##### v1
###### Usability
Our Review Process

#### Additional Publication Details

Title ISBN Edition Publisher Year
Ready Math Practice Problem Solving Grade K Student Book (2016) 978-1-4957-1678-2 Curriculum Associates 2016
Ready Math Practice Problem Solving Grade K Teacher Guide (2016) 978-1-4957-1679-9 Curriculum Associates 2016
Ready CCSS Math Instruction Grade K Student Book (2017) 978-1-4957-2002-4 Curriculum Associates 2017
Ready CCSS Math Instruction Grade K Teacher Resource Book (2017) 978-1-4957-2012-3 Curriculum Associates 2017
Ready CCSS Mathematics Assessments Grade 2 Student Book (2014) 978-0-7609-8658-5 Curriculum Associates 2014
Ready CCSS Mathematics Assessments Grade 2 Teacher Resource Book (2014) 978-0-7609-8665-3 Curriculum Associates 2014
Ready Math Practice Problem Solving Grade 2 Teacher Guide (2016) 978-0-7609-9592-1 Curriculum Associates 2016
Ready CCSS Math Instruction Grade 2 Student Book (2017) 978-1-4957-0549-6 Curriculum Associates 2017
Ready CCSS Math Instruction Grade 2 Teacher Resource Book (2017) 978-1-4957-0577-9 Curriculum Associates 2017
Ready Mathematics Student Book 978-1-4957-3587-5 Student Edition Curriculum Associates 2017
Ready Mathematics Teacher Resource Book 978-1-4957-3590-5 Teacher Edition Curriculum Associates 2017
Ready Math Practice Problem Solving Grade 1 Student Book (2016) 978-1-4957-1680-5 Curriculum Associates 2016
Ready Math Practice Problem Solving Grade 1 Teacher Guide (2016) 978-1-4957-1681-2 Curriculum Associates 2016
Ready CCSS Math Instruction Grade 1 Student Book (2017) 978-1-4957-2003-1 Curriculum Associates 2017
Ready CCSS Math Instruction Grade 1 Teacher Resource Book (2017) 978-1-4957-2013-0 Curriculum Associates 2017
Ready Mathematics Student Book 978-1-4957-3588-2 Student Edition Curriculum Associates 2017
Ready Mathematics Teacher Resource Book 978-1-4957-3591-2 Teacher Edition Curriculum Associates 2017
Ready Common Core Mathematics Grade 3 978-0-7609-8900-5 Curriculum Associates
Ready Math Practice Problem Solving Grade 3 Teacher Guide (2016) 978-0-7609-9593-8 Curriculum Associates 2016
Ready CCSS Math Instruction Grade 3 Student Book (2016) 978-1-4957-0550-2 Curriculum Associates 2016
Ready 4 Common Core Mathematics Instruction (2014) 978-1-4957-0551-9 Curriculum Associates 2014
Ready CCSS Math Instruction Grade 3 Teacher Resource Book (2016) 978-1-4957-0578-6 Curriculum Associates 2016
Ready Math Student Edition 978-0-7609-8902-9 Curriculum Associates
Ready Math Practice Problem Solving Grade 5 Student Book (2016) 978-0-7609-9226-5 Curriculum Associates 2016
Ready Math Practice Problem Solving Grade 5 Teacher Guide (2016) 978-0-7609-9595-2 Curriculum Associates 2016
Ready CCSS Math Instruction Grade 5 Student Book (2016) 978-1-4957-0552-6 Curriculum Associates 2016
Ready CCSS Math Instruction Grade 5 Teacher Resource Book (2016) 978-1-4957-0580-9 Curriculum Associates 2016
Ready 4 Mathematics Assessments (2014) 978-0-7609-8901-2 Curriculum Associates 2014
Ready Math Practice Problem Solving Grade 4 Student Book (2016) 978-0-7609-9225-8 Curriculum Associates 2016
Ready Math Practice Problem Solving Grade 4 Teacher Guide (2016) 978-0-7609-9594-5 Curriculum Associates 2016
Ready Mathematics Student Book 978-1-4957-3589-9 Student Edition Curriculum Associates 2017
Ready Mathematics Teacher Resource Book 978-1-4957-3592-9 Teacher Edition Curriculum Associates 2017
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## Report for 4th Grade

### Overall Summary

The instructional materials for Ready Grade 4 meet the expectation for alignment to the CCSS. In Gateway 1, the instructional materials meet the expectations for focus by assessing grade-level content and spending at least 65% of class time on the major clusters of the grade, and they are coherent and consistent with the Standards. In Gateway 2, the instructional materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, and they connect the Standards for Mathematical Content and the Standards for Mathematical Practice.

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

### Focus & Coherence

The instructional materials for Ready Grade 4 meet the expectation for focusing on the major work of the grade and having a sequence of topics that is consistent with the logical structure of mathematics. The materials do not assess topics before the grade level indicated, 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 for Ready Grade 4 meet the 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 Grade 4 meet the expectations for assessing grade-level content.

The program provides Interim Assessments available in the student edition and online for each unit. There is a separate Ready Assessments book containing three assessments. There are also two versions (Form A and Form B) of the Mid-Unit and Unit assessments for each of the units.

There are three above grade-level questions found in the assessments:

• For Unit 2 Assessment Question 5 the expression provided as a solution by the materials is written with parentheses so that students would add before dividing. Using a numerical expression written with parentheses is aligned to 5.OA.1.
• In the Ready Assessments book Assessment 3 Question 40 the expression provided as a solution by the materials is written with parentheses so that students would add before multiplying. A numerical expression written with parentheses is aligned to 5.OA.1.
• Unit 5 Assessment Forms A and B Question 4d asks students to add fractions with unlike denominators (5.NF.2).

Overall, unit assessment items are aligned to Grade 4 standards. The above grade-level assessment questions could be removed or modified by the teacher without affecting the sequence of learning for students.

#### 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 for Ready Grade 4 meet the expectation for students and teachers using the materials as designed devoting the majority of class time to the major work of the grade. Overall, the 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 Grade 4 meet the expectations for spending the majority of the time on the major clusters of the grade. This includes all the clusters in 4.NBT and 4.NF along with 4.OA.A. To determine focus on major work, three perspectives were evaluated: the number of units devoted to major work, the number of lessons devoted to major work, and the number of instructional days devoted to major work. Of the three perspectives, the number of instructional days is most representative and was used to determine the score for this indicator.

