2nd Grade - Gateway 1

The materials reviewed for i-Ready Classroom Mathematics Grade 2 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 2 materials contain five units, with each unit providing numerous opportunities for both formative and summative assessments. Summative assessment items include:

• Unit 2, Assess, Unit Assessment, Form A, Item 1, “A store has 38 red flags and 34 blue flags for sale. The store sells some flags. Now there are 45 flags left at the store. How many flags did the store sell? Show your work. The store sold ____ flags.” (2.OA.1)

• Unit 3, Assess, Mid-Unit Assessment, Form A, Item 8, “Which numbers are greater than 342? Choose all the correct answers.” Answer choices include: 351, 432, 234, 343, 423, and 339.  (2.NBT.4)

• Unit 4, Assess, Mid-Unit Assessment, Form A, Problem 8, “Use a ruler to measure the length of each stick in centimeters. Then compare the lengths. Write your answers in the blanks. ____ centimeters ____ centimeters. The bottom stick is ___ centimeters longer than the top stick.” An image of two sticks are shown for students to measure. (2.MD.4)

• Unit 5, Assess, Unit Assessment, Form B, Item 1, “Yvonne has a triangle. How many angles does it have? Write your answer in the blank. ___ angles.” (2.G.1)

The materials reviewed for i-Ready Classroom Mathematics Grade 2 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 1, Lessons 1 and 2, engage students with the full intent and extensive work with 2.OA.2. (Fluently add and subtract within 20 using mental strategies…). Lesson 1, Mental Math Strategies for Addition, Session 1, students “Explore the idea that there are different ways to add within 20.” and “Understand that making a ten is one strategy that can be used to find the sum.” Explore, “In this lesson, you will use different strategies to add numbers in your head. Use what you know to try to solve the problem below. Jason is taking a jeepney to school. There are 8 people on the jeepney. Then 4 more people get on. How many people in all are on the jeepney?” Connect It, Problem 2c, Show how to make a ten to find 8+5. Complete each equation with the unknown number. 8+___=10; 10+___=13; So, 8+5=___. In Session 2, Additional Practice, Practice Adding by Counting On or Making a Ten, Problem 6, “Find 9+2 by counting on or making a ten. Show your work. Explain why you chose that strategy.” In Sessions 3 and 4, students continue using various strategies to add within 20. Lesson 2, Mental Math Strategies for Subtraction, Session 1, students “Explore the idea that subtraction with a two-digit number can be done in steps.” and “Understand that you can break apart a number to make subtraction easier.” Explore, “In this lesson, you will use different strategies to subtract numbers in your head. Use what you know to try to solve the problem below. Alo has 14 stamps. He uses 6 stamps to mail letters to his shichu who lives in Arizona. How many stamps does Alo have left?” Session 2, Apply It, Problem 6, “Use what you just learned to solve these problems. Show how to find 12-7=? by counting on.” Problem 7, “Find 15-7 by making a ten using equations.” Problem 8, “Use the answer from problem 7 to fill in the squares on the open number line.” In Session 3 and 4, students continue using strategies (relationship between addition and subtraction, fact families, number bonds, etc.) to solve addition and subtraction problems. Session 4, Refine, Apply It, Problem 3, “Which equations are in the fact family for the number bond? Choose all that apply. A. 12=7+5; B. 19=12+7; C. 7=12-5; D. 12=5+7; E. 5=12-7.” Problem 4, “Jamila takes box braids out of her hair. She starts with 18 braids and takes out 9 braids. How many braids are left in Jamila’s hair?” Answer choices: 17, 11, 9 and 7. 

