2nd Grade - Gateway 1

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet the expectations that they assess grade-level content. 

i-Ready Teach and Assess is the portal through which both assessments and the Ready Classroom Mathematics Teacher Toolbox are housed. Unit Assessments are found in the Ready Classroom Mathematics Teacher Toolbox, Classroom Resources, Assess. Comprehension Checks are found in i-Ready, Teach and Assess, Assessment. 

The series is divided into units, and each unit has numerous opportunities for both formative and summative assessments that can be administered in online and/or paper and pencil formats. The online Teacher Toolbox includes two versions of Unit Assessments: Form A and Form B. Form A assessments are editable in each one of the units. The Form A assessments also have the grade level standard identified with a brief narrative of possible ways students could solve the item, and/or reasoning as to why specific multiple choice options are not accurate. Form A assessments also include a standards correlation chart, DOK levels, as well as a correlation to the lesson(s) related to each assessment question. Form B assessments do not include these features.

An additional assessment opportunity is provided through the online i-Ready Comprehension Check portal. This feature presents opportunities for teachers to load class rosters and collect data, and is described as “an alternative to the print Mid-Unit or Unit Assessment. For each of these assessments, the tables (below) provide a Depth of Knowledge (DOK), standard(s) addressed, and the corresponding lesson(s) assessed by each Item.” 

Above grade-level content addressing probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments. Examples of assessment items from the Classroom Resources tab aligned to Grade 2 CCSS include:

• In Unit 3, Assess, Mid-Unit Assessment - Form A Teacher, Item 4 states, “Skip-count to complete the number pattern. Write your answer in the blanks.” The pattern begins with 178, __, 198, __, __, 228 (2.NBT.2).
• In Unit 4, Assess, Mid-Unit Assessment - Form A Teacher, Item 12 states, “Fred wants to measure the height of his bedroom door in feet. Should he use a ruler or a measuring tape? Explain your choice.” The student will explain what they mentally see, a ruler or tape to measure heights of larger objects. (2.MD.1)
• In Unit 5, Assess, End of Unit, Unit Assessment - Form A Teacher, Item 2 states, “What are two different ways to find the total number of squares in the partitioned rectangle?” There is a rectangle given that has 3 columns and five rows. Students show that they can do “3 + 3 + 3 + 3 + 3” and “5 + 5 + 5” to count all the squares in the rectangle. (2.G.2)

Examples of assessment items from the Assess and Teach tab aligned to Grade 2 CCSS include:

• In Comprehension Checks, Comprehension Checks Details, Grade 2, Unit 1 (Lessons 4-5), Preview, Item 7 states, “Selena has 12 crayons. She finds 6 more. Then she gives 4 to a friend. How many crayons does Selena have now?” The choices given are 2, 10, 14, or 18. (2.OA.1).
• In Comprehension Checks Details, Grade 2, Unit 3 (Lessons 17-10), Preview, Item 3 states, “Decide if each comparison is true or false. Choose True or False for each comparison. 3 hundreds + 9 tens=309.” (2.NBT.4)
• In Comprehension Checks, Comprehension Checks Details, Grade 2, Unit 4, (Lessons 26-27), Preview, Item 3 states, “Look at the leaf and the paper clip. What is the best estimate of the leaf?” A paper clip of 1 inch is above the leaf. Students’ choices are: “1 inch, 2 inches, 4 inches, 8 inches.” (2.MD.3)

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for spending a majority of instructional time on major work of the grade. To evaluate focus on the grade, alignment to the major work with all of the clusters in 2.NBT, along with clusters 2.OA.A, 2.OA.B, 2.MD.A, and 2.MD.B were examined at the levels of unit, lesson, and instructional days. Of the three levels, instructional days were determined to be the most representative of the amount of instructional time spent on major work of the grade. 

Evidence: 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 3 of 5 units, which is approximately 60%.
• The number of lessons devoted to major work of the grade (including review days, assessments, and supporting work connected to the major work) is 26 of 37, which is approximately 70%. (Lessons in this series are taught over a number of instructional days.)
• The number of instructional days devoted to major work (including review days, assessments, and supporting work connected to the major work) is 132 of 179, which is approximately 73%. 

