At Home in College Revisiting Proportional Thinking and Linking up with Variables and Equations.

Day 1: Goals

Start Two fluency sprints: o 1 minute each o Note how many correct in each trial

Example 1& 2 What is the pattern or process that you recall or notice when converting percents to fractions? If I gave you a number as a fraction, could you tell me what percent the fraction represents? How would you do this? What mathematical process is occurring for the percent to convert to a decimal? If I gave you a number as a decimal, could you tell me what percent the decimal represents? How would you do this?

Card Activity

Closing

Day 2 Goals

Opening

The number or quantity that another number or quantity is being compared to is called the whole. The number or quantity that is compared to the whole is called the part because it is part (or a piece) of the whole quantity In our comparison of the value of a nickel coin to the value of a dollar, which quantity is considered the part and which is considered the whole? Explain your answer.

To help us keep track of quantities and their corresponding percents, we can use arrows to show the correspondences in our sequences of reasoning:

Ex.2

Closing

Lesson 3: Goals

Closing What formula can we use to relate the part, whole, and percent? Why did the word “part” change to “quantity” in the percent formula? What are the advantages of using an algebraic representation to solve percent problems? Explain how to decide on which quantity in a problem should represent the whole.

Lesson 4: Goals Students solve percent problems when one quantity is a certain percent more or less than another Students solve percent problems involving a percent increase or decrease.

Looking back at our answers to the Opening Exercise, what percent is represented by one ring? If Cassandra gets the ring for her birthday, by what percent did her ring collection increase? Compare the number of new rings to the original total Use an algebraic equation to model this situation. The quantity is represented by the number of new rings

Percent Decrease

Example 4

Visually…

Closing

Lesson 5: Goals

Which quantity in this problem represents the whole?

Solution

Closing

Lesson 6: Goals Students solve various types of percent problems by identifying the type of percent problem and applying appropriate strategies Students extend mental math practices to mentally calculate the part, the percent, or the whole in percent word problems.

Fluency Sprint Two Rounds, One minute each

Closing

Lesson 7 Goals Students understand the terms original price, selling price, markup, markdown, markup rate, and markdown rate. Students identify the original price as the whole and use their knowledge of percent and proportional relationships to solve multistep markup and markdown problems Students understand equations for markup and markdown problems and use them to solve markup and markdown problems

Definitions

Problem

Example 1: Which quantity is the “whole” quantity in this problem? How do 140% and 1.4 correspond in this situation? What does a “markup” mean? Does it matter in what order we take the discount? Why or why not?

Find the sales price of the bicycle.

In all, by how much has the bicycle been discounted in dollars? Explain After both discounts were taken, what was the total percent discount?

Exercises 1-3

Closing How do you find the markup and markdown of an item? Discuss two ways to apply two discount rates to the price of an item when one discount follows the other.

Lesson 8 Goals

Three students measured a computer screen using a ruler. Their measurements are given below: Do you believe that the stated size of the screen, printed on the box, is the actual size of the screen? Using our sample data, how could you determine the error of each student’s measurement to the actual measurement? What is the difference between Connor’s Measurement 2 and the actual measurement? Which one is correct? Why? How can we make sure that the difference is always positive? Elaborate. StudentMeasurement 1 (in.)Measurement 2 (in.) Taylor Connor Jordan

Absolute Error

Questions Do you think the absolute error should be large or small? Why or why not? If we wanted to know the percent that our absolute error is of the exact value, what would this tell us? Can you derive a formula or rule to calculate the percent that our absolute error is of the exact value?

Percent Error

Questions

Closing Explain the difference between absolute error and percent error. Can either the absolute error or percent error be negative? Why or why not? What is the benefit of calculating or using the percent error?

Lesson 9: Goals Students solve percent problems where quantities and percents change. Students use a variety of methods to solve problems where quantities and percents change, including double number lines, visual models, and equations.

Visual Model

Closing What formula can we use to relate the part, whole, and percent? Describe at least two strategies for solving a changing percent problem using an equation.

Lesson 10: Goals

What is simple interest? How is it calculated? What pattern(s) do you notice from the table? Can you create a formula to represent the pattern from the table?

Interest

Closing Explain each variable of the simple interest formula. What would be the value of the time for a two-year period for a quarterly interest rate? Explain.

Lesson 11: Goals Students solve real-world percent problems involving tax, gratuities, commissions, and fees. Students solve word problems involving percent using equations, tables, and graphs. Students identify the constant of proportionality (tax rate, commission rate, etc.) in graphs, equations, tables, and in the context of the situation.

Situations

Closing

Lesson 12 Goals Students write and use algebraic expressions and equations to solve percent word problems related to populations of people and compilations. Please fill in the information in the table, and compute percentages as asked.

Discussion How did you calculate the percent of boys in the class? How did you calculate the percent of girls in the class? What is the difference between the percent of girls whose names begin with a vowel and the percent of students who are girls whose names begin with a vowel? Is there a relationship between the two? If the percent of boys whose names start with a vowel and percent of girls whose names start with a vowel were given and you were to find out the percent of all students whose names start with a vowel, what other information would be necessary?

Closing What is the importance of defining the variable for percent population problems? How do tape diagrams help to solve for percent population problems? Give examples of equivalent expressions from this lesson, and explain how they reveal different information about the situation.