• Unit 3, Lessons 16, 17, and 18, engage students with the full intent and extensive work with  2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction…). Lesson 16, Add Three-Digit Numbers, Session 1, Explore, Try It, students add hundreds, tens, and ones. “You already know about hundreds, tens, and ones in three-digit numbers. Now you will use strategies to add three-digit numbers. Use what you know to try to solve the problem below. Tayen and her grandmother are making a jingle dress. Tayen’s grandmother puts 234 cones on the dress. Tayen puts 131 cones on the dress. How many cones do Tayen and her grandmother put on the dress?” Students use different strategies to solve the problem, then discuss their strategies with a partner. Connect It, Problem 2, “You can also show jumps on an open number line to add three-digit numbers. What is 248+143? Write the missing numbers on the open number line to find the sum.” There is an open number line with 248, 348, 388 labeled for the first two jumps. Session 2, Develop, Adding and Regrouping Ones, pg. 408, students “Explore different ways to understand adding three-digit numbers.” “There are 254 adults and 328 children helping to clean up their city. How many people are helping to clean up the city? Picture It: You can show your numbers in a quick drawing.” Image shows students how to draw base-ten blocks to model the numbers. “Model It: You can show jumps on an open number line.” An image shows students how they can use the open number line pictured. “Model It: You can break apart addends.” An image shows students how they can rewrite the numbers in expanded form. Session 2, Develop, Apply It, Problem 6, “Find the sum. Show your work. 167+426=.”  Lesson 17, Subtract Three-Digit Numbers, Session 1, Explore, Try It, students subtract hundreds, tens, and ones. “You know how to subtract two-digit numbers. Now you will learn to use place value to subtract three-digit numbers. Use what you know to try to solve the problem below. Anica has 368 pet pal cards. Tiva has 243 cards. How many more cards does Anica have than Tiva?” Session 2, Develop, pg. 432, “Explore different ways to understand subtracting three-digit numbers.” “One day there are 450 camp sites being used at Yosemite National Park. 218 of the sites have a camper. The rest have a tent. How many of the camp sites have a tent? Picture It: You can make a quick drawing.” An image shows students how they can draw base-ten blocks to represent the problem. “Model It: You can subtract hundreds, tens, and ones.” An image shows students how to subtract one place- value of the subtrahend at a time. “Model It: You can break apart the numbers.” An image shows students how to rewrite the problem in expanded form to subtract. Session 2, Additional Practice, Practice Regrouping Tens to Ones, Problem 4, “472 people see a dancing show. On Saturday, 248 people see the show. The rest see it on Sunday. How many people see the show on Sunday? Show your work.” Lesson 18, Use Addition and Subtraction Strategies With Three-Digit Numbers, Session 1, Additional Practice, Prepare for Using Strategies to Add and Subtract Three-Digit Numbers, Problem 1, students use strategies to add and subtract three-digit numbers. “Think about what you know about adding and subtracting. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.” Session 3, Additional Practice, Practice Using Subtraction Strategies with Three-Digit Numbers, Problem 1, “Max scores 372 points in a computer game. Valeria scores 481 points in the same game. How many fewer points does Max Score than Valeria? Find 481-372. First regroup 1 ten as 10 ones in 481. Then subtract. 481=400+___+___-372=300+___+___=___+0+___.”  Session 4, Refine, Apply It, Problem 2, “A store has 328 bags of pumpkin seeds and 519 bags of sunflower seeds for sale. How many bags of seeds does the store have in all? Show your work.” Problem 3, “A male California sea lion weighs 436 pounds. A female sea lion weighs 219 pounds less than the male. How many pounds does the female sea lion weigh?” Answer choices: 217, 227, 645, and 655.

• Unit 4, Lessons 20 and 21, engage students with the full intent and extensive work with  2.MD.1 (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes). Students measure and estimate lengths in standard units. Lesson 20, Measure in Inches and Centimeters, Session 1, Explore, Connect It, Problem 3, students determine the more useful way to measure an item.  “Kofi says it is more useful to measure a shoelace with a ruler than with paper clips. Explain why.” Session 2, Additional Practice, Practice Measuring in Inches and Centimeters, Problem 3, “Use a ruler to measure the length of the root vegetable in centimeters. What is the length of the root vegetable?” Session 3, Refine, Apply It, Problem 5, “Use a ruler. What is the length of the piece of celery?” Answer choices: 9 centimeters, 10 centimeters, 11 centimeters, and 12 centimeters. Lesson 21, Measure in Feet and Meters, Session 1, Explore, Connect It, Problem 2, “Rulers often show both inches and centimeters. Many rulers show 12 inches. This is equal to 1 foot. a. How many inches are in the ruler? b. How many centimeters are on the ruler?” Session 2, Develop, Apply It, Problem 6, “Caton measures his wagon. He says that it is about 2 feet long. Carmela says that it is about 3 feet long. Who is correct? Explain your answer.” Session 3, Develop, Apply It,  Problem 5, students decide if it is better to measure with a centimeter ruler or a meter stick. “Circle the objects that are easier to measure with a centimeter ruler. Underline the objects that are easier to measure with a meter stick.” Answers include: picnic table, toothbrush, sofa, crayon, piano, and slice of bread. Session 4, Refine, Apply It, Problem 9, students are given additional practice choosing the correct measurement tool between rulers, and meter sticks, and measuring tape. “Jabari wants to measure the length of a parking spot in meters. He says the best tool to use is a ruler. Do you agree? Why or why not?”