An instructional day analysis is most representative of the instructional materials because most lessons are taught over 4 to 5 days with review and assessment included. As a result, approximately 73% of the instructional materials focus on the major work of the grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

i-Ready Teach and Assess is the portal through which the Ready Classroom Mathematics Teacher Toolbox is housed. Supporting standards/clusters are connected to the major standards/clusters of the grade. For example:

• Lesson 4, Session 2, Develop, provides a connection between supporting cluster 2.MD.D (Represent and interpret data) and major cluster 2.OA.A (Represent and solve problems involving addition and subtraction) by using a graph to answer addition and subtraction problems. For example, Problem 6 states, “How many fewer students choose taco than pizza?” On the same page is a bar graph providing the data needed to answer the question. The graph shows 7 students choose pizza and 4 students choose tacos. Using this information, students will subtract “7 - 4 = 3” to solve. 
• Lesson 10, Session 4, Develop, provides a connection between the supporting cluster 2.MD.C (Work with time and money) and the major cluster 2.OA.A (Represent and solve problems involving addition and subtraction) by having students use money to solve addition and subtraction problems.  For example, Problem 1 states, “Write an addition equation to show how much Kane starts with.” The problem provides the blank equation “____+____+____=____.” The page above this one has the following story problem, “Liam has $100 bill. Kane has two $20 bills and one $5 bill. Kane gets more money for his birthday. Now he has the same amount of money as Liam. How much money does Kane get for his birthday?” Students will need to add “20 + 20 + 5 = 45” in the equation provided.
• In Lesson 31, Session 1, Explore Adding Using Arrays, the Learning Target states, “Understand subtraction as an unknown addend problem.” This connects 2.OA.C (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) with 2.NBT.A.2 (Count within 1000; skip-count by 5s, 10s, and 100s). Students set up arrays and repeated addition equations to find out how many objects are in an array. In Session 2, Develop, Try It, students put stickers in an array, “Each row has 5 stickers. Each column has 4 stickers. How many stickers are there in all?” Students skip count by 5s to come up with a solution of 20.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 182 days. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. 

i-Ready Teach and Assess is the portal through which teachers access the Ready Classroom Mathematics Teacher Toolbox. Pacing information from the publisher regarding viability for one school year can be found in the documents titled “Yearly Pacing” found in the Program Implementation tab on the home page for each grade level and in the Lesson Overview documents found under the Classroom Resource tab for each lesson. The sessions shown in the Lesson Overview documents do not match the Yearly Pacing. Yearly Pacing includes a list of units, lessons within each unit, and the number of days each lesson encompasses, a note that sessions are 45-60 minutes in length and number of days for assessments. The Grade 2 Lesson Overview documents show 147 days of instruction, 9 days for assessment, 10 days for “Math in Action” lessons, and 5 days for i-Ready diagnostic assessments. In addition to the days of math instruction, “Lesson 0” is included with 5 days of instruction at the beginning of the year to teach and establish instructional routines. Review days are also provided at the end of each unit for a total of 5 review days. This is a total of 182 days. 

 Pacing information is also verified in the Classroom Resources tab in each unit for each lesson in Lesson Overview and Family Connection which includes a Lesson Pacing Guide with more detailed information that lists sessions and minutes for each lesson.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for the materials being consistent with the progressions in the Standards. The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards.  

In i-Ready, Ready Classroom Mathematics, Classroom Resources, the materials clearly identify connections to prior and future grade-level work and progressions across grade levels. For example:

• In the beginning of each unit there is a Learning Progression flowchart which clearly identifies and connects the standards that are taught in the unit with information on “What lessons are children preparing for?” For instance, in Unit 2, Learning Progressions chart, Grade 1, Lesson 25, Add and Subtract Tens (1.NBT.C.4 and 1.NBT.C.6) links to Grade 1, Lesson 26, Understand 10 More and 10 Less (1.NBT.C.5); then to Grade 2, Lesson 6, Add Two-Digit Numbers (2.NBT.B.5 and 2.NBT.B.9) and Grade 2, Lesson 7, Subtract Two-Digit Numbers (2.NBT.B.5 and 2.NBT.B.9); and then to Grade 3, Lesson 3, Subtract Three-Digit Numbers (3.NBT.A.2) and Grade 4, Lesson 5, Subtract Whole Numbers (4.NBT.B.4). Content for future grades is identified in this way for lessons in all five units of the Grade 2 curriculum. 
• Each lesson includes a Learning Progression section that identifies related work from prior grades or prior units within the grade, work being done in the current lesson, and work to be done in future grades. For example, the Learning Progression section for Lesson 14 states “In Grade 1 students explore the concept of greater than and less than, comparing place values of two-digit numbers. They record comparisons using the symbols for inequalities. Students learn the meaning of the equal sign and apply it to equations. In Grade 2 students expand their understanding of numbers and place value as they explore three-digit numbers. They model, read, and write three-digit numbers in various forums, attending to the additional place-value position of the hundreds. Students further explore the concepts of equality and inequality as they measure and compare lengths. In this lesson students compare three-digit numbers through picture models, charts, and by using the terms greater than and less than. Numbers are applied to a variety of settings, extending the concept of number beyond physical quality. Students model situations involving inequalities using the appropriate symbol > or <. In Grade 3 and beyond, students apply their understanding of inequalities to fractions and decimals. They model inequalities on a number line and explore the meaning of the greater than, less than or equal to symbols used in algebraic sentences.”

The materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. For example:

• Lessons include between four and five sessions (days) focused on grade level tasks. During Develop, students explore ways to solve problems using multiple representations, digital tools, and prompts to reason and explain their thinking. In addition, the Develop and Refine sections of the lessons allow students to solve problems and discuss their solution methods. The independent practice and Math in Action lessons provides students the opportunity to work with problems in a variety of formats to integrate and extend concepts and skills
• In Unit 4, Lessons 20 and 21 address Standard 2.MD.1 (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes). In Lesson 20, Session 2, Develop, Apply It, Problem 8, “Tony says the crayon is 8 centimeters long. Explain what Tony did wrong. Then find the correct length of the crayon.” The Teacher materials state, “Error Alert: if students are unable to explain what Tony did wrong, then model the correct way to measure the crayon and compare the length with the result of counting the number of centimeters from 1 to 8.” Work on grade level is taught for the same standard providing two full lessons to cover the standard.
• In Unit 3, Lessons 12-19 address two- and three-digit numbers across 39 Sessions. In Lesson 12, students are introduced to three-digit numbers. Lesson 13 supports how to read and write those types of numbers. In Lesson 14, students compare three-digit numbers. In Lesson 15, students use mental math to add and subtract using the strategies of skip counting and adding/subtracting with 10 more or 10 less. In Lesson 16, students add three-digit numbers. In Lesson 17, students subtract three-digit numbers. In Lesson 18, students practice their strategies to add or subtract three-digit numbers. In Lesson 19, students add several two-digit numbers. 
• In Lesson 18, Session 2, Develop Fluency and Skills Practice includes 12 addition problems with three digit numbers. For example, Problem 12 states, “Show one way to complete the equation ________+________=754.” This last problem provides two unknown addends. 
• Additional components of the materials include math centers and enrichment activities which provide students with more time to work on grade level concepts. 

The materials provide explicit guidance for teachers and/or students that makes connection to prior knowledge in the Lesson Overview: Prerequisite Skills and at the beginning of some sessions with “Connect to prior knowledge.” For example:

• In Lesson 5, Prerequisite Skills states, “Solve one-step problems. Interpret a number line. Use a bar model to solve a one-step word problem.” For example, Session 3, Connect to Prior Knowledge states, “Have students use counters to show that 12 more than 6 is 18.” 
• In Lesson 32, Prerequisite Skills states, “Know doubles facts to 20. Skip-count by twos. Understand the meaning of equal groups.” In Session 1, Connect to Prior Knowledge states, “Have students make 2 equal groups and tell how they know the groups are equal.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meets expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. 

In i-Ready, Ready Classroom Mathematics, Program Implementation, there is a Correlations Guide. The guide lists each Cluster Heading and the standards for the grade, the Emphasis (Major, Supporting, or Additional), and the lessons which Focus, Develop, or Apply the standard. In Classroom Resources, each lesson includes a learning target that is visibly shaped by the CCSS Mathematics cluster headings.

Examples of where the mathematics in the materials make connections to cluster headings include:

• In Lesson 1, the Learning Target states, “Fluently add within 20 using mental strategies.” This Is shaped by 2.OA.B (Add and subtract within 20). 
• In Lesson 8, Lesson Overview, the Content Objective states, “Fluently break apart two-digit numbers into tens and ones as a place value strategy for addition and subtraction.” This connects to cluster heading 2.NBT.B (Use place value understanding and properties of operations to add and subtract). 
• In Lesson 16, the Learning Target states, “Add within 1000, using concrete models or drawings and strategies based on place value, properties of operations, relate the strategy to a written method.” This connects to cluster heading 2.NBT. B (Use place value understanding and properties of operations to add and subtract). 
• In Lesson 25, Session 1, the Learning Target states,  “Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units” is shaped by 2.MD.B (Relate addition and subtraction to length). 

Examples of connections between major domains, clusters, or standards in the Classroom Resources include: 

• Lesson 1, Session , connects 2.OA.A (Represent and solve problems involving addition and subtraction) to 2.OA.B (Add and subtract within 20), as students analyze one-step addition and subtraction word problems and write equations to represent the problems. Students also use fact families as a strategy to solve one-step problems, build number sense, and interpret models that represent one-step problems. 
• Lesson 15 connects the major cluster 2.NBT.A (Understand place value) and 2.NBT.B (Use place value understanding and properties of operations to add and subtract), as students “Write the missing number to show how to skip count from 235 by fives instead of tens.”
• Lesson 26, Session 1 connects with 2.OA.A (Represent and solve problems involving addition and subtraction) as students use the number line to add/subtract up to two-digit numbers with two-digit numbers. The materials state: “Show a length of 10 on the number line. Then show a length of 12 more on the number line. What is the total length shown on the number line?”