Proportional Reasoning Summative Task

Proportional Reasoning Summative Task.

Length: 3 days
Due: Friday December 12, 2014

You will need to save the following documents and save them in your google docs.  Make sure you give each document the propor name.

1. Summative Task
2. Report Outline
3. Rubric

Task

Unit 2 Proportional Reasoning Summative Task from Jessica Garcia

Report Outline

Throw a dinner party report from Jessica Garcia

Rubic

Intro into Percents and test make-ups

Percents

This chapter focuses on content from the Ratios and Proportional Relationships (RP) domain and addresses the following grade 7 standards: 7.RP.2, 7.RP.2, 7.RP.3, 7.EE.2, 7.EE.3.

Essential Question

Each chapter has an Essential Question that keeps students focused on the big idea of the chapter. For Chapter 2, the Essential Question is "How can percent help you understand situations involving money?"

Chapter Vocabulary 

discount (Lesson 7)
gratuity (Lesson 6)
markdown (Lesson 7)
markup (Lesson 6)
percent equation (Lesson 4)
percent error (Lesson 5)
percent of change (Lesson 5)
percent of decrease (Lesson 5)
percent of increase (Lesson 5)
percent proportion (Lesson 3)
principal (Lesson 8)
sales tax (Lesson 6)
selling price (Lesson 6)
simple interest (Lesson 8)
tip (Lesson 6)

Proportional and Reasoning Book Test.  Download for corrections.




P

Direct Variation

Common Core State Standards

7.RP.2   Recognize and represent proportional relationships between quantities.

7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Essential Question How can you determine if a linear function is a direct variation from an equation

Objective use direct variation to solve problems

Lesson Vocabulary

direct variation

constant of variation

constant of proportionality

Rate of change and slope Reteach

Assessment 2

Essential Question How can you find the unit rate from a line on a graph that goes through the origin?

Objective understand slope as it relates to rate of change

Objective identify slope using tables and graphs

Slope from Jessica Garcia

Rate of change and Slope

Common Core State Standards

7.RP.2   Recognize and represent proportional relationships between quantities.

7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Essential Question How can you find the unit rate from a line on a graph that goes through the origin?

Objective understand slope as it relates to rate of change

Objective identify slope using tables and graphs

Develop the Concept

Investigation

Rate of Change and Slope resource

Rate of Change and Slope worksheet

SOLVE PROPORTIONAL RELATIONSHIPS

Homework Review

Mid-Chapter 1 Check

Objective use proportions to solve problems

 Lesson Vocabulary

proportion

cross product


Bell Ringer

Opening: 

What is the ratio of shaded squares to total squares?

If you divide your rectangle into eighths, what is the ratio of shaded eighths to the total number of eighths?

What is another way to divide the rectangle into equal parts? What is the ratio of shaded parts to the total number of parts? 

 Reminder-

If two ratios are equivalent then they share the same unit rate.

Graph, Interpret and Compare Proportional Relationships

Do Now

Objective identify proportional relationships by graphing on the coordinate plane

Lesson Vocabulary

coordinate plane

quadrants

ordered pair

x-coordinate

y-coordinate

y-axis

origin

x-axis

Lesson Resources (click for videos)

Example 1: Display all possibilities in a proportional relationship by graphing

Week Outline Nov 17 - 21 2014

Monday: Proportional and Nonproportional Relationships

Tuesday:  Reteach/ Solving Proportional and Nonproportional Relationships

Wednesday: Solving Proportional and Nonproportional Relationships Activities

Thursday: Mid Chapter Assessment.  Prep before Assessment

Friday: Hands on activities, movement, laugher, thought, fun

 

PROPORTIONAL AND NONPROPORTIONAL RELATIONSHIPS

Building on the Essential Question

At the end of the lesson, students should be able to answer "What makes two quantities proportional?"

Objective identify proportional and nonproportional relationships

Lesson Vocabulary

proportional
nonproportional
equivalent ratios

There are several ways to determine whether or not a relationship is proportional.

• If ordered pairs of a relation show a constant ratio, it is a proportion.
• If the elements in the rows of a table for the relation have a constant ratio, it is a proportion.
• If there is a constant ratio between y- and x- coordinates of points on the graph of a relation, it is a proportion.
• If the relation can be expressed algebraically in the form y = kx, it is a proportion.

A relation that does not have these characteristics is not a proportion.

Converting Unit Rate: Group Presentations

Good Things

Do Now:

Today we will :

-Review Social Contract
-Finish our converting unit rate poster.
-Present our posters
-Make affirmation Envelopes 

Converting Unit Rate: Practice

Bell Ringer

Check your work. Answer to Bell Ringer

In class work:  Pair Check

Convert units using dimensional analys

Learning Goal: How can you show that two objects are proportional?

Lesson Objective: Convert Units of Measure between derived units to solve problems

DOL:

Vocabulary

Unit Ratio
Dimensional Analysis  Click for link.