• Grade 4 instruction is divided into six units. Unit 1 addresses 4.NBT. More than half of Unit 2 addresses 4.OA.A. Unit 3 addresses 4.NBT. Unit 4 addresses 4.NF. Therefore, 3.5 out of 6 units, approximately 58 percent, focus on major work of the grade.
• Grade 4 instruction is divided into 33 lessons. Twenty out of 33 lessons, approximately 61 percent, focus on major work of the grade. Seven of the 33 lessons focus on supporting work in support of the major work of the grade. Overall, approximately 82 percent of the lessons focus on major work of the grade.
• Grade 4 instruction consists of approximately 170 instructional days. Approximately 106 days focus on major work of the grade, and approximately 32 days focus on supporting work which supports the major work of the grade. Overall, approximately 81 percent of instructional days are spent on 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 for Ready Grade 4 meet the expectation for being coherent and consistent with the Standards. Overall, the instructional materials have supporting content that enhances focus and coherence, are consistent with the progressions in the Standards, and foster coherence through connections at a single grade, where appropriate and required by the 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 Grade 4 meet expectations for supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of the connections between supporting work and major work include the following:

• Unit 2 Lesson 7 Making line plots (4.MD.4) is connected to fractions on a number line (4.NF.A).
• Unit 5 Lesson 29 Measuring angles (4.MD.C) is connected to fractions (4.NF.B) by having students measure fractions of a full turn of angles.
• Unit 5 Lesson 26 Using the standard formula for area and perimeter (4.MD.3) is connected to grade-level work with multiplication (4.NBT.B).
• Unit 5 Lesson 25 Finding factor pairs (4.OA.4) is connected to the major work of using place value understanding and properties of operations to perform multi-digit arithmetic (4.NBT.B).
• Unit 5 Lesson 27 Creating line plots displaying data in fractions of units (4.MD.4) is connected to the major work of adding and subtracting fractions (4.NF.A and 4.NF.B).
• Unit 5 Lesson 23 Convert Measurements relates (4.MD.1) to use place value understanding and the properties of operations to perform multi-digit operations (4.NBT.5).
• Unit 5 Lesson 24 Time and Money (4.MD.A) is connected to the major work of using all four operations with whole numbers (4.OA.A), fractions and decimals (4.NF.B).
• Unit 5 Lesson 30 Adding and subtracting with angles (4.MD.C) is connected to the major work of using addition and subtraction to solve word problems (4.OA.3).

However, there are times when natural connections between supporting work is not used to enhance and support the major work of the grade. For example, in Unit 2 Lesson 7 the supporting standard 4.OA.4 does not connect to major work of the grade:

• Work with factors and multiples (4.OA.4) is not connected with comparing fractions, using number lines, and ordering common fractions (4.NF.A).
• Finding factors (4.OA.4) is not connected to major work of finding common denominators (4.NF.1).

##### 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 Grade 4 meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades. The suggested pacing includes 143 days of lessons, 12 days of Math in Action, and another 15 days for assessment making 170 days of materials. According to the Teacher Guide, pages A42-A43, each lesson is expected to last between 30-45 minutes.

##### 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 Grade 4 meet the expectation for being consistent with the progressions in the standards. Content from prior grades is identified or connected to grade-level work, and students are given extensive work with grade-level problems.

Overall, materials develop according to the grade-by-grade progressions in the Standards. Typically, material related to prior and future grades is clearly identified or related to grade-level work.

The materials relate grade-level concepts to prior knowledge from earlier grades. Each Lesson Overview provides a Learning Progression. The Learning Progression explains connections between prior grades and the lesson. For example, in Unit 1 Lesson 2 the progression states, “In earlier grades students used the greater than ($$>$$) and less ($$<$$) than symbols to compare whole numbers and to compare fractions.” Additionally, each unit begins with a progression overview document. This document connects grade level concepts to specific standards from prior grades, and this document also connects grade-level concepts to future standards. Student prior knowledge is activated and connected to new skills and concepts on the first day of each lesson in Use What You Know. For example, in Unit 2 Lesson 5 students are reminded that they "have looked at multiplication as joining equal groups" and are told that "(m)ultiplication is also a way to compare two numbers."

The instructional materials provide given extensive work with grade-level problems. Lessons provide grade-level problems for students. Students spend three, four, or five days in a lesson working with grade-level standards. During modeled and guided instruction, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. The guided practice allows students to solve problems and discuss their solution methods. The independent practice provides students the opportunity to work with problems in a variety of formats to integrate and extend concepts and skills. The Practice and Problem Solving Guide provides additional practice problems for each of the lessons, and the back of the Practice and Problem Solving Guide provides problems for additional skills practice. Each lesson also has math center activities which provide additional practice with grade-level problems.

##### 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 Grade 4 meet the expectations for fostering coherence through connections at a single grade, where appropriate and when the standards require. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings and opportunities to provide problems and activities that connect two or more clusters in a domain or two or more domains, when these connections are natural and important.

Instructional materials are clearly shaped by CCSSM cluster headings. The units are divided into instruction focused on domains. Grade 4 standards are clearly identified in the Table of Contents and a CCSSM Focus box found at the beginning of each lesson. Additionally, a CCSSM Correlation Chart identifies which lessons address specific standards. Instructional materials shaped by cluster headings include the following examples:

• Unit 1 Lesson 1 Understand Place Value is shaped by 4.NBT.A, generalize place value understandings for multi-digit whole numbers.
• Unit 2 Lesson 5 Understand Multiplication is shaped by 4.OA.A, use the four operations with whole numbers to solve problems.
• Unit 4 Lesson 13 Understand Equivalent Fractions is shaped by 4.NF.A, extend fraction equivalence and ordering.

Instructional 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 the connections are natural and important.

• In Unit 2 Lesson 10 Solving Multi-step Word Problems (4.OA.A) is connected to multiplying whole numbers (4.NBT.A and 4.NBT.B).
• In the Unit 4 Math in Action Use Fractions and Decimals understanding fraction equivalence (4.NF.A) is connected to building fractions from unit fractions (4.NF.B) and using decimal notation for fractions and comparing decimal fractions (4.NF.C).
• Unit 5 Lesson 27 Line Plots connects make a line plot to display a data set of measurements in fractions of a unit (4.MD.4), to understand a fraction a/b with a >1 as a sum of fractions 1/b (4.NF.3).

