ࡱ > bjbjww Z R | | T G < + g i i i i i i $ ( ʇ T i p g g k s 0]d B v un N S 0 < n : s s
~ < | : Grade 6 UNIT 1: Ratios and Unit Rates Suggested Number of Days for Entire UNIT: 35
Essential Question
Key ConceptsCross Curricular ConnectionsHow do we use ratios and unit rates to solve real-world mathematical problems?
Unit Vocabulary
Ratio
Rate
Unit Rate
Value of a Ratio
Equivalent Ratios
Percent
Associated Ratios
Double Number Line
Ratio TableRepresenting and Reasoning About Ratios
Collections of Equivalent Ratios
Unit Rates
Percent
*Assessments
Mid-Module Assessment: After Section B
(3 days -1 day for assessment, 1 day for assessment return, & 1 day for remediation)
End-of-Module Assessment: after Section D (3 days- 1, day for assessment, 1 day for assessment return, & 1 day for remediation).
HYPERLINK "http://www.engageny.org/resource/grade-6-mathematics-module-1" http://www.engageny.org/resource/grade-6-mathematics-module-1
Religion: Use the actual size of the parts of the Egyptian pyramids to make a scale model using ratios and proportions. Find the measurements of your own church and compare it to the pyramids.
Science: Use ratios and proportions to analyze the amount of calories each student consumes in a day. Students will need to determine the amount of calories per serving. They would also set up a proportion based on how many servings they would eat to determine the calories for each item. Consider what is appropriate for different body types.
Other: Engage in researching the golden ratio. Construct a well developed composition paper on the significance of the golden ratio and where we see it in our everyday lives.
Unit Outcome (Focus)
Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios. Use proportional reasoning to convert between measurements.
UNIT 1 SECTION A: Representing and Reasoning About Ratios Suggested Number of Days for SECTION: 8
Essential QuestionKey ConceptsStandards for Mathematical PracticeHow do we use ratios and unit rates to solve real-world mathematical problems?Ratios
Equivalent Ratios
Solving Problems by Finding Equivalent Ratios
Associated Ratios and the Value of a Ratio
Equivalent Ratios Defined Through the Value of a Ratio1. Make sense of problems and persevere in solving them
3. Construct viable arguments and critique the reasoning of others
6.Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning.
CommentsStandard No.Standard
( Major Standard ( Supporting Standard ( Additional StandardPriorityStudents develop fluidity in using multiple forms of ratio language and ratio notation. They construct viable arguments and communicate reasoning about ratio equivalence as they solve ratio problems in real world contexts (6.RP.3). As the first topic comes to a close, students develop a precise definition of the value of a ratio a:b, where b `" 0 a s t h e v a l u e a / b , a p p l y i n g p r e v i o u s u n d e r s t a n d i n g o f f r a c t i o n a s d i v i s i o n ( 5 . N F . 3 ) . T h e y c a n t h e n f o r m a l i z e t h e i r u n d e r s t a n d i n g o f e q u i v a l e n t r a t i o s a s r a t i o s h a v i n g t h e s a m e v a l u e .
6 . R P . 1
( D O K 2 )
6 . R P . 3 a
U n d e r s t a n d t h e c o n c e p t o f a r a t i o a n d u s e ratio language to describe a ratio relationship between two quantities.
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations
a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare.
(
(
UNIT 1 SECTION B: Collections of Equivalent Ratios Suggested Number of Days for SECTION: 7
Essential QuestionKey ConceptsStandards for Mathematical PracticeHow do we use ratios and unit rates to solve real-world mathematical problems?Tables of Equivalent Ratios
The Structure of Ratio Tables: Additive and Multiplicative
Comparing Ratios Using Ratio Table
From Ratio Tables to Double Number Line Diagrams
From Ratio Tables to Equations Using the Value of the Ratio
From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
A Synthesis of Representations of Equivalent Ratio Collections1. Make sense of problems and persevere in solving them
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
6.Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning.
CommentsStandard No.Standard
( Major Standard ( Supporting Standard ( Additional StandardPriorityStudents explore collections of equivalent ratios in real world contexts. They build ratio tables and study their additive and multiplicative structure (6.RP.3a). Students continue to apply reasoning to solve ratio problems while they explore representations of collections of equivalent ratios and relate those representations to the ratio table (6.RP.3). Building on their experience with number lines, students represent collections of equivalent ratios with a double number line model. They relate ratio tables to equations using the value of a ratio.
6.RP.3a
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations
a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare.
(
UNIT 1 SECTION C: Unit Rates Suggested Number of Days for SECTION: 8
Essential QuestionKey ConceptsStandards for Mathematical PracticeHow do we use ratios and unit rates to solve real-world mathematical problems?
From Ratios to Rates
From Rates to Ratios
Finding a Rate by Dividing Two Quantities
Comparison Shopping Unit Price and Related Measurement Conversions
Getting the Job Done Speed, Work and Measurement Units
Problem-Solving Using Rates, Unit Rates, and Conversions Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
4. Model with mathematics
Attend to precision
8. Look for and express regularity in repeated reasoning
Comments
Rate reasoning is central to the study of algebra and is a critical foundation for understanding slope in grades 7 & 8.Standard No.Standard
( Major Standard ( Supporting Standard ( Additional Standard
( Standard ends at this grade ( Fluency StandardPriority
6.RP.2
(DOK 2)
6.RP.3b
(DOK 2)
6.RP.3d
(DOK 2)
Understand the concept of a unit rate a/b associated with a ratio a:b with b `" 0 , a n d u s e r a t e l a n g u a g e i n t h e c o n t e x t o f a r a t i o r e l a t i o n s h i p .
U s e r a t i o a n d r a t e r e a s o n i n g t o s o l v e r e a l - w o r l d a n d m a t h e m a t i c a l p r o b l e m s , e . g . , b y r e a s o n i n g a b o u t t a b l e s o f e q u i v a l e n t r a t i o s , t a p e d i a g r a m s , d o u b l e n u m b e r l i n e d i a g r a m s , o r e q u a t i o n s
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
(
(
Students build further on their understanding of ratios and the value of a ratio as they come to understand that a ratio of 5 miles to 2 hours corresponds to a rate of 2.5 miles per hour, where the unit rate is the numerical part of the rate, 2.5, and miles per hour is the newly formed unit of measurement of the rate (6.RP.2). Students solve unit rate problems involving unit pricing, constant speed, and constant rates of work (6.RP.3b). They apply their understanding of rates to situations in the real world.
UNIT 1 SECTION D: Percent Suggested Number of Days for SECTION: 6
Essential QuestionKey Concept
Standards for Mathematical Practice
How do we use ratios and unit rates to solve real-world mathematical problems?Percent and Rates per 100
A Fraction as a Percent
Percent of a Quantity
Solving Percent Problems1. Make sense of problems and persevere in solving them
4. Model with mathematics
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoningCommentsStandard No.Standard
( Major Standard ( Supporting Standard ( Additional Standard
( Standard ends at this grade ( Fluency StandardPriorityStudents are introduced to percent and find percent of a quantity as a rate per 100. Students understand that N percent of a quantity has the same value as N/100 of that quantity. Students express a fraction as a percent, and find a percent of a quantity in real-world contexts. Students learn to express a ratio using the language of percent and to solve percent problems by selecting from familiar representations, such as tape diagrams and double number lines, or a combination of both (6.RP.3c).
