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Our Review Process

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### Overall Summary

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for Alignment to the CCSSM. The materials meet the expectations for Focus and Coherence by assessing grade-level content, spending the large majority of instructional time on major work of the grade, and they are coherent with the progressions of the standards, making meaningful connections between supporting and major work of the grade, are viable for a school year, and present all students with opportunities to engage in extensive work with grade-level problems to meet the full intent of grade-level standards. The materials meet the expectations for Rigor and Mathematical Practices as they meet the expectations for Rigor and Balance and meet the expectations for Practice-Content Connections. The materials balance the rigorous expectations of the Standards, and they attend to Practice-Content Connections, addressing all of the Mathematical Practice Standards; however, there are instances where these are over-identified.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for focusing on the major work of the grade and are coherent with the Standards. The materials do not assess topics before the grade-level, spend at least 65% of class time on the major clusters of the grade, and are coherent and consistent with the Standards.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content and, if applicable, content from earlier grades.

##### Indicator {{'1a' | indicatorName}}
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

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)

#### Criterion 1.2: Coherence

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet the expectations for students and teachers using the materials as designed and devoting the majority of class time to the major work of the grade. Overall, instructional materials spend at least 65% of class time on the major clusters of the grade.

##### Indicator {{'1b' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

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.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet the expectations for being coherent and consistent with the Standards. Overall, the instructional materials connect supporting content to enhance focus and coherence, are consistent with the progressions of the standards, foster connections at a single grade, where appropriate, and include extensive work with grade level problems to meet the full intent of grade-level standards.

##### Indicator {{'1c' | indicatorName}}
Supporting content enhances focus and coherence simultaneously by engaging students in 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.
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

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.

##### Indicator {{'1e' | indicatorName}}
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

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:

• 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.”
##### Indicator {{'1f' | indicatorName}}
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

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?”

### Rigor & Mathematical Practices

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet the expectations for alignment with the Standards’ expectations for rigor and the mathematical practices. The instructional materials attend to each of the three aspects of rigor individually, and also attend to balance among the three aspects. The instructional emphasize mathematical reasoning, attend to the full intent of each practice standard; however, there are instances where the practice standards are overidentified.

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet the expectations for reflecting the balances in the Standards, and helping students to meet the Standards’ rigorous expectations by helping students develop and demonstrate conceptual understanding, procedural skill and fluency, and application. The instructional materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications, and do not always treat the three aspects of rigor together or separately.

##### Indicator {{'2a' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop conceptual understanding. For example:

• In Lesson 17, Session 1, Explore, Try It, students build on what was learned in Lesson 16 with addition to solve subtraction strategies. The beginning of each session focuses on the use of visual/concrete models. Apply It focuses on the use of expanded form to teach the standard algorithm. Regrouping starts at Session 2 with tens and ones, Session 3 regroups hundreds to tens, Sessions 4 and 5 allow for regrouping anywhere in the problems.
• In Lesson 18, Session 1, Explore, students use whatever strategies they are comfortable with to solve three-digit number problems. Students review using open number lines and place value charts. Apply It states, “For all problems, encourage students to use a drawing, a model, or equations to support their thinking.” For Sessions 2-4, students are given choices to use the strategies they want. In Session 5, students have to solve two open number line problems in the Apply It problems.
• In Lesson 19, Session 2, Develop, Model It states, “Break each number into tens and ones. Then add pairs of numbers.” The problem shows the addends 16, 41, 22, and 39 written into a place value chart. Students are developing conceptual understanding of 2.NBT.6.

Examples of students independently demonstrating conceptual understanding include:

• In Lesson 5, Student Worktext, Session 2, Develop, Problem 5, Reflect states, “Look back at your Try it, strategies by classmates, and Picture it and Model it. Which models or strategies do you like best or solving two-step problems? Explain.” (2.NBT.9)
• In Lesson 16, Session 2, Develop, Apply It states, “For all problems, encourage students to break apart the addends into hundreds, tens and ones to find the solution.” (2.NBT.7)
• In Lesson 31, Student Worktext, Session 2, Develop, Try It states, “Mike puts some stickers into an array. Each row has 5 stickers. Each column has 4 stickers. How many stickers are there in all?” (2.OA.4)  Understanding arrays builds conceptual understanding for multiplication in later grades.
• In Interactive Practice, Understand Three Digit Numbers, students use virtual base ten blocks, place value charts, and expanded form to understand three-digit numbers. (2.NBT.1)
• In Interactive Practice, Understanding Partitioning Shapes, students reason about how shapes are partitioned and whether more pieces is the same as a greater amount of the whole. (2.G.3)
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. The materials include problems and questions, interactive games, and math center activities that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade.

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop procedural skill and fluency throughout the grade level. For example:

• In Lesson 1, Session 1, Explore states, “complete each equation to show how to make a ten to add 8+5.” Students then show “8+2=10, 10 +3=13, so, 8+5=13” by filling in the blanks with missing numbers.  Students build procedural skill by learning to make a 10 to add numbers with sums greater than 10.
• In Lesson 6, Session 1, Explore, Connect It, students use two different procedures with base-ten blocks for adding 27+15. In the first procedure, students “Go to the next ten” by showing “27+3=30, 30+10=40, 40+2=42.” In the second procedure, students “Add tens, then ones.” Students show that 20+10=30, 7+5=12, and 30+12=42.
• In Lesson 20, Session 2, Develop, Apply It states, “Tony says the crayon is 8 centimeters long. Explain what Tony did wrong. Then find the correct length of the crayon.” A picture of a crayon being measured by a ruler is shown, the crayon is being measured starting at the one inch mark. Students are developing the procedural skill of measuring from the 0 inch mark.

2.OA.2 (Fluently add and subtract within 20 using mental strategies. By the end of 2nd grade know from memory all sums of two one digit numbers) requires students to develop grade level fluency. This standard is addressed in several lessons, including:

• In Lesson 2, Session 4, Refine, Develop Fluency states, “Why: Support students’ facility with fact families. How: Have students write the four equations to represent the fact family below.”
• In Unit 1, Math in Action, Student Worktext states, “Beau wants to build a shelf to store his 16 robot motors. Look at his plan. Shelf Plan: Use up to 6 shelves. Put at least 3 and no more than 6 robot motors on each shelf. How many shelves should Beau make? How many motors should he put on each shelf?”