### Rigor & Mathematical Practices

The instructional materials for Ready Grade 4 meet the expectation for aligning with the CCSS expectations for rigor and mathematical practices. The instructional materials attend to each of the three aspects of rigor individually, and they also attend to the balance among the three aspects. The instructional materials emphasize mathematical reasoning, identify the Mathematical Practices (MPs), and attend to the full meaning of each practice standard.

##### 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 for Ready Grade 4 meet the expectation for reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations, by helping students develop 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 Grade 4 meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Students use pictures, manipulatives, and models to demonstrate conceptual understanding.

The Teacher Resource Book contains a section called Concept Extension that provides teachers with additional ways to support building students’ conceptual understanding. Examples of how the Concept Extension supports teachers in building conceptual understanding include:

• Unit 1 Lesson 3 provides guidance to teachers on how to connect regrouping in addition to regrouping in subtraction, using base ten blocks. (4.NBT.4).
• Unit 2 Lesson 7 provides guidance to teachers on how to use patterns to find all the factor pairs for a number (4.OA.4).
• Unit 4 Lesson 15 provides guidance to teachers on how to use number lines to help extend student understanding of decomposing fractions (4.NF.3).

Clusters 4.NF.A, 4.NF.B, and 4.NF.C focus on understanding fractions as numbers and fraction equivalence.

• In Unit 4 Lesson 14 Compare Fractions (4.NF.2) students use note cards and divide them into thirds, fourths, fifths, and tenths to compare fractions. During this lesson, groups of students also use number lines to compare fractions.
• In Unit 4 Lesson 16 Add and Subtract Fractions (4.NF.3) students cut a piece of notebook paper into 12 equal strips and practice adding twelfths. Students use number lines to add fractions. Students divide paper plates into eighths, shade ⅝, and cut out 2 eighths using scissors to determine how much is remaining.
• In Unit 4 Lesson 20 Fractions as Tenths and Hundredths (4.NF.5) students use pennies and dimes to model tenths and hundredths.

##### 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 Grade 4 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The materials provide opportunities to attend to procedural skill and fluency throughout the course, including fluency of adding and subtracting within 1,000,000 (4.NBT.4).

All lessons provide an opportunity for students to use computation skills. Each lesson contains a Building Fluency section which is designed to be used twice during a lesson. The Student Practice and Problem-Solving Book contain fluency practice pages, and Math Center Activities are included in the Teacher Toolbox which include activities for both procedural skill and fluency.

• Unit 1 Lesson 3 addresses adding and subtracting whole numbers within 1,000,000 (4.NBT.4).
• Unit 1 Math in Action integrates adding and subtracting within 1,000,000 (4.NBT.4).
• In Unit 4 Lessons 16 and 17 students add fractions with like denominators and compare fractions with different numerators and denominators (4.NF.3).

iReady Door 24 Plus is a free iPad app for fact fluency practice and is only available on the Apple platform. The game includes the fluencies for Grade 4.

##### 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 Grade 4 meet the expectation for being 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.

Opportunities to work with engaging applications are provided throughout the instructional materials. Each unit contains a Math in Action where students are exposed to non-routine problems that contain many points of entry, have more than one possible solution, integrate multiple standards, and include a Persevere on Your Own section. During guided practice Try It and independent practice Practice by Myself, students apply what they have learned to solve real-world problems. Most lessons also have an online interactive tutorial for students which features real-world applications. In addition, there are Problem Solving Connection problems where students solve multi-step word problems with whole numbers (4.OA.3), solve real world problems using addition and subtraction of fractions (4.NF.3d), and solve real world problems using multiplication of fractions (4.NF.4c). The following are examples of the applications included in the instructional materials:

• In Unit 2 Lesson 10 students are presented with multiple opportunities to solve problems posed with whole numbers using the four operations in contexts that include miles walked in a 3-week period, planting flowers in pots, and reading books.
• In Unit 4 Lesson 17 Practice & Problem Solving Book students solve real-world problems using addition and subtraction of fractions in contexts that include mixing together a fruit salad, distance traveled during a trip, and determining how much fabric is used in a costume.
• Unit 4 Lesson 20 Practice & Problem Solving Book page 214: “Mila has 100 math problems to finish this week. She solved 2/10 of the problems on Monday and 25/100 of the problems on Tuesday. Which day did she solve more problems? What fraction of the problems did she solve on Monday and Tuesday? Has she completed more than ½ her problems?”

##### 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 Grade 4 meet the expectations for balancing the three aspects of rigor. Overall, the three aspects of rigor are not always treated together and are not always treated separately within the materials.

Each lesson contains opportunities for students to build conceptual understanding, procedural skills and fluency, and apply their learning in real-world problems. Lessons are designed so students engage with all three components of rigor at different points in the lesson. During Guided Instruction and Guided Practice, students explore alternative solution pathways to master procedural fluency. During Independent Practice, students apply the concept in real world applications where they need to use both the procedural skills and their understanding of the concept to solve problems with multiple solutions and explain/compare their solutions.

For example, in Unit 5 Lesson 24 Time and Money students explain procedures for finding elapsed time, total time, conversion between units of time, money spent/saved and conversion between units of money. Through Guided and Independent Practice, students demonstrate multiple strategies to solve time and money problems, building fluency. In Independent practice, students also demonstrate conceptual understanding through error analysis. Teachers receive guidance to set up a classroom store, and students use the store as a place to apply what they have learned about money to a real-world, ongoing application. In the Unit 5 Lesson 24 Quiz students encounter routine procedural problems, evaluate the veracity of numerous expressions to represent a situation, and, using the information from the procedural and conceptual tasks, determine if the goal will be reached.

Math in Action lessons occur at the end of most units. These lessons focus on application problems where students apply procedural fluency and conceptual understanding to solve problems in a non-routine, real-world context.

#### 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 for Ready Grade 4 meet the expectation for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. Overall, the materials identify and attend to the full meaning of the MPs, emphasize mathematical reasoning by prompting students to construct viable arguments and analyze the arguments of others, assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others, and attend to the specialized language of mathematics.

