3rd Grade - Gateway 1

The materials reviewed for i-Ready Classroom Mathematics Grade 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The i-Ready Classroom Mathematics assessments are found in the Teacher Toolbox and include Mid-Unit and Unit Assessments. The Grade 3 materials contain six units, with each unit providing numerous opportunities for both formative and summative assessments. Summative assessment items include:

• Unit 1, Assess, Unit Assessment, Form A, Item 9, “Clark scores 146 points bowling. Kia scores 179 points bowling. How many points do they score in all? Show your work. Solution _____.” (3.NBT.2)

• Unit 3, Assess, Unit Assessment, Form A, Item 10, “A cafeteria worker stacks 54 trays. They make 9 stacks of trays. How many trays are in each stack? Write related multiplication and division equations to find the number of trays in each stack. Use t for the unknown number. Solution _____.” (3.OA.3)

• Unit 3, Assess, Mid-Unit Assessment, Form A, Item 2, “Jed builds a square sandbox. One side has a length of 8 feet. How much space will Jed’s sandbox cover?” (3.MD.7)

• Unit 4, Assess, Mid-Unit Assessment, Form B, Item 1, “How many equal parts are between 0 and 1? Write your answer in the blank.” A picture is shown of a number line with hash marks labeled 0 and 1 on each end, partitioned into 4 equal parts. (3.NF.2)

• Unit 6, Assess, Unit Assessment, Form A, Item 8, “Use these shapes for Part A and Part B. Part A Pilar says both shapes belong in the same group. What group could both shapes belong to? Explain your reasoning. Part B Nen says both shapes do not belong in the same group. What group could only one shape belong to? Explain your reasoning.” An image of an equilateral triangle and a parallelogram are shown. (3.G.1)

The materials reviewed for i-Ready Classroom Mathematics 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 Program Overview, Program Organization document, “The lessons in i-Ready Classroom Mathematics span multiple days and integrate several standards to help students make connections and develop a deep understanding.” There are three types of lessons: 1. Strategy Lessons, which comprise the majority of lessons in the program and “help students make important connections and deepen their understanding while acquiring and developing mathematical skills and strategies,” 2. Understand Lessons, which “begin with the word “Understand” focus primarily on conceptual understanding and occur at key points in the instructional sequence,” and 3. Math in Action Lessons, which occur at the end of each unit and “review and apply unit content and teach students how to develop complete responses to a performance task.” 

The i-Ready Classroom Mathematics materials provide a consistent structure within each lesson, which is a session or “day”, and each “plays a different role in supporting student understanding.” “Each session takes 45-60 minutes to complete and includes time for instruction, practice, and differentiation.” Day 1 consists of an Explore session which “connects prior knowledge and introduces new content.” Days 2-4 consist of Develop sessions which “build multi-dimensional understanding using rich tasks, problem solving, discourse and multiple representations.” Day 5 consists of a Refine session which “strengthen skills and understanding with in-class practice time” and “reteach, reinforce, and extend learning.” The materials present all students with opportunities to meet the full intent and engage in extensive work with each grade-level standard. Examples include:

• Unit 2, Lesson 9, Use Place Value to Multiply, and Math in Action, engage students with the full intent and extensive work with 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.) Students use place value understanding and properties of operations to multiply one-digit numbers by multiples of 10. Session 1, Explore, Try It, students multiply one-digit numbers by multiples of ten by skip-counting and counting on by groups of 10. “There are 4 stacks of books on a table. Each stack has 20 books. How many books are there in all?” Students use the problem to explore different strategies for solving including, skip-counting by tens, twenties, and using unit form (2 tens, 4 tens, 6 tens, 8 tens). Session 2, Develop, Try It, students rewrite a multiple as the product of 10 and another whole number. “A clothing shop has 4 racks of dashikis. There are 40 dashikis on each rack. How many dashikis does the shop have in all?” Session 2, Develop, Apply It, Problem 8, “Multiply 60\times8. Show your work.” Session 3, Apply It, Problem 2, “Multiply 6\times90. Show your work.”  Math in Action, Solve Multiplication and Division Problems, Persevere on Your Own, Monthly Gifts, “Brandi tells local companies they can support the theater department at the local college. Brandi asks the companies to sign up to make monthly gifts. She wants to raise at least $800 in 6 months from these gifts. Here are the gift amounts: $10 each month, $20 dollars each month, $50 each month. How can Brandi raise at least $800 in 6 months? Solve It, Help Brandi find a way to raise money. Find out how much each monthly gift raises in 6 months. Then find a way to raise at least $800 in 6 months. Tell how you know that your answer works.”

