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##### A Story of Ratios

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**A Story of Ratios**Grade 7 – Module 4 Session 1**Agenda**Introduction to the Module Concept Development Module Review**Grade 7 Module 4 Overview**Module Overview (p. 3) • Questions to address: • How many topics are there and what are those topics? • How many days are required for lessons? Assessments? Remediation and return? • What are some of the important topics and concepts discussed in the narrative?**Topic AFinding the Whole**Topic A Opener (p. 11) What concepts do you expect to see in Topic A?**Lesson 1: Percent**Lesson 1 / Student Outcomes • Students understand that percent is the number and that the symbol means percent. • Students convert between fraction, decimal, and percent; including percents that are less than or greater than . • Students write a non-whole number percent as a complex fraction.**Percent**Lesson 1 / Opening Exercise Color in a 10 x 10 grid to represent each fraction:**Percent**Lesson 1 / Opening Exercise What are equivalent representations of ?**Percent**Lesson 1 / Opening Exercise What are equivalent representations of**Percent**Lesson 1 / Example 1 Use the meaning of the word “percent” to write each percent as a fraction and then a decimal. Percent Fraction Decimal**Consider this…**The following is not from the module, but is to help make a point… I will name a sequence of colors and for each one, do one of the following: If I name a red color, raise your right hand high. If I name a blue color, clap your hands together once.**Lesson 2: Part of a Whole as a Percent**Lesson 2 / Student Outcomes • Students understand that the whole is , and use the formula to problem-solve when given two terms out of three from the part, whole, and percent. • Students solve word problems involving percent using expressions, equations, numeric, and visual models.**Part of a Whole as a Percent**Lesson 2 / Example 1 and Exercise 1 Example 1: In Ty’s math class, 20% of the students earned an A on a test. If there were 30 students in the class, how many got an A?**Part of a Whole as a Percent**Lesson 2 / Discussion Is the expression equivalent to from our steps in Example 1? What does represent? What does represent? What does their product represent?**Lesson 3: Comparing Quantities w/ Percent**Lesson 3 / Student Outcomes • Students use the context of a word problem to determine which of two quantities represents the whole. • Students understand that the whole is 100% and think of one quantity as a percent of another using the formula , to problem solve when given two terms out of three from a quantity, whole, and percent. • When comparing two quantities, students compute percent more or percent less using algebraic, numeric, and visual models.**Comparing Quantities with Percent**Lesson 3 / Example 1(a) and (b) Six club members decided to evenly split the total number of bracelets to be produced [300 bracelets]. Of the 54 bracelets produced over the weekend, Anna produced 32 bracelets. Compare the number of bracelets that Emily produced [22] as a percent of those that Anna produced. Compare the number of bracelets that Anna produced as a percent of the number that Emily produced.**Comparing Quantities with Percent**Lesson 3 / Example 1(a) and (b) What percent more did Anna produce in bracelets that Emily? What percent fewer did Emily produce in bracelets than Anna?**Lesson 4: Percent Increase and Decrease**Lesson 4 / Student Outcomes • 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.**Percent Increase and Decrease**Lesson 4 / Discussion A sales representative is taking 10% off of your bill as an apology for any inconveniences.**Lesson 5: Find One Hundred Percent Given Another Percent**Lesson 5 / Student Outcomes • Students find 100% of a quantity (the whole) when given an quantity that is a percent of the whole by using a variety of methods including finding 1%, equations, mental math using factors of 100, and double number line models. • Students solve word problems involving finding 100% of a given quantity with and without using equations.**Find One Hundred Percent Given Another Percent**Lesson 5 / Opening Exercise What are the whole number factors of 100? What are the multiples of those factors (up to 100)? How many multiples are there of each factor (up to 100)?**Find One Hundred Percent Given Another Percent**Lesson 5 / Exercise 2 Nick currently has 7,200 points in his fantasy baseball league which is 20% more points than Adam has. How many points does Adam have?**Mental Math using Factors of 100**Lesson 5 / Example 2 If is ___% of a number, what is that number? How did you find your answer?**Lesson 6: Fluency with Percents**Lesson 6 / Student Outcomes • 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.**Lesson 6: Fluency with Percents**Lesson 6 / Exercise 2 • Richard works from 11:00 a.m. to 3:00 a.m. His dinner break is of the way through his work shift. What time is Richard’s dinner break?**Topic BPercent Problems Including More than One Whole**Topic B Opener (p. 101) What concepts do you expect to see in Topic B?**Lesson 7: Markup and Markdown Problems**Lesson 7 / Student Outcomes • 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 multi-step markup and markdown problems. • Students understand equations for markup and markdown problems and use them to solve markup and markdown problems.**Markup and Markdown Problems**Lesson 7 / Example 2 Black Friday: A mountain bike is discounted by 30% and then discounted an additional 10% for shoppers who arrive before 5:00 a.m. Find the sales price of the bicycle. In all, by how much has the price of the bicycle been discounted in dollars? Explain. After both discounts were taken, what was the total percent discount?