The instructional materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. Within each lesson, there are Fluency and Skills Practice pages that children complete on their own.  Some examples of when students get opportunities to demonstrate procedural skill and fluency in Classroom Resources include:

• In Lesson 2 Fluency and Skills Practice, eight problems show a subtraction equation and the related addition equation (ex. 12-3=?, 3+?=12) and Problem 9 states, “In problem 6, how did you use your first answer to find your second answer?”
• In Lesson 6 Fluency and Skills Practice, seven pairs of problems are presented where one shows the numbers decomposed as tens and ones and the other problem that shows two addends. For example, Problem 1 shows 30+7+50+3 and Problem 2 shows 37+53, and Problem 15 states, “How does the information in number 9 help you solve number 10?” (2.NBT.5)
• Learning Games which provide independent practice include:
• In Match, students match the card that has two numbers or a number and dots that are being added/subtracted to the other card that shows the correct answer.
• In Hungry Fish, students combine the numbers in the bubble together until they equal the amount shown on the fish. Levels Addition 11-15, 16-20, 21-30, 31-100, 10s and 100s and Subtraction 11-15, 16-20, 21-30, 31-100, 10s, and 100s are appropriate for Grade 2.
• In the Math Center Activities, there are games provided to work on adding within 20.
• The Lesson 1 game, Make a Ten, focuses on solving missing addend equations so that the student can solve, his/her partner checks, and then he/she moves the marker on the game board.
• In Lesson 2 game, Use Mental Math to Subtract, students pick a card, put connecting cubes together, break off some and hide them, and then the partner has to guess how many are hidden.
• In the Math Center Activities, there are games provided to work on adding with 100, including:
• In the Lesson 2 game Doubles and Near Doubles, students use dice to roll and double numbers covering a game board based as students play.
• In the Lesson 6 game 100 or Not, students use number cards to make two-digit numbers to add. If their solution is within 100, students get a counter.
• In the Lesson 8 game First to 5 (or 10), students play using an operation pile and number card pile. Students draw an operation (+ or -) and then two number cards.
##### Indicator {{'2c' | indicatorName}}
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The instructional materials include some opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level.

Opportunities for students to independently demonstrate the use of mathematics flexibly are present in a variety of contexts. The instructional materials demonstrate multiple opportunities for students to engage in routine application of mathematics of the grade level in the i-Ready, Assess & Teach, Classroom Resources, including:

• In Lesson 3, Session 1, Explore states, “Fola has 8 berries. Her dad gives her some more berries. Now, Fola has 13 berries. How many berries did Fola’s dad give her?” (2.OA.1)
• In Lesson 3, Student Worktext, Session 3, Develop, Problem 7 states, “Explain how you would solve this problem. Ken has 10 toy cars. He has 4 more toy cars than Sarah. How many toy cars does Sarah have?” (2.OA.1)
• In Lesson 6, Session 3, Develop states, “Directions- Read and try to solve the problems below. There are 48 students on Bus A and 43 students on Bus B. How many students are on both buses?”
• In Lesson 7 Subtract Two-Digit Numbers, Session 2, Develop states, “Directions- Read and try to solve the problem below. There are 54 children at camp. 27 are girls. How many boys are at camp?”
• In Lesson 8, Session 3, Develop states, “Directions- Use what you learned to solve these problems. Problem- There are 65 cherries in a bowl. Dan eats 12 cherries with his lunch. How many cherries are in the bowl now?”
• In Lesson 25, Student Worktext, Session 3, Develop, Problem 6 states, “Luisa has a piece of yarn that is 38 inches long. Daryl has a piece of yarn that is 4 inches shorter than Luisa’s. They need 75 inches of yarn for their craft project. Do they have enough yarn? Explain your answer.”
• In Lesson 25, Session 3, Develop states, “Ed has two dog leashes. The purple leash is 84 inches long. The red leash is 75 inches long. How much shorter is the red leash than the purple leash?”

The instructional materials include multiple opportunities for students to engage in non- routine application of mathematical skills and knowledge of the grade level.

For example, in Classroom Resources:

• In Unit 1, Math in Action states, “Solve each problem on a separate sheet of paper. Example Problem- Beau has 17 jars. He needs at least 8, but no more than 12 jars for a Science project. He will put the rest of the jars on a shelf. How many jars could Beau use for the science project? How many will be left to put on the shelf?” (The problem shows a picture of 18 jars.)
• In Lesson 3, Session 5, Refine, Apply It, Problem 5 states, “Write a problem that can be solved using the bar model at the right. (6, ?, 8) Then show how to solve your problem.” This non-routine problem gives a sample student solution of “I have 8 stuffed toys. 6 are bears. The rest are dogs. How many stuffed dogs do I have? I can write and solve an equation 8 - 6 = 2; I have 2 stuffed dogs.”
• In Unit 2, Math in Action, Session 1 states, “Zoo Tours: A total of 58 people sign up for a tour of the zoo today. Alex has to make groups for the tour. Look at the notes. Zoo Tour Notes - tour groups must have at least 12 people, Tour groups can have no more than 20 people, There can be up to 4 groups in one day.”
• The Unit 2 Performance Task provides an opportunity for students to solve a non-routine application problem. Students are tasked with finding out how many of each type of cupcake Nicole bakes. The materials state: “Nicole bakes chocolate and vanilla cupcakes for a party. Some of the cupcakes have frosting. The rest have no frosting. Use the clues to find out how many of each cupcake Nicole bakes.” Students are then given clues to figure out the problem.
##### Indicator {{'2d' | indicatorName}}
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

All three aspects of rigor are present independently throughout the program materials. The instructional materials attend to conceptual understanding, procedural skill and fluency, and application independently throughout the grade level.

Students engage in instruction and activities to develop conceptual understanding of grade level mathematics:

• In Lesson 3, Session 1, Explore, Connect to Prior Knowledge, students practice conceptual understanding of part-part-whole. The directions state, “Why: Support students' understanding of part-part-whole relationships to prepare for solving addition and subtraction word problems. How: Have students use counters to show 14 as the sum of any two of its addends.”

Students engage in instruction to develop procedural skills and fluency appropriate for Grade 2:

• In Lesson 31, Session 2, Develop, Picture It & Model It, students are given an array of stickers. Students show that they can add 4 together 5 times or add 5 together 4 times. Students continue to practice drawing arrays and finding two ways to write repeated addition problems for each problem in the rest of this Session.

Students use mathematical understanding and skill to solve application problems:

• In Lesson 18, Session 1, Explore states, “You know how to add and subtract three-digit numbers. Use what you know to try to solve the problem below. Ms. Mendez’s class has 243 storybooks. Then the class gets some new storybooks. Now the class has 372 storybooks. How many new storybooks does Ms. Mendez’s class get?” Students apply the skills they have learned about adding and subtracting to a problem with three-digits.

Multiple aspects of rigor are engaged simultaneously at times to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

Examples where two or more of the aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials include:

• In Lesson 3, Session 3, Explore, students develop conceptual understanding of solving one-step word problems by using a ten-frame to solve the problem. As students develop conceptual understanding of building tens to help in adding, they also gain fluency in grade level appropriate addition. Students also apply their understanding and procedural skill to solve mathematics applications to real-world word problems.
• In Lesson 4, Student Worktext, Session 2, Develop, students use their conceptual understanding of reading bar graphs and creating equations to solve the problem. For example, “Martin asks the students in his class: What is your favorite sport? He makes a picture graph and a bar graph to show his results. How many students does Martin ask?” Students are applying their understanding of bar graphs and equations to application problems.
• In Lesson 27, Session 3, Develop, Additional Practice, Problem 5, students measure lengths of ribbon to organize and label the measurements in a line plot. This is an example of both real world application and procedural skills together within one problem.

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for Practice-Content  connections. Overall, the materials attend to the full meaning of the mathematical practices, however; there are instances where the practice standards are over-identified.