##### Indicator {{'2e' | indicatorName}}
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 Grade 4 meet the expectations for identifying the Mathematical Practices (MPs) and using them to enrich the mathematics content within and throughout the grade.

The MPs for each lesson are identified in the CCSS Focus section as part of the Lesson Overview. SMP TIPs are found in the Teacher Resource Book throughout the lessons, and these tips highlight the integration of particular MPs within the lessons. The MPs are also identified for each lesson in the Table of Contents for the Teacher Resource Book on pages A4-A7.

Some examples of where the MPs are identified and used to enrich the mathematics content include:

• Unit 2 Lesson 9: MPs 1, 2, 4, 5, 6, and 7 are identified in the Lesson Overview. The SMP TIP in the lesson for MP2 states, “Writing multi-step equations to represent word problems requires students to reason abstractly and quantitatively. To successfully complete this problem, students need to see that 2 + 1 is more than just an addition fact to be computed. They must see 2 + 1 as the quantity of hours worked in one day that will then be multiplied by the number of days worked.”
• Unit 4 Lesson 14: MPs 1, 2, 4, 5, and 7 are identified in the Lesson Overview. The SMP TIP for MP4 states, “Some students may be tempted to use the model alone as justification for saying that Adriana ate more. Encourage them to use the model mathematically by reasoning about the number of parts and sizes of the parts. Discuss how the number of parts in each bar relates to the denominators and how the number of shaded parts relates to the numerators.” The SMP TIP for MP7 states, “Students must apply knowledge of equivalent fractions to solve this problem. Encourage them to look for and make use of structure as they search for a viable common denominator. Ask: Could you rewrite 2/100 as tenths? [No. You would have to divide 2 by 10.] How could you rewrite 8/10 as hundredths? [Multiply both the numerator and denominator by 10 to get 80/100.]” The SMP TIP in the lesson for MP5 states, “Help students use benchmark fractions strategically. When students discuss their comparison, guide them to consider what benchmark fraction will be most helpful in solving a given problem. For example, in problems 10-13, 1 is a useful benchmark because both fractions in the problem are near 1 on a number line.”
• Unit 5 Lesson 23: MPs 2, 5, 6, and 8 are identified in the Lesson Overview. The SMP TIP in the lesson for MP8 states, “Point out to the students that there is repeated reasoning involved when converting from a larger unit to a smaller unit. The number given in the larger unit will always be multiplied by the number of smaller units that make up one larger unit.”

##### Indicator {{'2f' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Ready Grade 4 meet the expectation for carefully attending to the full meaning of each practice standard. Overall, the materials attend to aspects of the mathematical practices (MPs) during different lessons throughout the grade, so when taken as a whole, the instructional materials attend to the full meaning of each MP.

Examples of where the instructional materials attend to each of the MPs include:

• MP1: In Unit 5 Lesson 26 students make sense of and persevere in solving problems while finding missing side lengths when the perimeter is given.
• MP2: In Unit 2 Lesson 5 students reason abstractly and quantitatively as they translate between words, symbols, and bar models that represent the same multiplicative comparison. In Unit 2 Lesson 10 students reason abstractly and quantitatively as they reason about the remainder and what it means.
• MP4: In Unit 3 Lesson 12 students solve problems that involve division of whole numbers. The students can model the division problems with equations, bar diagrams, or an area model, and the students can use the model they choose to revise their initial solution if there are errors or it doesn’t make sense.
• MP5: In Unit 5 Lesson 25 students have the opportunity to choose from different tools as they engage with problems involving length. The SMP TIP in the lesson for MP5 states, “Encourage students to use and/or draw visual models when confronted with various problems. A visual model can be a useful tool in deciding the necessary steps to finding a solution. Visual models often make the problem seem more ‘real’ and less abstract.”
• MP7: In the Unit 1 Math in Action students discuss where they see place value in their solution to a problem and how their understanding of place value helps them understand the solution. In Unit 4 Lesson 13 students use the structure of fractions to determine what happens when fractions are multiplied or divided.
• MP8: In Unit 6 Lesson 32 students use repeated reasoning to classify a rhombus. The SMP TIP in the lesson for MP8 states, “Students have had many opportunities to identify right, acute, and obtuse angles. Students should be able to correctly place a rhombus in the Venn diagram using the patterns they have seen with other quadrilaterals.”

##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
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 Grade 4 meet the expectation for prompting students to construct viable arguments and analyze the evidence of others. Overall, the materials offer students multiple opportunities to construct viable arguments and/or analyze the arguments of others throughout the materials.

Examples where students are prompted to construct viable arguments and analyze the arguments of others include:

• Unit 1 Math in Action students construct an argument as to why their estimate is reasonable for the expected number of visitors to a blog post about video games.
• Unit 3 Lesson 12 Question 16 students choose the correct answer out of four for a word problem. Then students answer: “Awan chose D as the correct answer. How did he get the answer? How can you tell that Awan’s answer doesn’t make sense?”
• Unit 4 Lesson 14 Practice and Problem Solving Workbook students are asked, “Can two fractions with the same numerator and different denominators be equal? Explain using words and numbers.”

##### Indicator {{'2g.ii' | indicatorName}}
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 Grade 4 meet the expectation for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others concerning key grade level mathematics detailed in the content standards. The materials provide teachers with SMP TIPs to help facilitate students to construct arguments and/or analyze the arguments of others.

Examples where teachers are supported to help students construct viable arguments and analyze the arguments of others include:

• Unit 2 Math In Action has a note for teachers during Plan It and Solve It that states, “Put students in pairs to discuss solution ideas. Ask them to also discuss the Reflect questions about Mathematical Practices. Remind students that there are always different ways to answer these questions.”
• Unit 3 Math In Action SMP Tip states: “Encourage students to explain and justify their ideas and to ask each other questions about their suggestions. Prompt them to demonstrate how their ideas could lead toward a solution.”

##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Ready Grade 4 meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of Mathematics.

