A Story of Ratios

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NYS COMMON CORE MATHEMATICS CURRICULUM

A Story of RatiosGrade 7 – Module 4 Overview TrainingRCSD February 25 and February 27, 2014


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



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?



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

:



SPRINTS-WHAT is a Sprint?

• Read paper from Bill Davidson• Share thoughts about reading• Watch video• Discuss• Share thoughts on implementing in our classrooms



What standards/clusters are in this module?

http://www.engageny.org/sites/default/files/resource/attachments/grade-7-math-guide.pdf



Curriculum Overview of 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)



Topic AFinding the WholeWhat concepts do you expect to see in

Topic A?

Topic A Opener (p. 11)



Lesson 1: Percent

Lesson 1 / Student Outcomes



Percent

Lesson 1 / Opening Exercise



Percent

Lesson 1 / Example 1



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




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



Part of a Whole as a Percent

Lesson 2 / Discussion



Lesson 3: Comparing Quantities w/ Percent




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)



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)



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.




Percent Increase and DecreaseA sales representative is taking 10% off of your bill as an apology for any

inconveniences.

Lesson 4 / Discussion



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.




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



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



Mental Math using Factors of 100




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: Fluency with Percents




Topic BPercent Problems Including More than One WholeWhat concepts do you expect to see in

Topic B?

Topic B Opener (p. 101)



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.




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?




Markup and Markdown Problems

Lesson 7 / Exercise (4)



Lesson 8: Percent Error Problems




Understanding Percent Error




Understanding Percent ErrorHow Far Off?• Use the formula for absolute error to find the absolute errors of the given

measurements.




Percent Error Problems




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.




Solving Problems when the Percent Changes




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 10: Simple Interest




Understanding Simple Interest


Time (in years) Balance (in dollars)

1 104.50

2 109.00

3 113.50

4 118.00

5 122.50



Simple InterestComplete Lesson 10, Problem Set #3

Lesson 10 / Problem Set #3



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.




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.




Mid-Module AssessmentComplete Problem #1 from the Mid-Module Assessment

Mid-Module Assessment / Problem #1



A Story of RatiosGrade 7 – Module 4Session 1



Topic CScale DrawingsWhat concepts do you expect to see in

Topic C?

Topic C Opener (p. 170)



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.




The Scale Factor as a Percent for a Scale Drawing




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



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.




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?




Changing Scales




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.




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 15: Solving Area Problems Using Scale Drawings




Solving Area Problems Using Scale Drawings

What percent of the area of the large disk lies outside the smaller disk?




Solving Area Problems Using Scale Drawings




Topic DPopulation, Mixture, and Counting Problems Involving Percents

What concepts do you expect to see in Topic D?

Topic D Opener (p. 227)



Lesson 16: Population Problems• Students write and use algebraic expressions and equations to solve

percentage word problems related to populations of people and compilations.




Population Problems




Lesson 17: Mixture Problems• Students write and use algebraic expressions and equations to solve

percent word problems related to mixtures.




Mixture Problems

Lesson 17 / Exercise 1a



Mixture Problems




Lesson 18: Counting Problems• Students solve counting problems related to computing percentages.




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



End-of-Module Assessment

End-of-Module Assessment



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.



Key Points



A Story of RatiosGrade 7 – Module 4Session 1

A Story of Ratios

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Transcript of A Story of Ratios