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The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Program Implementation, “Standards for Mathematical Practices in Every Lesson” states that the Deepen Understanding part of lessons describes that the Student Worktext learning targets are linked to the MPs.  Each lesson routine is outlined with the specific MPs that are addressed. Try It focuses on MPs 1, 2, 4, 5, and 6; Discuss It focuses on MPs 2, 3, and 6; and Connect It focuses on MPs 2, 4, and 5. These routines are present in each lesson, however teachers are not provided with specific guidance or direction as to how each routine in each lesson is engaging students with the practices. For example, in Unit 5, Lesson 30, the Correlation document indicates that MP 1, 2, 3, 4, 5, 6, 7, and 8 are emphasized in the Lesson. The CCSS Focus in the Lesson Overview indicates that MP 4, 5, 7, and 8 are emphasized in the lesson.  Only MP7 is tagged in the Lesson where this MP is included. The materials state, “In addition to SMPs 1, 2, 3, 4, 5, and 6, which are integrated into the instructional routine, the Teacher’s Guide includes additional opportunities for children to develop habits of mind described by the Standards for Mathematical Practice.”

Mathematical Practices are explicitly connected to the mathematical content. Examples of connections include:

• In Lesson 5, Session 3, Develop, Deepen Understanding, MP 2 states,  “When discussing the explanation and the picture, consider how the representations of the information in the problem are shown. Ask: Meg says there are 6 soccer balls in the big bag. What did she do wrong? Listen for: Meg may have subtracted 3 from 9 because the problem gives 2 numbers (3,9) and the word fewer. There are more soccer balls in the big bag than the small bag, but 9 is not less than 6. Meg found 3 fewer than 9 instead of finding the number for which 9 is 3 fewer. Ask: How could Meg restate the problem to help her understand it better? Listen for: Students may comment that 3 fewer in the small bag means 3 more in the big bag, that the larger number is unknown, or that adding 3 to the number of balls in the small bag gives the number in the big bag. Generalize: Have students share their reasoning for identifying the whole and parts of a word problem. Listen for understanding that word problems may be restated to more easily relate them to models and equations.”
• In Lesson 7, Session 3, Develop, the Deepen Understanding section provides guidance for MP5 to help students use tools. The materials state, “When discussing the Model Its, prompt students to consider how each Model It shows subtracting the same two-digit number. Ask: Where does the first Model It show regrouping a ten? Could you show subtracting 15 in the first Model it without regrouping? Where does the second Model it show regrouping a ten? Why are there only 5 ones taken away in Step 2 of the second Model it? What do you notice about the last group of blocks shown for both models?”
• In Lesson 15, Session 3, Develop, Deepen Understanding, MP 8 states, “Ask: How is adding 4+1 like adding 4 hundreds +1 hundred? How can you use 4+1 to find 400+100? How can you use 4+1 to find 400 more than 432? Generalize: Can you use a basic fact to add 100 to any three-digit number?” Students look for and express regularity in repeated reasoning because they use known facts to add three-digit numbers.
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Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for carefully attending to the full meaning of each practice standard.

The instructional materials attend to the full meaning of each mathematical practice in i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources.

Ready Classroom Mathematics materials fully meet the intent of the following math practices:

Math Practice 1: Make sense of problems and persevere in solving them.

• In Math In Action, Unit One, the Purpose section states, “Students examine a problem that involves using addition and subtraction to find a number of shelves and the number of items per shelf. They discuss the problem to understand what it is asking and brainstorm different approaches. Then they refer to a problem-solving checklist to analyze a sample solution and identify what makes it a good solution.”
• In Math in Action, Unit Four, the Purpose section states, “Students examine a problem that involves measuring and understanding units of measurement to create a design for decorating a pencil box with buttons. They discuss the problem to understand what it is asking and brainstorm different approaches. Then they refer to a problem-solving checklist to analyze a sample solution and identify what makes it a good solution.”

Math Practice 2 Reason abstractly and quantitatively.

• In Lesson 4, Session 2, Develop, Deepen Understanding, the directions state, “MP2 Reason abstractly and quantitatively. When discussing the Favorite Sports bar graph, prompt students to consider other questions that can be answered from the graph. Generalize: Do you think this always true? How do the bars for Baseball and Football support your answer? Ask for volunteers to explain their reasoning. Listen for understanding that greater numbers correspond to taller bars and lesser numbers correspond to shorter bars.”
• In Lesson 6, Session 1, Explore states, “In this session, students draw on their knowledge of place value and adding one-digit numbers to add two-digit numbers. They examine a model of two-digit numbers and explore strategies to add those numbers. They look ahead to adding two-digit numbers using base-ten blocks, going to the next ten, and adding tens and then ones.” Try it, Make Sense of the Problem states, “Present the problem and guide students as needed to understand that 27 is the number of cans at the start and 15 is the change in the number of cans. Students may want to use base-ten blocks (tens and ones), connecting cubes, number bonds, bar models or open number lines.”  Discuss it, Support Partner Discussion states, “Encourage students to name or model the strategy they used to solve the problem. Look for, and prompt as necessary, understanding of: Two groups being joined to form a larger group regrouping 10 ones as 1 ten and making a ten to add.”
• In Lesson 13, Session 2, Develop states, “In this session, students solve a problem that requires them to find the total value of 2 hundreds, 1 ten, and 3 ones. Students model the quantities either on paper or with manipulatives. The purpose of this problem is to have students develop strategies for connecting digits to the values that they represent so that they can find the value of three digit numbers.” The Student WorkText page states, “Read and try to solve the problem below. Amir plays a board game that uses play money. He wins 1 tens bill, 2 hundreds bills and 3 ones bills. What is the total value of the bills Amir wins? The materials state, “Students use base-ten blocks, play money bills, hundreds place value charts, 200 charts and/or and open number line. After students try it, they discuss their answers, strategies and have partner discussion.”

Math Practice 4: Model with mathematics.

• In Lesson 8, Session 2, Develop states, “At the fair 39 students wait in line for a ride. Then some more students join the line. Now there are 93 students in line. How many more students join the line?” Students use two representations, a number line and adding up to the next 10. Deepen Understanding states, “When discussing the two subtraction equations used to represent the word problem, prompt students to consider how the equations are connected.”
• In Unit 4: Math in Action: Use Measurement, Deepen Understanding, Using Diagrams and Equations states, “Bella saves buttons to decorate things she makes. Bella wants to glue some buttons on the top of a pencil box. Each button is the same distance across. How can Bella decorate the pencil box? Draw a picture/ Tell how many buttons she needs.” Students look at multiple solutions and solve the problem another way. The materials state, “As you discuss the sample solution, prompt students to look for connections between the addition equations and the diagram. Have them describe what part of the diagram each number represents. Ask, How do the equations represent the buttons and the spaces? Listen for 7 and 9 represent the lengths of the sides of the pencil box top. The addends represent the buttons and the 1-centimeter spaces between them. Ask, What would happen to the design if you decided to use more space between the buttons? Less space? Explain. Listen for More space leads to fewer buttons, and less spaces leaves room for more buttons on each side. There could be no space left between buttons or different amounts of space between them.”

Math Practice 5: Use appropriate tools strategically.

• In Lesson 9, Student Worktext, Session 3, Develop, Try It, in the math toolkit students are given a choice of using base-ten blocks, number bonds, bar models, hundreds charts, or open number lines to solve, “Some books are on a shelf. Students take 24 books from the shelf. Then there are 38 books on the shelf. How many books are on the shelf to begin with?”
• In Lesson 32, Student Worktext, Session 2, Develop, Try It, in the math toolkit students are given a choice of using counters, hundreds charts, number lines, or sticky notes to solve, “Ms. Ruiz brings 15 footballs and 14 soccer balls to gym class. Which number is odd?”