• The Student Practice and Problem Solving Book has notes at the bottom of the pages where mathematical vocabulary is defined.
• The Teacher Resource Book has Lesson Vocabulary for each lesson with mathematical terms and their definitions.
• Teachers are prompted in the Teacher Resource Book to have students use precise mathematical language. For example, Unit 4 Lesson 20 Mathematical Discourse 1 states, “Discuss the meaning of “4/10 of a dollar” [40 cents, or 4 dimes] and “50/100 of a dollar” [50 cents, or 5 dimes].”
• Each lesson has an “English Language Learners” section in the Teacher Resource Book that contains some ways to support vocabulary development for all students.
• Lessons contain language objectives. For example, Unit 2 Lesson 7 states, “Orally define and use in discussion the key mathematical terms factor, factor pair, multiple, composite number, and prime number.”

### 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 for Ready Grade 4 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 exercises that are 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.

##### Indicator {{'3a' | indicatorName}}
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 Grade 4 meet expectations for distinguishing between problems and exercises. Each problem or exercise has a purpose.

Students are learning new mathematics and solving problems in the beginning stages of each lesson in the Use What You Know, Find Out More, Reflect, Picture It, and Model It sections. At the conclusion of lesson instruction, students complete exercises in the Guided Practice and Independent Practice that engage them in exercises to practice skills and in problems to apply learning.

The instructional materials provide problems and exercises in both the Ready Instruction book and the Practice and Problem Solving Book. For example, in Unit 3 Lesson 12 Modeled and Guided Instruction students complete division problems using an area model and partial products methods that include making meaning of remainders. During Guided Practice students solve division exercises with remainders using area models and partial quotients. During Independent Practice students solve multiple choice problems that require them to demonstrate their use and understanding of division with and without remainders.

##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed for Ready Grade 4 meet the expectations that the design of assignments is not haphazard and that the exercises are given in intentional sequences.

Problem sets and daily practice exercises relate to the mathematical concept developed in each lesson. The sequence of topics in each unit is intentionally planned to move from working with concrete and pictorial representations to more abstract work with numbers and computation. Each unit has a progressions chart showing what students have learned in previous grades connected to what they will learn in Grade 4 and how this will relate to what they will learn in future grades. Each lesson has a Learning Progression section in the lesson overview of the Teacher Resource Book which states what was learned in the previous grade, what students are learning in Grade 4 how it relates the current lesson, and what will happen in the next grades.

Concepts are explored and developed in daily lessons and reinforced through partner work and independent practice. Lessons are designed using a scaffolded approach. Students are guided by the teacher in the beginning of instruction, move toward work with partners or in small groups, and finally work independently. For example, in Unit 3 lessons are sequenced to build understanding of and fluency with multiplication and division with multi-digit whole numbers. Instruction begins in Lesson 11 with students multiplying one-digit and two-digit numbers by multiples of ten before multiplying two two-digit factors using area models, partial sums and the standard algorithm. In Lesson 12 students divide using the same area model representations and are asked to provide the related multiplication equations. Finally, students use the various strategies learned for multiplying and dividing in Unit 3 to complete the Math In Action lesson where they use and apply all operations with whole numbers as well as estimation.

##### Indicator {{'3c' | indicatorName}}
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 Grade 4 meets expectations that there is a variety in what students are asked to produce.

Students are expected to respond and produce solutions in various ways. They are asked not only to produce answers but to provide evidence through drawings, representations, and written explanations. Students are often asked to analyze and defend the work of others. They must justify their conclusions with verbal statements and mathematical reasoning.

Lessons are designed with a consistent routine that includes whole group, partner, and independent work. The Picture It, Model It, Connect It, and Try It portions of each lesson require students to represent the problem in a drawing and make connections between the drawing and the equations. The Pair/Share portion of each lesson asks students to discuss their approaches to solving problems with another student, promoting students to justify their work and reason through the work of others. Question types vary and include multiple choice, true/false, draw a model, short answer, solve, explain, find the mistake, and multi-step performance tasks. Students are asked to produce various answers for the mathematical content that is the focus of each lesson. For example, in Lesson 25 students complete open-ended questions based on reading a short paragraph, use bar models, pictures, and number lines to solve problems, solve problems involving measurement conversions, and answer multiple choice questions.

##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for Ready Grade 4 meet expectations for providing manipulatives that are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

In the Hands-On Activities found within each lesson students use a variety of manipulatives including number cubes, unit cubes, fact triangles, hundreds charts, base-ten blocks, place value charts, number cards, clocks, stopwatches, volume containers, pattern blocks, and square tiles. Students are frequently asked to look at a manipulative model and create a math equation from the representation. For example, in Lesson 20 students add fractions of tenths and hundredths by looking at pictures of base-ten blocks shaded to represent the fractions.

Throughout the materials, various manipulatives are introduced and used in lessons. Their use is appropriate for the mathematics content represented. For example, in Lesson 17 students use fraction circles to model addition of fractions in the Hands on Activity. Students discuss and make sense of the models, connecting them to the written expression the teacher is instructed to write on the board.

##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The visual design of the instructional materials reviewed for Ready Grade 4 is not distracting or chaotic, and supports students in engaging thoughtfully with the subject.

The format of each lesson is consistent in both the Teacher Resource Book and Student Instruction Book. The pictures within the Student Instruction Book and the Interactive Tutorials on the Ready Teacher Toolbox are colorful, engaging, and represent items that are relevant to children.

The students have adequate space to work within the Student Instruction Book and Practice and Problem Solving Book. Each lesson for the teacher and student has a consistent layout throughout the series. The pictures match the concepts addressed. For example, Unit 4 Lesson 14 has two Interactive Tutorials. Fraction-tration has an objective for students to compare two fractions with different denominators by creating common denominators, or by comparing to a benchmark fraction. As the tutorial loads, a “chat” appears at the bottom of the page with comments about fractions and links to other sites. The animation begins with students dragging fraction tiles into two columns: less than 1 and greater than 1. They are then asked to make comparisons between fractions. They compare fractions to benchmark fraction (i.e. ½) and identify equivalent fractions. If a student gets an incorrect answer, a number line pops up to help them connect the visual picture to the fraction and the number line. The animation continues with students continuing to make comparisons and sort fractions as greater than or less than the benchmark fractions. This is an engaging way for students to compare and order fractions.

#### 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 for Ready Grade 4 meet the 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.