• Unit 2 and Unit 3, Lessons 12 and 17, engage students with the full intent and extensive work with 3.OA.4 (Determine the unknown whole number in a multiplication or division equation relating three whole numbers.) Students determine the unknown whole number in a multiplication or division equation relating three whole numbers. Lesson 12, Multiplication and Division Facts, Session 2, Develop, Try It, students work with division facts. “Aki wants to make 5 sled dog teams. There are 40 sled dogs, and the teams must have the same number of dogs. She wants to find out how many sled dogs to put on each team. Aki writes: 40\div5=___. How many sled dogs should Aki put on each team?” Session 2, Additional Practice, Practice Working with Division Facts, Problem 7, “Pala has 24 trading cards. He gives away all his cards to friends. He gives 8 cards to each friend. Use this information to solve problems 7-9. Use the number line to show how many friends Pala gave cards to.” Problem 8, “Write two different division facts for the story. ____ and ____.” Problem 9, “Write the multiplication facts that belong to the same fact family.” Session 3, Develop, Try It, “Complete the facts. 2\times___=10, 24\div6=___, ___\times6=48, and ___\div1=8.” Apply It, Problem 8, “Lila and Will pick 16 California poppies. They share them equally. Which facts could be used to find the number of poppies each person gets? Choose all that apply.” Answer choices: 4\times4=16, 2\times8=16, 16\div2=8, 16\div4=4, and 16\div8=2. Session 4, Refine, Apply It, Problem 6, “Does putting the number 8 in the box make each equation true? 9\times__=64, 6\times__=48, 56\div__=8, 32\div___=4.” Unit 3, Lesson 17, Solve One-Step Word Problems Using Multiplication and Division, Session 2, Additional Practice, Practice Solving Problems About Equal Groups, Problem 2, “Complete the multiplication and division equations for this problem. Write the value of h. 18\div___=h, h\times___=18, h=___.” Session 3, Additional Practice, Practice Solving Problems About Arrays, Problem 2,  “In the art room, there are 20 baskets. The baskets are arranged in 4 equal rows. How many baskets are in each row? Complete the division equation to solve the problem. b stands for the unknown number. 20\div___=b, so b=___.” 

• Unit 4, Lesson 20, Understand What a Fraction Is, Sessions 1-3, engage students with the full intent and extensive work with 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 develop an understanding of what a fraction is by naming fractions by the number of equal parts in a whole, understanding and identifying the denominator and numerator, identifying unit fractions, and understanding that they build other fractions. Students write and name fractions that describe shapes that have been partitioned into equal parts with one or more parts shaded. Lesson 20, Session 1, Explore, Model It, Problem 6, “Explain why the denominator, 4, does not change when you are counting by the unit fraction  \frac{1}{4} to reach \frac{3}{4}.” Session 2, Develop, Connect It, Problem 7, “Look at the rectangle. a. What unit fraction names each part? b. Shade 4 parts of the rectangle. Write the fraction you shaded.” A picture of a rectangle partitioned into 8 equal parts is provided. Session 2, Additional Practice, Practice Describing the Parts of a Whole with Fractions, Problem 3, “Shade this shape to show \frac{3}{4}.” Problem 4, “Shade this shape to show  \frac{2}{6}.” Problem 5, “Shade three parts of this shape. What fraction did you shade?” Problem 6, “Shade 7 parts of this shape. What fraction did you shade?” Four shapes are shown. The first is a rectangle partitioned into 4 equal parts.  The next is a parallelogram partitioned into 6 equal parts. The next is a circle partitioned into 8 equal parts. The last is a rectangle partitioned into 8 equal parts.” Session 3, Refine, Apply It, Problem 5, “Trang has a circle divided into equal parts. One part is shaded, and the other three parts are not. Trang says her circle shows the fraction  \frac{1}{3}. Is she correct? Draw a picture to help you explain.”