**Markup and Markdown Problems**Lesson 7 / Exercise (4) Exercise 4: Write an equation to determine the selling price, , on an item that is originally price dollars after a markup of 25%. Create a table (and label it) showing five possible solutions to your equation. Create a graph (and label it) of your equation. Interpret the points and .**Lesson 8: Percent Error Problems**Lesson 8 / Student Outcomes • Given the exact value, , of a quantity and an approximate value, , of the quantity, students use the absolute error, , to compute the percent error by using the formula . • Students understand the meaning of percent error: the percent the absolute error is of the exact value. • Students understand that when an exact value is not known, an estimate of the percent error can still be computed when given a range determined by two inclusive values; (e.g., if there are known to be between 6,000 and 7,000 black bears in New York, but the exact number is not known, the percent error can be estimated at most , which is .**Understanding Percent Error**Lesson 8 / Example 1 • How Far Off? • Using a 12-inch ruler, measure the diagonal of a sheet of paper and record your value.**Understanding Percent Error**Lesson 8 / Example 1 • How Far Off? • Use the formula for absolute error to find the absolute errors of the given measurements.**Percent Error Problems**Lesson 8 / Example 3 The attendance at a musical event was counted several times. All counts were between and . If the actual attendance number is between and , inclusive, what is the most and least the percent error could be? Explain your answer.**Lesson 9: Problem Solving when the Percent Changes**Lesson 9 / Student Outcomes • 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.**Solving Problems when the Percent Changes**Lesson 9 / Example 1 Tom’s money is of Sally’s money. After Sally spent and Tom saved all of his money, Tom’s money is more than Sally’s money. How much money did each have at the beginning?**Problem Solving when the Percent Changes**Lesson 9 / Example 3 Kimberly and Mike have an equal amount of money. After Kimberly spent $50 and Mike spent $25, Mike’s money is 50% more than Kimberly’s. How much money did Mike and Kimberly have at first?**Lesson 10: Simple Interest**Lesson 10 / Student Outcomes • Students solve simple interest problems using the formula: , where , , , and . • When using the formula , students recognize that units for both interest and time must be compatible; students convert the units when necessary.**Understanding Simple Interest**Lesson 10 / Example 1 Larry invests $100 in a savings plan. The plan pays interest each year on his $100 account balance. The following chart shows the balance on his account after each year for the next five years. He did not make any deposits or withdrawals during this time.**Simple Interest**Lesson 10 / Problem Set #3 Complete Lesson 10, Problem Set #3**Lesson 11: Tax, Commissions, Fees, and other Real-World**Percent Problems Lesson 11 / Student Outcomes • 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 (the tax rate, commission rate, etc.) in graphs, equations, tables, and in the context of the situation.**Tax, Commissions, Fees, and other Real-World Percent**Problems Lesson 11 / Exercise 5 • Complete modeling Exercise 5 (parts a, b, and c) from lesson 11. • Write up your solutions on poster paper to present to the group.**Mid-Module Assessment**Mid-Module Assessment / Problem #1 Complete Problem #1 from the Mid-Module Assessment**A Story of Ratios**Grade 7 – Module 4 Session 1**Topic CScale Drawings**Topic C Opener (p. 170) What concepts do you expect to see in Topic C?**Lesson 12: The Scale Factor as a Percent for a Scale**Drawing Lesson 12 / Student Outcomes • Given a scale factor in percent, students make a scale drawing of a picture or geometric figure using that scale, recognizing that the enlarged or reduced distances in a scale drawing are proportional to the corresponding distances in the original picture. • Students understand scale factor to be the constant of proportionality. • Student make scale drawings in which the horizontal and vertical scales are different.**The Scale Factor as a Percent for a Scale Drawing**Lesson 12 / Exercise 1 Create a scale drawing of the following drawing using a horizontal scale factor of , and a vertical scale factor of .**The Scale Factor as a Percent for a Scale Drawing**Lesson 12 / Problem Set #2 Create a scale drawing of the original drawing given below with a horizontal scale factor of 80% and a vertical scale factor of 175%. Write numerical equations to find the horizontal and vertical distances.**Lesson 13: Changing Scales**Lesson 13 / Student Outcomes • Given Drawing 1, and Drawing 2 (a scale model of Drawing 1 with scale factor), students understand that Drawing 1 is also a scale model of Drawing 2, and compute the scale factor. • Given three drawings that are scale drawings of each other, and two scale factors, students compute the other related scale factor.**Changing Scales**Lesson 13 / Example 2 A regular octagon is an eight-sided polygon with side lengths that are all equal. All three octagons are scale drawings of each other. Use the chart and the side lengths to compute each scale factor as a percent. How can we check our answers?**Changing Scales**Lesson 13 / Example 3 The scale factor from Drawing 1 to Drawing 2 is and the scale factor from Drawing 1 to Drawing 3 is . Drawing 2 is also a scale drawing of Drawing 3. Is Drawing 2 a reduction or an enlargement of Drawing 3? Justify your answer using the scale factor. The drawing is not necessarily drawn to scale.