3rd Grade - Gateway 1

The materials reviewed for Eureka Math² Grade 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The Assessment System includes lesson-embedded Exit Tickets, Topic Quizzes, and Module Assessments. According to the Implementation Guide, “Exit Tickets are not graded. They are paper based so that you can quickly review and sort them. Typical Topic Quizzes consist of 4-6 items that assess proficiency with the major concepts from the topic. You may find it useful to grade Topic Quizzes. Typical Module Assessments consist of 6-10 items that assess proficiency with the major concepts, skills, and applications taught in the module. Module Assessments represent the most important content taught in the module. These assessments use a variety of question types, such as constructed response, multiple select, multiple choice, single answer, and multi-part. There are two analogous versions of each Module Assessment available digitally. Analogous versions target the same material at the same level of cognitive complexity.” Examples of summative Module Assessments items that assess grade-level standards include:

• Module 1, Module Assessment 2, Item 3, “Pablo puts photos in his photo album. He puts the photos in 3 rows of 6. How many photos does Pablo put in his photo album altogether? Part A. Click in the box to make an array to represent the problem. Part B. Which equations can be used to solve the problem? Select the two correct answers. 1. 6\div3= , 2. 6\times3= , 3. 3\times3= , 4. 6+6+6= , 5. 3+3+3+3+3= . Part C. How many photos does Pablo put in his photo album altogether? Pablo puts photos in his photo album altogether.” (3.OA.1)

• Module 2, Module Assessment 1, Item 6, “Create two 3-digit numbers that both round to the same hundred. Drag one digit into each box to create your numbers.” (3.NBT.1)

• Module 4, Module Assessment 1, Item 8, “One wall in Mia's bedroom is 10 feet long and 10 feet wide. Mia puts two paintings on the wall. One is 3 feet long and 2 feet wide. The other is 1 foot long and 2 feet wide. What is the area of the wall that is not covered by the paintings?” (3.MD.7d)

• Module 5, Module Assessment 1, Item 4, “Amy partitions a rectangle into 6 equal parts. She wants to color \frac{2}{6} of the rectangle green. How many parts should Amy color green? Explain how you know?” (3.NF.1)

• Module 6, Module Assessment 1, Item 3, students are provided with a grid figure and asked, “Create a quadrilateral that is not a rectangle and that has at least one right angle.” (3.G.1)

The materials reviewed for Eureka Math² Grade 3 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

According to the Grades 3-5 Implementation Guide, “Each lesson is structured in four sections: Fluency, Launch, Learn, and Land. Lessons are designed for one 60-minute instructional period. Fluency provides distributed practice with previously learned material. It is designed to prepare students for new learning by activating prior knowledge and bridging small learning gaps. Launch creates an accessible entry point to the day’s learning through activities that build context and often create productive struggle that leads to a need for the learning that follows. Every Launch ends with a transition statement that sets the goal for the day’s learning. Learn presents new learning related to the lesson objective, usually through a series of instructional segments. This lesson component takes most of the instructional time. Suggested facilitation styles vary and may include direct instruction, guided instruction, group work, partner activities, interactive video, and digital elements. The Problem Set, an opportunity for independent practice, is included in Learn. Land helps you facilitate a brief discussion to close the lesson. Suggested questions, including key questions related to the objective, help students synthesize the day’s learning.” 

Instructional materials engage all students in extensive work with grade-level problems through the consistent lesson structure. Examples include:

• Module 1, Multiplication and Division with Units of 2, 3, 4, 5, and 10, Lesson 6 engage students in extensive work with 3.OA.2 (Interpret whole-number quotients of whole numbers…). Fluency, Choral Response: Equal Parts, students identify and describe equal parts of a shape to further student’s understanding of geometric concepts learned in Grade 2. Teachers display the shape of a circle and ask, “What is the name of this shape? This is 1 whole circle. How many equal parts is the whole partitioned into? Students describe how their modeling changes based on what is known.” Teachers show students a circle partitioned into halves and ask, “How many equal parts is the whole partitioned into? Is the whole partitioned into halves, thirds, or fourths?” Launch, “students determine 5 as either the number of groups or the number in each group” and answer, “Is 5 the number of groups or the number in each group?” Teachers invite students to turn and talk about how they know whether 5 is the number of groups or the number in each group. Teachers frame the next part of the lesson, “Today, we will represent equal sharing using what we know about the number of groups and the number in each group.” Learn, Equally Share Crackers, Classwork, Problem 1, students model, discuss, and compare division problems. Teachers give each pair of students 5 paper plates, 10 crackers, and direct students to read Problem 1 chorally. “Use 10 crackers to make equal shares with 5 crackers in each group. a. Draw to show how you equally shared the crackers and then complete the sentences. b. The total number is ___. c. The number in each group is ___. d. The number of equal groups is ___.” Land, Debrief, Problem  2, students explore measurement and division problems using visual models. Teachers are directed to use prompts to guide a discussion about the two interpretations of division. “What does the number 5 represent in problems 1 and 3? In problems 2 and 4? Why is it helpful to think about what the numbers in an equal-sharing problem represent?”

