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A Story of Ratios

Explore key topics on finding whole, parts of a whole as percent, comparing quantities, percent increase/decrease, and fluency with percents. Understand curriculum guidance and useful insights for effective module delivery.

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A Story of Ratios

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  1. A Story of Ratios Grade 7 – Module 4 Overview Training RCSD February 25 and February 27, 2014

  2. Agenda

  3. Pacing Update • Handouts - Module 3 Guidance, Module 4 Guidance • Review Module 3 and Module 4 Guidance. • Discuss at your table: • Are the guidance documents for mod 3 and 4 helpful to you? • If so, how? • If not, how could they be more useful?

  4. Pacing Update continued: • Math 7 Pacing Guide Update • Review Pacing Guide Update. • How many days until NYS testing? • How the school schedule falls (Super. Day, Spring Break) • Where you are in the curriculum now? • ELA exam dates and impact on instructional Days • Other thoughts, plans, etc… ELA Exam 4/1-4/3 • Superintendent’s Day 3/14 SPRING BREAK Math Exam 4/30-5/2 • :

  5. SPRINTS- • WHAT is a Sprint? • Read paper from Bill Davidson • Share thoughts about reading • Watch video • Discuss • Share thoughts on implementing in our classrooms

  6. What standards/clusters are in this module? • http://www.engageny.org/sites/default/files/resource/attachments/grade-7-math-guide.pdf

  7. Curriculum Overview of A Story of Ratios

  8. 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)

  9. Topic AFinding the Whole • What concepts do you expect to see in Topic A? • Topic A Opener (p. 11)

  10. Lesson 1: Percent • Lesson 1 / Student Outcomes

  11. Percent • Lesson 1 / Opening Exercise

  12. Percent • Lesson 1 / Opening Exercise

  13. Percent • Lesson 1 / Opening Exercise

  14. Percent • Lesson 1 / Example 1

  15. 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.

  16. Lesson 2: Part of a Whole as a Percent • Lesson 2 / Student Outcomes

  17. 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

  18. Part of a Whole as a Percent • Lesson 2 / Discussion

  19. Lesson 3: Comparing Quantities w/ Percent • Lesson 3 / Student Outcomes

  20. 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)

  21. 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)

  22. 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

  23. Percent Increase and Decrease • A sales representative is taking 10% off of your bill as an apology for any inconveniences. • Lesson 4 / Discussion

  24. 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

  25. 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

  26. 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

  27. Mental Math using Factors of 100 • Lesson 5 / Example 2

  28. 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

  29. Lesson 6: Fluency with Percents • Lesson 6 / Exercise 2

  30. Topic BPercent Problems Including More than One Whole • What concepts do you expect to see in Topic B? • Topic B Opener (p. 101)

  31. 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

  32. 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. • 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? • Lesson 7 / Example 2

  33. Markup and Markdown Problems • Lesson 7 / Exercise (4)

  34. Lesson 8: Percent Error Problems • Lesson 8 / Student Outcomes

  35. Understanding Percent Error • Lesson 8 / Example 1

  36. 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

  37. Percent Error Problems • Lesson 8 / Example 3

  38. 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

  39. Solving Problems when the Percent Changes • Lesson 9 / Example 1

  40. 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

  41. Lesson 10: Simple Interest • Lesson 10 / Student Outcomes

  42. Understanding Simple Interest • Lesson 10 / Example 1

  43. Simple Interest • Complete Lesson 10, Problem Set #3 • Lesson 10 / Problem Set #3

  44. 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

  45. 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

  46. Mid-Module Assessment • Complete Problem #1 from the Mid-Module Assessment • Mid-Module Assessment / Problem #1

  47. A Story of Ratios Grade 7 – Module 4 Session 1

  48. Topic CScale Drawings • What concepts do you expect to see in Topic C? • Topic C Opener (p. 170)

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