Math Practice 6: Attend to Precision

• In Lesson 4, Session 2, Develop, Deepen Understanding section provides guidance to ensure students can attend to precision. This section states, “When discussing organizing Lynn’s data set, emphasize the need for precision in recording data when graphing. Ask, Why do you think it is important to organize the data before making a picture graph or bar graph? Listen for, Sorting and counting the data makes it easier to count the totals in the groups. The numbers in each group need to be correct to be sure the graph will be correct.”
• In Lesson 26, Session 3, Develop, Try It, students attend to precision as they use a number line to solve, “Lucas is 49 inches tall. His little sister is 27 inches tall. Use the number line to find how much taller Lucas is than his sister.”

Math Practice 7: Look for and make use of structure.

• In Lesson 15, Session 2, Develop, Deepen Understanding, the directions state, “MP7 Look for structure. When discussing the number line model, prompt students to consider how the number line is labeled to model skip counting by tens.”
• In Lesson 16, Session 2, Develop, Deepen Understanding, the directions state, “MP7 Look for structure. Generalize: How could you use an open number line to add any three-digit numbers? Listen for understanding that when adding any 2 three-digit numbers, the problem can be solved on an open number line by starting at one addend and then making jumps to show adding the hundreds, tens and ones of the other addend.”

Math Practice 8: Look for and express regularity in repeated reasoning.

• In Lesson 1, Session 3, Develop, Deepen Understanding, the directions state, “MP8 Use repeated reasoning. Generalize: Can you use doubles plus one to find the sum of any two numbers that are 1 apart? Explain. Have students share their reasoning. Listen for understanding that when addends are 1 apart, doubling the lesser of the two addends then adding one more can simplify finding the sum of the addends.”
• In Lesson 2, Session 3 Develop, Deepen Understanding, the directions state, “MP8 Use repeated reasoning. When discussing the number bond model, prompt students to look for patterns between fact families that have the same whole.”
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Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade level mathematics.

Student materials consistently prompt students to construct viable arguments and to analyze the arguments of others. In the Program Implementation tab, Implementation Support, Try-Discuss-Connect Routine Resources, teachers find different ways to encourage Math Practice 3 in their math classrooms. Try It provides Three Reads routine, Co-Craft Questions and Problems, and Turn and Talk routine. Discuss It provides the Turn and Talk, Collect and Display, Say It Another Way, and Compare and Connect routines. Connect It provides Collect and Display, Turn and Talk, and Say It Another Way routines. Second grade curriculum includes Math In Action sections that allow children to read other students' solutions of math problems and analyze them themselves. They reflect on what was done well and what could be done differently.

These routines provide students with opportunities to construct viable arguments. Examples include:

• In Lesson 2, Student Worktext, Session 1, Explore states, “Chen has 14 stamps. He uses 6 of them to mail letters. How many stamps does Chen have left?” During the whole class discussion, students have modeled this problem with counters. Students answer follow up questions: “How do [student’s name] and [student’s name] models show the starting amount and the amount subtracted? How do they show the number of stamps Chen has left?”
• In Lesson 13, Student Worktext, Session 2 Develop, Item 4 states, “Reflect: Look back at your Try It, strategies by classmates, and Picture It and Model It. Which models or strategies do you like best for solving two-step problems? Explain.” Students then write their critiques and explanations in their worktext.
• In Lesson 28, Session 2, Develop, Reflect, Item 3 states, “Look back at your Try It, strategies by classmates, and Model Its. Which models or strategies do you like best for naming and drawing shapes you see? Explain.” Students then write their critiques and explanations in their worktext The directions for Reflect in the teacher section states, “If time allows, have students share their preferences with a partner.”

Ready Classroom Mathematics materials give students opportunities to analyze the mathematical arguments of others. Examples include:

• In Lesson 5, Student Worktext, Session 4, Refine, Item 3 states, “Bev gets 6 dollars from her mom and 4 dollars from her dad. She wants to buy a game that costs 18 dollars. How many more dollars does Bev need? (A-2 B-8 C-10 D14) Allie chose C as the correct answer. How did Allie get her answer?”
• In Lesson 10, Student Worktext, Session 1, Explore, students solve, “Lee, Seth, and Jack each have 5 coins. Lee’s coins are worth 1 cent each: 1¢ 1¢ 1¢ 1¢ 1¢. Seth’s coins are worth 5 cents each: 5¢ 5¢ 5¢ 5¢ 5¢. Jack’s coins are worth 10 cents each: 10¢ 10¢ 10¢ 10¢ 10¢. Which child has the most money?” “Discuss it Support Partner Discussion To reinforce the values of different coins, encourage students to say the value of each coin as they talk to each other.”
• In Lesson 6, Reinforce, Math Center Activities, On Level Activity states, “100 or Not! What You Need 10 Counters, Digit Cards 0-9 (2 sets). FInd 24+36. What You Do:  1. Take turns. Shuffle the Digit Cards and place them face down in a pile. 2. Take 2 cards and make a two-digit number. Take 2 more cards and make a different two-digit number. 3. Add the 2 two-digit numbers. 4. Your partner checks your answer. 5. If the sum is less than 100, take a counter. If the sum is 100 or greater, then do not take a counter. 6. Return cards to the bottom of the pile. Repeat. 7. The first partner to get 5 counters wins.”
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Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Ready Classroom Mathematics instructional materials support teachers to engage students in constructing viable arguments. Examples include:

• In Lesson 3, Session 3, Develop, the teacher is provided with the following questions to support engaging students in constructing viable arguments, “How does the number of soccer balls in the small bag compare to the number of soccer balls in the large bag?”
• In Lesson 32, Session 2, Develop, Discuss It, Support Partner Discussion states in Common Misconception, teachers are directed to “Look for students who group the 15 footballs in 3 equal groups or 5 equal groups to justify the 15 is even, instead of making two equal groups.”
• In Unit 2, Math In Action states, “Review Yoop’s solution to the Zoo Tours problem on the previous page. Ask: How can you summarize the steps in Yoop’s solution? Listen for: Put 12 people each in 4 groups, find the total number of people in the 4 groups, subtract the total from the people who signed up for the tour, and then split up and put these 10 leftover people into the 4 groups. Ask: What are some different steps you could use to solve the problem? Listen for: Use the greatest number of people they can put into a group and then add to find how many groups are needed.”

Ready Classroom Mathematics instructional materials support teachers to engage students in analyzing the arguments of others. Examples include:

• In Lesson 9, Session 1, Explore, Support Whole Class Discussion states, “Prompt students to note the relationship between the numbers in each model and the numbers in the problem. Ask How do [student name]’s and [student names]’s solutions show the start? THe change? The total? Listen for 7 is the total. 49 is the number from which you jump to 75 on the number line. The change is unknown and can be found by subtracting 49 from 75.”
• In Lesson 1, Session 2, Develop, Discuss It, Support Partner Discussion states, “Encourage students to talk about the model or strategy they chose and to use the terms start and change as they discuss their solutions.” Guided questions are listed: “How is your strategy the same as your partner’s? How is it different? What do you like about your partner’s strategy? What do you disagree with?”
• In Unit 2 Math in Action, Session 2, Solve It states, “Have students work in pairs to discuss their preliminary solutions. Then they are confident that their plan will work, have students independently write their solution on a blank sheet of paper.” Reflect states, “Have students work with a partner to share their thinking and discuss the Reflect questions.”
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Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that materials explicitly attend to the specialized language of mathematics. The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols.