What we will learn today?
To convert on rate to an equivalent rate by multiplying by a unit ratio or its reciprocal.

1. How can you find the number of feet in 2 yard?
2. How many feet are in 1 2/3 yards?
3. How can you find the number of inches in 1 yard?

refer to page 117 in your planner.

Copy down steps!

Practice Problems

1.       A remote control car travels at a rate of 10 feet per second.  How many inches per second.  How many inches per second is this?

2.       A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this?

3.       A gull can fly at a speed of 22 miles per hour. About how many feet per hour can the gull fly?

4.       An AMTRAK train travels at 125 miles per hour. Convert the speed miles per minute.  Round to the nearest tenth.

5.       Marvin walks is at a speed of 7 feet per second.  How many feet per hour is this?

6.       The average speed of one team in a relay race is about 10 miles per hour.  What is the speed in feet per second?

Evidence of Learning:

Lorenzo rides his bike at a rate of  yards per second. About how many miles per hour can Lorenzo ride his bike?

Charlie runs at a speed of 3 yards per second.  About how many miles per hour does charlie run?

HW : Volume 1 Chapter 1 pg 29 #'s 1-6

Energy of Life

What does daily diet consist of for a citizen in the US?

ChooseMyPlate

 week 1: Rotations

critical reading

Group 1-Writing Reflection

Group 2- Building

Group 3- Experimental Design Outline

How do fractions apply to unit rates?

Real Life Unit Rates.

• Step 1:  Write as a fraction.
• Step 2: Divide top and bottom by denominator
• Step 3: Label

How can you show that two objects are proportional?

Objective  Determine unit rates 

Goal How is a rate a measure of one quantity per unit of another quantity?

Lesson Vocabulary

rate
unit rate

Develop the Concept

• What is the speed limit on the highway?
• If you drive at that speed limit, how far will you travel in one hour? 
• If a student earned $12 in 2 hours, how much would she earn in one hour? 
• If 8 pounds of dog food cost $12, how much will one pound cost? 

Proportion Vocab and Long Divison

 Complete graphic organizers for Ratios and Proportional Reasoning Vocabulary

 Google → Math Definition for _____________

•  Complex fractions 
• Coordinate plane 
• Cross products 
• Equivalent ratios 
• Direct variation 
• Nonproportional 
• Proportion 
• Ordered pair 
• Origin 
• Quadrants 
• Rate Rate of change 
• Slope 
• Unit rate 
• x-axis 
• y-axis
•  x coordinates 
• y coordinate

Ratios and Proportional Reasoning

What we will be doing today...

Check List:

1.) Complete Integers Assessment on 
     Quia <-- click for link

2.) Complete graphic organizers for Ratios and Proportional Reasoning  Vocabulary

Google → Math Definition for _____________

• Complex fractions
• Coordinate plane
• Cross products
• Equivalent ratios
• Direct variation
• Nonproportional
• Proportion
• Ordered pair
• Origin
• Quadrants
• Rate
• Rate of change
• Slope
• Unit rate
• x-axis
• y-axis
• x coordinates
• y coordinate

3. Play Math GAMES!!

Google

•“MathSnacks Ratio Rumble” <-- click for link

•“Arcademics- Ratio and Proportion” <-- click for link

Converting decimals to fractions and percents

Tell Me something Good!!



Bell Ringer: What are the Rules for the following,

1. Adding and Subtracting Integers?
2. Multiplying and Dividing Integers?

Write down the rules on the index card on your desk.

What today will look like:

1. Finish your integer practice worksheet from yesterday.
2. Take an assessment on Integers

• Click HERE for quiz link 

     3. If you finish early.  You will watch the video below on Fractions, Decimals, and Percents.

• Follow along with the video.
• You should be taking notes.
• You should be trying each example.

If you have questions at all today in class, 

PLEASE ASK FOR HELP!!

 

How do you use the Pueblo City Bus Map?

Bell Ringer:

Ms. Garcia is thinking about buying a new fuel efficient vehicle.  Help her make her decision.

Toyota Prius gets 44 miles per gallon.  The cheapest gas by her home is $3.55.

What is the gas price per mile?

If Ms. Garcia buys the Prius and drives to Denver and back, about 335 miles…

How much will it coast her?

Show all work.  

Class Activity 

-Fact fluency Activities: Division (Fluently divide multi-digit numbers using the standard algorithm.)

Lesson:

Exploring Transportation Daily Challenge

Using the bus map, figure out which buses and transfers you would take to get from your house to Pueblo Mall, City Park, and the south side library.

How much would it cost you in bus fares to get to each location?

How would that price change if you were disabled?

How about if you were over the age of 65?

http://pueblo.us/index.aspx?NID=492

From which bus line is this video recorded from?

How much money are you spending on gas per day?

Yesterday we learned how to calculate how many miles your family member drives per day...per week.  Today we are going estimate how much they spend in gas.

Lesson 2: How much money are you spending on gas per day?...per week?