6.RP.3c
(DOK 1)
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
d. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
(
Possible Activities EQUIVALENT RATIO BINGO: Create a list of 30+ problems involving ratios (make sure they all have different answers). Write the problems and answers on index cards. Write the answers on the board. Have students randomly write 24 of the answers on a blank bingo card (cards can be reused or exchanged). Place the index cards face down. Take turns choosing a card and reading the problem to the students. You may want to also write the problem on the board so that students can reference it later if they need more time. Students should mark off the correct answer on their game boards using chips or paper scraps. Traditional bingo rules apply. Make sure you have the winning students read off their answers. Bingo card can be downloaded at HYPERLINK "http://www.rethinkmathematics.com"www.rethinkmathematics.com Click on Math Games and download the Equivalent Fractions Game for game boards.
EQUIVALENT RATIO BOARD GAME: (2 person game) One player throws two dice and makes a proper fraction with the numbers rolled (smaller number as numerator). The player then finds an equivalent ratio on the board and covers it with a marker. If an opponents marker is already there, it may be removed. If a player rolls doubles, he or she loses a turn. The first player to get three markers in a row wins! Create boards of equivalent r a t i o s u s i n g t h e r o l l o f a d i c e o r d o w n l o a d a p r e m a d e b o a r d o n l i n e ( s e e b e l o w ) . E x : R o l l a 6 a n d 2 . F r a c t i o n i s 2 / 6 . E q u i v a l e n t r a t i o c a n c o v e r 4 / 1 2 o r 1 / 3 . D o w n l o a d p r e - m a d e b o a r d s a t H Y P E R L I N K " h t t p : / / l e a r n z i l l i o n . c o m / l e s s o n s / 5 8 0 - v i s u a l i z e - p a r t t o p a r t -ratios-using-pictures"http://learnzillion.com/lessons/580-visualize-parttopart-ratios-using-pictures
GAMES AT RECESS: The students in Mr. Hills class played games at recess.
6 boys played soccer
4 girls played soccer
2 boys jumped rope
8 girls jumped rope
Afterward, Mr. Hill asked the students to compare the boys and girls playing different games. For the entire problem, visit HYPERLINK "http://www.illustrativemathematics.org/illustrations/76"http://www.illustrativemathematics.org/illustrations/76
Resources
VISUALIZE PART-TO-TOTAL RATIOS USING PICTURES In this lesson you will learn to visualize a part-to-total ratio using pictures.
HYPERLINK "http://learnzillion.com/lessons/581-visualize-parttototal-ratios-using-pictures"http://learnzillion.com/lessons/581-visualize-parttototal-ratios-using-pictures
THE GOLDEN RATION: In this lesson, one of a multi-part unit from Illuminations, students learn and understand the concept of ratio. They learn about the Golden Ratio, used by the painter Leonardo da Vinci in his work, while exploring different ratios to see whether the Golden Ratio holds true. HYPERLINK "http://thinkfinity.org/%09%09%09http:/illuminations.nctm.org/LessonDetail.aspx?ID=L510" \t "_blank"http://illuminations.nctm.org/LessonDetail.aspx?ID=L510
Engage NY Grade 6 Module 1 Link: HYPERLINK "http://www.engageny.org/resource/grade-6-mathematics-module-1" http://www.engageny.org/resource/grade-6-mathematics-module-1
Possible Activities
CONVERTING UNIT RATES ACTIVITY: Have students collect data on unit rates by timing themselves doing a variety of activities (saying the alphabet, hops on one foot in one minute, etc.). Have them use these rates to find out how many hops on one foot they can do in one hour; or how many times they can say the alphabet in 45 minutes, etc.?
COMPARISON SHOPPING: Bring in the Sunday ads for different grocery stores items (student can also view ads online). Challenge the students to comparison shop to find the best deal using unit cost. A short movie explaining comparison shopping can be viewed online (see right).
Ex: 5 oranges for $3.50 or 2 for $1.75. Which is the better deal?
Ex: $4.50 for 24 ounces of pasta and $5.00 for 30 ounces of pasta. Which is the better deal?
ROAD TRIP ACTIVITY: (groups of 3-5) Each group of students will choose and research a city in the Unites States. They will plan to travel to the city via car. The students will research which car they will purchase (or rent) for the drive and how many gallons of gas the car gets per mile. The student will then go on a virtual road trip! They can calculate how many miles they traveled and how much gas they bought. They can chart their unit rate of miles per gallon as well as graph their course. They can find the ratio of miles to the gallon as well as distance travelled per day. Extend: Students can track expenses: How much total money they spent, including hotels and food, etc. They can also receive speed bumps along the way, such as your team received a flat tire on the 64thmile of day 2. What do you do? What is the added cost?
PRICE PER POUND AND POUNDS PER DOLLAR The grocery store sells beans in bulk. The grocer's sign above the beans says, 5pounds for$4. At this store, you can buy any number of pounds of beans at this same rate, and all prices include tax. For entire problem, visit: HYPERLINK "http://www.illustrativemathematics.org/illustrations/549"http://www.illustrativemathematics.org/illustrations/549Resources
COMPARISON SHOPPING: A short movie explaining comparison shopping. Go to HYPERLINK "http://www.brainpop.com"www.brainpop.com Click on Math, select Free Movies, and choose Comparing Prices.
UNDERSTAND RATES AS A TYPE OF RATIO In this lesson you will learn how rates are part of the ratio family by reviewing the qualities of a ratio
HYPERLINK "http://learnzillion.com/lessons/839-understand-rates-as-a-type-of-ratio"http://learnzillion.com/lessons/839-understand-rates-as-a-type-of-ratio
TRAVEL IN THE SOLAR SYSTEM: This lesson, from Illuminations, affords students the opportunity to think about two aspects of the time required to complete space travel within the solar system. First, students consider the amount of time that space travelers must spend on the journey. Second, students think about what kinds of events might occur on Earth while the space travelers are on their journey. Thinking about both situations improves students' concept of time and distance as well as their understanding of the solar system. HYPERLINK "http://thinkfinity.org/%09%09%09http:/illuminations.nctm.org/LessonDetail.aspx?ID=L281" \t "_blank"http://illuminations.nctm.org/LessonDetail.aspx?ID=L281
Possible Activities PROPORTIONS: Challenge students to discover proportions (equivalent ratios) and to plan a lesson with examples and models to present to the class. Resources found online at www.homeschoolmath.net. Click on Lessons then scroll down to Middle and choose How to Teach Proportions.
I HAVE, WHO HAS? An activity for the entire class to practice solving problems. The students are each given a card or two. Each card contains a number on the top and a problem to solve on the bottom. The answer to the problem leads to the next card; if cards are created they need to be completed all at once. This is a great game to reinforce mental math with unit rates or percent to decimal to fraction conversions. Game cards can also be downloaded online (see right).
Ex: I have ___, who has a ratio equivalent to 3:7? The student with 9:21 on their card responds: I have 9:21, who has ratio equivalent to 2:9? The student with 4:18 on their card responds and the game continues until all of the cards are called.