• Module 2, Place Value Concepts Through Metric Measurement, Lesson 14 engage students in extensive work with 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or relationships between addition and subtraction). Fluency, Choral Response: Place Value, students use place value and the value of a given number to say the number in expanded form to find sums and differences. Teachers display the number 137 and ask, “What is the digit in the tens place? What is the value of the 3 in this number? What is 137 in expanded form?” Learn, Add Like Units of One-and Two-digit Numbers, students add without regrouping using place value. “Write 22+5=___ with a number bond. How is this model similar to the unit form equation? How does this work help you add like units, or tens to tens and ones to ones.” Learn, Subtract  Like Units in Unit Form, students subtract using place value in unit form. “Write the following problems 7 ones - 4 ones = ___ones; 9 tens - 3 tens = ___ tens; 5 tens 7 ones - 6 ones = ___ tens ___ones; 7 tens 6 ones - 2 tens 4 ones = ___ tens ___ ones.” 

• Module 6, Geometry, Measurement and Data, Lessons 2, 5, and 6 engage students in extensive work with 3.MD.1 (Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram). Lesson 2, Fluency, Choral Response: Time on the Clock, students tell time to the nearest five minutes using an analog clock to develop fluency with reading and measuring time to the nearest minute. Teachers display a picture of the clock that shows 8:15 and ask, “What time does the clock show?“ A clock showing 8:15 is provided. Lesson 5, Land, Exit Ticket, ”Solve each problem. Show your strategy, Eva and Gabe start playing a game at 10:23 a.m. They finish playing the game at 11:18 a.m. How many minutes did  Eva and Gabe play the game?” Lesson 6, Learn, Word Problems Involving Time, students compare solution strategies as they solve time word problems. Classwork, Problem 1, “Show your strategy to solve each problem. James lifts weights from 11:45 a.m. to 12:20 p.m. and then goes for a run for 35 minutes. How many minutes does James exercise in all?” Classwork, Problem 2, “The train from Station A to Station B leaves at 7:24 a.m. The trip usually takes 34 minutes.Today, the train is 4 minutes late. Will the train arrive at Station B before 8:00 a.m. or after 8:00 a.m.? How do you know?” 

Instructional materials provide opportunities for all students to engage with the full intent of all Grade 3 standards. Examples include: 

• Module 3, Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9, Lessons 3 and 9 engages students with the full intent of 3.OA.5 (Apply properties of operations as strategies to multiply and divide). Lesson 3, Fluency, Whiteboard Exchange: Interpreting Tape Diagrams, “students interpret a tape diagram modeling measurement or partitive division and write an equation to build an understanding of two interpretations of division.” Teachers are directed to display the tape diagram with a group size of five and a total of 40. “What is the total? Let’s use the tape diagram to find how many fives are in 40. Does this tape diagram show the number of groups or the size of each group? Write a division equation to represent this tape diagram where the quotient is the number of groups.” Land, Debrief, “students count by units of 8 to multiply and divide by using arrays.” Teachers are directed to facilitate a discussion about strategies for multiplying and dividing with 8? “What strategies can you use to multiply and divide by 8? How do you decide which strategy to use to multiply or divide by 8?” Lesson 9, Learn, Problem Set, Problem 1, “Circle to show the equal groups in each array. Then circle the expression that represents the equal groups. 3 groups of 2\times4.” 

