7th grade eureka module 2 b. kasandbox. Module 5. org G7-M2-SE-1. Engage NY Eureka Math 7th Grade Module 2 Lesson 5 Answer Key Eureka Math Grade 7 Module 2 Lesson 5 Example Answer Key. OVERVIEW. C Eureka Math. Grade 2 Module 7 Problem Solving with Length, Money, and Data. Rational Numbers Topic A - Addition and Subtraction of Integers and Rational Numbers Engage NY Eureka Math 7th Grade Module 2 Lesson 13 Answer Key Eureka Math Grade 7 Module 2 Lesson 13 Example Answer Key. Lesson 2 7•2 Lesson 2: U sing the umber ine to Model the A ddition of ntegers This video covers concepts taught in Module 2, Lesson 10 of 7th grade Eureka Math (Engage NY). 1 through 6, in 6 volumes Module 1 : Ratios and proportional relationships -- Module 2 : Rational numbers -- Module 3 : Expressions and equations -- Module 4 : Percent and proportional relationships -- Module 5 : Statistics and probability -- Module 6 : Geometry Parent Overview - 7th Grade Eureka Math. Module 3. Explain your choice using pictures or words. Eureka Math and EngageNY resource for 7th grade. 2015 S. Example 2: A Numeric Approach to Finding a Part, Given a Percent of the Whole In Ty’s English class, 70% of the students completed an essay by the due date. GRADE . TASK: Using the above information, semiannual statements, register, and beginning This book may be purchased from the publisher at eureka-math. 2, 7. AP Statistics. Mid-Module Assessment Task 7•2 Module 2: Rational Numbers Name Date 1. Using the values from the chart in Problem 1, which is the least and which is the greatest? Explain how you arrived at your answers. Engage NY Eureka Math 7th Grade Module 2 Lesson 18 Answer Key Eureka Math Grade 7 Module 2 Lesson 18 Exercise Answer Key. 10 9 8 7 6 5 4 3 2 1 G7-M1-UTE-1. This video covers concepts taught in Module 2, Lesson 15 of 7th grade Eureka Math (Engage NY). She started counting at 10, and then she counted until she was on the number -4 on the number line. She started counting at 10, and then This work is derived from Eureka Math ™ and licensed by Great Minds. The temperature in the morning Eureka Math, Learn Practice Succeed, Grade 7 Module 2, c. Introduction to This work by EMBARC. Answer: 3 + 5 = 8. C. Statistics and Probability . Multi-Digit Whole Multi-Digit Whole Number and Decimal Fraction Operations. NS. Engage NY Eureka Math 7th Grade Module 2 Lesson 23 Answer Key Eureka Math Grade 7 Module 2 Lesson 23 Exercise Answer Key. Rational Numbers. Answer: Engage NY Eureka Math 7th Grade Module 4 Lesson 2 Answer Key Eureka Math Grade 7 Module 4 Lesson 2 Example Answer Key. Find the scale factor Grade 7 Module 2 Topic C Lesson 17 Exit Ticket Qty: 30 Lesson 18 Exit Ticket Qty: 30 Lesson 19 Exit Ticket Qty: 30 ©2015 Great Minds. EngageNY Math Grade 7 Module 4 Answer Key | Eureka Math 7th Grade Module 4 Answer Key. Engage NY Eureka Math 7th Grade Module 2 Lesson 8 Answer Key Eureka Math Grade 7 Module 2 Lesson 8 Example Answer Key. In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers ( 6. ISBN 978-1-64054-356-0 Printed in the U. . Grade 7 Student texts, mod. Student workbook - Mod 1. Lead Eureka Math® Grade 7 Supplemental Materials April 2020. Step 2: Count the number of units from the endpoint you started on to the other endpoint. 7 . Transitioning from Integer Multiplication Rules to Integer Division Rules Students make an integer multiplication facts bubble by expanding upon the four related math facts they wrote down. The numbers used throughout this example are a sample response. 2 Table of Contents Module and Topic Level Materials Grade 7 Module 3 Overview Narrative, pp. Eureka Math 2 Equip™ (Level 1–Algebra I) begins with a diagnostic Pre-Module digital assessment that identifies a student’s last point of success with the essential Engage NY Eureka Math 7th Grade Module 2 Lesson 2 Answer Key Eureka Math Grade 7 Module 2 Lesson 2 Example Answer Key. Topic A: Mental Strategies for Multi-Digit Whole N This work by EMBARC. 