ADVANCED PAPER POOL: This reproducible worksheet, from an Illuminations lesson, presents a table on which students record their predictions about the behavior of pool balls on pool tables of different dimensions. Three related questions accompany the table. HYPERLINK "http://thinkfinity.org/%09%09%09http:/illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Advanced.pdf" \t "_blank"http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Advanced.pdf
ResourcesPREPARING TO TEACH PROPORTIONAL REASONING: What do your students already know about ratio, proportion, and scale? Do they have the knowledge and skills necessary to understand the mathematics of proportional reasoning? Teaching Module 1 focuses on eight skills students should master before exploring Scale City: HYPERLINK "http://www.teachersdomain.org/resource/scl10.plr.module1/"http://www.teachersdomain.org/resource/scl10.plr.module1/
Engage NY Grade 6 Module 1 Link: HYPERLINK "http://www.engageny.org/resource/grade-6-mathematics-module-1" http://www.engageny.org/resource/grade-6-mathematics-module-1
Possible Activities
GO TO THE STORE: Write on the whiteboard, cut out, or print pictures of items that are for sale. Explain to the students that they have to buy any combination of four items. The students are then challenged to find the total of the items plus sales tax. Extend: Can they calculate their total if select items are on sale (i.e. 25% off)?
GRID AND PERCENT IT: In this Illuminations lesson, students solve various types of percent problems using a 10 x 10 grid, a common model for visualizing percents. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L249
PERCENT SLOPE TOOL: This reproducible activity, from an Illuminations lesson, provides a template by which students can create a tool for calculating the slope of real-world inclines. HYPERLINK "http://thinkfinity.org/%09%09%09http:/illuminations.nctm.org/Lessons/OnFire/OnFire-AS-PerSlopeTool.pdf" \t "_blank"http://illuminations.nctm.org/Lessons/OnFire/OnFire-AS-PerSlopeTool.pdf
Resources
FIND THE PART WHEN THE PERCENT AND TOTAL ARE KNOWN: In this lesson you will learn to calculate the part when you know the percent and the total by using a double number line: HYPERLINK "http://learnzillion.com/lessons/596-find-the-part-when-the-percent-and-total-are-known"http://learnzillion.com/lessons/596-find-the-part-when-the-percent-and-total-are-known
BIG MATH AND FRIES: This Illuminations lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items. HYPERLINK "http://thinkfinity.org/%09%09%09http:/illuminations.nctm.org/LessonDetail.aspx?id=L849" \t "_blank"http://illuminations.nctm.org/LessonDetail.aspx?id=L849
Engage NY Grade 6 Module 1 Link: HYPERLINK "http://www.engageny.org/resource/grade-6-mathematics-module-1" http://www.engageny.org/resource/grade-6-mathematics-module-1
Possible Activities
I HAVE, WHO HAS? An activity for the entire class to practice solving problems. The students are each given a card or two. Each card contains a number on the top and a problem to solve on the bottom. The answer to the problem leads to the next card; if cards are created they need to be completed all at once. This is a great game to reinforce mental math with unit rates or percent to decimal to fraction conversions. Game cards can also be downloaded online (see right).
Ex: I have ___, who has a ratio equivalent to 3:7? The student with 9:21 on their card responds: I have 9:21, who has ratio equivalent to 2:9? The student with 4:18 on their card responds and the game continues until all of the cards are called.
MEASURING UP: This unit explores the concepts of proportional reasoning, ratio, and indirect measurement. Students engage in a variety of activities that involve taking their own measurements, exploring different ratios, and examining similar figures. Students convert measurements into customary and metric units. These activities immerse students in problem solving, reasoning, and making connections to real-life situations. HYPERLINK "http://illuminations.nctm.org/LessonDetail.aspx?id=U148"http://illuminations.nctm.org/LessonDetail.aspx?id=U148
Resources
CONVERT MEASUREMENT UNITS USING RATIO TABLES: In this lesson you will learn to convert measurement units by using ratio tables.
HYPERLINK "http://learnzillion.com/lessons/592-convert-measurement-units-using-ratio-tables"http://learnzillion.com/lessons/592-convert-measurement-units-using-ratio-tables
CELL SIZE AND SCALE: This & ' 1 D E L O Q S T U g h i t u v ٲ~qdYLٲ?L h~ hO 5B*ph h~ hx
5B*ph h~ h B*ph h~ hS 5B*ph h~ hgt 5B*ph h~ h|q 5B*ph h~ h4]D 5B*ph h~ hno 5B*ph h~ h? 5B*ph h~ htE 5B*ph h~ h 5B*ph h~ h?W 5B*ph h~ hg 5B*ph h~ hjN 5B*ph h~ h 5B*ph T U h i v I kd $$If l F #5
t 0 6 4 4
l a yt bl $
$ d $If a$gd bl
5d gd
. 0 7 9 J L ^ ` k l T
l
" ǺǺǺǺǺǺǺǺǺǭwjwjX "j h~ h( B*U^J ph h~ h( B*aJ ph h~ h( 5B*aJ ph h~ h( B*^J ph h~ h]Q B*^J ph h~ h; B*^J ph h~ ht/ B*^J ph h~ h( 5B*ph h~ h( B*ph h~ h; B*ph h~ hg B*ph h~ htE B*ph h~ htE 5B*ph " 0 9 L ` l d $7$ 8$ H$ If gd bl
& F d $7$ 8$ H$ If gd bl $If gd(
$$If gd( $
$ d $If a$gd(
$ d $If gd bl T
b c $ % }
~
- .
$ d $If gd bl
$ d $If gd( $
$ d $If a$gd( d $7$ 8$ H$ If gd bl
" # ` a c l % - ~
, - . / 0 1 E F G \ ] źźźvi\OB h~ htK B*^J ph h~ h]Q B*^J ph h~ h]Q 5B*ph h~ hx
5B*ph h~ htK 5B*ph h~ hZ B*ph h~ hx
B*ph h~ hFE B*ph h~ htE B*ph h~ h]Q B*ph h~ hg B*ph h~ hg 5B*ph h~ h( B*^J ph h~ h( 0J B*^J ph "j h~ h( B*U^J ph . / 0 F G ] ^ o e R R R R d $7$ 8$ H$ If gd bl d gd kd $$If l GF #5
t 0 6 4 4
l a yt bl ] ^ ` a h o s W X ^ _ : ~ + , A ϵϨϛϐzzozaS j oh~ h{ B*ph j nh~ h{ B*ph h~ hB$6 B*ph h~ h_ B*ph h~ h B*ph h~ h{ B*ph h~ hFE 5B*ph h~ hno 5B*ph h~ hB$6 5B*ph h~ h 5B*ph h~ h{ 5B*ph h~ h B*ph h~ hx
B*ph h~ h\w B*^J ph ^ _ ` w ` ` ` $
$ d $If a$gd bl
5d gd
$ d gd j kdR $$If l ' 5 H6
t 0 6 4 4
l a yt bl X _ q n Z C C C C C
& F!
