Reflection: Staircase of Complexity Percentages of Numbers (Lesson one in lesson progression) - Section 6: Homework


It was interesting to me that the students did not pick up right away the first problem is exactly the same as the second.  The first problem is a simple one step equation that they needed to solve.  This came easy to them because they know that of means to multiply and thus they were able to rewrite as an equation and solve.  I found that some of my students struggle when there is text involved and they then need to navigate the text in order to pull out the information needed to create the equation.  We are working hard with unpacking the problem, using that information to navigate through the text in order to translate it into an equation to solve the problem.  Unpacking and translating the text are two strategies that have heavy focus in my instruction. 

When a student unpacks a problem they will:

1.) Circle any power verbs (i.e identify, determine, show, explain)

2.) Underline what the power verb tells them to do.

3.) Box all numbers or variables that are needed to solve the problem. 

When doing this it is important for students to be able to identify numbers needed and numbers that are not needed to solve the problem.  For example, Malissa purchased a 72 inch flat screen and used 90% of her savings.  Malissa had $1200.00 in savings.  How much did Malissa pay for the t.v.  Students will be tempted to box 72.  When students do this I emphasize the importance in reading the problem first before unpacking the problem.

4.) Circle all questions that the problem ask.

5.) Highlight vocabulary that is important to solving the problem.  (i.e How much more, "of" in the context of multiply.  This is another tricky one.  For example, students will need to know the difference when "of" is used as 90% of her savings, and The regular price "of" the Jordans is $180.00.  In the second example, "of" is used for the sentence to be grammatically correct and has no math connotation. 

6.) Create a checklist from the power verbs and questions circled.  

  Interesting Observation! Students struggle with APPLICATION.
  Staircase of Complexity: Interesting Observation! Students struggle with APPLICATION.
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Percentages of Numbers (Lesson one in lesson progression)

Unit 3: Proportional Reasoning with Percents
Lesson 3 of 16

Objective: 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.

  Print Lesson
Math, Percentages, Number Sense and Operations, proportions, Fractions, mathematical practices, equation, Reading Strategies, unpacking the question, Mathematical content translation, multiplying percents, percent, real world
  45 minutes
ercentage of numbers
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