kean fall 10 lesson plan1 - duplin county schools...explanation: complete worksheets as whole group...

Rowan IMPACT Project

District ________Lindenwold_____________________________

Unit�Overview�Template Content Area: Ratios and Proportional Thinking (Comparing and Scaling) Unit Title: Making Sense of Proportions/ Everyday Use of Proportions (Investigation 4) Target Course/Grade Level: Math/7th grade Unit Summary: In this unit the students will be given problems where they are required to make comparisons or find missing values using proportional reasoning that they may come across in everyday life. Primary interdisciplinary connections: Science, Social Studies, Home Ec and various other shop classes 21st century themes: Global Awareness - Application of skill in real life context Unit Rationale: The skills in this unit lay the foundation for students to be able to write ratios, set up and solve proportions in order to make wise choices when comparing quantities and be able to find missing quantities. The skills learned in this unit will be used daily in both other classes and in everyday life.

Learning�Targets Standards: CCSI: Mathematics, CCSI: Grade 7, Ratios & Proportional Relationships 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems.

� 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

� 2. Recognize and represent proportional relationships between quantities. 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.

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

� 2c. Represent proportional relationships by equations. � 2d. Explain what a point (x, y) on the graph of a proportional relationship means

in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

� 3. Use proportional relationships to solve multistep ratio and percent problems.

Content Statements: How to develop ratios, fractions, rates and unit rates to answer questions When to use various forms of comparisons. How to form and interpret ratios in various situations. How to set up proportions. How to connect unit rate and proportional reasoning to real life situations. How to connect unit rates in real life situations. CPI # Cumulative Progress Indicator (CPI) 7. RP Analyze proportional relationships and use them to solve real-world and mathematical

problems.


Unit Essential Questions: x What is a ratio? x What is a ratio as a measure of an attribute in a

real world situation? x How are ratios related to fractions? x How are ratios related to division? x What is a proportion? x What is rate and how is it related to proportional

reasoning? x When is it appropriate to reason proportionally?

Unit Enduring Understandings x A ratio is a multiplicative comparison of two

quantities. x Forming a ratio as a measure of a real-world

attribute involves isolating that attribute from other attributes and understanding the effect of changing each quantity on the attribute of interest.

x Ratios can often be meaningfully interpreted as fractions.

x Ratios can be meaningfully reinterpreted as quotients (unit rate).

x A proportion is a relationship of equality between two ratios. In a proportion, the ratio of 2 quantities remains constant as the corresponding values of the quantities change.

x A rate is a set of infinitely many equivalent ratios. x Superficial cues present in the context of a

problem do not provide sufficient evidence of proportional relationships between quantities.

Unit Learning Targets Students will ...

x Develop ratios, fractions, rates and unit rates to answer questions. x Use appropriate form of comparison. x Set up and solve proportions. x Graph situations involving rates x Interpret ratios, rates and other comparisons.

Evidence�of�Learning�Summative Assessment: Total Unit (Ratios and Proportional Thinking) – Supervisor created benchmark tests modeled after NJ ASK at mid unit approx. 2-3 weeks and end of unit approx. 5-6 weeks Equipment needed: Calculator, computer, smartboard, document camera Teacher Resources: Comparing and Scaling text, CMP teacher resource CD, various internet sites


Formative Assessments x Supervisor created pre-assessment x Teacher created quizzes x Student completion/explanation of HW/CW x Exit ticket answers

x Teacher/student discussion x Student computer work

Lesson�Plans��Lesson Timeframe

Lesson 1 Making Comparisons and Writing Ratios

4 hours/days for lessons, 1 day quiz

Lesson 2 Comparing Ratios, Percents, and Fractions

6 hours/days for lessons, 1 day mid-unit Benchmark test

Lesson 3 Comparing and Scaling Rates

6 hours/days for lessons, 1 day quiz

Lesson 4 Making Sense of Proportions

6 hours/days for lessons, 1 day End Unit Benchmark test

Teacher Notes: Certain students may not be able to pull number out of word problems to set up proportions. These students will need more direction one on one or not be given word problems. When completing whole group lessons answers and examples should be modeled on the document camera to ensure initial understanding. Curriculum Development Resources: See links listed in UDL resources. Unit Authors: Michelle Kean Date: 12/10/10


�Lesson�Plan�1�Template�

Content Area: Math – Ratios and Proportional Reasoning Grade: 7 Lesson Title: Everyday Use of Proportions Timeframe: 2 hours/days

Lesson�Components�

21st Century Themes X Global Awareness Financial, Economic,

Business, and Entrepreneurial Literacy

Civic Literacy Health Literacy

21st Century Skills Creativity and

Innovation X Critical Thinking and

Problem Solving Communication

and Collaboration Information

Literacy Media Literacy ICT Literacy X Life and Career Skills

Interdisciplinary Connections: Science, Social Studies, Various Home Ec and Shop Classes Integration of Technology: Calculator, computer, smartboard, document camera and various web sites noted below.