$ d $If gd_
$ d $If gd bl kd $$If l F N #5 f (
t 0 4 4
l a yt bl : ~
$ d $If ^ gd_
$ d $If gdB$6
$ d $If gd bl X a n W W W B W
< $ d $If gd bl $
$ d $If a$gd bl kd $$If l F N #5 f (
t 0 4 4
l a yt bl A B X a b B H
& , x z | L δδδΩ朏wi^P j nh~ h_ B*ph h~ hX/ B*ph j nh~ hX/ B*ph h~ h_ B*^J ph h~ hQ B*ph h~ h 5B*ph h~ hQ 5B*ph h~ hFE B*ph h~ h_ 6B*ph h~ h_ 5B*ph h~ h_ B*ph h~ h{ 5B*ph h~ h{ B*ph j h~ h{ B*ph a b z | ] T @ @ @ @ @
$ d $If gd bl $If gdB$6 kdo $$If l \ N F25 8 !
t 0 4 4
l a yt bl L M N $
$ d $If a$gd bl d $7$ 8$ H$ If gd_
$ d $If gd_
$ d $If gd bl S ? + +
$ d $If gd bl
$ d $If gd_ kdR $$If l 4 \ N F25 `8 `! `
t 0 4 4
l a p
yt bl u u | 9 ?
! ! ! ! ! ! ! 9" " ··wjwjw·]jwjw h~ hB$6 B*^J ph h~ hq! 5B*ph h~ hq! B*ph j h~ hB$6 B*ph j oh~ hB$6 B*ph j nh~ hB$6 B*ph h~ h r B*ph h~ hB$6 B*ph h~ hB$6 5B*ph h~ h{ 5B*ph h~ hCW. B*ph h~ hwY 5B*ph h~ h{ B*ph $ E -
$ d $If ^ gd_ kd` $$If l 4 \ N F25 8 !
t 0 4 4
l a yt bl
$ d $If gd bl E 6 6
$ d gd kdg $$If l 4 M \ N F25 8 !
t 0 4 4
l a yt_
$ d $If gd bl D W d H kdh $$If l F N #5 f (
t 0 4 4
l a yt1. $
$ d $If a$gd1.
5d gdB$6 / R ] 6 s t
$ d $If ^ gd1.
$ d $If gd r
& F!
$ d $If gdB$6
& F!
$ d $If gd1.
$ d $If gd1. t u ~ n W W W B W
< $ d $If gd1. $
$ d $If a$gd1. kd+ $$If l F N #5 f (
t 0 4 4
l a yt1.
] T @ @ @ @
$ d $If gd1. $If gdq! kd $$If l \ N F25 8 !
t 0 4 4
l a yt1. ! ! ! ! ! ! ! ! ! $
$ d $If a$gd1.
$ d $If gd1. d $7$ 8$ H$ If gd1. ! ! ! ! S D : d gdq!
$ d gd kd $$If l 4 \ N F25 `8 `! `
t 0 4 4
l a p
yt1. ! " " 9" :" " " W C C
$ d $If gd1. kd
$$If l F N #5 f (
t 0 4 4
l a yt1. $
$ d $If a$gd1. " " " " " $# ]# # # # $ '$ c$ n
$ d $If ^`gd1.
& F
$ d $If ^gd1.
$ d $If gd""
& F
$ d $If ^gd1.
& F
$ d $If gdq!
$ d $If gd7 " " # $ e$ n$ $ $ $ $
% % #% $% :% ;% Y% Z% m% v% w% x% z% % % % % % % % % % % % % ķqķdd h~ h r 5B*ph j zh~ hq! B*ph j h~ hq! B*ph j h~ hq! B*ph j oh~ hq! B*ph j nh~ hq! B*ph h~ hq! 5B*ph h~ h7 5B*ph h~ h"" 5B*ph h~ h"" B*ph h~ hq! B*ph h~ h7 B*ph "c$ d$ e$ n$ $ R ; '
$ d $If gd"" $
$ d $If a$gd"" kd $$If l F N #5 f (
t 0 4 4
l a yt1.
$ d $If ^`gd1. $ $ $ :% m% v%
< $ d $If gd1. $
$ d $If a$gd1. v% w% x% y% z% % ] F 2 2 2
$ d $If gd1. $
$ d $If a$gd1. kdu $$If l \ N F25 8 !
t 0 4 4
l a yt1. % % % % % % % % % % % % % % % % % & & & ( ( ( ( (
$ d $If gdq!
$ d $If gd1. % & ( Z( ( ( ( ( ( ( ( ( {) |) ~) ) ) ) ) ) ) N* W* * * * ·ߡ~p߷bWJWJW h~ h"" 6B*ph h~ h"" B*ph j nh~ h7 B*ph j nh~ hq! B*ph h~ hq! 5B*ph *h~ h7 B*^J fH ph q
*h~ h r B*^J fH ph q
h~ h7 B*ph h~ hq! 6B*]^J ph h~ hq! B*^J ph h~ hq! B*ph *h~ hq! B*^J fH ph q
( z) {) |) }) ~) ) ) ) ) ) ) ) $
$ d $If a$gd7 $
$ d $If a$gd1.
$ d $If gd1.
$ d $If gd7 ) ) + + + + S ? ? ? ?
$ d $If gd1. kdX
$$If l 4 \ N F25 `8 `! `
t 0 4 4
l a p
yt"" * * 8+ ?+ + + *, - - - - - - - - - .
. . ). *. . . . . . . 0 0 "0 %0 50 60 εçÙË}rrererXr h~ h r 5B*ph h~ h r 6B*ph h~ h r B*ph j zh~ h[ B*ph j h~ h[ B*ph j h~ h[ B*ph j oh~ h[ B*ph j nh~ h[ B*ph h~ h[ B*ph h~ h[ 5B*ph h~ hq! 5B*ph h~ h"" B*ph h~ h"" 5B*ph + + + + + Y > * *
$ d $If gd1. $
$ d $If ^ a$gd1. kdf $$If l 4 l\ N F25 8 !
t 0 4 4
l a yt1. + + + + + E 6 , d gd[
$ d gdq! kdm $$If l 4 < \ N F25 8 !
t 0 4 4
l a yt1.
$ d $If gd1. + + + , , *, +,
$ d $If gd1. $
$ d $If a$gd[ $
$ d $If a$gd1.
5d gd[ +, ,, {, , , , , - p \ E E E E \
& F
$ d $If gd1.
$ d $If gd1. kdn $$If l F N #5 f (
t 0 4 4
l a yt1. - /- V- - - - - - \ E E E $
$ d $If a$gd1. kd, $$If l F N #5 f (
t 0 4 4
l a yt1.
$ d $If gd1. - - . ). *. 3 kd $$If l \ N F25 8 !
t 0 4 4
l a yt1. $
$ d $If a$gd1.
< $ d $If gd1. *. #0 $0 %0 -0 50 60 70 0 0 1 1 1 1 $
$ d $If a$gd1.
$ d $If gd r
$ d $If gd1.