##### Indicator {{'3f' | indicatorName}}
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 Grade 4 meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. Support is provided in the following ways:

• Step by Step in each lesson organizes content into chunks for student learning and includes guiding questions, key points, and teacher prompts. For example, in Lesson 15 students explore fractions on a number line. During Guided Instruction teachers are prompted to ask: “Can you think of another way to show finding a difference on a number line?” Teachers are told, “Students may mention adding up to subtract.”
• The Mathematical Discourse section in each lesson includes questions to engage students and advance their mathematical understanding. For example, Lesson 11 Mathematical Discourse asks: “If you have a multiplication problem such as 100 x 12, will it change your answer if you write it as 12 x 100?” Teachers receive information on why the answers are the same and how this is an example of the commutative property. “Students may understand the concept, but may not know the name. It states that regardless of the order in which you multiply two numbers, the product is always the same.”

##### Indicator {{'3g' | indicatorName}}
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 Grade 4 meet expectations that they 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 provide resources to support teacher planning.

• The Teacher Resource Book provides a separate pacing guide for the year, month, week, and day.
• The Unit Overview page includes lesson titles, page numbers, the primary and supporting standards, prerequisite skills, content objectives, learning progressions, lesson vocabulary, and a detailed pacing guide for whole and small group instruction for each lesson.
• Two Common Core correlation charts, Ready Instruction Correlation and Interim Assessment Correlation, are included.
• The Cognitive Rigor and Ready Chart lists specific questions identified as DOK level 3.

The Teacher Resource Book contains components to assist with lesson delivery.

• At a Glance explains what students will be doing during each component of the lesson.
• Step by Step organizes the lesson into chunks and provides guiding questions.
• SMP Tips highlight specific Standards for Mathematical Practice.
• Mathematical Discourse includes questions to engage students and advance their learning. Possible answers and key ideas to listen for in student responses are included.
• Try It Solutions provide complete explanations and multiple solutions.
• Concept Extensions, ELL Support, and Visual Models provide support, suggestions, and strategies to engage students with activities that support varied abilities.
• Solutions in the Independent Practice section includes a correct response, at least one possible solution method, and the DOK level for the problems.
• Quick Check and Remediation includes an exit slip to monitor understanding. A chart includes error analysis and remediation suggestions.
• Hands-On Activity extends the concepts and skills using manipulatives and a collaborative group approach.
• Challenge Activity extends the learning of those students who have mastered the skills and concepts.

The Teacher Toolbox found online contains the following technology components to assist with lesson delivery:

• Interactive Tutorials are referenced as part of Day 1 instruction for most lessons and provide interactive video clips for delivery of student mathematical learning.
• i-Ready Door 24 Plus is a free iPad app for fact fluency practice but is not explicitly included in the Teacher Resource Book for instruction.

i-Ready (available for additional purchase and used by most Ready users) is an Online Diagnostic and Instruction component.

##### 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 Grade 4 meet expectations for containing a teacher’s edition in print and online that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their knowledge of the subject, as necessary.

In each lesson, information is provided for the teacher to understand and make connections between the mathematical content and practices, errors or misconceptions that may arise, and the rationale behind specific lesson parts.

• In Unit 4 Lesson 22 the SMP TIP for MP8 states, “Students make use of regularity in repeated reasoning by applying the same processes that they developed in earlier grades to compare whole numbers. Ask students why this process works for decimals but not for fractions. [Decimals use the principles and patterns of base ten place value, but fractions often have denominators that are not multiples of ten.]”
• In Unit 6 Lesson 33 the Learning Progression states, “In this lesson students build on their understanding to reason about lines of symmetry in two-dimensional figures. … In Grade 5 students will extend their understanding of geometric concepts when they solve mathematical problems using the coordinate plane.”

Throughout Ready Grade 4 there is guidance for teachers that identifies and connects the underlying mathematics of a lesson. These are written in adult language.

##### 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 Grade 4 meet expectations for containing a print teacher’s edition (in print and in the on-line Teacher Toolbox) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Each unit begins with a Lessons Progressions Chart. This chart begins by listing lessons that students are building upon. These lessons can come from previous grades and from Grade 4. For example, Unit 4 Lesson 15 builds upon Grade 3 Lessons 16 and 17 and Grade 4 Lesson 13. The chart also lists lessons that students are preparing for. For example, Unit 6 Lesson 32 is preparing students for Grade 5 Lessons 30 and 31.

Each Lesson Overview includes a Learning Progression section. This section begins with an explanation of how the lesson builds on prior knowledge from Grade 3. The Learning Progression explains the lesson's overall connection to Grade 4 and the mathematical content of the lesson. This section also explains connections to Grade 5 and, if appropriate, to other future grades.

##### 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 Grade 4 provide a list of lessons in both the printed and digital versions of the Teacher Resource Book that cross-reference lessons and standards and provide an estimated instructional time for each unit, chapter, and lesson.

• A Year-Long Pacing Guide recommends the number of days for each lesson, including assessments. Lessons include recommended minutes per day.
• The Unit Overview provides the focus standard for each lesson.
• The Correlation Chart correlates the Common Core Standards with each instructional lesson.

##### 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 Ready Grade 4 instructional 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 Practice and Problem Solving Book includes a Family Letter for each lesson. The letter includes an explanation of the math and an activity for the family to use at home. A Spanish version of the letter is available online in the Teacher Toolbox.

##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Ready Grade 4 instructional materials contain explanations of the instructional approaches of the program and identification of research-based strategies.

The Teacher Resource Book contains the following explanations of the program instructional approaches:

• “Answering the Demands of the Common Core with Ready” details how the program addresses the shifts in the standards.
• “Supporting Research” provides the instructional methods used by Ready, examples of where these methods are found in the program, and research that supports these methods.
• “Cognitive Rigor and Ready” provides a table that combines the hierarchies of learning of Webb (Depth of Thinking) and Bloom (Types of Thinking) and provides a table that charts where higher-complexity items can be found within lessons.
• References are provided at the back of the Teacher Edition. This list details key research reports on math instruction and learning.

#### Criterion 3.3: Assessment

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

The instructional materials for Ready Grade 4 partially meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide opportunities for identifying and addressing common student errors and misconceptions, ongoing review and practice with feedback, and having assessments with standards clearly denoted. The instructional materials do not consistently provide strategies for gathering information about students’ prior knowledge or include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers.