Goals/Objectives/CPIs�

Students: x Will set up and solve proportions with 80% accuracy. x Use proportional reasoning to find missing information with 80% accuracy. x Use appropriate forms of comparison with 80% accuracy. x Explain or give examples of how comparison and proportional reasoning are used in everyday life with

80% accuracy. Learning�Activities/Instructional�Strategies 1. Engagement: http://www.youtube.com/watch?v=c6IjYT3fUK0 2. Exploration: http://www.brainpop.com/math/ratioproportionandpercent/ratios/preview.weml

3. Explanation: Complete worksheets as whole group activities. 1 whole group lesson per day. (See

attached whole group work Day 1 and Day 2.)

4. Elaboration: Give students choice board to further explore proportional thinking on their own. 1 choice board per day. (See attached Choice Boards for Day 1 and Day 2.)

5. Evaluation: Exit Ticket – List one way in which comparisons or proportional reasoning can be used in your everyday life.

Formative�Assessment�Tasks

x Brain Pop Quiz x Class discussion and Classwork x Choice Work x Exit Ticket


Universal Design for Learning Options Multiple Means of Representation See resources below

1. Perception 2. Language & symbols 3. Comprehension

Multiple Means of Action and Expression See resources below 1. Physical activity 2. Expressive skills and fluency 3. Executive functions

Multiple Means of Engagement 1. Recruiting interest 2. Sustaining effort and persistence 3. Self-regulation x Resources x http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/game.shtml x http://www.quia.com/rr/35675.html?AP_rand=1630204544 x http://lindenwoldk12.rubiconatlas.org/c/etc/getFile.php?originalFile=Drawing%2BRatios.pdf&Fil

eID=2FF26FE0-0C2F-45B5-AA5E-92FB5AEE7FEC&download=Drawing+Ratios.pdf& x http://lindenwoldk12.rubiconatlas.org/c/etc/getFile.php?originalFile=Writing%2BRatios.pdf&File

ID=49968E53-A9E4-4351-965F-9C4D0E773FC7&download=Writing+Ratios.pdf& x http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=261 x http://lindenwoldk12.rubiconatlas.org/c/etc/getFile.php?originalFile=Scaling%2BUp%2Bor%2BD

own%2B%2528Ratios%2Band%2BProportional%2BRelationships%2529.doc&FileID=607EC0EA-BA6E-49EE-AFEB-658FF1F0205B&download=Scaling+Up+or+Down+%28Ratios+and+Proportional+Relationships%29.doc&

x http://www.mathtv.com/index.php?playlist=16217 x http://math.rice.edu/~lanius/proportions/index.html x http://sites.google.com/site/cmpatrowan/home/grade7/compare-scale x http://www.helpingwithmath.com/resources/wor_ratio_proportion.htm x http://mathforum.org/escotpow/puzzles/galactic/applet.html x http://lindenwoldk12.rubiconatlas.org/c/etc/getFile.php?originalFile=Money%2BExchange%2BR

atio%2BRecording%2BSheet.docx&FileID=6A0CF433-AE9C-444A-95DD-A5E07EBEBCBD&download=Money+Exchange+Ratio+Recording+Sheet.docx&

x http://standards.nctm.org/document/eexamples/chap5/5.2/index.htm#APPLET x http://illuminations.nctm.org/ActivityDetail.aspx?ID=178 x http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/game.shtml x http://www.youtube.com/watch?v=c6IjYT3fUK0 x http://lindenwoldk12.rubiconatlas.org/c/etc/getFile.php?originalFile=Ratios%2Band%2BProporati

ons%2BReview.docx&FileID=2023ECCC-A65D-4273-A624-FB0238381E15&download=Ratios+and+Proporations+Review.docx&


Name _______________________________ Date ___________________________ Proportions (Group Instruction Day 1)

A proportion is an equation that states two ratios are equal. 21 =

42

Getting Ready: Dogs outnumber cats in an area by a ratio of 9 to 8. There are 180 dogs in the area how many cats are there? The problem below shows a proportion being used to find out how many cats are in the area.

Why was the original ratio of 89 multiplied

by 2020 ? __________________________

________________________________

________________________________

________________________________

Practice:

1. Calculators are on sale at a price of $1,000 for 20. How many can be purchased for $1,250? Set up a proportion and solve to get your answer.

2. Country music is the primary format for 20% (20 out of 100) of American

radio stations. There are about 10,600 radio stations in the US. About how many of the stations play country music? Show two ways to get your onswer.


Use the reasoning you used to solve 1 and 2 to solve the following proportions for x.