• Module 4, Multiplication and Area, Lessons 2, 3 and 16 engage students with the full intent of 3.MD.5 (Recognize area as an attribute of plane figures and understand concepts of area measurement). Lesson 2, Learn, Area and Square Units, students model covering a shape with 1-inch squares to find its area in square units. Teachers ask, “What do you notice about the number of squares it takes to cover polygons A and C? Are the squares you used to cover polygons A and C the same size? What can we say about the amount of space taken up by polygons A and C? The amount of flat space a shape takes up is called its area. Because polygons A and C take up the same amount of space, they have the same area. Their areas are equal.” Land, Exit Ticket, Problem 1, “Find the area of each shape. Each (square) represents 1 square unit. 1. Shape A is ___ square units.” Lesson 3, Launch, “students apply attributes of polygons to make different shapes that have the same area.” There are four different pictures of polygons displayed. Learn, students develop an understanding of why different shapes can have the same area. The teacher is instructed to direct students to polygon H. “How many squares does it take to cover polygon H? What is the area of polygon H in square units?  What other shapes in our set of polygons have an area of 6 square units?” Lesson 16, Fluency, Choral Response: Find the Area, students find the area of a composite figure in square units to build fluency with understanding area (Topic A). A rectangle divided into eight square units is displayed. Teachers are directed to display the figure with an area of square units. “What is the area of the figure?” Students repeat the process with four more different figure configurations, showing 9 square units, 10 square units, and 12 square units. Learn, Area of Four Equal Parts, “students decompose a square into equal parts and find the area of the parts.” Teachers direct students to one of their grids, “We will use the paper squares to represent the Babylonian squares, What do you notice?, What are the side lengths of the square? What is the area of the square?”

• Module 5, Fractions as Numbers, Lesson 1, engages students with the full intent of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole). Lesson 1, Launch students identify shapes as they partition shapes into equal parts and name the fractional unit. Teacher displays partitioned shapes one at a time and asks, “Is the shape partitioned into equal parts or unequal parts? If the shape is partitioned into equal parts, how can we name the equal parts?” Learn, Draw to Equally Share More Than One Object, students solve equal-parts word problem where more than one object is shared and where the solution involves fractional units. Teacher displays the problem, “4 friends have 13 granola bars to share equally,” and asks, “How many bars will each get?” Teacher directs students to work with a partner and use the Read-Draw-Write process to solve problems, asking the following questions as partners work, “What will happen with the extra granola bar? How could the friends equally share the extra granola bar?  How much does this friend get? What about this other friend? Does everyone get an equal amount or number? Is there another way you could equally share the granola bars?” Teacher gathers the class for partners to share their work, asking, “How did you share the bars so that each friend got an equal amount? Notice how the bars are partitioned. How many equal parts are there? How did you show how the leftover granola bar was partitioned? What did you name the parts? The fourths are units. We can count them, just as we count measurement units, such as inches and milliliters, and place value units, such as ones and tens. What are some other units we’ve counted this year? Fractional units are the units we count when we partition a whole into equal parts. Fourths are fractional units. What are some other fractional units? How do you know everyone gets an equal amount, or an equal number of units? 1 fourth is a fraction. When you have a number of fractional units, it’s called a fraction. Do these parts look like fourths of a whole granola bar? Can I really say the drawing shows fourths? Size is important when we make drawings of parts. We need to be as precise as possible when drawing equal parts of a whole.”

The materials reviewed for Eureka Math² Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major work of each grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade. 

• The number of modules devoted to the major work of the grade (including assessments and supporting work connected to the major work) is 4.5 out of 6, approximately 75%.

• The number of lessons devoted to the major work of the grade (including supporting work connected to the major work) is 102 out of 140, approximately 73%.

• The number of days devoted to the major work of the grade (including assessments and supporting work connected to the major work) is 116 out of 140, approximately 83%. 

A lesson-level analysis is most representative of the instructional materials as the lessons include major work and supporting work connected to major work. As a result, approximately 73% of the instructional materials focus on major work of the grade.

The materials reviewed for Eureka Math² Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed so supporting standards are connected to the major work standards and teachers can locate these connections on a tab called, “Achievement Descriptors and Standards” within lessons. Examples include:

• Module 2, Topic D, Lesson 25: Solve two-step word problems, Learn, Two-Step Word Problem Using Addition and Subtraction, Classwork, Problem 1, connects the supporting work of 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to the major work of 3.OA.8 (Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding). Students use self-selected representations and strategies to solve two-step addition and subtraction word problems. Teacher prompts students to use the Read-Draw-Write process and select their own solution strategies and materials. ”Use the Read–Draw–Write process to solve each part of the problem. Eva’s cherries weigh 434 grams less than her apples. Eva’s apples weigh 670 grams. a. How much do Eva’s cherries weigh? b. What do Eva’s cherries and apples weigh in total?” 