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

The instructional materials reviewed for Ready Grade 4 partially meet expectations for supporting teachers with strategies for gathering information about students’ prior knowledge within and across grade levels.

Prerequisite skills are listed for each unit and lesson. At the beginning of each unit in the Student Instruction Book students check off skills they already know in the “Self Check.” Filling out the checklist is explicitly called out in the “Step By Step” section at the beginning of the unit in the Teacher Resource Book. Prerequisite support lessons are provided for the teacher within each lesson to review prerequisite concepts or fill in gaps in student knowledge.

However, there are no pretests included within the program or systematic way to gather information about student prior knowledge. The i-Ready online component (available for additional purchase and used by most Ready users) is the tool provided to gather information about prior knowledge.

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

The instructional materials reviewed for Ready Grade 4 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• The Quick Check and Remediation section at the end of a lesson presents a question to monitor understanding of the content of the lesson. This section includes a chart of incorrect answers, common errors, and remediation suggestions.
• Lesson Quizzes provide the teacher with a Common Misconceptions and Errors section that describes common misconceptions and errors.
• Within lessons themselves, directions instruct teachers to watch for specific errors and misconceptions, and suggestions are provided to address these errors and misconceptions. For example, in Lesson 5 students are assessed on multiplicative comparison and the following misconceptions are noted: “Students may find a sum or difference instead of finding the comparison; they may confuse the meaning of the factors in the model; or they may look at the position of the factors without considering the meaning of the context.”

##### 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 Grade 4 meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Each lesson provides approximately one week of instruction. Over the course of the week, responsibility for the learning process transfers from the teacher to the student. Students move from scaffolded support to independent problem solving. Review and practice is incorporated in each lesson within the Ready Instruction Book and in each homework assignment within the Practice and Problem Solving Book.

Feedback is provided to students throughout lessons. Frequent feedback opportunities to address skills and concepts are provided in the Teacher Resource Book. The Quick Check and Remediation activity within each lesson provides teachers with sample errors and remediation strategies to address those errors. Assessments and Performance tasks include rubrics that can also be used to provide feedback.

##### 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 Grade 4 meet the expectation for offering ongoing formative and summative assessments that clearly denote which standards are being emphasized.

• Standards are clearly noted within assessments found in the Mathematics Assessments Teachers Guide.
• An Interim Assessment is provided for each unit. Interim assessments provide standards correlations for each item. This information can be found on the Interim Assessment Correlations chart in the Teacher Resource Book.
• Unit Assessments provide standards correlations for each item. Unit Assessments and correlations are found online in the Teacher Toolbox.
• Lesson quizzes and quick checks are provided for most lessons. These quizzes assess the specific standards being taught in the lesson.

##### 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 Grade 4 partially meet expectations for the inclusion of rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Rubrics are used throughout the course. Rubrics can be found within lessons for some independent practice activities, in quizzes, mid- and unit assessments, Math in Action, unit performance tasks, and in the Assessment Book. The rubrics and scoring guidelines are easy to understand and interpret.

Within lessons rubrics and scoring guidelines do provide guidance for teachers to follow-up, and throughout Ready there is guidance for teachers on behaviors to look for, error alerts, and misconceptions. However, the lesson quizzes, mid- and unit assessments, interim assessments, and the Assessment Books provide little guidance for teachers on how to interpret student performance or suggestions for follow-up. For example, scoring rubrics are provided for Math in Action Lessons and Unit Performance Tasks, but follow-up suggestions based on scoring criteria are not provided.

##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials reviewed for Ready Grade 4 encourage students to monitor their own progress.

• There is a self-check for students at the beginning of each unit. It is to be marked both before the unit and then again after the unit. This process is explicitly noted in the Step by Step of the Teacher Resource Book.
• There is a self-check for students at the end of each lesson with a reminder to go back to the unit self-check to see if there is anything they can check off.

#### Criterion 3.4: Differentiation

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

The instructional materials for Ready Grade 4 meet the expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide a balanced portrayal of various demographic and personal characteristics. The instructional materials also consistently provide: strategies to help teachers sequence or scaffold lessons; strategies for meeting the needs of a range of learners; tasks with multiple entry-points; support, accommodations, and modifications for English Language Learners and other special populations; and opportunities for advanced students to investigate mathematics content at greater depth.

##### 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 Grade 4 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Each lesson follows a gradual release model in which scaffolded support is withdrawn as students gain mastery. Each lesson consists of four components: Introduction, Modeled and Guided Instruction, Guided Practice, and Independent Practice.
• Lessons are sequenced to build from conceptual understanding, using concrete and pictorial representations to more abstract representations.
• The marginal notes in the Teacher Resource book often suggest ways to support students as a whole and subgroups of students who might need extra support. Notes include sections on vocabulary, concept extensions, visual models, hands-on activities, and real-world connections.
• Each lesson contains a Differentiated Instruction page which contains an Intervention Activity, On-Level Activity, and a Challenge Activity.
• Center Activity PDF’s can be found online in the Teacher Toolbox to help further differentiation.

##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instruction materials reviewed for Ready Grade 4, meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

The Teacher Resource Book contains the following support:

• Each lesson includes a section called Small Group Differentiation that consists of three subsections: Reteach, Teacher-led Activities, and Student-Led Activities. Specific lessons from earlier in the material, as well as the previous grade-level material in the series, are identified and can be used to review or fill in gaps in student knowledge. Student–led Math Center activities in three different levels are referenced for additional instruction, if needed.
• The marginal notes in the Teacher Resource Book suggest ways to support students as a whole and provide specific strategies for subgroups of students who might need extra support. This includes sections on vocabulary, concept extensions, visual models, hands-on activities, and challenge activities.
• The Math In Action section for each unit has a Differentiated Instruction page that includes an Intervention and a Challenge Activity.
• The student Practice and Problem Solving book includes three levels of problems (basic, medium, challenge) that include verbal, visual, and symbolic representations.

##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

Grade 4 Ready instructional materials meet expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

When solving problems, students often choose their own solution strategy and/or representation. The embedded tasks are presented using multiple representations (drawings, charts, graphs, numbers or words) and different solution strategies.

