Percent, Piece, Whole

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Objective

SWBAT determine parts, percent, and whole and learn two approaches to percent problem solving.

Big Idea

students practice fluency in percent conversions and calculate percents of wholes through a visual and numeric approach

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. Their Do Now assignment is faced down, and students are asked NOT to turn the paper over. They must write their names on the back side of this paper without turning it over. I explain that we will be starting classes with “sprints” for this percents unit to keep their skills in converting sharp. I also explain that when they turn over the paper they will need to convert fractions to percents, percents to decimals, and percents to fractions. These sprints are built from materials available on the EngageNY state website developed to support the common core curriculum. For more resources within this module (Percent and Proportional Relationships) visit this link.
Determining the amount of time to give students for this task was difficult. I started out giving them 5 minutes for this first sprint and noticed that many kids simply gave up because they wouldn’t finish within 5 minutes. I extended the time a couple of times (on different days) to 6-8 minutes, but I feel that this defeats the purpose of a “sprint” (speed).

A strategy I found the most helpful was to stagger the awards given so that students have incremental goals. Most days, I decided to give just 5 minutes, but reward students with:

  • 1 achievement point if they completed an entire column
  • 2 achievement points if they completed an entire column and 80% or more of the answers were correct
  • 3 achievement points if they completed BOTH columns AND 80% of the answers of more were correct
  • 4 achievement points if they completed BOTH columns and ALL of the answers were correct

This strategy worked best because it challenged students at different levels. Even the students who struggled academically the most with these conversions pushed themselves to complete an entire column and saw progress.

In the last 4 – 5 minutes of this section, I go snake around the room cold calling different students to give me the answers to each conversion. If all students did not reach a certain point or do not have an answer for any given conversion, I quickly review a strategy that would save them time and give the answers myself.

 

Guided Practice

10 minutes

Students receive the “Task” assignment for today. We will begin this Task together through some guided practice and then students will get time to work independently and with neighbors.

I like to begin each major unit with a push for conceptual understanding of the questions. Thus, we begin with a chart where all I want students to do is identify the “whole” in each question. For example, in the first example in the table the question states: 15 is what percent of 90?

I explain to students that there are three parts we need to be aware of in problems like this, the percent, the piece, and the whole. Before answering any of these types of questions, we must check in with ourselves to identify the percent, the piece, and the whole.

 

After letting students discuss which the whole piece is in the second example within the table (56), we share out our answers. Student must then work with neighbors to identify the whole unit in the rest of the examples in the table. A timer will be set with 3 minutes to complete this activity.

After time expires, I ask for the answers and write them on the Smartboard.

Task

20 minutes

Next I set a timer for 5 minutes. Students must work silently and independently to identify the piece, the whole and the percent in each of the examples in the second table. I am walking around during this time to provide feedback and extra help to students who need it. I am also asking students to put answers up on the Smartboard for others to see. At the end of 5 minutes I should have all answers up on the SmartBoard. All students’ attention will be required back at the board.

I will take 5 minutes to do a guided example of the “Visual Approach” to solving these problems. IT involves bar models.

 

After modeling the visual approach, a timer will be set with 5 minutes to complete the next example with partners. I will have a student take 2 minutes to model the solution at the board.

Finally, I model the numeric approach to finding the percent of a whole. I warn students that this method is best for finding the percent of a whole, where the information missing is the piece. Simply choosing the numeric approach because they want to avoid the difficult, conceptual bar model is dangerous when the percent or the whole are missing.

I am also including the teacher resource from the EngageNY website which has more tips for scaffolding and questioning through these activities.

Closing

10 minutes

Students are given the last 10 minutes of this class period to work silently and independently on their homework. A half sheet of paper is given to them and they must write their name on it. Then, they must copy their answer ONLY to the next problem,

A bag of candy contains 300 pieces of which 28% are red. How many pieces are red?

Which quantity represents the whole?

The directions and expectations are clearly written on the board as:

  • Work silently until the end of class to complete the HW section of your Task
  • Write your name on the half sheet of paper
  • Write you answers only to the first two questions:

How many pieces are red?

Which quantity represents the whole?

Students should get a 5 minute warning before the end of class if they have not yet started writing on their half sheet of paper. I will be using these sheets as exit tickets to inform my planning for the next day and determine if students need more practice finding the percent of a whole and identifying it.