In the Program Implementation tab, an Academic Vocabulary Glossary is provided. This is set up with the vocabulary explicit to each unit.  In the Classroom Resources tab, there is a “Build Your Vocabulary” Sheet that goes along with each unit to help develop the vocabulary within the unit. This page can be found in the Beginning of the Unit link for each unit. There is also a “Connect Language Development to Mathematics” that helps to develop language routines with students..

The Ready Classroom Mathematics materials provide explicit instruction on the use of mathematical language. In the Classroom Resource tab, evidence includes:

• In Unit 1 “Beginning of Unit Tab” tab, there is a Build Your Vocabulary page and a Connect Language Development to Mathematics page. The Build Your Vocabulary page is a student work page designed to introduce the vocabulary for the unit. The Connect Language Development to Mathematics page provides information on how to use the student vocabulary page. This page has a vocabulary routine that extends to other units. The routine calls for the following to be done with each vocabulary word: Assess prior knowledge, Say (pronounce) the word, Define the word, and Use the word. This routine is defined only in the Connect Language Development in Unit 1 but is referenced in later units.
• On the Build Your Vocabulary page students are given two different sets of words, “My Math Words” and “My Academic Words.” The guidance provided to the teacher under the Connect Language Development to Mathematics page states, “My Math Words in all units, My Math Words provides access to prior knowledge and understanding of critical math words and phrases through teacher-guided activities. My Academic Words in Units 4-6, My Academic Words provides an early entry point to those all-purpose academic words students will engage with throughout their study of mathematics. Use the Academic Vocabulary Routine to provide explicit instruction and active engagement.” The Academic Vocabulary Routine directions are then provided and broken up into four parts. The four parts listed are, “Assess Prior Knowledge, Pronounce the Words, Define the Words, Use the Words.”
• In Lesson 2, Session 3 Develop, Develop Language states, “Why: Develop the multiple meanings of the word left, focusing on the meaning relevant to the problem. How: Using examples of the word in context, explain that the word left has three meanings:
• She left the cafeteria (past tense of “to leave”)
• There are no crayons left in the box (What remains)
• She turned left at the corner (direction; opposite of right)

Ask students to identify the meaning of the word left as it is used in the problem.”

• In Lesson 3, Session 3, Develop, the materials provide explicit instruction on the use of mathematical language. Teachers clarify the meaning and usage of the word fewer. The materials state, “Have students talk with partners to compare the number of different items or persons in the classroom using the word fewer. There are fewer erasers than pencils on the desk. There are fewer girls than boys sitting down. Explain that the word fewer is used when comparing things that can be counted, while the word less is used for things that cannot be counted. Examples: less milk, fewer cups.
• In Lesson 13, Session 2, Develop, Develop Language states, “Why: Support students’ understanding of the term expanded form. How: Explain to students that when something expands, it gets longer. The expanded form of a number is a longer way of writing it, by separating out the units, tens, and hundreds. For example, the longer or expanded form of 284 is 200+80+4. By using expanded form, you can clearly see that there are 2 hundreds, 8 tens, and 4 ones.”

Ready Classroom Mathematics materials support students to learn and use precise and accurate terminology. IIn the Classroom Resource tab, evidence includes:

• There is a “Build Your Vocabulary” Sheet that goes along with each unit to help develop the vocabulary within the unit. This page can be found in the Beginning of the Unit link for each unit.
• Lesson Vocabulary is listed on every Lesson Overview page for each section. For example, Lesson 6, Lesson Overview, the following Lesson Vocabulary is listed:
• Regroup: to put together or break apart ones, tens, or hundreds. For example, 10 ones can be regrouped as 1 ten, or 1 hundred can be regrouped as 10 ones.
• In Lesson 30, Session 1, Additional Practice has a Support Vocabulary Development section which the teacher uses to build the understanding of partitioning rectangles (e.g., “What is it?” “What I know about it.” 3 area models to partition).

In the Program Implementation tab there is:

• An Academic Vocabulary Glossary with the vocabulary explicit to each unit.
• A Teacher’s Guide Table of Contents provides the overall view of each unit. In each unit there is a Build Your Vocabulary section with the vocabulary addressed in the unit.

In the Program Implementation materials and throughout lessons in Ready Classroom Mathematics, students are provided with graphic organizers that assist with mathematical language to ensure students are using precise vocabulary. There are five different graphic organizers provided throughout the lessons which allow students to organize learning concepts and vocabulary through definitions, illustrations, examples, etc.

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet the expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercised that given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent.

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The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for distinguishing between problems and exercises.

There are several practice pages provided with each lesson. After receiving guidance from the teacher in the Try It section of each lesson, students can demonstrate their understanding in a variety of ways. Students solve problems to learn new mathematics in the Explore sessions of each lesson. These ideas are further developed in Develop sessions, where students solve problems in the Try It and Connect It sections. In the Refine session, students complete exercises where they apply their learning. For example:

• In Grade 2, Lesson 25, Session 1, Explore, students explore adding and subtracting lengths by using what they know about adding and subtracting two digit numbers in the problem, “The tail of a toy alligator is 6 inches shorter than the rest of its body. The rest of its body is 32 inches long. How long is the alligator’s tail?” In Session 2, students practice the skill by solving problems involving beads. In Sessions 3 and 4 students move to solving two step problems involving length.
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Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for designing assignments not being haphazard and exercises given in intentional sequences.

The sequence of lessons in each topic is designed to move from concrete and pictorial representation toward abstract work with numbers. Each unit has a Unit Flow and Progressions Video that highlights the work of the unit and how it fits in the progression of mathematics across grade levels.

Each unit also has a Learning Progression Chart that shows which lessons are building upon and which lessons students are preparing for within the unit. Each lesson has learning progression information which highlights work done in previous grade levels, as well as the work to be done in this lesson and subsequent lessons.

Each lesson has a consistent structure that builds towards independence. For example,

• In Grade 2, Lesson 27, Session 3, students are given the problem, “Julia spills a box of spaghetti. She picks up the broken pieces. Measure each piece using centimeters. Show how the measurement data might be organized.” Teachers are prompted to provide guiding questions such as “What happens when spaghetti falls on the floor? Are all the pieces the same size?” Students then work in pairs to discuss how they organized their data and how they chose to display the data. Students then explore different ways to display data. Finally, during Apply It and the Exit Ticket students practice and independently show their understanding.

Lessons within units build upon each other. For example:

• In Grade 2, Unit 2 includes the following lessons and topics: Lesson 6: Add Two Digit Numbers, Lesson 7: Subtract Two Digit Numbers, Lesson 8: Use Addition and Subtraction Strategies with Two Digit Numbers, Lesson 9: Solve Word Problems with Two Digit Numbers, Lesson 10: Solve Word Problems Involving Money, and Lesson 11: Tell Time and Write Time
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There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for having a variety in what students are asked to produce.