2015. Grade 7 Module 1; Grade 7 Module 2; Grade 7 Modules 3 & 4; Grade 7 Modules 5 & 6 ; Eureka 8th Grade Spanish Workbook. ** Module 1 - Ratios and Proportions. This is a Eureka Math Affirm has more than 450 assessments for Grade 1 through Precalculus. Skip to content. Lesson 1 Engage NY Eureka Math 7th Grade Module 2 Lesson 10 Answer Key Eureka Math Grade 7 Module 2 Lesson 10 Example Answer Key. Topic quizzes and Mid-Module and End-of-Module Assessments are fully aligned with the Eureka Math assessments. EMBARC is an independent organization and is not affiliated with, or sponsored or endorsed by, Great Minds. The Eureka Math 2 digital platform provides teachers with everything they need to plan, teach, assign work, assess for understanding, and analyze assessment data. Grade 2 Module 8 Collapse all Expand all. Eureka Math Grade 7 Module 4 Percent and Proportional Relationships. General Info. Eureka Math™ Grade 7, Module 2 Student File_A Contains copy-ready classwork and homework as well as templates (including cut outs) This work is derived from Eureka Math ™ and licensed by Great Minds. Using the Commutative and Associative Properties to Efficiently Multiply Quick and easy learning is possible with our Eureka Math Grade 7 Answer Key. Grade 7 General Resources. Teacher Edition. Show and explain your steps. Write the value of your hand in the Total column. Start Round 1 by selecting four cards. Eureka Math Grade 7 Module 6 Teacher Edition FL State Adoption Bid # 3691. Downloadable Resources Page. Step 1: Students construct three similar integer multiplication problems, two problems using one negative Module 1 : Ratios and proportional relationships -- Module 2 : Rational numbers -- Module 3 : Expressions and equations -- Module 4 : Percent and proportional relationships -- Module 5 : Statistics and probability -- Module Lesson 1 : Opposite Quantities Combine to Make Zero 2 7•2 3. Eureka Math Grade 7 Module 5 Lesson 1 Answer Key; Eureka Math Grade 7 Module 5 Lesson 2 Answer Key; Eureka Math Eureka Math. Use one expression per space. Counting On to Express the Sum as Absolute Value on a Number Line. 8th Grade . eureka-math. 0 This video covers concepts taught in Module 2, Lesson 13 of 7th grade Eureka Math (Engage NY). Instruct students to record the values of their cards on the images in Part A. Eureka Math Grade 7 Module 5 Statistics and Probability . John’s father asked him to compare several different cell phone plans and identify which 7th Grade . 2 5 % 2. Go Math Menu Toggle. 7th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Module 6; 8th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Grade 5 Module 2. Eureka Essentials: Grade 2 URL An outline of learning goals, key ideas, pacing suggestions, and more! Teach Eureka Lesson Breakdown Engage NY Eureka Math 7th Grade Module 4 Lesson 13 Answer Key Eureka Math Grade 7 Module 4 Lesson 13 Example Answer Key. 2018 Published by 7th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Module 6; 8th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Grade 7 Module 5 Collapse all Expand all. Find the IXL skills that are right for you below! Module 2. Teacher Edition Eureka Math® Grade 2 Modules 1 & 2 In Grade 2 Module 1, Application Problems begin in Topic B. org G7-M2-TE-1. Tic-Tac-Toe Review Fill in the 9 spaces with one expression from the list below. Example 1: Modeling Addition on the Number Line Complete the steps to find the sum of -2+3 by filling in the blanks. View our PRIVACY POLICY Engage NY Eureka Math 7th Grade Module 2 Lesson 20 Answer Key Eureka Math Grade 7 Module 2 Lesson 20 Task Answer Key. Grade 7 Module 1: Ratios and Proportional Relationships. 2016 2. 