NYS COMMON CORE MATHEMATICS CURRICULUM A Story of

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 7 – Module 4 Session 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Agenda Introduction to the Module Concept Development Module Review © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Curriculum Overview of A Story of Ratios © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Grade 7 Module 4 Overview 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? Module Overview (p. 3) © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Topic A Finding the Whole What concepts do you expect to see in Topic A? Topic A Opener (p. 11) © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1: Percent Lesson 1 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Percent Lesson 1 / Opening Exercise © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Percent Lesson 1 / Opening Exercise © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Percent Lesson 1 / Opening Exercise © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Percent Lesson 1 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios 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. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 2: Part of a Whole as a Percent Lesson 2 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Part of a Whole as a Percent 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? Lesson 2 / Example 1 and Exercise 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Part of a Whole as a Percent Lesson 2 / Discussion © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 3: Comparing Quantities w/ Percent Lesson 3 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Comparing Quantities with Percent 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. Lesson 3 / Example 1(a) and (b) © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Comparing Quantities with Percent What percent more did Anna produce in bracelets that Emily? What percent fewer did Emily produce in bracelets than Anna? Lesson 3 / Example 1(a) and (b) © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 4: Percent Increase and Decrease • 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. Lesson 4 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Percent Increase and Decrease A sales representative is taking 10% off of your bill as an apology for any inconveniences. Lesson 4 / Discussion © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 5: Find One Hundred Percent Given Another Percent • 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. Lesson 5 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Find One Hundred Percent Given Another Percent 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)? Lesson 5 / Opening Exercise © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Find One Hundred Percent Given Another Percent 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? Lesson 5 / Exercise 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mental Math using Factors of 100 Lesson 5 / Example 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 6: Fluency with Percents • 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 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6: Fluency with Percents Lesson 6 / Exercise 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Topic B Percent Problems Including More than One Whole What concepts do you expect to see in Topic B? Topic B Opener (p. 101) © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 7: Markup and Markdown Problems • 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. Lesson 7 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Markup and Markdown Problems Black Friday: A mountain bike is discounted by 30% and then discounted an additional 10% for shoppers who arrive before 5: 00 a. m. a) Find the sales price of the bicycle. b) In all, by how much has the price of the bicycle been discounted in dollars? Explain. c) After both discounts were taken, what was the total percent discount? Lesson 7 / Example 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Markup and Markdown Problems Lesson 7 / Exercise (4) © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8: Percent Error Problems Lesson 8 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Understanding Percent Error Lesson 8 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Percent Error How Far Off? • Use the formula for absolute error to find the absolute errors of the given measurements. Lesson 8 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Percent Error Problems Lesson 8 / Example 3 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 9: Problem Solving when the Percent Changes • 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. Lesson 9 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Solving Problems when the Percent Changes Lesson 9 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Problem Solving when the Percent Changes 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 9 / Example 3 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10: Simple Interest Lesson 10 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

A Story of Ratios NYS COMMON CORE MATHEMATICS CURRICULUM Understanding Simple Interest Time (in years) Balance (in dollars) 1 104. 50 2 109. 00 3 113. 50 4 118. 00 5 122. 50 Lesson 10 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Simple Interest Complete Lesson 10, Problem Set #3 Lesson 10 / Problem Set #3 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 11: Tax, Commissions, Fees, and other Real-World Percent Problems • 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. Lesson 11 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Tax, Commissions, Fees, and other Real-World Percent Problems • Complete modeling Exercise 5 (parts a, b, and c) from lesson 11. • Write up your solutions on poster paper to present to the group. Lesson 11 / Exercise 5 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Complete Problem #1 from the Mid-Module Assessment / Problem #1 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 7 – Module 4 Session 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Topic C Scale Drawings What concepts do you expect to see in Topic C? Topic C Opener (p. 170) © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 12: The Scale Factor as a Percent for a Scale Drawing • 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. Lesson 12 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Scale Factor as a Percent for a Scale Drawing Lesson 12 / Exercise 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Scale Factor as a Percent for a Scale Drawing 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 12 / Problem Set #2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 13: Changing Scales • 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. Lesson 13 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Changing Scales 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? Lesson 13 / Example 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Changing Scales Lesson 13 / Example 3 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 14: Computing Actual Lengths from a Scale Drawing • Given a scale drawing, students compute the lengths in the actual picture using the scale factor. Lesson 14 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Computing Actual Lengths from a Scale Drawing The distance around the entire small boat is 28. 4 units. The larger figure is a scale drawing of the smaller sketch of the boat. State the scale factor as a percent, and then use the scale factor to find the distance around the scale drawing. Lesson 14 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 15: Solving Area Problems Using Scale Drawings Lesson 15 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Solving Area Problems Using Scale Drawings What percent of the area of the large disk lies outside the smaller disk? Lesson 15 / Example 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Solving Area Problems Using Scale Drawings Lesson 15 / Example 4 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Topic D Population, Mixture, and Counting Problems Involving Percents What concepts do you expect to see in Topic D? Topic D Opener (p. 227) © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 16: Population Problems • Students write and use algebraic expressions and equations to solve percentage word problems related to populations of people and compilations. Lesson 16 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Population Problems Lesson 16 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Population Problems Lesson 16 / Example 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Population Problems Lesson 16 / Example 3 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 17: Mixture Problems • Students write and use algebraic expressions and equations to solve percent word problems related to mixtures. Lesson 17 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Mixture Problems Lesson 17 / Exercise 1 a © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Mixture Problems Lesson 17 / Exercise 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 18: Counting Problems • Students solve counting problems related to computing percentages. Lesson 18 / Student Outcomes © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Counting Problems 1. How many 4 -letter passwords can be formed using the letters “A” and “B”? 2. What percentage of the 4 -letter passwords contain: a) No “A’s”? b) Exactly one “A”? c) Exactly 2 “A’s”? d) Exactly 3 “A’s”? e) 4 “A’s”? Lesson 18 / Exercises 1 -2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Your Biggest Takeaway Take a moment to reflect on today’s module focus session and prepare 1 or 2 key takeaways that you think are important to share with the group. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Key Points © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Key Points © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 7 – Module 4 Session 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org