Students are expected to respond to problems in a variety of ways, including produce answers, use models, drawings, and equations to support their explanations. Students are asked to justify their solutions with a partner and participate in discussions with Discuss It and Pair/Share prompts. Students respond to different problem types in the Refine section of the lessons, including short answer explanations, multiple choice, fill in the blank, and drawings. For example:

• In Grade 2, Lesson 17, Session 2, Develop, students respond to problems in multiple ways when subtracting three digit numbers. There are problems where students solve word problems, do quick draws, and use partial sums.
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Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for manipulatives being faithful representations of the mathematical objects they represent.

There are a variety of manipulatives in the Math Tool Kit available during lessons, and students are introduced to these in appropriate contexts for the concept being developed.

• In Grade 2, Lesson 12, Session 2, Develop, students use base ten blocks and place value charts to understand three-digit numbers.
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The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet the expectations for the visual design not being distracting or chaotic.

The student pages provide ample space for students to show work and write explanations. The layout of the lessons is consistent throughout all of the lessons and the student materials are present in the teacher edition. For example:

• In Grade 2, Lesson 11, the Fluency and Skills Practice Page states, “What time does the clock show? Write the same time on the digital clock.” Students are provided with graphics of a clock with a time. The graphics are clear and not distracting to the understanding of the concept.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for supporting teacher learning and understanding of the Standards. The instructional materials support: planning and providing learning experiences with quality questions; contain ample and useful notations and suggestions on how to present the content; and contain explanations of the grade-level mathematics in the context of the overall mathematics curriculum.

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Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing teachers with questions that are designed to elicit students’ mathematical understanding and thinking.

• In Grade 2, Lesson 22, Session 2, Develop, questions are posed for the teacher to ask students. The questions are in italics and easy for the teacher to see. In Discuss It, Support Whole Class Discussion, the following questions are provided: “Why are there more centimeters than inches in the measurements? How will the number of inches compare to the number of centimeters when measuring the length of any object? Why?”
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Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meets expectations for including ample notes and useful annotations and suggestions on how to present the content in the student edition.

The Program Implementation tab includes a “Digital Math Tools - Support Videos” section. This section includes support videos for counters and connecting cubes, base ten introduction, base ten: add and subtract, number line, multiplication models, perimeter and area, fraction models: add and subtract, and fraction models: compare and multiply.

In Classroom Resources, guidance for teachers supports the delivery of the content, as well as information on student responses for each section of the lesson. For example:

##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for containing a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject as necessary.

In Classroom Resources at the beginning of each unit, Learning Progressions, Math Background, and Unit Flow and Progression Videos provide information for teachers on mathematics and models. For example:

• In Grade 2, Unit 2, Beginning of Unit, Teach, the Unit Flow and Progression Video builds teacher understanding on using models connected with the mathematics of the unit.
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for containing a teacher’s edition that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.

The Ready Classroom Mathematics materials include a “Learning Progression,” section in the teacher edition for each lesson that describes how the grade-level appropriate standard is developed in previous grades as well as how it will extend in the next grade. For example:

• In Grade 2, Lesson 15, Full Lesson, Standards 2.NBT.2 and 2.NBT.8  are listed and defined. Under the Learning Progression section on the same page which describes the progression, students will learn about addition and subtraction fluency, it starts with In Grade 1, moves to In Grade 2, In This Lesson, and In Grade 3.
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 contain an online portal that cross-references standards and provides a pacing guide for each lesson. Specifically, under the Program Implementation tab there are Teacher’s Guide, Table of Contents, Program Overview, Correlations, and Yearly Pacing resources to assist the teacher. Moreover, under the correlation resource there are correlations by state standard, correlations by ready classroom mathematics lessons, math in action correlations, standards for mathematical practices correlations, unit review correlations, and ELA standard correlations.

##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement. Family Letters for each lesson are found in the “Lesson Overview and Family Letter” tab at the beginning of each lesson. These letters explain the learning target and include an activity they can do at home. In the teacher edition, there is a “Connect to Family” section. For example:

• In Grade 2, Lesson 16, the Family Letter provides background information on adding three-digit numbers and an activity for families to do with their child.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 contain explanations of the instructional approaches of the program and identification of the research-based strategies. Under the Program Implementation Tab, there is a Supporting Research tab. Here, teachers can find supporting research charts including: “Ready Classroom Mathematics is built on research from a variety of federal initiatives, national mathematics organizations, and experts in mathematics.” The chart lists instructional routines, mathematical practices, collaborative learning, and mathematical discourse. For each one of those items, the publishers have listed examples and corresponding research.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide opportunities for addressing common student errors and misconceptions, ongoing review and practice with feedback, clearly denote the standards being assessed, and provide rubrics and guidance for teachers to interpret student performance and suggestions for follow-up. The instructional materials provide some opportunities to gather information on students’ prior knowledge.

##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

The materials in Ready Classroom Mathematics list prerequisite skills for each lesson in the Lesson overview. Prerequisite Lessons are provided with each lesson to review concepts or to provide students with instruction in areas that may be gaps in their learning. For example:

• In Grade 2, Lesson 29, the Prerequisite Lesson is: Grade 1 Lesson 34: Putting Shapes Together, Sessions 1-5.

In addition to identifying prerequisite skills for each lesson, Explore, at the beginning of each lesson, connects students’ prior knowledge with the content of the lesson. In some Warm-up questions there is a tag “Prerequisite” noting that the question is assessing prior knowledge.

The instructional materials include adaptive Diagnostic Assessments with Prerequisite  Reports found in i-Ready, Reports.

##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

The Ready Classroom Mathematics materials provide strategies for teachers to identify and address common student errors and misconceptions. For example,

• ]]In Grade 2, Lesson 24, Session 1, Explore, the Common Misconception states, “Look for students who are not comfortable using a ruler to find length. As students present solutions, have them specify how they used the ruler with the picture or the line segments to measure the two lengths.”
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Over the course of a lesson, which includes multiple sessions, materials engage students with multiple activities to review, practice, and independently demonstrate the grade-level mathematical concepts and skills.

Feedback is provided to students as they progress through the Sessions. Frequent feedback opportunities to address skills and concepts are provided in the Classroom Resources tab, within each lesson and its sessions. The Reteach - Tools for Instruction within each lesson provides teachers with sample errors and remediation strategies to address those errors. In addition, throughout the lesson sessions, potential misconceptions are highlighted with guidance for teachers to provide feedback and new opportunities for practice. For example:

• In Grade 2, Lesson 18, Reteach, Tools for Instruction, Check for Understanding states, “If you observe the student adds 543 + 864, the student may have difficulty identifying the missing part of the problem. Then try guiding the student through making a bar model for the situation and writing equations to match before finding its solution.”
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for offering ongoing formative and summative assessments that clearly denote which standard is being emphasized.

• Standards are clearly noted within the assessments found at the end of each lesson. Standards are provided alongside the questions as well as the Depth of Knowledge level. Unit Assessment Correlations are available with the question number, DOK, Standard, and Lesson.
• A Mid-Unit Assessment is provided for longer units. Mid-Unit Assessments also provide standards correlations for each item. These can be found in the Classroom Resources tab, End of Unit, Assess, Lesson Quizzes, and Unit Assessments.
• Formative assessments are also available:
• Lesson quizzes, exit tickets, and quick checks are provided for most lessons. These quizzes assess the specific standard(s) being taught in the lesson.
• Within the sessions are Check For Understanding supports that include a statement as to why the check is being done. The why relates back to the standard being taught in the activities for that session.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for including aligned rubrics and scoring guidelines to support teachers in interpreting student performance and sometimes provide for follow-up instruction.