60 70 0 0 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 P5 l5 x9 z9 : : f: g: i: x: ; ; ; ; ; 꾰zzqzzzqzg^zz h bl hFE ^J h bl hFE 5^J h bl hFE 0J j h bl hFE U h bl hFE h bl hFE 5h h[ 5 h h[ h~ h[ 5B*ph j nh~ h[ B*ph h~ h[ B*ph *h~ h r B*^J fH ph q
h~ h r B*ph *h~ h[ B*^J fH ph q
#1 1 1 1 U > ' $
$ d $If a$gd[ $
$ d $If a$gd1. kd $$If l 4 \ N F25 `8 `! `
t 0 4 4
l a p
yt1. 1 1 1 1 1 1 H 1
& F
$ d $If gd1. kd $$If l 4 Z\ N F25 8 !
t 0 4 4
l a yt1.
$ d $If gd1. 1 1 1 1 1 1 1 H 9 9
$ d gd[ kd $$If l 4 \ N F25 8 !
t 0 4 4
l a yt1.
$ d $If gd1. 1 1 1 P5 Q5 h: i: l W W 8 8 $
< $ d $s&P#$/ If a$gdFE d $s&P#$/ If gdFE t kd $$If l y 5H6
t
6Ps 0 6 4 4
l a ytFE $
< $ d $s&P#$/ If a$gdFE i: : : : ; ; < < < U t kd $$If l 5 H6
t
6Ps 0 6 4 4
l a ytFE
< $ d $s&P#$/ If gdFE d $s&P#$/ 7$ 8$ H$ If gdFE ; < < < < $< &< S< T< < < < = = R= S= U= f= |> }> > > $? %? &? '? (? H? I? J? V? ? ? ? ? ? ? ? ? ƻƻui h0i hc 0J 5^J hc hc 5^J j hc 5U^J
hc 5^J h bl hc 0J hc hFE h bl hFE 0J h bl hFE B*PJ ^J ph333 h bl hFE PJ ^J h bl hFE 5PJ ^J h bl hFE 5 h bl hFE h bl hFE ^J j h bl hFE Uh bl hFE 0J ^J &< $< %< &< < T= U= l W B W W d- $s&P#$/ If gdFE d $s&P#$/ If gdFE t kd1 $$If l 5H6
t
6Ps 0 6 4 4
l a ytFE $
< $ d $s&P#$/ If a$gdFE U= &? '? (? ? ? ? ? S t kd $$If l " 5 H6
t
6Ps 0 6 4 4
l a ytFE d $s&P#$/ If gdFE d $If gdc d $s&P#$/ If gdFE ? ? ? ? ? ] * 2 $
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If a$gdFE t kd} $$If l $ 6C7
t
6P 0 C76 4 4
l a ytFE $
< $ d $&P#$/ If a$gdFE
$ d gd ? ? ? ? @ EA XA B C CF jF OG PG G G G G G G G G G G %H &H IH JH ZH [H H H +I ,I -I I I I I I I I ·謟謁uu謁u h bl hFE 5PJ ^J h bl hFE 0J ^J h bl hFE ^J h bl hFE 5^J h bl hFE 0J PJ ^J j h bl hFE Uh bl hFE PJ ^J h bl hFE 5PJ \^J h bl hFE B*ph h bl hFE 5B*ph h bl hFE h bl hFE 5h h"G 5 (? ? CA EA ZB B B B CF h h h 3
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If ^gdFE /
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If gdFE 2 $
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If a$gdFE CF G G G o P $
< $ d $&P#$/ If a$gdFE t kd& $$If l 6 C7
t
6P 0 C76 4 4
l a ytFE d d d $&P#$/ @&If [$\$gdFE G G G H H ,I I s ^ ^ I ^ d- $&P#$/ If gdFE d $&P#$/ If gdFE $d $&P#$/ If a$gdFE t kd $$If l o 6 C7
t
6P 0 C76 4 4
l a ytFE I I L L L L a R
$ d gd t kd $$If l 6 C7
t
6P 0 C76 4 4
l a ytFE d $&P#$/ If gdFE d $&P#$/ If gdFE I I K K K PL QL L L L L L L L L L L L NM M M M P P Q Q Q R R ]R ^R _R `R aR kR lR R S ʻӫӠӠʠӳyl h bl hFE B*^J ph333 h bl hFE 5KH$ PJ ^J h bl hFE 5PJ ^J h bl hFE 5B*ph h bl hFE B*ph h h 5h bl hFE 5 h bl hFE B*PJ ^J ph f h bl hFE 0J h bl hFE j h bl hFE Uh bl hFE PJ ^J h bl hFE B*PJ ^J ph333 %L L L M M O P l < < < < /
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If gdFE t kd9 $$If l y 5H6
t
6P 0 6 4 4
l a ytFE $
< $ d $&P#$/ If a$gdFE P P _R `R aR F t kd $$If l F 5 H6
t
6P 0 6 4 4
l a ytFE d $&P#$/ If gdFE /
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If gdFE aR kR lR (T )T T l W W W d $&P#$/ If gdc t kd $$If l o 5H6
t
6P 0 6 4 4
l a ytFE $
< $ d $&P#$/ If a$gdFE S S S S S %T &T IT JT KT WT T T T T T T T T T T T T T U EV XV ƺʰʺʕ݀xppeT h bl hFE 5B*PJ ^J ph333 h bl hFE B*ph h bl hFE 5h h 5 h h h bl hFE 5KH$ PJ ^J h bl hFE B*]^J ph333 h0i hc 0J 5^J hc hc 5^J j hc 5U^J hc
hc 5^J h bl hFE 0J ]^J h bl hFE j h bl hFE U h bl hFE 6B*]^J ph333 T T T T T T T g X X X
$ d gd t kd< $$If l 5 H6
t
6P 0 6 4 4
l a ytFE $ d d d $&P#$-D / @&If M
[$\$gdFE T T T T DV EV l < < /
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If gdFE t kd $$If l y 5H6
t
6P 0 6 4 4
l a ytFE $
< $ d $&P#$/ If a$gdFE EV lW W W (Y *Y +Y ,Y F t kd $$If l F 5 H6
t
6P 0 6 4 4
l a ytFE /
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If gdFE d $&P#$/ If gdFE XV lW W W ^X _X X X &Y 'Y *Y +Y ,Y 7Y 8Y lY Y Y JZ KZ Z Z Z Z [ [ !\ "\ Z\ [\ \\ ]\ }\ ~\ \ \ \ \ \ ˹˹Ħ֛珈xnx hc hc 5^J j hc 5U^J hc
hc 5^J h bl hFE 5PJ ^J h bl hFE PJ ^J h bl hFE 5h bl hFE B*ph h bl hFE 0J ^J h bl hFE j h bl hFE U h bl hFE 5B*PJ ^J ph333 h bl hFE 0J h bl hFE B*PJ ^J ph333 &,Y 6Y 7Y 8Y Z Z \\ ]\ l W W B W d $&P#$/ If gdFE d- $&P#$/ If gdFE t kd9 $$If l 5 H6
t
6P 0 6 4 4
l a ytFE $
< $ d $&P#$/ If a$gdFE \ ] ]
] ] ]
] ] ] ] ] (] )] 9] _ ` a a a a %b &b 'b (b )b 3b 5b ab cb fb b b c »xlaRa h bl hFE B*PJ ^J ph333 h bl hFE PJ ^J h bl hFE 5PJ ^J h bl hFE 0J j h bl hFE Uh bl hFE B*ph h bl hFE 5B*ph h bl hFE 5h h 5 h h h bl hFE h bl hc 5PJ ^J hc 5PJ ^J hFE 5PJ ^J
hc 5^J j hc 5U^J h0i hc 0J 5^J ]\
] ] ]
] ] ] ] ] h Y Y Y
$ d gd t kd $$If l ' 5 H6
t
6P 0 6 4 4
l a ytFE d- $&P#$/ If gdFE d $If gdc ] ] '] (] )] _ l < /
& 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If gdFE t kd $$If l y 5H6
t
6P 0 6 4 4
l a ytFE $
< $ d $&P#$/ If a$gdFE _ _ _ 'b (b .
