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Transcript of A Story of Ratios
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of RatiosGrade 7 – Module 4 Overview TrainingRCSD February 25 and February 27, 2014
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
AgendaTUESDAY•Warm-up – Mid-Module Assessment Questions
•Pacing Update – Discussion
•All about Sprints – Reading, Video, Discuss
•Module 4 overview -Concept Development
•Topic A
THURSDAY•Warm-up – End-of-Module Assessment Questions
•Recap of Important Parts of Module
•Topic B
•Topic C
•Topic D
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Pacing UpdateHandouts - 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?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
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
:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
SPRINTS-WHAT is a Sprint?
• Read paper from Bill Davidson• Share thoughts about reading• Watch video• Discuss• Share thoughts on implementing in our classrooms
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
What standards/clusters are in this module?
http://www.engageny.org/sites/default/files/resource/attachments/grade-7-math-guide.pdf
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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 A Story of Ratios
Grade 7 Module 4 OverviewQuestions 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
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Topic AFinding the WholeWhat concepts do you expect to see in
Topic A?
Topic A Opener (p. 11)
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Lesson 1: Percent
Lesson 1 / Student Outcomes
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Percent
Lesson 1 / Opening Exercise
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Percent
Lesson 1 / Opening Exercise
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Percent
Lesson 1 / Opening Exercise
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Percent
Lesson 1 / Example 1
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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 PercentExample 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 A Story of Ratios
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
© 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
Lesson 2 / Discussion
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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 PercentSix 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 PercentWhat 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 DecreaseA sales representative is taking 10% off of your bill as an apology for any
inconveniences.
Lesson 4 / Discussion
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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 PercentWhat 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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Find One Hundred Percent Given Another PercentNick 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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Mental Math using Factors of 100
Lesson 5 / Example 2
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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 A Story of Ratios
Lesson 6: Fluency with Percents
Lesson 6 / Exercise 2
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Topic BPercent Problems Including More than One WholeWhat concepts do you expect to see in
Topic B?
Topic B Opener (p. 101)
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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 ProblemsBlack 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)
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Lesson 8: Percent Error Problems
Lesson 8 / Student Outcomes
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Understanding Percent Error
Lesson 8 / Example 1
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Understanding Percent ErrorHow Far Off?• Use the formula for absolute error to find the absolute errors of the given
measurements.
Lesson 8 / Example 1
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Percent Error Problems
Lesson 8 / Example 3
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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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Solving Problems when the Percent Changes
Lesson 9 / Example 1
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Problem Solving when the Percent ChangesKimberly 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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Lesson 10: Simple Interest
Lesson 10 / Student Outcomes
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Understanding Simple Interest
Lesson 10 / Example 1
Time (in years) Balance (in dollars)
1 104.50
2 109.00
3 113.50
4 118.00
5 122.50
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Simple InterestComplete Lesson 10, Problem Set #3
Lesson 10 / Problem Set #3
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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
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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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Mid-Module AssessmentComplete Problem #1 from the Mid-Module Assessment
Mid-Module Assessment / Problem #1
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NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of RatiosGrade 7 – Module 4Session 1
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Topic CScale DrawingsWhat concepts do you expect to see in
Topic C?
Topic C Opener (p. 170)
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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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
The Scale Factor as a Percent for a Scale Drawing
Lesson 12 / Exercise 1
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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 ScalesA 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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Changing Scales
Lesson 13 / Example 3
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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
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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
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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
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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 A Story of Ratios
Topic DPopulation, 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
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 A Story of Ratios
Population Problems
Lesson 16 / Example 1
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Population Problems
Lesson 16 / Example 2
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Population Problems
Lesson 16 / Example 3
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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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Mixture Problems
Lesson 17 / Exercise 1a
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Mixture Problems
Lesson 17 / Exercise 2
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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 Problems1. 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
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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
End-of-Module Assessment
End-of-Module Assessment
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Your Biggest TakeawayTake 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 A Story of Ratios
Key Points
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
Key Points