• Unit 5, Lesson 28, Recognize and Draw Shapes, Sessions 1-4, engage students with the full intent and extensive work with 2.G.1 as they “use the number of sides and angles to identify, name and classify polygons. Students reason logically when they generalize attributes of shapes and in determining when an attribute can be applied to all of one kind of polygon, some of them or none.” Session 1, Explore, Connect It, Problem 2, “The number of sides, vertices (corners), and angles tells what group a shape belongs to. a. Which arrow is pointing to a side?___ a vertex?___ an angle?___ b. The shape formed by two sides at an angle is a vertex. How many vertices does this shape have? c. A quadrilateral is a shape with 4 sides, 4 vertices, and 4 angles. Name a quadrilateral shape.” Reflect, Problem 3, “A pentagon has 5 sides, 5 vertices, and 5 angles. Is the shape above a pentagon. Explain.” An image of a pentagon is shown. Session 2, Develop, students, “Recognize and draw shapes with specified attributes and recognize that shapes have a specific number of sides, angles, and vertices.” Apply It, Problem 4, “Look at the number of sides, angles, and vertices of each shape below. Sort the shapes. Write each shape’s letter in the correct column.” 12 shapes are provided and labeled with letters A-L. Column categories include triangles, quadrilaterals, pentagons, and hexagons. Session 3, Develop, Connect It, Problem 1, “Look at the first Picture It. How many faces does a cube have?” Problem 5, “Pick up a cube. How many edges does a cube have? How many vertices? A cube has ___ edges and ___ vertices.” Session 4, Refine, Apply It, Problem 1, “Draw a shape that has 5 sides. Write the name of the shape. Show your work.” Problem 9, “Draw a shape that has between 3 and 6 sides. Use the dots below. What is the name of your shape? Explain how you know.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 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 4 of 5 units, approximately 80%.

• The number of Lessons (Strategy and Math in Action) devoted to major work of the grade, including supporting work connected to major work is 31 of 37, approximately 84%. 

• 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 122 of 141, approximately 87%.

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 87% of the instructional materials focus on the major work of the grade.

The materials reviewed for i-Ready Classroom Mathematics Grade 2 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 4, Draw and Use Bar Graphs and Picture Graphs, Sessions 3-4, connects the supporting work of 2.MD.10 (Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions…), as students create and use bar graphs in order to complete addition and subtraction problems. In Session 3, Develop, Apply It, Problems 5-7, “Apply It. Use what you just learned to solve these problems.” Problem 5, “Make a bar graph to show the favorite color data.” Problem 6, “Make a picture graph to show the favorite color data. Problem 6, Make a picture graph to show the favorite color data.” Problem 7, “One student changes their favorite color from blue to green. How will this change your bar graph? How will this change your picture graph?” In Session 4, Refine, Apply It,  Problem 2, “Yuko makes this graph on Sunday morning. Then she reads 2 more books that day. Fill in the graph to show how many books she read in all on Sunday.” Problem 3, “How many fewer books did Yuko read on Friday than on Saturday?”

• Unit 2, Lesson 11, Tell and Write Time, Session 1, Explore, Connect It, Problems 1-3, connect the supporting work of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) to the major work standard of 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s), as students skip count by 5s in order to read and write time to the nearest 5 minutes. Problem 1, “What time does Kia play the banjo? Problem 2, “a. What number did the hour hand just go past? b. What number is the minute hand pointing to?, c. Skip-count by fives to find the number of minutes.” Problem 3, “Why can you skip-count by fives to show there are 60 minutes in an hour?”

• Unit 5, Lesson 31, Add Using Arrays, Session 2, Develop, Apply It, Problems 7-8, connect the supporting work of 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends) to the major work of 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s), as students find the total number of objects arranged in rectangular arrays in order to count within 1000 and skip count by 5s, 10s, and 100s. Problem 7, “Andre makes an array of toy cars. Write two equations you could use to find the total number of cars in Andre’s array. Show your work.” Problem 8, “A phone has 4 rows of buttons. Each row has 3 buttons. Draw an array to show the buttons on the phone. Then write and solve an equation to find the total number of buttons on the phone. Show your work.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 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 1, Lesson 3, Solve One-Step Word Problems, Session 2, Develop, Apply it, Problems 6-7, connect the major work of 2.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 2.OA.B (Add and subtract within 20), as students solve word problems using numbers within 20. Problem 6, “Ming goes to the store. He buys 12 carrots. 7 are purple. The rest are orange. How many orange carrots does Ming have? Write an equation to solve. Show your work.” Problem 7, “Tam has 13 books to give away. How many can he give to his brother and how many to his cousin? Show your work.”