• Unit 5, Lesson 27, Time, Sessions 1-5, engage students with the full intent and 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 27, Explore, Session 1, Additional Practice, Prepare for Working With Time, Problem 3, “Solve the problem. Show your work. Anwar starts watching a movie at the time shown on the clock. What time does the clock show?” Session 2, Develop, Apply It, Problem 7, “It is 7 minutes before 2 PM. Draw the hands on the clock at the right to show the time. Then write the time on the digital clock below. Be sure to include AM or PM.” Session 3, Additional Practice, Practice Finding the End Time in Word Problems, Problem 2, “Galeno gets in line for the Safari Ride at 11:55 AM. He waits in line for 8 minutes. The ride lasts 7 minutes. What time does he get off the ride? There is a number line shown with tick marks for each minute. Time shown on the timeline are 11:45, 12:00, and 12:15.” Session 4, Additional Practice, Practice Finding the Start Time in Word Problems, Problem 3, “A movie starts at 5:15 PM. Tarlo wants to get to the theater 25 minutes before the movie starts. It takes 10 minutes to drive to the theater from Tarlo’s home. What time should Tarlo leave home? Show your work.” Session 5, Refine, Apply It, Problem 6, “Kacy plays two games of checkers with her brother. The first game takes 12 minutes, and the second game takes 18 minutes. They put the game away at 7:55 PM. What time did they start playing checkers? Show your work. They started playing checkers at ____.”

• Unit 6, Lessons 30 and 31, engage students with the full intent and extensive work with 3.G.1 (Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category…). Students understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Students also recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Lesson 30, Understand Categories of Shapes, Session 3, Refine, Apply It, Problem 2, “Explain Zahara says that all rectangles belong in the group some right angles. Caton says that all rectangles belong in the group all right angles. Who is correct? Explain.” Problem 3, “Illustrate Draw a shape that belongs to both of these groups: all sides are the same length and no right angles.” Lesson 31, Classify Quadrilaterals, Session 1, Explore, Try It, “A rhombus is one kind of quadrilateral. A rectangle is another kind of quadrilateral. How are the rhombus and the rectangle shown below the same? How are they different?” Session 1, Additional Practice, Prepare for Classifying Quadrilaterals, Problem 3, “Parallelograms and squares are quadrilaterals. How are the parallelogram and the square shown the same? How are they different?” Session 2, Explore, Apply It, Problem 8, “The Incas designed buildings with doors and windows shaped like trapezoids. One way to define a trapezoid is a quadrilateral with at least one pair of parallel sides. Draw two different trapezoids.” Session 3, Develop, Apply It, Problem 8, “Draw a quadrilateral in which all sides are not the same length, opposite sides are the same length, and there are no right angles. Then name the quadrilateral.” Session 4, Refine, Apply It, Problem 6, “Use the grid below. Draw a quadrilateral that belongs to at least two of these groups: parallelogram, rectangle, or square. Explain why your shape belongs to these groups.Show your work.”

The materials reviewed for i-Ready Classroom Mathematics Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of the grade. 

• The approximate number of Units devoted to major work of the grade, including supporting work connected to major work is 5 of 6 units, approximately 83%.

• The number of Lessons (Strategy and Math in Action) devoted to major work of the grade, including supporting work connected to major work is 33 of 39, approximately 85%. 

• The number of instructional days (including Strategy and Math in Action Lessons, Mid-Unit Assessments, and Unit assessments) devoted to major work of the grade, including supporting work connected to major work is 127 of 150, approximately 85%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of Strategy Lessons, Math in Action Lessons, and Unit Assessments. As a result, approximately 85% of the instructional materials focus on the major work of the grade.

The materials reviewed for i-Ready Classroom Mathematics Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

The materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Within Program Implementation, Correlations, Content Focus in the Common Core State Standards (CCSS), teachers are encouraged to "Use the tables to help inform i-Ready Classroom Mathematics instructional pacing so that students spend the majority of their time on the work of the major clusters, with time spent on supporting and additional clusters used to enhance that work." Examples of connections include:

• Unit 1, Lesson 2, Add Three-Digit Numbers, Session 4, Refine, Apply It, Problem 4, connects 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…), as students understand how to add and subtract three-digit numbers in order to solve two-step word problems using the four operations. Apply It, Problem 4, “Andre and his parents drive to see his older sister graduate from basic training. They drive 129 miles on Tuesday. They drive 78 more miles on Wednesday than on Tuesday. How many miles do they drive in all on Tuesday and Wednesday?” Answer choices: 51 miles, 207 miles, 285 miles, 336 miles.