• Module 4, Topic A, Lesson 5: Relate side lengths to the number of tiles on side, Fluency, Whiteboard Exchange: Polygons and Attributes, connects the supporting standard 3.G.1 (Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category…) to the major work of 3.MD.5 (Recognize area as an attribute of plane figures and understand concepts of area measurement), 3.MD.5a (A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area), 3.MD.5b (A plane figure which can be covered without gaps or overlaps by 𝑛 unit squares is said to have an area of 𝑛 square units), and 3.MD.6 (Measure areas by counting unit square, square cm, square m, square in, square ft, and improvised units). Students develop understanding of polygons and their attributes as they sketch a polygon with a given attribute and find other polygons with the same attributes. Teacher displays the attribute: four sides. “Sketch a polygon with 4 sides.” Teacher displays the three polygons labeled with letters. “Which of the polygons have 4 sides? Write the letter or letters.” Teacher displays the polygons A and B circled and directs students to repeat the process with the following sequence: “Attribute: at least 1 pair of parallel sides; Attribute: 2 pairs of parallel sides; Attribute: opposite sides have equal length. Attribute: 4 sides have equal length.” Learn, Measure Side Lengths of a Rectangle, Students use the relationship between the side length of square tiles to side length of rectangles. Teacher directs students to place 4 inch tiles at the start of the inch side of the ruler and asks, “When we use the ruler to measure the length of these tiles, what unit do we use? What is the length?” A picture of a ruler and inch tiles representing a rectangle is shown. Learn, Label Side Lengths of a Rectangle. Teacher points to the 5-inch side and asks the following questions: “How many tiles did you use to make this side? How many inches long do you think this side is?” Teacher guides students to use a ruler to measure and label the side length as 5 in. Do you think we need to label the opposite side too? Why? What is the area of the rectangle? How do you know?”

• Module 5, Topic A, Lesson 4: Partition a whole into fractional units pictorially and identify the unit fraction, Launch, connects the supporting work of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole) to the major work of 3.NF.1 (Understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into “b” equal parts; understand a fraction \frac{a}{b} as the quantity formed by 𝑎 parts of size \frac{1}{b}). Students identify and relate numbers of equal parts to fractional units. The teacher displays the picture of the yellow hexagon and the next picture (1 half) and asks, “How much of the hexagon is red? Half, How many halves?” Teacher displays the last picture in the halves sequence and invites students to count as each halve is pointed to, and asks, “How much of the hexagon is red? How many halves make 1?” Learn, Identify and Count Fractional Units, “Display the picture of the rectangle with 1 half shaded. Trace the outline of the rectangle and ask the following series of questions: Are there equal parts? How many equal parts are there? What is the fractional unit? What is each part called? What is the unit fraction? Count the parts to make 1. Repeat the process with the pictures of the shapes that show 1 fifth, 1 third, and 1 eighth shaded. Remove the scaffolding questions as students are ready. Consider drawing additional examples as needed.”

The materials reviewed for Eureka Math² Grade 3 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Grade 3 lessons are coherent and consistent with the Standards. Teachers can locate standard connections on a tab called, “Achievement Descriptors and Standards” within lessons. Examples include:

• Module 1, Topic E, Lesson 19: Use the distributive property to break apart multiplication problems into known facts, Learn, Classwork, Problem 2, connects the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division) to the major work of 3.OA.C (Multiply and divide within 100). Students utilize the break apart method and distributive property to solve multiplication problems. “Direct students to problem 2. Miss Diaz’s class is going on a field trip. The bus has 8 rows of 4 seats. How many seats are on the bus? Guide students through the process of using the break apart and distribute strategy by breaking apart the rows to find out how many seats are on the bus. 8\times4=(5\times4)+(3\times4)=20+12=32. There are 32 seats on the bus. Consider the following possible sequence: What multiplication fact represents the entire array? Write 8\times4 below the array. Let’s use the break apart and distribute strategy to break apart the 8 rows of 4. Break the array into 5 rows of 4 and 3 rows of 4 by shading 5 rows of 4 with your pencil.”

• Module 2, Topic C, Lesson 13: Collect and represent data in a scaled bar graph and solve related problems, connects the supporting work of 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic) to the supporting work of 3.MD.B (Represent and interpret data). Students collect data, create scaled bar graphs to represent data, then solve problems based on the data represented in their graphs. Horizontal Scaled Bar Graph, Classwork, “Complete the table to show the number of students who chose each favorite school lunch. Represent the data on a horizontal bar graph. Create a scale for the graph.” The teacher is prompted to ask the following questions: “Which lunch choice was chosen by the most students? How many students chose it? If each tick mark represents 2 students, will the number of students who chose (the option chosen by the most students) fit on the graph? How do you know? If the number of students who chose (the option chosen by the most students) fits on the graph, will the number of students who chose each of the other choices fit on the graph? How do you know? We do not need to label every tick mark. Let’s count by twos to label the tick marks for 10 and 20.”

