Percentages of Numbers (Lesson one in lesson progression)

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SWBAT solve real world word problems involving percentages of numbers.

Big Idea

Students will have the opportunity to grapple through complex word problems using MP 1, 2, 4, and 6.

Pre Lesson Teacher Notes

Please navigate through the pre Teacher Guided Notes.  I know there is a lot of text involved, however it gives a good insight into the lesson and the routine of the lesson. 

This lesson will follow with 5 other lessons that will allow you to culminate the percentage unit with a performance task.  Each of these lessons will allow students to focus on one objective within the percentage unit in order for students to build mastery.  The objective of doing each of these lessons consecutively is so that students are able to answer multi-step, complex, rigorous, word problems that combine each objective in one problem.  Lower level learners will struggle with solving a multi-objective problem if they do not have mastery with each objective.  Students will appreciate being able to scaffold the complex problems using their understanding of each objective and feel empowered in doing so.  You may choose to teach each of these lessons in any order you feel is best suited for your class.  The lessons are Percentages of Numbers, Discount, Sales Tax, Additional Discounts, and Tip.  There will be two separate lessons included in this unit of Percentage of Increase and Percentage of Decrease that you may opt to teach in conjunction with these lessons.  I culminate these lessons with a performance task that is used as a summative assessment.  It is refreshing to get away from the traditional summative assessments and use a performance task to assess mastery of several objectives taught. 

When teaching this lesson as well as the accompanying lessons over percentages, you will have a consistent routine that will give students an opportunity to understand when the mathematical practices are being used, how to use them, and appreciate the power these practices have in gaining a deeper understanding of complex questions.  Students will appreciate having a routine built into the lessons taught.  They will be able to get started right away with the lesson, and begin to work independently.  This will allow you to be a facilitator when necessary and give direct instruction when necessary. 

In these lessons, you will focus on content area vocabulary, word problem strategies, scaffolding questions, unpacking the question, and critical thinking in real world scenarios.  The computation will be done with the calculator.  We will focus more on understanding what the problem is asking the students to do and how to create the equations to answer the questions accurately.  Each of these lessons will have the same routines.  You will have a large emphasis on MP 1, 2, 3, 4, and 6.  Each lesson will have a bell ringer that will focus on MP 1, 4, and 2, a student activity that will focus on MP 3 and 6, a whole group discussion that will be driven by direct instruction, that will focus on MP 6, and a closing.  Not all will have an assigned homework task. Each task will focus on one rich word problem that will be scaffolded down according to the needs of the class. 

With each of these lessons, my students are grouped homogenously.  I’ve grouped these students in groups of 4.  I identified who should be paired up using their Star Math assessments, data gathered using teacher made assessments, understanding of how my students think, and ability level as a whole.  I have two groups that are considered high level learners, a middle group, and two lower level groups who tend to need more attention from me.  Grouping students this way allows the students to utilize one another on the same level. One student will not take over the conversation.  This allows students to feel comfortable because they are paired up with their peers that are like thinkers and are typically on the same level.  Students are not intimidated by one another.  This is an amazing strategy that will afford you the opportunity to differentiate your instruction effectively.

In each of these lessons, I give my students guided notes that are already printed.  I have my students cut out the notes, and the example problems (problems used for their bell ringer) and glue them into their Interactive Math Journals.  In my reflection I will add student examples that will give you an idea of how this is done.  This will cut down on time needed for students to copy notes, and afford an opportunity for students to write down their own thinking to accompany the given notes which will deepen student understanding. 

Bell RInger

10 minutes

As the students enter the room, hand them the problem that will focus on the objective of the day.  Students will work independently for 10 minutes.  During this time students should practice MP 1, 2, 4, and 5.  Walking the room gauging student understanding will benefit the type of open ended questioning you will want to ask during the student activity.  This will also drive your whole group instruction.  Start students with unpacking the problem. This will allow students to identify important information from the problem to help give them a starting point.  Please see my strategy folder on how students unpack a word problem.  

Student Activity

15 minutes

After students have had an opportunity to grapple through the problem on their own for 10 minutes, have them discuss their work with one another in their designated groups.  In the above pre lesson guided notes I discuss how I group my students to maximize this time.  Mathematical practice 3 comes into play heavily during this time.  Students should also focus on solving the problem with their peers accurately.  This places heavy emphasis on MP 6. As you teach each of these lessons, students will be able to practice MP 5 as they use the notes given to help with each upcoming objective that is being taught.  Students will be given 15 minutes to discuss their findings together.  During this time you will want to visit each group to listen to their mathematical discussions, ask guided questions that will help them navigate through the problem, and gather data that will help you guide your whole group discussion.  With your lower level learners you may want to take this opportunity to give small group direct instruction so that they may offer rich discussion during the whole group instruction and to pin point what the scaffolding questions you need to ask during the whole group instruction.  My reflection will give you specific questions I came up with to help student mastery.  

Whole Group Discussion

15 minutes

: During this time, your goal is for students to share out what was discussed during the student activity.  This is the time in which all students are able to learn from one another at one time.  Students will share what process they used to solve the problem, what difficulties they are having with the problem, what successes they had while solving the problem, and which strategies were used to accomplish the task.  As you walked the room you were able to gauge what questions you will ask during this time.  For this specific lesson students are asked to find the percent of questions Mandy answered correctly on her test.

 Helpful hints:  Students should know that the word “of” means to multiply.  When dealing with percentages, multiplication is usually their friend.  This will be their go to operation.  If you take the statement “Mandy answered 80% of her questions on her math test correctly” and have the students translate this into an equation, they will be able to solve what the problem is asking of them.  I break this statement down by asking these questions:

“What does 'of' mean to do?  Students should respond with “to multiply”. 

I begin to have my students create an equation.  I always tell them to leave any percentages or numbers as they are.  We are focused on translating words into numbers and operations to create an equation.  Many of my students will write the multiplication symbol either directly above the word 'of' in the statement or write on top of the word. 

The equation begins as 80% x ____.  For students to understand what they are multiplying 80% by I asked them what does the text tell us? 80% of what?  Students will respond with 80% of her questions. 

I guide students through the text and ask them to find within the text how many questions were on the test.  When students unpack this question, they should have placed a box around all numbers that were important in solving this problem.  This is a great visual for students to block out unnecessary information that will not be pertinent to answering the question.  Students should have boxed 45 questions.  This will be the translation for “her questions”.  Now students have a full equation that they will be able to solve. 

80% x 45= _________________

It is important for students to understand what the response will represent.  I then refer back to the text of the problem and ask what does 80% of her questions mean?  They will respond with the number of questions that Mandy answered correctly. 

During the time the students unpack the question this information was underlined.  Now, once students correctly solve the equation and are able to articulate what the response represents, I ask what did the problem ask us to do?  While students unpacked the problem, they should identify what the problem is asking them to do by either circling power verbs or the questions.  This problem asks how many questions did Mandy answer correctly and incorrectly.  Students will create a checklist from what they circled.  As they answer each item on their checklist they are assuring themselves to earn the maximum amount of points that are assigned to each problem.  Students should recognize that they should be able to subtract the number correct from the total to get the number of questions incorrect. 

This is a direct instructional time period.  


5 minutes

During your closing summarize what has been learned in the lesson.  For this lesson, students should understand how to translate mathematical text into equations, how to interpret what the text is asking them to do,  and how to identify what their computational results mean in reference to the question.  


Assign students the two problems that are included in this section.  One of the problems is an equation to solve using the understanding gained from the lesson today, the next problem is applying the computation into a word problem.  My reflection will give you insight on how this is not easy for lower level students and ways to regroup instruction for students who continue to struggle with application.