# 0`
P@ d $&P#$/ 1$ 7$ 8$ H$ If gdFE 5
& F
# 0`
P@ vd $&P#$/ 1$ 7$ 8$ H$ If ^vgdFE (b )b 3b l $
< $ d $&P#$/ If a$gdFE t kd(! $$If l F 5 H6
t
6P 0 6 4 4
l a ytFE 3b 4b 5b b ec fc I J v a v v v v L d $&P#$/ If gdFE d- $&P#$/ If gdFE d $&P#$/ If gdFE t kd! $$If l 5 H6
t
6P 0 6 4 4
l a ytFE c c cc dc fc yc {c c G H I J ` 8 9 : rmha]Q j hc 5U^J hc
hc 5^J hc 5 hFE 5-h bl hFE B*CJ OJ PJ QJ ^J aJ ph333 h bl hFE PJ ^J h bl hFE 5PJ ^J h bl hFE 5h bl hFE 0J h bl hFE B*^J ph333 Uh bl hFE ^J h bl hFE 5B*^J ph333 h bl hFE 5^J h bl hFE h bl hFE 0J ^J j h bl hFE U simple interactive from the University of Utah's Genetic Science Learning Center gives you the opportunity to see how various small things compare to one another. HYPERLINK "http://thinkfinity.org/%09%09%09http:/sciencenetlinks.com/tools/cell-size-and-scale/" \t "_blank"http://sciencenetlinks.com/tools/cell-size-and-scale/
DISCOVERING GALLON MAN: In this lesson, one of a multi-part unit from Illuminations, students experiment with units of liquid measure used in the customary system of measurement. They also practice making conversions of length and weight. HYPERLINK "http://thinkfinity.org/%09%09%09http:/illuminations.nctm.org/LessonDetail.aspx?ID=L513" \t "_blank"http://illuminations.nctm.org/LessonDetail.aspx?ID=L513
Engage NY Grade 6 Module 1 Link: HYPERLINK "http://www.engageny.org/resource/grade-6-mathematics-module-1" http://www.engageny.org/resource/grade-6-mathematics-module-1
Archdiocese of New York Page PAGE \* MERGEFORMAT 10 2014-2015
h ^ d gdCP t kd|" $$If l 5 H6
t
6P 0 6 4 4
l a ytFE d $If gdc d $&P#$/ If gdFE
P R S »xc[WS h9 h#_ h[ CJ aJ (j h hU CJ UaJ mH nH u h2 CJ aJ mH nH uh h CJ aJ j h hU CJ UaJ h bl CJ aJ h CJ aJ h" j h" U h h h bl hFE h bl hc 5 hc 5h0i hc 0J 5^J j hc 5U^J hc hc 5^J
hc 5^J d gdCP
H$p5ABgd bl d gddR h h h" 5 1h 0:p G = /!8"8#8$8% 5 1h 0:p G = /!8"8#8$8% 5 1h 0:p G = /!8"8#8$8% 5 1h 0:p G = /!8"8#8$8% 5 1h 0:p G = /!8"8#8$8% $$If !v h5 55#v :V l
t 0 6, 5 / yt bl $$If !v h5 55#v :V l G
t 0 65 / / yt bl $$If !v h5 H6#v H6:V l '
t 0 65 H6/ yt bl $$If !v h5 5f5(#v #vf#v(:V l
t 0 , 5 5f5(/ yt bl $$If !v h5 5f5(#v #vf#v(:V l
t 0 5 5f5(/ / yt bl $$If !v h5 585!5#v #v8#v!#v:V l
t 0 , 5 585!5/ / yt bl $$If !v h5 585!5#v #v8#v!#v:V l 4
t 0 +++5 585!5/ / / p
yt bl $$If !v h5 585!5#v #v8#v!#v:V l 4
t 0 +++, 5 585!5/ / / yt bl $$If !v h5 585!5#v #v8#v!#v:V l 4M
t 0 +++5 585!5/ / / yt_ $$If !v h5 5f5(#v #vf#v(:V l
t 0 , 5 5f5(/ yt1. $$If !v h5 5f5(#v #vf#v(:V l
t 0 5 5f5(/ / yt1. $$If !v h5 585!5#v #v8#v!#v:V l
t 0 , 5 585!5/ / yt1. $$If !v h5 585!5#v #v8#v!#v:V l 4
t 0 +++5 585!5/ / / p
yt1. $$If !v h5 5f5(#v #vf#v(:V l
t 0 , 5 5f5(/ yt1. $$If !v h5 5f5(#v #vf#v(:V l
t 0 5 5f5(/ / yt1. $$If !v h5 585!5#v #v8#v!#v:V l
t 0 , 5 585!5/ / yt1. $$If !v h5 585!5#v #v8#v!#v:V l 4
t 0 +++5 585!5/ / / p
yt"" $$If !v h5 585!5#v #v8#v!#v:V l 4l
t 0 +++, 5 585!5/ / / yt1. $$If !v h5 585!5#v #v8#v!#v:V l 4<
t 0 +++5 585!5/ / / yt1. $$If !v h5 5f5(#v #vf#v(:V l
t 0 , 5 5f5(/ yt1. $$If !v h5 5f5(#v #vf#v(:V l
t 0 5 5f5(/ / yt1. $$If !v h5 585!5#v #v8#v!#v:V l
t 0 , 5 585!5/ / yt1. $$If !v h5 585!5#v #v8#v!#v:V l 4
t 0 +++5 585!5/ / / p
yt1. $$If !v h5 585!5#v #v8#v!#v:V l 4Z
t 0 +++, 5 585!5/ / / yt1. $$If !v h5 585!5#v #v8#v!#v:V l 4
t 0 +++5 585!5/ / / yt1. $$If !v h5 H6#v H6:V l y
t
6Ps 0 6 , 5 H6/ ytFE $$If !v h5 H6#v H6:V l
t
6Ps 0 6 5 H6/ / ytFE $$If !v h5 H6#v H6:V l
t
6Ps 0 6 , 5 H6/ ytFE $$If !v h5 H6#v H6:V l "
t
6Ps 0 6 5 H6/ ytFE $$If !v h5 C7#v C7:V l $
t
6P 0 C76 , 5 C7/ ytFE $$If !v h5 C7#v C7:V l
t
6P 0 C76 5 C7/ / ytFE $$If !v h5 C7#v C7:V l o
t
6P 0 C76 5 C7/ / ytFE $$If !v h5 C7#v C7:V l
t
6P 0 C76 5 C7/ / ytFE $$If !v h5 H6#v H6:V l y
t