• Module 6, Topic A, Lesson 6: Solve time word problems and use time data to create a line plot, Learn, Word Problems Involving Time, Classwork, Problem 3, connects the major work of 3.MD.A (Solve Problems Involving Measurement and Estimation Of Intervals Of Time, Liquid Volumes, and Masses of Objects) to the major work of 3.OA.D (Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic). Students solve problems involving time, “David wants to watch a movie before he goes to bed. He needs to be in bed at 9:00 p.m. It takes him 17 minutes to get ready for bed. The movie is 93 minutes long. What time should he start the movie?” Land, Debrief, “How are the models we use for solving time problems the same? How are they different? What strategies can be used to solve different types of time problems? How can line plots help us look at time data?”

The materials reviewed for Eureka Math² Grade 3 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from future grades is identified within materials and related to grade-level work. These references are consistently included within Topic and Module Overviews to reveal coherence across modules and grade levels. Some Teacher Notes within lessons also include connections to future concepts. Examples of connections to future concepts include:

• Module 2: Place Value Concepts Through Metric Measurement, Module Overview, connects 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to work in future grades. “In Grade 4 Module 1, students apply their understanding of measurement units to convert weight, liquid volume, and length measurements from larger units to smaller units. Students generalize place value and rounding concepts and relationships to larger, multi-digit numbers. They add and subtract multi-digit numbers by using the standard algorithms for addition and subtraction.”

• Module 3: Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9, Module Overview, connects 3.NBT.3 (Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations) to work in future grades. “In Grade 4, Module 2, students apply grade 3 strategies for multiplication and division to multiply and divide numbers of up to 4 digits by one-digit numbers. Students complete measurement conversions and solve multiplicative comparison and multi-step word problems. Students advance their prior experiences with the properties of operations by identifying factors, multiples, and prime numbers within 100."

• Module 5: Topic A, Lesson 15: Identify fractions on a ruler as numbers on a number line, Learn, Teacher Notes connects 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram) to work in future grades. "Students formally describe fractions greater than 1 as mixed numbers in grade 4. The emphasis here is on representing measurements with whole numbers and some fractional units (e.g., 5 and \frac{1}{2} inches). In the next lesson, students drop the word and as they represent fractional measurements greater than 1 on the number line to make line plots.”

Materials relate grade-level concepts from Grade 3 explicitly to prior knowledge. These references can be found consistently within Topic and Module Overviews and less commonly within teacher notes at the lesson level. In Grade 3, prior connections are often made to content from previous modules within the grade. Examples include:

• Module 1: Multiplication and Division with Units of 2, 3, 4, 5, and 10, Module Overview, Before This Module, connects 3.OA.1 (Interpret products of whole numbers) to previous work from Grade 2. "In grade 2, students complete foundational work for multiplication and division. They form equal groups, write repeated addition sentences, arrange objects in rows and columns to form arrays up to 5 by 5, and discover how adding the number of objects in the rows or columns relates to repeated addition. At first, arrays are made with gaps between rows and columns and, later, are made with no gaps. Students build and manipulate arrays and use part–total language to express the composition and decomposition. Grade 3 module 1 elevates the work of grade 2 through formal introduction of multiplication and division."

• Module 2: Place Value Concepts Through Metric Measurement, Module Overview, Before This Module, connects 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) and 3.MD.2 (Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units) to previous work from Grade 2. "In grade 2, students describe and apply place value concepts to two- and three-digit numbers. They count and bundle ones, tens, and hundreds up to 1,000. Students read and write numbers in standard, unit, and expanded forms and apply place value understanding to add and subtract two- and three-digit numbers by using a variety of strategies. Simplifying strategies consist of composing and decomposing tens and hundreds to make problems easier to compute mentally and developing various written methods to record student thinking. Students also estimate and measure length by using a variety of tools and units in the customary and metric systems of measurement. Grade 3 uses familiar place value concepts to expand student understanding of metric measurement of weight and liquid volume and to develop fluency in addition and subtraction within 1,000.”

• Module 6: Geometry, Measurement, and Data, Module Overview, Before This Module, connects 3.MD.1 (Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes) to previous work from Grade 2, Module 3. "In Grade 2, Module 3, students tell and write time to the nearest five minutes, use a.m. and p.m., and describe quarter hours by using quarter past and quarter to. In grade 3 module 2, students create scaled bar graphs to represent categorical data. In module 4, students identify attributes of quadrilaterals, including right angles and parallel sides. Students also name different types of quadrilaterals by using attributes. They define and recognize area as an attribute of polygons and determine the areas of rectangles by using side lengths. Students represent area data on line plots. In module 5, students partition wholes into fractional parts on the number line. They use rulers to measure to the nearest quarter inch and plot fractional length data on line plots."