Rubrics are provided for Mid-Unit Assessments, Unit Assessments, Unit Performance Tasks, Lesson Quizzes, and Math in Action. (grade 2 and above) The rubrics and scoring guidelines support teachers to interpret student performance. Assessment answer keys are provided alongside the questions along with the DOK level for the item. For multiple choice answers, the correct answer and explanations for incorrect choices are given, including the most common misconceptions.

Reports from i-Ready diagnostic assessments and comprehension checks assist teachers in providing follow-up instruction for misconceptions and mathematical errors. The electronic reports also include links to assist in reteaching items missed. Within lessons, rubrics and scoring guidelines provide guidance for teachers to follow-up and, throughout Ready Classroom Mathematics, there is guidance for teachers on behaviors to look for, error alerts, and Common Misconceptions.

• Unit Assessments include a Unit Assessment Teacher Guide that provides instructors with solutions, points possible, the exact standard covered, and the depth of knowledge (DOK) level for each item.
• The Scoring Guide for the problems in the scoring table include: DOK, points of scoring, standard addressed, and lesson assessed by each problem.
• The Scoring Rubrics includes points and expectations for short response, multiple select, choice matrix, extended response, and fill-in-the-blank items.
• Assessment Practice provides some support for follow-up by identifying standards that need further study and reinforcement. Assessment Practice Answer Key and Correlations identify the standard which each question has been designed to evaluate.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 encourage students to monitor their own progress.

Each Unit Opener has a Self-Check page for students to select the skills/concepts they think they already know and understand. End of Unit opportunities for self-reflection are provided at each grade level for all units. Assessments can be completed using an answer form that allows for students to correct the assessment orally after completion, review answers, and explain concepts students may not fully understand. Dialogue is fully supported inside the classroom to address student misconceptions and give students opportunities for both self- and peer assessment.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials consistently provide: strategies to help teachers sequence and scaffold lessons; to meet the needs of a range of learners; tasks with multiple entry points; supports and accommodations for English Language Learners and special populations; and opportunities for advanced students to investigate mathematics content at a deeper level. The instructional materials provide a balanced portrayal of various demographic and personal characteristics, and include suggestions for grouping strategies.

##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The sessions within a lesson follow the sequence of Explore, Develop, and Refine. Within a session, there is a sequence of Start, followed by Try It, Model It, or Apply It; Discuss; Connect; and Close.

• Start is designed to build fluency or connect to prior knowledge.
• Try It is designed to give students an opportunity to explore the concept on their own.
• Model It is designed to allow students the opportunity to explore the concept through manipulatives or drawings.
• Apply It is designed to give students an opportunity to practice the skill on their own.
• Discuss is designed to allow students to talk to other students about the concept and compare what they did with each other.
• Connect It is designed to help students connect the concept to real-life.
• Close is designed to solidify the learning for the day and to check for understanding through the use of an exit ticket.

Each lesson includes a Differentiated Instruction Teacher Toolbox that includes Reteach (Tools for Instruction), Reinforce (Math Center Activities), and Extend (Enrichment Activities). For example, the Lesson 1 Overview states:

• Reteach- “Children who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction.”
• Reinforce- “Children who require additional practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities.” This is available in three versions: on-level, below-level, and above-level.
• Extend- “Children who have achieved proficiency with concepts and skills are ready for additional challenges will benefit from group collaborative games and activities to extend understanding.”
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing teachers with strategies to meet the needs of a range of learners.

Each lesson provides opportunity for differentiation in small group lessons, interactive digital tutorials, support for teachers to address common misconceptions at different points throughout lessons. For example:

• The Differentiated Instruction opportunities provide support to reteach students who need additional support, reinforce learning for students who need additional practice, and extend learning for students who have achieved proficiency and are ready for further challenges.
• The Language Development sections for English Language Learners provides even more differentiated support for students who are at different levels of English proficiency.
• Community and Cultural Responsiveness activities build bridges between the mathematics students are learning to investigations of authentic contexts and issues. For example, students apply mathematics they have learned to objects and activities found in parks.

The materials also support learning with a variety of different experiences to develop connections in each lesson. For example:

• Lessons use manipulative objects such as counters and connecting cubes for hands-on experiences where students are actively applying and representing mathematics with hands-on objects.
• Partner and Whole group discussion are incorporated in all sessions to provide dialogue surrounding the mathematics being done.
• Visual representations and physical representations using mathematics manipulatives are used throughout each session.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

The materials present word problems at the beginning of most lessons in the Try It part of the session, which provides multiple points of entry for students. During Model It, students can model the problem in whichever way they like. Examples of problems that provide multiple entry points, different representations, and/or solution pathways include:

• In Grade 2, Lesson 7, Student Worktext, Session 3, Develop, Try It states, “Ming has 42 toy animals. She gives 15 animals to her friends. How many toy animals does Ming have left?”
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations to engage students in regular and active participation in learning mathematics.

In Program Implementation, Implementation Support there are resources, including:

• A Multilingual Glossary
• A Bilingual Glossary
• WIDA PRIME V2 Correlation
• Try-Discuss-Connect Routine Resources

In Classroom Resources, Teachers Edition, Language Development is identified for each lesson. This differentiated instruction chart provides guidance for teachers at three levels of differentiation that identifies specific strategies (e.g., Speaking/Writing, Reading/Writing) directly connected to lesson sessions and activities. During sessions, specific strategies target additional supports for students to support engagement in lesson activities. For example:

• Prerequisite lessons are identified for most lessons and include specific supports for ELLs.
• Develop Language includes Why (rationale for the suggestions) and How (strategies and guidance on how to engage students) sections, along with explanations as needed.
• Discuss It provides supports for all students to engage in mathematical discourse.
• Differentiated Instruction is included for most lessons and includes activities for intervention, on-level, and challenge.
• Math Center activities provide multiple levels of content.
• Math in Action lessons in Grade 2 and higher build background in a variety of contexts to ensure access for all.
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing opportunities for proficient and advanced students to participate in enrichment activities for a deeper challenge.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Classroom Resources, Teacher, Lesson Pacing Guide includes Small Group Differentiation Activities, and highlights Extend, Enrichment Activity. These Enrichment Activities can be found during the Refine session in the lesson, and include a Challenge Activity related to the content of the lesson. For example:

• In Grade 2, Lesson 16, Extend states, “Show students the following sum: 360+230=330+260. Make sure they notice that the groups of ten have been switched, being paired with a different hundred. Challenge students to determine if switching the tens in this way will always work even when there are digits other than zero in the ones place. Require students to justify whether switching the tens does or does not always work…”
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for providing a balanced portrayal of demographic and personal characteristics representing a variety of backgrounds.

In the Program Implementation tab, a multilingual, bilingual, and academic glossary are provided. Throughout the materials there are examples of animated pictures of children that have varied skin tone, features, hair color, and hair types such as pictures of children with brown skin and black hair, light skin and blond hair, and brown skin and brown hair. Pictures with more than one child show interactions between children with varied skin and hair colors such as one with light brown skin and black hair and the other with dark brown skin and black hair. The pictures of objects included are pencils, cars, soccer balls, footballs, apples, bananas, crayons, goldfish, rocks, flowers and other objects commonly known to most students. A variety of names representing different ethnic and cultural backgrounds are used, including:  Rosa and Ryan, Nick and Nora, Dave and Ari, Roberto and Rena, Fran and Pete, Gabe and Rose, Darious, Sam, Lexi, Paco, Julija, Lana, and Kyle.