7th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Module 6; 8th Grade; Home; Module 1; Module 2; Module 3; Module 4; Grade 5 Module 2 Collapse all Expand all. Use the diagrams below to find the scale factor and then find the area of Engage NY Eureka Math 7th Grade Module 6 Lesson 6 Answer Key Eureka Math Grade 7 Module 6 Lesson 6 Exploratory Challenge Answer Key Use a ruler, protractor, and compass to complete the following problems. Answer: positive There’s exponentially more to Eureka Math 2 than can fit on the pages of a book. org 10 9 8 7 6 5 4 3 2 1 Eureka Math™ Grade 7, Module 5 Teacher Edition. Module 6. Module 1. 2018 Published by Engage NY Eureka Math 7th Grade Module 2 Mid Module Assessment Answer Key Eureka Math Grade 7 Module 2 Mid Module Assessment Task Answer Key. org are unblocked. ISBN 978-1-64054-357-7 Printed in the U. 7 GRADE Mathematics Curriculum GRADE 7 • MODULE 5 Module 5: Statistics and Probability Table of Contents. 10 9 8 7 6 5 4 3 2 1 G7-M2-UTE-1. Example 2: A Numeric Approach to Finding a Part, Given a Percent of the Whole . 1, 7. Set up and solve an equation to find the value of p and r. Online based upon Eureka Math and is licensed under a Creative Commons Attribution Engage NY Eureka Math 7th Grade Module 3 Lesson 21 Answer Key Eureka Math Grade 7 Module 3 Lesson 21 Example Answer Key Example 1: Lateral Area of a Right Prism A right triangular prism, Skip to content. 2018 Published by Eureka Math™ Grade 8 Module 2 Teacher Edition. Exercise 1. Answer: Engage NY Eureka Math 7th Grade Module 2 Lesson 19 Answer Key Eureka Math Grade 7 Module 2 Lesson 19 Example Answer Key. There are 30 students in Ty’s English class. In the space below, create a word problem that involves integer multiplication. 2018 Published by Eureka Math. They each got Module Overview 7•2. ISBN 978-1-64054-359-1 Printed in the U. Students’ answers depend on the cards they pick. org and *. org. Model the equation using straight arrows called vectors on the number line below. 10 9 8 7 6 5 4 3 2 1 G7-M5-UTE-1. Two lines meet at a point that is also the endpoint of a ray. This book may be purchased from the publisher at eureka-math. Follow the steps for each round of play. A. Diamond used a number line to add. 3. Module 3 : Expressions and Equations 1. Use the 8 card and its additive inverse to write a real-world story problem about their sum. Grade 2 Module 2 Collapse all Expand all. Eureka Math. 10 9 8 7 6 5 4 3 2 1 G7-M6-UTE-1. org G7-M4-ETP-P5-1. Grade 7 Module 2: Rational Numbers. Circle the most appropriate tool to measure their throws. 0 At UnboundEd, we walk side-by-side with educators on their professional learning journey, helping them cultivate the mindsets, knowledge, and skills to deliver grade-level, engaging, affirming, and meaningful —GLEAM™— instruction. Exploring Subtraction with the Integer Game Play the Integer Game in your group. Expressions and Equations . Texas Go Math; Big Ideas Math; 7th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Module 6; 8th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Grade 7 Module 6 Collapse all Expand all. Parent Tips - mod 1 topic A. ©2015 Great Minds. *FREE* shipping on qualifying offers. Module 2: Rational Numbers . Exercises Youth Group Trip. Designed with Universal Design for Learning (UDL) at its core, Engage NY Eureka Math 7th Grade Module 2 Lesson 15 Answer Key Eureka Math Grade 7 Module 2 Lesson 15 Exercise Answer Key. com. 7th Grade . Eureka Math Grade 7 Module 5 Topic A Calculating and Interpreting Probabilities. Mathematics Curriculum . S. The Office of Standards and Instruction provides resources to support districts and schools as they develop and implement high-quality, culturally responsive instruction designed to help all students achieve the expectations set forth in the NYS Learning Standards. Grade 2 Module 1 Collapse all Expand all. Samantha and Bill are having a beanbag throwing contest and need to measure each of their throws. 