Students will be able to calculate any whole number percent of a number mentally.

Big Idea

From 10% students can build 30%, 120%, 5%, etc.

Intro & Rationale

The purpose of this lesson is for my students to engage in mental calculations with percentages.

When I first started teaching I noticed that my students did not do percent calculations the way adults do. (Nor do textbooks teach percent calculations in the way that adults do it!) As I watched my students using a pencil and paper algorithm I realized two things:

  1. The textbook process is complicated for students
  2. In the textbook process there are many opportunities to make mistakes

In my experience, mental calculations are much faster and generally make more sense to students. When students understand that most percents can be built from 10 Percent they become much more flexible and accurate in their calculations. Moreover, by solving problems mentally students often think about the relationships between the numbers, observing patterns and making generalizations.

Warm up

30 minutes

Students begin today's Warm up when they enter class:

Angel sells electronics at Best Buy. For every $100 of electronics that he sells he will be paid a $10 bonus (over his regular hourly pay). What percent of sales is his bonus? How much bonus pay will he recieve if he sells $6000 worth of merchandise?

I expect students to solve this problem in multiple ways. But, I have written the problem in such a way that I anticipate equivalent fractions will be part of the conversation. I know that one misconception my students often have is that if the denominator is a dollar amount (or some other label) that it can't also be the percent. I want my students to understand that a percent is just a special ratio comparing to a quantity of 100 and that the quantity arises from the context of the problem.

As always I have students share their answers first in their Math Family Group. Then, we will discuss the problem as a class. As they share multiple methods for finding 10%, I expect my students to make connections between their own strategy and the structure that reasoning with percents gives to a problem (MP7).  I have included two video examples illustrating my students' thinking about the problem:

Exploration with white boards

30 minutes

Next, I introduce my Cup Model and I teach students how to "fill the cup." On one side of the cup is the percent full and the other side (opposite ends of the water line) is the quantity in ml. The idea is to build (Scaling up) from 10%. 

  1. I draw the cup with a water line at the top and tell them the capacity when full. 
  2. I tell my students the cup is only 10% full and draw a waterline to represent what that would look like, asking them how much water is in the cup, and I write the amount. 
  3. I draw a new water line and ask how many ml. of water would fill the cup 30%, 50%, etc. 
  4. Students write their answers on their individual white board and raise it up on the count of three so I can assess.

As my students are working out their strategy I circulate to see what they are coming up with. Some students will use repeated addition (10% + 10% + 10%), others will multiply (10% x 3), and others will add parts (10% + 10% + 30% = 50%).

When teaching my students to use this model I start with powers of ten (800 ml., 1200ml.) and stick with percents that are multiples of 10. As my students gain confidence, I start to ask about 5%, 25%, 75%, etc. Most years, the progression moves quickly once a student has shared the halving method for finding 50%.

If there is time to take things a step further: I tell my students how much liquid the cup holds when it is 20% full and I ask them, "How much liquid can the cup hold?"