6P 0 6 , 5 H6/ ytFE $$If !v h5 H6#v H6:V l F
t
6P 0 6 5 H6/ / ytFE $$If !v h5 H6#v H6:V l o
t
6P 0 6 , 5 H6/ ytFE $$If !v h5 H6#v H6:V l
t
6P 0 6 5 H6/ ytFE $$If !v h5 H6#v H6:V l y
t
6P 0 6 , 5 H6/ ytFE $$If !v h5 H6#v H6:V l F
t
6P 0 6 5 H6/ / ytFE $$If !v h5 H6#v H6:V l
t
6P 0 6 5 H6/ ytFE $$If !v h5 H6#v H6:V l '
t
6P 0 6 5 H6/ ytFE $$If !v h5 H6#v H6:V l y
t
6P 0 6 , 5 H6/ ytFE $$If !v h5 H6#v H6:V l F
t
6P 0 6 5 H6/ / ytFE $$If !v h5 H6#v H6:V l
t
6P 0 6 5 H6/ ytFE $$If !v h5 H6#v H6:V l
t
6P 0 6 5 H6/ ytFE j! 6 6 6 6 6 6 6 6 6 v v v v v v v v v 6 6 6 6 6 6 > 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 h H 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 2 0 @ P ` p 2 ( 0 @ P ` p 0 @ P ` p 0 @ P ` p 0 @ P ` p 0 @ P ` p 0 @ P ` p 8 X V ~ OJ PJ QJ _HmH nH sH tH J ` J w N o r m a l d CJ _HaJ mH sH tH d 2 d Kx H e a d i n g 3 d d d @&[$\$ 5CJ OJ PJ QJ \^J aJ D A` D
D e f a u l t P a r a g r a p h F o n t R i@ R 0 T a b l e N o r m a l 4
l 4 a ( k (
0 N o L i s t B B tE 0 P l a c e h o l d e r T e x t B*ph R R tE 0 B a l l o o n T e x t d CJ OJ QJ ^J aJ N N tE 0 B a l l o o n T e x t C h a r CJ OJ QJ ^J aJ t #t tE
T a b l e G r i d 7 :V 0 d @ @ 2@ x
L i s t P a r a g r a p h ^m$ > B> dR 0 H e a d e r d H$ . Q. dR 0 H e a d e r C h a r > @ b> dR 0 F o o t e r d H$ . q. dR 0 F o o t e r C h a r 6 U@ 6 H y p e r l i n k >*B*ph ` ` D
3 N Y C T e x t d ( F @8 CJ OJ PJ QJ ^J B B c> a p p l e - c o n v e r t e d - s p a c e ` ^ ` Kx 0 N o r m a l ( W e b ) d d d [$\$ CJ OJ PJ QJ ^J aJ Z Z Kx m a t h j a x 1 2 56;<@ CJ Z\]aJ r @ R R Kx H e a d i n g 3 C h a r 5CJ OJ PJ QJ \^J aJ d O d ( n y - l i s t - b u l l e t s
& F# d < < 1$ B*PJ ^J ph# X O X _ n y - p a r a g r a p h d x x 1$ B*PJ ^J ph# T T _ n y - p a r a g r a p h C h a r B*CJ PJ ^J aJ ph# PK ! [Content_Types].xmlj0Eжr(Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi} ;~@(Hu* Dנz/0ǰ $ X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭? PK ! ֧ 6 _rels/.relsj0 }Q%v/C/} (h"O
= C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_ 6LR7`0̞O,En7Lib/Se е PK ! ky theme/theme/themeManager.xml M
@}w7c(Ebˮ CAǠҟ7՛K
Y,
e.|,H ,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+&
8 PK ! P theme/theme/theme1.xmlYOo6w toc'vuر-Mn iP@I}úama[إ4:l ЯGRX^6؊>$ !)O^rC$y@ /yH*)UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSe bORD۫qu gZo~ٺlAplxpT0+[}`j zA V2Fi@qv֬5\|ʜ̭NleXd sjcs7f
W+Ն7` g ȘJj|h(KD-
dXiJ؇(x$( :;˹! I_TS 1?E ??ZBΪmU/ ?~xY'y5g&/ɋ>GMGeD3Vq%'#q$8K )fw 9:ĵ
x}rxwr:\TZaG*y8IjbRc|XŻǿI
u3KGnD 1NIBs
RuK>V.E L+M2#'fi ~V vl{u8z H
* :( W ☕
~JTe\O*tHGHY }KNP*ݾ˦ TѼ9/#A7qZ $*c?qUnwN%Oi4 =3ڗP
1Pm \\9Mؓ2aD];Yt\[x]}Wr|]g-
eW
)6-rC Sj
id DЇAΜIqbJ#x꺃 6k#ASh&ʌt(Q% p%m&]caS l=X\P1Mh9MVdDAaVB[݈fJíP|8 քAV^f
Hn- "d>znNJ ة>b&2vKyϼD:,AGm\nziÙ .uχYC6OMf3or$5N HT[XF64T,ќM0E)`#5XY`פ ;%1U٥m;R>QD DcpU'&LE/pm%]8firS4d 7y\`JnίI R 3U~7+#m qBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCM m<.vp IYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07% < ҍ PK !
ѐ ' theme/theme/_rels/themeManager.xml.relsM
0wooӺ&݈Э5
6?$Q
,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{ P8g/ ]QAsم(#L[ PK- ! [Content_Types].xmlPK- ! ֧ 6 + _rels/.relsPK- ! ky theme/theme/themeManager.xmlPK- ! P theme/theme/theme1.xmlPK- !
ѐ ' theme/theme/_rels/themeManager.xml.relsPK ]
w' H@ H P %[ 7 n Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q T " ] A " % * 60 ; ? I S XV \ c 2 4 7 9 > B M R U ] c g l p t v | . ^ a t ! ! " c$ $ v% % ( ) + + + +, - - *. 1 1 1 1 i: < U= ? ? CF G I L P aR T T EV ,Y ]\ ] _ (b 3b 3 5 6 8 : ; < = ? @ A C D E F G H I J K L N O P Q S T V W X Y Z [ \ ^ _ ` a b d e f h i j k m n o q r s u w x y z { " ` o* * * v- - . T/ / / `0 0 1 62 2 2 3 O3 3 ; N; ; ; < < < := = ?