5, 6. This video covers concepts taught in Module 2, Lesson 7 of 7th grade Eureka Math (Engage NY). Place the tail of the • Module 1: Ratios and Proportional Relationships » Module 2: Rational Numbers • Module 3: Expressions and Equations • Module 4: Percent and Proportional Relationships • Module 5: Statistics and Probability • Module 6: Geometry LET’S CHECK IT OUT! MODULE 2 FOCUS In this 23-lesson module, students build on their If you're seeing this message, it means we're having trouble loading external resources on our website. ruler paper clips meter stick centimeter cubes b. Addition and Subtraction of Length Units. e- ureka math. Mid-Module Assessment Task 7•2 Module 2: Rational Numbers Engage NY Eureka Math 7th Grade Module 1 Lesson 2 Answer Key Eureka Math Grade 7 Module 1 Lesson 2 Example Answer Key. All other modules will be in order. Engage NY Eureka Math 7th Grade Module 2 Lesson 16 Answer Key Eureka Math Grade 7 Module 2 Lesson 16 Example Answer Key. → Counting up starting at 0 corresponds to positive ___ numbers. Eureka Math 2 Sets a New Standard for Inclusive Learning . A STORY OF RATIOS 1 ©2015 Great Minds. 1 through 6, in 6 volumes. This test covers all of the standards included in a Eureka assessment. 2) as they collect like terms with rational number coefficients This video covers concepts taught in Module 1, Lesson 2 of 7th grade Eureka Math (Engage NY). kastatic. Exploring Area Relationships. You can use this test as the actual test, a practice test, or a study guide. 3, 7. Engage NY Eureka Math 7th Grade Module 2 Lesson 12 Answer Key Eureka Math Grade 7 Module 2 Lesson 12 Example Answer Key. Eureka Math Grade 7 Module 5 Teacher Edition FL State Adoption Bid # 3691. Grade 7 Module 2 Lessons 1–23 Eureka Math™ Homework Helper 2015–2016. At UnboundEd, we walk side-by-side with educators on their professional learning journey, helping them cultivate the mindsets, knowledge, and skills to deliver grade-level, engaging, affirming, and meaningful —GLEAM™— instruction. 0 This video covers concepts taught in Module 2, Lesson 6 of 7th grade Eureka Math (Engage NY). Place the tail of the arrow on 12. For his birthday, Zack and three of his friends went to a movie. Formula for the Distance Between Two Rational Numbers Find the distance between -3 and 2. Representing Sums of Rational Numbers on a Number Line a. 8. Question 1. Lesson 2 7•2 Lesson 2: U sing the umber ine to Model the A ddition of ntegers Engage NY Eureka Math 7th Grade Module 2 Lesson 17 Answer Key Eureka Math Grade 7 Module 2 Lesson 17 Opening Exercise Answer Key. parent tips - Eureka Math. a. Eureka Math Grade 7 Module 2 Teacher Edition FL State Adoption Bid # 3691. 3-4 the opportunity to practice knowledge of operations with rational numbers gained in Module 2 (7. 2015-16 Lesson 1 : Opposite Quantities Combine to Make Zero 7•2 G7-M2-Lesson 1: Opposite Quantities Combine to Make Zero Positions on the Number Line 1. 1. Unit Conversions This work by EMBARC. Assessments are different from those in the print edition of the curriculum. Parent roadmap **Please note, we will be starting with Module 2 this year, followed by 3, then 1. ISBN 978-1-64054-355-3 Printed in the U. He did the amazing work of converting all the assessments into Google Docs to make customization Engage NY Eureka Math 7th Grade Module 2 Lesson 1 Answer Key Eureka Math Grade 7 Module 2 Lesson 1 Example Answer Key. Items cover Depth of Knowledge levels 1–3. 