The following shapes are similar. Use proportions to find missing side x and missing side y.

a. Side x ____________________________________________ b. Side y ____________________________________________ Find the height of the tree using proportions.


Name __________________________________ Date ____________________________ Everyday Use of Proportions (Group Instruction Day 2) In our everyday lives and in many occupations we often need to solve proportion problems.

1. Jogging 5 miles burns about 500 calories. How many miles will Quashawn need to jog to burn off the 1,200-calorie lunch he ate?

2. Quashawn jogs about 8 miles in 2 hours. How long will it take him to jog 12

miles? 3. Dominay gives vitamins to her adult dogs. The recommended dosage is 2

teaspoons per day for adult dogs weighing 20 pounds. She needs to give vitamins to Bruiser who weighs 75 pounds and to Dust Ball who weighs 7 pounds. What is the correct dosage for each dog?

a. Bruiser: ____________________________________ b. Dust Ball: ___________________________________

4. Shaakira and Jesica walk 1 mile in about 15 minutes. They keep this pace for

several hours.

a. How far do they walk in 90 minutes?


b. How far do they walk in 65 minutes

5. Ernest makes 10 of his first 15 shots in a free-throw contest. If he

continues at the same rate how many free-throws does he make in 60 attempts?

How many shots would he make if he tried 80 times? How many shots does Ernest have to attempt to make 30 free-throws?


Proportional Reasoning Choice Board Day 1

For the remainder of the period you can choose to do any two

of the following activities: *For any computer site you choose please turn in a paper with

at least 5 problems you completed. Choice 1: http://www.ixl.com/math/practice/grade-7-solve-proportions-word-problems

Choice 2: http://www.classzone.com/cz/books/math_thematics1_08/resources/applications/animations/html/g6_8_3.html

Choice 3: http://www.classzone.com/cz/books/math_thematics2_08/resources/applications/animations/html/g7_9_2.html

Choice 4: http://mathtv.com/ Select: Basic Math then Proportions then Solving Proportions

Choice 5 : Worksheet: Comparison Strategies


Name ____________________________________ Date _________________________ Comparison Strategies Using the following recipes for orange juice answer the questions below.

1. Which recipe will make juice that is the most “orangey”? __________ 2. Which recipe will make juice that is the least “orangey”? __________

3. What comparison statement is correct?

95 of Mix B is concentrate

145 of Mix b is concentrate


Use the picnic table pictures to answer the following questions.

a. suppose the pizzas are shared equally by everyone at each table. Does someone at the small table get same amount as someone at a large table? _________ Each person at the small table gets __________ pieces. Each person at the large table gets __________ pieces.

b. Which table relates to 83 ? _______________

What do the 3 and the 8 mean? ________________________________________________ ________________________________________________________________________

Is 83 a part to whole comparison or a part to part comparison?

________________________


Proportional Reasoning Choice Board Day 2

For the remainder of the period you can choose to do any two

of the following activities: *For any computer site you choose please turn in a paper with

at least 5 problems you completed. Choice 1: http://www.ixl.com/math/practice/grade-7-solve-proportions-word-problems

Choice 2: http://mathslice.com/ratios_ws.php

Choice 3: http://www.classzone.com/cz/books/math_thematics1_08/get_chapter_group.htm?cin=3&rg=ani_math&at=animations&var=animations Choice 4: http://mathtv.com/ Select: Basic Math then Proportions then Applications

Choice 5 : Worksheet: Proportion Strategies


Name __________________________________ Date ______________________ Proportion Strategies So far in this investigation you have solved proportions with nice, easy numbers. Now we are going to solve proportions that are not so nice or easy. This will take what you learned and challenge you to a higher level.

1. A jet takes ten miles to descend (go down) 4,000 feet. How many miles does it take for the jet to descend 5,280 feet?

2. Jessy works at a restaurant and eats one enchilada for lunch every day that he works. He figures that he ate 240 enchiladas last year. 3 enchiladas have a total of 705 calories. How many calories, from enchiladas, did he eat last year?

3. In Clementon Elementary School, there are 58 6th graders, 76 7th graders and 38 8th graders. The school council is made up of 35 students who are chosen to represent all 3 grades equally.

a. Write a fraction to represent the number of students in each grade

level. 6th graders ________________ 7th graders ________________ 8th graders ________________


b. Use the fractions from part a to set up proportions that will help you determine how many students from each grade should be on the student council.

6th graders ___________________ 7th graders ___________________ 8th graders ___________________

4. Reymundo wants to estimate the number of beans in a large jar. He takes out 100 beans and marks them. He then returns them to the jar and mixes them with the unmarked beans. Rey picks 30 beans out of the jar and 2 are marked. Set up a proportion to estimate the number of beans in the jar.

kean fall 10 lesson plan1 - duplin county schools...explanation: complete worksheets as whole group...

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