• Unit 4, Lesson 26, Measure Length and Plot Data on Line Plots, Session 1 and 4, connect supporting work of 3.MD.4 (Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves or quarters) to the major work of 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram), as students measure objects to the nearest whole inch, half inch, and quarter inch in order to understand a fraction as a number on the number line. Session 1, Explore, Connect It, Problem 2, “ a. You can count by half inches on the ruler.  Fill in the blanks below by counting by half inches from 0 to 3 inches. 0 inches, \frac{1}{2} inches, 1 inch, ___ inches, ___ inches, ___ inches, ___ inches.” There is an image of a ruler marked with 0-3 inches. Each inch is divided into fourths.  There is a number line under the ruler labeled with fourths, halves and wholes. “b. What are the lengths of the top and bottom green beans to the nearest half inch? Top ____  Bottom ____.” There is an image of two green beans shown. There is an image of a ruler marked with 0-3 inches. Each inch is divided into fourths. There is also a number line under the ruler labeled with fourths, halves, and wholes. Session 4, Refine, Apply It, Problem 6, “Use an inch ruler for this problem. Part A, Measure the leaves to the nearest \frac{1}{4} inch. Record the lengths in the table. Part B, Complete the line plot using the measurements you recorded in the table.” There are images of leaves to be measured along with a table to put the measurement of each leaf in. There is a line plot titled “Leaf Lengths” with “Length (in inches)” labeled below the line plot.

• Unit 6, Lesson 33, Partition Shapes into Parts with Equal Areas, Session 1 and 2, connect 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}) and 3.MD.5 (Recognize area as an attribute of plane figures and understand concepts of area measurement), as students partition rectangles and describe the area as a fractional part of the area of the whole rectangle. Session 1, Explore, Connect It, Problem 2, “You can break apart the same shape into equal parts in a lot of ways. You can use fractions to describe the area that each part covers. Look at the rectangles below. The shaded areas of all four rectangles are both alike and different. a. What fraction of the area of rectangle A is shaded? What fraction of the area of rectangle B is shaded? What fraction of the area of rectangle C is shaded? What fraction of the area of rectangle D is shaded? b. For rectangles C and D, what unit fraction is equivalent to the fraction shown by the shaded parts?” Four rectangles are provided. The first two are partitioned into fourths in different ways with one fourth shaded. The second two are partitioned into eighths in different ways with two eighths shaded. Session 2, Additional Practice, Practice Partitioning Shapes into Equal Parts, Problem 8, “Divide rectangle D into 4 equal parts and divide rectangle E into 8 equal parts.” Problem 9, “Shade \frac{1}{4}of the area of each rectangle in problem 8.” There is an image of two congruent rectangles for students to partition and shade.

The materials reviewed for i-Ready Classroom Mathematics 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.

The materials are designed so major standards/clusters are connected to the major standards/ clusters of the grade as well as supporting standards/clusters being connected to supporting standards/clusters. Within Program Implementation, Correlations, Content Focus in the Common Core State Standards (CCSS), teachers are encouraged to "Use the tables to help inform i-Ready Classroom Mathematics instructional pacing so that students spend the majority of their time on the work of the major clusters, with time spent on supporting and additional clusters used to enhance that work.” Examples of connections include:

• Unit 2, Lesson 5, Multiply with 0,2, 5, and 10, Develop, Session 2, connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.B (Understand the properties of multiplication and the relationship between multiplication and division) and to the major work of 3.OA.C (Multiply and Divide within 100), as students find products with factors of 2, 5, and 10 by using skip-counting, equal group models, and arrays. Connect It, Problem 1, “Look at both Model Its. What multiplication equations can you write for the number of antennas and number of buttons?” Problem 2, “How do both types of models use skip counting?” Problem 3, “If you take the antenna array in the second Model It and turn it, what would the equation be for each way the array is shown?” Session 2, Apply It, Problem 9, “An airport bus has 8 rows of travelers. Each row has 5 travelers. How many travelers are on the bus?”

• Unit 2, Lesson 12, Session 1, Explore, Connect It, Problem 2, connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division), as students use multiplication to help solve division problems. “Fact families for multiplication and division are groups of related equations. All the equations, or facts, use the same three numbers. If you know one fact in a family, you can find all the others. a. Say you need to solve ___\div9=6. You can write the facts in this family to find one that you might know. Use the array to help you complete this fact family. 6\times9=___, 9\times6=___, ___\div=9, ___\div9=6 b. Look back at the problem on the previous page. Write the complete fact family using the three numbers for this situation.”