0 International License. Example 1: Rule for Adding Integers with Same Signs a. Engage NY Eureka Math 7th Grade Module 2 Lesson 3 Answer Key Eureka Math Grade 7 Module 2 Lesson 3 Example Answer Key. i. They contextualize learning as students apply strategies to solving simple add to, take from, put together/take apart problem types using the Read-Draw- Grade 7 Module 2 Topic C Lesson 17 Exit Ticket Qty: 30 Lesson 18 Exit Ticket Qty: 30 Lesson 19 Exit Ticket Qty: 30 ©2015 Great Minds. If you're seeing this message, it means we're having trouble loading external resources on our website. Table of Contents. How long is the arrow that represents 3? Answer: 3 units. I created these tests for my own students. Module 2. Eureka Essentials: Grade 2 URL An outline of learning goals, key ideas, pacing suggestions, and more! Teach Eureka Lesson Breakdown URL. Lesson 2 : S. Eureka Math Grade 7 Module 4 Topic A Finding the Whole. In a complete sentence, describe the relevant angle relationships in the diagram. Engage NY Eureka Math 7th Grade Module 2 Lesson 7 Answer Key Eureka Math Grade 7 Module 2 Lesson 7 Example Answer Key. Refer to the integer game when answering the following questions. 10 9 8 7 6 5 4 3 2 1 G7-M3-UTE-1. Sums and Differences to 100. Engage NY Eureka Math 7th Grade Module 1 Lesson 19 Answer Key Eureka Math Grade 7 Module 1 Lesson 19 Example Answer Key. Using the division button on your calculator, explore various quotients of integers 1 through 11. 4a) Eureka Math Module 2: Rational Numbers 7 Lesson 1 – Opposite Quantities Combine to Make Zero Essential Questions: Exercise 1: Positive and Negative Numbers Review With your Students make an integer multiplication facts bubble by expanding upon the four related math facts they wrote down. 1-02. You will use 9 of the expressions: 12-4x 8x+4-12x 8(\(\frac{1}{2}\) x -2) 12-6x+2x-4x+4 EngageNY Math Grade 7 Module 5 Answer Key | Eureka Math 7th Grade Module 5 Answer Key. Answer: It means that if you have a sum and want to take the opposite, for Module 2: Addition and Subtraction of Length Units End-of-Module Assessment Task 2 {2 2. operations from Module 2 is demonstrated as students collect like terms containing both positive and Quick and easy learning is possible with our Eureka Math Grade 7 Answer Key. Eureka Math Module 1 - Ratios and Proportional Relationships 3 Example 2: Our Class by Gender Number of Boys Number of Girls Ratio of Boys to Girls Class 1 Class 2 Class 3 Class 4 Class 5 Whole 7th Grade Class Create a pair of equivalent ratios by making a comparison of quantities discussed in this example Lesson 2 7 •4. Represent each of the following expressions as one rational number. Eureka Math Grade 7 Module 2 End of Module Assessment Answer Key. 2015 9781640549739, 1640549730 [Great Minds] on Amazon. Represent the sum of 3+5 using arrows on the number line. Grade 8 Module 1; Engage NY Eureka Math 7th Grade Module 2 Lesson 9 Answer Key Eureka Math Grade 7 Module 2 Lesson 9 Example Answer Key. Example 2. Eureka Math Grade 7 Module 4 Lesson 1 Answer Key; Eureka Math Grade 7 Module 4 Lesson 2 Answer Key; Eureka Math Grade 7 Engage NY Eureka Math 7th Grade Module 5 Lesson 2 Answer Key Eureka Math Grade 7 Module 5 Lesson 2 Example Answer Key. Grade Topic C: Applying Operations with Rational Numbers to Expressions and Equations (7. Extending Whole Number Multiplication to the Integers Part A: Complete quadrants I and IV of the table below to show how sets of matching integer cards will affect a player’s score in the Integer Game. Eureka Essentials: Grade 5 URL An outline of learning goals, key ideas, pacing Engage NY Eureka Math 7th Grade Module 2 Lesson 6 Answer Key Eureka Math Grade 7 Module 2 Lesson 6 Example Answer Key. Online based upon Eureka Math and is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4. Eureka Math Grade 7 Module 1 Teacher Edition FL State Adoption Bid # 3691. The youth group is going on a trip to an amusement park in another part of the state. This module is comprised of 23 lessons; 7 days are reserved for administering the Mid- and End-of-Module Assessments, returning the assessments, and remediating or providing further Engage NY Math 7th Grade Module 2 Topic C Applying Operations with Rational Numbers to Expressions and Equations. If you're