• Unit 3, Lesson 19, Add Several Two-Digit Numbers, Session 2, Additional Practice, Problems 4-6 connect the major work of 2.NBT.A (Understand place value.) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract.), as students use place value understanding to add four 2-digit numbers. “A fruit stand has 47 apples and 49 pears for sale. It also has 53 peaches and 62 plums. Problem 4, Break each number into tens and ones. 47=___+___53=___+___49=___+___ 52=___+ ___. Problem 5, How many pieces of fruit are there in all? Show your work. Problem 6, Lateefah babysits for 4 days. She earns $29, $34, $36, and $52. What is the total amount of money Lateefah earns? Show your work.”

• Unit 4, Lesson 24, Compare Lengths, Session 3, Develop, Apply It, Problem 6, connects the major work of 2.MD.A (Measure and estimate lengths in standard units.) to the major work of 2.MD.B (Relate addition and subtraction to length.), as students measure lengths and add or subtract lengths to solve problems. “What is the difference in lengths of the pieces of ribbon, in centimeters? Show your work.” An image of 2 ribbons of different lengths is shown. 

• Unit 5, Lesson 30, Partition Rectangles, Session 2, Additional Practice, Problems 5 and 8, connects the supporting work of 2.OA.C (Work with equal groups of objects to gain foundations for multiplication.) to the supporting work of 2.G.A (Reason with shapes and their attributes.), as students use repeated addition to find the number of squares partitioned in a rectangle. Problem 5, “Write an equation to find how many squares are in the rectangle. ___ +___+___=___ How many squares are in the rectangle? ___ squares.” An image is shown of a rectangle partitioned into 2 rows of 3 squares. Problem 8, “Yolanda plans two games on the blacktop playground. She draws two rectangles that are the same size. Draw lines to show two different ways to break apart the rectangles into same-size squares.”

• Unit 5, Lesson 31, Add Using Arrays, Session 3, Refine, Apply It, Problems 7 and 9, connects the supporting work of 2.OA.C (Work with equal groups of objects to gain foundations for multiplication.) to the supporting work of 2.MD.C (Work with time and money.), as students refine strategies for solving problems using arrays. Problem 7, “Alita’s loteria board forms an array. It has 4 rows and 4 pictures in each row. Draw an array to represent the board. Show how to use a doubles fact to find the total number of pictures.” Problem 9, “Explain how to write two different equations to find the total number of pennies.” An image of 2 rows with 5 pennies in each row is shown.

The materials reviewed for i-Ready Classroom Mathematics Grade 2 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 2: Numbers Within 100, Lesson 10: Overview, Solve Word Problems Involving Money, Learning Progression, “In Grade 2 students explore concepts of money with coins and denominations of bills. In Grade 3 and beyond, students will continue to solve problems involving money. They recognize that coins represent a fraction of a dollar and use the decimal point to separate dollars from cents.”

• Unit 4: Length, Measurement, Addition and Subtraction, and Line Plots, Lesson 22: Overview, Understand Measurement with Different Units, Learning Progression, “In Grade 3 choosing an appropriate unit will continue to be important as students begin to measure volumes and weights in addition to lengths. Students will apply what they know about measuring lengths to problems involving perimeter and area.”

• Unit 5: Shapes and Arrays: Partitioning and Tiling Shapes, Arrays, Evens and Odds, Lesson 29: Overview, Understand Partitioning Shapes into Halves, Thirds, and Fourths, Learning Progression, “In Grade 3 students focus on fractions as equal areas of a shape in preparation for using an area model in Grade 4. They read and write fractions on a number line. Students expand their understanding of fractions to sixths and eighths. They compare fractions in varied ways and find equivalences, preparing them for adding fractions.” 

Examples of connections made to prior grades include:

• Unit 2: Numbers Within 100, Lesson 11: Overview, Tell and Write Time, Learning Progression, “In Grade 1 students explore time by reading an analog and a digital clock, telling time in hours and half hours. They write time using a colon to separate the hour and minutes. In Grade 2 students expand on their understanding of time and reading a clock as they explore duration and passage of time.”

• Unit 3: Numbers Within 1,000 Place Value, Addition, and Subtraction, Lesson 13: Overview, Read and Write Three-Digit Numbers, Learning Progression, “In Grade 1 students explore the concept of place value by bundling 10 ones to make groups of 10. They learn to read numbers between 9 and 99 and write them using proper digit placement.” 

• Unit 5: Shapes and Arrays: Partitioning and Tiling Shapes, Arrays, Evens and Odds, Lesson 32: Overview, Odd and Even Numbers, Learning Progression, “In Grade 1 students skip-count by 10s and learn doubles and doubles + 1 facts. They also examine the concept of equality and equal shares.”