@ C@ KE E F _G G G H PH H L L L M N [N lO O P 8P P P cU U U oV V W W JX X rY Y Z ?Z Z Z %[ XXXXXXXXXXXXXXXXXXXXXXX) A D T ! L # A A @ 0 (
B
S ? 1 1 2 3 Z Z Z Z Z Z Z Z Z Z Z [ #[ &[
: ': Q Q Z Z Z Z Z Z Z Z Z #[ &[ 3 3 3 3 a ] ^ a c # :$ <$ % % & k' k' w' w' 3 3 3 3 3 3 G@ G@ H H P P Z Z Z Z Z Z Z Z [ [ [ [ [ ![ &[ $ 9?I"b L ܮ} m>
| }4 (n+M JJL$_ 5QC!J o/P%DD a_)6 D\I*D -10 >J3x. [15 9( 4r;\؊ \Awڊ SMI"b ZS.I rVFv taX00h ,_~Z"tƱ 'tc:Pz Tet8 sAk /uk j-3lR4O `3m VOpvxL ZWpk8 J oq J3 -1 j-3l =[w D\I* rV \A 5QC! %u m>
ZWp J ##x a_) {`~ 9? VOp sAk L Te (n+ $ $ r 2^ : 8f L ݒ E 3)M S+Hu> $K^l i$K J .xK9 \ `$ hcPG 9P
f O O .] XafX ? yQ P
'63 # `/D 8Z_&*%- & SMn oS e bk
A4 o
8b ax
*Zw W0
?ww sPPn 0hc J Q B\ J dnI"`, ; 0UGF Adp" ,T.| "#(* {
Z| 8bS+H cHA +E 22 u>b1 g$ , J oS PG 3)M+_% ]?xV of `TH >M sP ^)
K9 Q ? HA B [3 Q! ( {!Ev i!ET dp"zYY $m"c O O `$ 3$!6s9 +_% hZ'8 ] (
7 n F/ w = _ ^n FE O WA J wY t/ #{ x
[ 2 ; ; >3 3\ Z 7 "" | $ X3 4| #_ b 66 ?: H ' { ( X 1. 8 P c D : E U Y Z 9 g 7 c> S -' Z Z @ d
, - 9W %[ ` @ ` ` 0 @ ` & ` P @ ` 8 ` t @ ` @ U n k n o w n G * Ax T i m e s N e w R o m a n 5 S y m b o l 3. * Cx A r i a l A. A r i a l N a r r o w ; W i n g d i n g s ? W i n g d i n g s 2 7. @ C a l i b r i ;. * Cx H e l v e t i c a 5. . [` ) T a h o m a K M y r i a d P r o C o r b e l ?= * Cx C o u r i e r N e w A $ B C a m b r i a M a t h " 1 h P*P*1
DM
.
DM
. 88 20 Z Z ;Q HP $P tE * ! x x F e d E x O f f i c e l o c a l u s e r $
! " # Oh +'0 < x
$ , 4 FedEx Office Normal.dotm localuser 2 Microsoft Office Word @ @ Ʒ8]@ *d@ *d
DM ՜. +,D ՜. +,P h p
( FedEx Office and Print Services, Inc. . Z Title 8 @ _PID_HLINKS A D T B > h t t p : / / w w w . e n g a g e n y . o r g / r e s o u r c e / g r a d e - 6 - m a t h e m a t i c s - m o d u l e - 1 : w ? W h t t p : / / t h i n k f i n i t y . o r g / % 0 9 % 0 9 % 0 9 h t t p : / i l l u m i n a t i o n s . n c t m . o r g / L e s s o n D e t a i l . a s p x ? I D = L 5 1 3 F < U h t t p : / / t h i n k f i n i t y . o r g / % 0 9 % 0 9 % 0 9 h t t p : / s c i e n c e n e t l i n k s . c o m / t o o l s / c e l l - s i z e - a n d - s c a l e / _ 9 Q h t t p : / / l e a r n z i l l i o n . c o m / l e s s o n s / 5 9 2 - c o n v e r t - m e a s u r e m e n t - u n i t s - u s i n g - r a t i o - t a b l e s ~ 7 6 8 h t t p : / / i l l u m i n a t i o n s . n c t m . o r g / L e s s o n D e t a i l . a s p x ? i d = U 1 4 8 D T 3 > h t t p : / / w w w . e n g a g e n y . o r g / r e s o u r c e / g r a d e - 6 - m a t h e m a t i c s - m o d u l e - 1 ? p 0 W h t t p : / / t h i n k f i n i t y . o r g / % 0 9 % 0 9 % 0 9 h t t p : / i l l u m i n a t i o n s . n c t m . o r g / L e s s o n D e t a i l . a s p x ? i d = L 8 4 9 m ? - W h t t p : / / l e a r n z i l l i o n . c o m / l e s s o n s / 5 9 6 - f i n d - t h e - p a r t - w h e n - t h e - p e r c e n t - a n d - t o t a l - a r e - k n o w n b y * g h t t p : / / t h i n k f i n i t y . o r g / % 0 9 % 0 9 % 0 9 h t t p : / i l l u m i n a t i o n s . n c t m . o r g / L e s s o n s / O n F i r e / O n F i r e - A S - P e r S l o p e T o o l . p d f D T ' > h t t p : / / w w w . e n g a g e n y . o r g / r e s o u r c e / g r a d e - 6 - m a t h e m a t i c s - m o d u l e - 1 Q S $ : h t t p : / / w w w . t e a c h e r s d o m a i n . o r g / r e s o u r c e / s c l 1 0 . p l r . m o d u l e 1 / M R ! i h t t p : / / t h i n k f i n i t y . o r g / % 0 9 % 0 9 % 0 9 h t t p : / i l l u m i n a t i o n s . n c t m . o r g / L e s s o n s / P a p e r P o o l / P a p e r P o o l - A S - A d v a n c e d . p d f 3 r W h t t p : / / t h i n k f i n i t y . o r g / % 0 9 % 0 9 % 0 9 h t t p : / i l l u m i n a t i o n s . n c t m . o r g / L e s s o n D e t a i l . a s p x ? I D = L 2 8 1 % : H h t t p : / / l e a r n z i l l i o n . c o m / l e s s o n s / 8 3 9 - u n d e r s t a n d - r a t e s - a s - a - t y p e - o f - r a t i o E G h t t p : / / w w w . b r a i n p o p . c o m / @ B 9 h t t p : / / w w w . i l l u s t r a t i v e m a t h e m a t i c s . o r g / i l l u s t r a t i o n s / 5 4 9 D T > h t t p : / / w w w . e n g a g e n y . o r g / r e s o u r c e / g r a d e - 6 - m a t h e m a t i c s - m o d u l e - 1 : t W h t t p : / / t h i n k f i n i t y . o r g / % 0 9 % 0 9 % 0 9 h t t p : / i l l u m i n a t i o n s . n c t m . o r g / L e s s o n D e t a i l . a s p x ? I D = L 5 1 0 o s P h t t p : / / l e a r n z i l l i o n . c o m / l e s s o n s / 5 8 1 - v i s u a l i z e - p a r t t o t o t a l - r a t i o s - u s i n g - p i c t u r e s t y 8 h t t p : / / w w w . i l l u s t r a t i v e m a t h e m a t i c s . o r g / i l l u s t r a t i o n s / 7 6 5 . O h t t p : / / l e a r n z i l l i o n . c o m / l e s s o n s / 5 8 0 - v i s u a l i z e - p a r t t o p a r t - r a t i o s - u s i n g - p i c t u r e s : 2 # h t t p : / / w w w . r e t h i n k m a t h e m a t i c s . c o m / D T > h t t p : / / w w w . e n g a g e n y . o r g / r e s o u r c e / g r a d e - 6 - m a t h e m a t i c s - m o d u l e - 1
! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~ R o o t E n t r y F d D a t a
# 1 T a b l e W o r d D o c u m e n t S u m m a r y I n f o r m a t i o n ( D o c u m e n t S u m m a r y I n f o r m a t i o n 8 , C o m p O b j y
F' Microsoft Office Word 97-2003 Document
MSWordDoc Word.Document.8 9q