behind a web filter, please make sure that the domains *. A fellow Eureka Math user, Daniel Kaufmann, created this wonderful spreadsheet of all the module assessments. What direction does it point Engage NY Eureka Math 7th Grade Module 2 Lesson 11 Answer Key Eureka Math Grade 7 Module 2 Lesson 11 Example Answer Key. Overcome all your difficulties in maths and fill up the knowledge gap by practicing the problems from our Eureka Math 7th Grade Solution Key. Above Header. Example 2: Animal Crackers A student brought a very large jar of animal crackers to share with students in class. Grade 7 • Module 2 . Earning two prestigious CAST certifications, Eureka Math² promotes inclusive, engaging learning. Go 7th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Module 6; 8th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Grade 4 Module 2 Collapse all Expand all. The students who are willing to become master in math by solving the problems from Eureka Math Answer Key for 7th Grade. Step 1: Start on an endpoint. 1. 2018 Published by 7th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Module 6; 8th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Grade 7 Module 4 This work by EMBARC. Can All Rational Numbers Be Written as Decimals? a. Engage NY Eureka Math 7th Grade Module 6 Lesson 2 Answer Key Eureka Math Grade 7 Module 6 Lesson 2 Example Answer Key. Part of a Whole as a Percent . 2016 ó { ð Trim Box = 612 x 783 pt 7th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Module 6; 8th Grade; Home; Module 1; Module 2; Module 3; Module 4; Module 5; Grade 1 Module 2 Collapse all Expand all. This work is derived from Eureka Math ™ and licensed by Great Minds. Part A: Students pick four cards. Grade 6 Module 2; Grade 6 Module 3 Workbook and Homework; Grade 6 Module 3; Grade 6 Module 4; Grade 6 Module 5; Grade 6 Module 6; Eureka 7th Grade Spanish Workbook. In Ty’s English class, 70% of the students completed an essay by the due date. Write an equation to model the situation. org G7-M2-ETP-P2-1. Counting Up and Counting Down on the Number Line Use the number line below to practice counting up and counting down. Home. 80 percent of items are auto This video covers concepts taught in Module 2, Lesson 5 of 7th grade Eureka Math (Engage NY). 0-05. GRADE 7 • MODULE. I would use the Eureka Math assessments as practice tests. Eureka Math Grade 7 Module 3 Teacher Edition FL State Adoption Bid # 3691. Skill plan for Eureka Math - 7th grade IXL provides skill alignments with recommended IXL skills for each module. Eureka Math: A Story of Ratios Contributors Michael Allwood, Curriculum Writer Tiah Alphonso, Program Manager—Curriculum Production Catriona Anderson, Program Manager—Implementation Support Beau Bailey, Curriculum Writer Engage NY Eureka Math 7th Grade Module 2 Lesson 14 Answer Key Eureka Math Grade 7 Module 2 Lesson 14 Example Answer Key. The scale factor from Drawing 1 to Drawing 2 is 60%. A STORY OF RATIOS. Answer: Answers will vary. EE. Example 1. Diagnostic, Pre-Module Assessments Powered by Eureka Math 2 Equip. Time, Shapes, and Fractions as Equal Parts of Shapes. Representations of Rational Numbers in the Real World Following the Opening Exercise and class discussion, describe why we need to know how to represent rational numbers in different ways. 3 . This work by EMBARC. Teacher access includes the following: Digital access to all content available in the Teach, Learn, and Apply print materials Engage NY Eureka Math 7th Grade Module 2 Lesson 4 Answer Key Eureka Math Grade 7 Module 2 Lesson 4 Example Answer Key. ISBN 978-1-64054-360-7 Printed in the U. 10 9 8 7 6 5 4 3 2 1. Teacher's editions, mod. Module 4. B. Eureka Math ™ Grade 7, Module 3. Pay by the Ounce Frozen Yogurt The purpose of this example is for students to understand when measures of one quantity are proportional to measures of another quantity.