Exploring Transportation Daily Challenge

If your parents travel only by car, how much does this cost them in gas per day? How about per week?

Using previously calculated mileage, teach students to calculate how much it costs to travel by car using the cost of gas.

Examples

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost in dollars for this car to travel 2,727 typical miles?

Pueblo: Gas per mile

http://www.coloradogasprices.com/Pueblo/index.aspx

Western Convenience $ 3.47

Alta Convenience $ 3.56

Loaf 'N Jug $3.60

Sinclair $ 3.64

Gas price per mile for common vehicleshttp://www.nytimes.com/packages/html/business/20060510_LEONHARDT/cost_per_mile.html


Outline of today:

You will have 20 minutes to complete your poster board of miles travel per day, week, month and year.

Next,  there will be two 16 minute rotations.

Rotation 1: Multiplication and Division Challenges.

Rotation 2: Using previously calculated mileage, teach students to calculate how much it costs to travel by car using the cost of gas.

 Formative Assessment The Three-Minute Pause provides a chance for students to stop, reflect on the concepts and ideas that have just been introduced, make connections to prior knowledge or experience, and seek clarification.
 I changed my attitude about... 
 I become more aware of... 
 I was surprised about... 
 I felt... 
 I related to...

Average miles per day...per week in a car.

 Figure out how much gas costs per gallon in Pueblo. What is your family’s means of transportation? How many miles do they travel per day? If someone in your family drives, ask them how many miles they would estimate they drive per day.

Lesson 1: Can you calculate how many miles your family member drives per week?  Teach students to calculate miles driven per week when given miles driven per day. There will be three 15 minute rotations.

Rotation 1:  Division Challenge (Fact fluency Activities: Division and multiplication) 

Who can make the most shoots?  Change every 2 minutes.

·         Use the division flash cards.  Every time you get a division problem right you get to take a shot on the MJ.  Rebound your own shot.  Keep track of score in your notebooks

 Or

Hula Hoop Division Challenge- Who can hula longer? Change every 2 minutes.

·         Use the division flash cards. You get to minutes to hula hoop, count how many division cards you get right.  Keep track of your score in your notebooks.

After using the division cards twice, you may switch to the multiplication flash cards.  Good luck

Rotation 2:  Teach students to calculate miles driven per day, per week, per month when given miles driven per day.We will create an example using google maps.  I made up starting and ending point.  Then as a group will answer the following questions.

1.     What’s the average miles your family travels in one day?

2.     Can you calculate how many miles your family member drives per week?

3.     What about the average miles for one month?

4.     Calculate 6 months?

5.     Calculate 1 year?

Rotation 3: Calculating average miles driven for your family.

What you need.

·         Blank sheet of paper.

·         Colored pencils

Directions: Similar to station 2…

·         Using google maps calculate (round trip) how many miles your guardian travels to work or school or in a car for one day.

·         Make a map showing your start and finish locations.

·         Indicate the miles on map.

·         You will be doing calculations on you maps so make sure you leave yourself room to write.

·         Once you have found your round trip miles then answer the following questions.  You must show all you work.

1.     What’s the average miles your family travels in one day?

2.     Can you calculate how many miles your family member drives per week?

3.     What about the average miles for one month?

4.     Calculate 6 months?

5.     Calculate 1 year?

Keep in mind, you only want to count the day your guardian is going to that same location (work, school, the store).

Also, remember how many days are in a week? How many days are in a month?  How many days are in a year?

Exploring Transportation Daily Challenge 

Can you calculate how many miles your family member drives per week ...per month? Teach students to calculate miles driven per week when given miles driven per day.


 Formative Assessment The Three-Minute Pause provides a chance for students to stop, reflect on the concepts and ideas that have just been introduced, make connections to prior knowledge or experience, and seek clarification. 
 I changed my attitude about... 
 I become more aware of... 
 I was surprised about...
 I felt... related to...

Introduction into Transportation.

Welcome  what today will look like...

Social Contract

Discuss 4 Questions

Review Good Things

Getting to know you activities

Introduction into Transportation

Bell Ringer:

Fact fluency Activities: Multiplication (Fluently multiply multi-digit whole numbers using the standard algorithm)

Card Games: Multiplication War

Lesson:

• Getting to Know you- Two truths and One lie about the summer.
• Introduction into Transportation

Exploring Transportation Daily Challenge
Figure out how much gas costs per gallon in Pueblo. What is your family’s means of transportation? How many miles do they travel per day? If someone in your family drives, ask them how many miles they would estimate they drive per day.

http://prezi.com/kzy1rcmp8xkm/?utm_campaign=share&utm_medium=copy

Formative Assessment

 The Three-Minute Pause provides a chance for students to stop, reflect on the concepts and ideas that have just been introduced, make connections to prior knowledge or experience, and seek clarification.

•  I changed my attitude about... 
• I become more aware of... 
• I was surprised about... 
• I felt... 
•  related to...