• Unit 3, Lesson 19, Scaled Graphs, Session 5, Refine, Apply It, Problems 2-3, connect 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) as students explore the idea that skip-counting and multiplication can help you read a picture graph. Problem 2, “Use the picture graph to solve problems 2 and 3. How much more snow fell in February and March combined than fell in November and December combined? Show your work.” Problem 3, “Which two months combined have the same amount of snowfall as February?” Answer choices: January and March, November and January, November and December, and December and March. A bar graph titled “Snowfall in New York City this Winter” is shown with Snowfall in inches and Months labeled. Units count by twos up to 14.

• Unit 5, Lesson 28, Liquid Volume, Session 3, Additional Practice, Practice Solving Word Problems About Liquid Volume, Problem 7, connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) and the major work of 3.OA.C (Multiply and divide within 100), the major work of 3.MD.A (Solve problems involving measurements and estimation of intervals of time, liquid volumes, and masses of objects) toas students solve one-step word problems involving volume (capacity). “A cow on Pabla’s family farm makes 32 liters of milk in one day. Pabla uses a 4-liter bucket to collect the milk. How many buckets of milk does she collect? Show your work.”

• Unit 6, Lesson 32, Area and Perimeter of Shapes, Session 2, Additional Practice, Practice Finding an Unknown Side Length, Problem 7, 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.D (Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.), as students add side lengths to find the perimeter of rectangles. “Takoda and his mother are building a sandbox in the shape of a hexagon. Each of the 6 sides of the hexagon is 6 feet long. What is the perimeter of the sandbox?”

The materials reviewed for i-Ready Classroom Mathematics 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.

Each Unit contains a Beginning of Unit section that provides numerous resources including a Lesson Progression and Math Background document for the teacher. The Lesson Progression identifies: “Which lessons are students building upon?”, “Which lessons are students preparing for?”, along with connections to prior and future work. The Math Background identifies “Information to unpack the learning progressions and make connections between key concepts.”

Examples of connections made to future grades include:

• Unit 3: Multiplication: Finding Area, Solving Word Problems, and Using Scaled Graphs, Lesson 18: Overview, Solve Two-Step Word Problems Using the Four Operations, Learning Progression, “In this lesson students model and solve two-step word problems involving all four operations and calculations with up to three-digit numbers. Students continue to use drawings, diagrams, words, tables, and equations with unknowns to represent situations in word problems…In Grade 4 students will model and solve multi-step word problems involving all four operations. Students will continue to write and solve equations with letters for unknowns, including division equations that require students to interpret the meaning of remainders.”

• Unit 5: Measurement: Time, Liquid Volume, and Mass, Lesson 28: Overview, Liquid Volume, Learning Progression, “In this lesson students are formally introduced to the concept of liquid volume. They learn how to relate the amount of liquid in 1 liter to the amount of liquid in containers they are familiar with…In Grade 4 students will further develop their understanding of liquid volume when they learn to convert liters to milliliters.”

• Unit 6: Shapes: Attributes and Categories, Perimeter and Area, and Partitioning, Lesson 30: Overview, Understand Categories of Shapes, Learning Progression, “In Grade 3 students discover that shapes can be described in more precise ways than just by the number of sides and angles and recognize that shapes can also be categorized by the attributes or characteristics. In Grade 4 students will classify shapes according to the presence or absence of parallel and perpendicular sides and angles of a specified size.”

Examples of connections made to prior grades include:

• Unit 2: Multiplication and Division: Concepts, Relationships, and Patterns, Lesson 13: Overview, Understand Patterns, Learning Progression, “In this lesson students extend their thinking about patterns by exploring patterns in a sequence of shapes and then in a number chart…In Grade 2 students explored patterns of odd and even numbers in a number chart.”

• Unit 4, Fractions: Equivalence and Comparison, Measurement, and Data, Lesson 20: Overview, Understand What a Fraction Is, Learning Progression, “In Grade 3 students develop a more formal understanding of fractions…In Grade 2 students used fraction language to describe dividing shapes into equal parts. They divided squares, circles, and rectangles into equal parts and named the parts as halves, thirds, and fourths. Through their work with models, students began to understand the concept of dividing a whole into equal parts.”

• Unit 6: Shapes: Attributes and Categories, Perimeter and Area, and Partitioning, Lesson 33: Overview, Partition Shapes into Parts with Equal Areas, Learning Progression, “In Grade 2 students divided shapes into equal parts, used fraction language such as halves, thirds, and fourths to describe the equal parts, and recognized that the combined equal parts make up the whole. In this lesson students first divide rectangles into equal parts. They recognize that equal parts have equal areas by combining their understanding of fractions as equal parts of a whole with their understanding of area of rectangles.”