##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 provide a variety of opportunities for different grouping strategies.

Each lesson session includes supports for partner discussion and whole class discussion. Some examples of discussions throughout the materials include: “Have pairs explain how they modeled and solved the problems. Compare and Connect the different representations and have children identify how they are related. Ask your partner: Do you agree with me? Why or why not? Tell your partner: I started by…” These discussion starters are used throughout the materials in all grades. Opportunities for grouping are also supported in the differentiated instruction and language development activities. The teacher materials offer support for whole class discussions and independent activities throughout the instruction.

##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 provide support to draw upon home language and culture to facilitate learning. The materials offer a multilingual mathematics glossary that defines common mathematical terms in ten different languages. There are student discourse tools in both English and Spanish to support those two most common languages. There are family letters in Spanish, as well as in English, that support parents in learning mathematics at home.

Interactive Learning Games are available in English and Spanish.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 integrate technology in ways that engage students in the Mathematical Practices. The digital materials are web-based and compatible with multiple internet browsers, and include opportunities to assess students’ mathematical knowledge and procedural skill. The digital materials do not include opportunities to personalize learning for students, but do present some opportunities for customization for local use. The instructional materials do not include opportunities for teachers and/or students to collaborate with each other.

##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

The instructional materials reviewed  for Ready Classroom Mathematics Grade 2 digital materials are web-based and compatible with multiple Internet browsers and operating systems. These materials also allow for the use of handheld and mobile devices. System requirements can be accessed by clicking the question mark at the top right-hand corner when signed in to the teacher website and clicking on the link to the system requirements PDF.

According to the PDF provided by the publisher, the materials are compatible with Windows 7 SP!, Windows 10 1802 (April 2018 update) or higher, MacOS X 10.11, MacOS 10.12-10.14, Google Chrome OS. Supported browsers include Internet Explorer on Mac and Google Chrome operating systems, Microsoft Edge, Microsoft Safari, Firefox, and Google Chrome. The publisher recommends Google Chrome with auto-updates enabled for the best experience. In addition, there is an app for iPads titled “i-Ready for Students.” The app is not supported for iPad minis. The app is not available for other tablets or the iPhone. However, when attempted, many of the tools can be viewed on other mobile devices through the website accessed through the browsers listed.

##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 materials include online comprehension checks for each lesson. Comprehension checks have five problems and are a mixture of problem types, including multiple-choice, multiple select, fill in the blank, and drag and drop. Middle and End of Unit Assessments are also available for each unit in a digital version with similar formatting. Those assessments are customizable and allow teachers to eliminate or combine assessment items. The learning games offer teachers reports on three types of data that include time spent on activities, student performance on math skills, and other qualitative data such as student perseverance through difficult tasks. Reports for comprehension checks are available for individual students and at the class level.

##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 can be customized for individual learners or users through the digital platform using adaptive or innovative technologies.

In i-Ready, Assess and Teach, Assessment, teachers can customize Interactive Practice assignments. In i-Ready, Reports, Learning Games can also be customized. i-Ready Instruction, available for an additional purchase, includes additional opportunities to customize content. In i-Ready, Assess and Teach, Classroom Resources, Lesson Quizzes, Fluency and Skills activities, and powerpoint slides for each lesson are customizable.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 materials provide limited opportunities for teachers to customize lessons for local use. Ready Classroom Mathematics Teacher Resources include Small Group Differentiation using Prerequisite Lessons, Tools for Instruction, Math Center Activities, and Enrichment Activities. These are teacher-led activities for use with small groups requiring additional instruction and/or review prerequisite concepts. Middle and End of Unit Assessments have one editable form, digital assessments are customizable, and fluency pages have an editable form as well.

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 provide no explicit guidance for opportunities for collaboration using technology. No opportunities are provided for teacher-to-student collaboration or student-to-student collaboration. There are no technical features that allow collaboration between teacher and student or between students.

##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

The materials include Interactive Tutorials with most lessons that are animated interactive lessons assigned to students in their personalized instructional plan. These tutorials include integrative technology such as interactive tools and digital math manipulatives to engage students in the Mathematical Practices.

Some lessons include multiple interactive tutorials related to the content of the lesson. Students work through the videos and answer questions. Students can use the lesson view to skip to different parts of the lesson. There is a pen for student use, as well as a notepad and a dictionary.

Digital Math Tools are provided to be used throughout the program. Tools available in the grades K-5 program include Counters, Connecting Cubes, Base Ten Blocks Tool, Number Line Tool, Multiplication Models Tool, Perimeter and Area Tool, and Fraction Models Tool. In general, tools are representative of concrete manipulatives.

Seven learning games are provided for student practice of concepts and skills. There is a document called “Learning Games Lessons Correlations” in the Program Implementation Guide, in the Digital Resource Correlations section, that provides information for teachers about which games support which lesson content.

Interactive Practice is provided for student practice of concepts. The practice is provided for some lessons but not all. In each Interactive Practice, students are given problems to solve which build on their conceptual understanding and help consolidate their knowledge.

## Report Overview

### Summary of Alignment & Usability for i-Ready Classroom Mathematics | Math

#### Math K-2

Note: The product name of this title was updated from “Ready Classroom Mathematics” to “i-Ready Classroom Mathematics” in January 2021. The name change has not impacted the EdReports review of the product.

The instructional materials reviewed for Ready Classroom Mathematics K-2 series meet expectations for Alignment to the CCSSM. The materials meet the expectations for Focus and Coherence by assessing grade-level content, spending the large majority of instructional time on major work of the grade, and they are coherent with the progressions of the standards, making meaningful connections between supporting and major work of the grade, are viable for a school year, and present all students with opportunities to engage in extensive work with grade level problems to meet the full intent of grade level standards. The materials meet the expectations for Rigor and Mathematical Practices as they meet the expectations for Rigor and Balance and meet the expectations for Practice-Content Connections. The materials balance the rigorous expectations of the Standards, and they attend to Practice-Content Connections, addressing all of the Mathematical Practice Standards; however, there are instances where these are over-identified.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

Note: The product name of this title was updated from “Ready Classroom Mathematics” to “i-Ready Classroom Mathematics” in January 2021. The name change has not impacted the EdReports review of the product.

The instructional materials reviewed for Ready Classroom Mathematics 3-5 series meet expectations for Alignment to the CCSSM. The materials meet the expectations for Focus and Coherence by assessing grade-level content, spending the large majority of instructional time on major work of the grade, and they are coherent with the progressions of the standards, making meaningful connections between supporting and major work of the grade, are viable for a school year, and present all students with opportunities to engage in extensive work with grade level problems to meet the full intent of grade level standards. The materials meet the expectations for Rigor and Mathematical Practices as they meet the expectations for Rigor and Balance and meet the expectations for Practice-Content Connections. The materials balance the rigorous expectations of the Standards, and they attend to Practice-Content Connections, addressing all of the Mathematical Practice Standards, however, there are instances where these are over-identified.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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###### Usability
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