• In Unit 2 Lesson 6 students are guided through a multiplication word problem using a bar model and the context of the problem to build the equation.
• In Unit 4 Lesson 20 Hands-on Activity students use 10-inch squares of paper to mark intervals of 10 vertically to create and explore a model of tenths and then horizontally to explore hundredths. In Lesson 21 Visual Model the teacher uses a place value chart and guides students in finding parallels between tens and tenths, and hundreds and hundredths.
• Unit 3 Math in Action features open-ended problems with many entry points and more than one possible solution. For example, students are given data about worms (how much they eat in one day, cost of 1050 and 2950 worms, and how much food is available). Students then tell how many and what size package of worms can be purchased to use the amount of food available. Students are encouraged to solve the problem in different ways.

##### 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 Grade 4 meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

The Teacher Resource Book and online Teacher Toolbox contain the following support:

• ELL Support Tips are found in the margin notes of each lesson of the Teacher Resource Book. For example, Unit 2 Lesson 9: “Throughout this lesson you will need to provide extra support to give English Language Learners confidence to participate in class discussions. Give all students time to think through their response to a question. Wait at least 5 seconds, and up to 30 seconds, before calling on any student to answer. If a student’s comment is unclear try 're-voicing' the student’s comment.”
• Prerequisite lessons include specific ELL support as needed. For example, in Unit 4 Lesson 20 there is one prerequisite lesson. Prerequisite Lesson 14 (Grade 3) includes an English language Learners support that states: “Some students, especially ELL students, may need additional support with understanding and using the word unit. Connect the term to the base-ten blocks they use. Remind them the ones blocks are called 'unit' cubes.”
• A Differentiated Instruction page is included in some lessons of the Teacher Resource Book. For example, Unit 5 Lesson 28 Understand Angles includes an Intervention Activity, On-Level Activity, and a Challenge Activity.
• Math Center Activities are provided On Level, Below Level, and Above Level.

##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials reviewed for Ready Grade 4 meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Materials offer the following instructional support for advanced learners:

• Each lesson of the Teacher Resource Book provides a Challenge Activity that provides students who have mastered the concepts and skills of the lesson with a more sophisticated problem. For example, in Unit 3 Lesson 12 Challenge Activity students are solving two-step word problems involving division. Three problems with contexts that include remainders are given. For example, “Jeremy had a bag of 300 raisins. He kept 20 for himself. He wanted to evenly split the rest among 7 friends. How many raisins was Jeremy able to give each of his friends?”
• The Math In Action section for each unit of the Teacher Resource Book has a Differentiated Instruction page that includes a Challenge Activity. For example, Unit 4 Math in Action: Use Fractions and Decimals Challenge Activity Sports Picture Frame asks students if they can design a frame from five craft sticks without changing the instructions. If it cannot be done, students must explain how the instructions could be changed to complete the project.
• A Differentiated Instruction page that provides Challenge activities is included in some lessons of the Teacher Resource Book. For example, Unit 1 Lesson 1 Understand Place Value includes a Challenge Activity to find numbers around them and present the numbers using base-ten clues in two different ways. Students also write each number in standard form, word form, and expanded form.

##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials reviewed for Ready Grade 4 meet the expectation for providing a balanced portrayal of various demographic and personal characteristics.

• The names and situations in the story problems represent a variety of cultural groups.
• Student edition pictures include students from a variety of cultures.
• The Let’s Talk About It section in each lesson includes four faces of various demographics and represents both genders.
• The application problems include real-world situations that are appropriate to a variety of cultural and gender groups.
• Interactive tutorials found online in the Teacher Toolbox represent students of both genders and various ethnicities.

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

The instructional materials reviewed for Ready Grade 4 provide opportunities for teachers to use a variety of grouping strategies.

The following strategies are found in the Teacher Resource Book:

• The Gradual Release model incorporates teacher led whole and small group instruction for each lesson.
• Pair/Share Tips found in the margin notes prompt students to compare answers and reason with a partner.
• The online Teacher Toolbox provides protocols for the Think-Share-Compare Activities.
• Margin notes within each lesson suggest appropriate grouping strategy - whole, small group, pairs, or individually - in different parts of the lesson.
• The online Teacher Toolbox provides math center activities for each lesson.

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

The instructional materials reviewed for Ready Grade 4 provide limited support for teachers to draw upon home language and culture to facilitate learning.

• The online Teacher Toolbox provides a Spanish version of the family letters included in the Practice and Problem Solving book.
• Some English Language Learner support sections found in the margin notes discuss making the connection between the English vocabulary and the Spanish cognate.

#### 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 for Ready Grade 4 integrate technology in ways that engage students in the Mathematical Practices. The digital materials are web-based and compatible with multiple internet browsers, but they do not include opportunities to assess student mathematical understandings and knowledge of procedural skills. The digital materials do not include opportunities for teachers to personalize learning for all students, and the materials offer some opportunities for customized, 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 Ready Grade 4 digital materials are web-based and compatible with multiple internet browsers. The Teacher Resource Book, Teacher Toolbox, and Student Books are platform neutral and can be accessed on tablets and mobile devices. The i-Ready Door 24 Plus is used for fact fluency, and practice is only available for iPads.

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

The instructional materials for Ready Grade 4 do not include opportunities to assess students’ mathematical understanding and knowledge of procedural skills using technology.

i-Ready is an online diagnostic and monitoring tool (available for additional purchase and used by most Ready users). i-Ready has two components. i-Ready Diagnostic is an adaptive diagnostic, and i-Ready Standards Mastery is designed to provide information about mastery of individual grade-level standards.

##### 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 Ready Grade 4 digital instructional materials cannot be customized for individual learners or users. An additional purchase of i-Ready (available for additional purchase and used by most Ready users) does provide adaptive diagnostic and growth measures to support personalized instruction.

There are limited opportunities for the teacher to customize lessons for local use. Ready Teacher Resources include Reteach Ready Instruction Prerequisite Lessons, Tools for Instruction, and Math Center Activities. Prerequisite Lessons and Tools for Instruction are teacher-led activities for use with small groups requiring additional instruction and/or review of prerequisite concepts. Math Center Activities are student-led activities.

##### Indicator {{'3ad' | indicatorName}}
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 Ready Grade 4 instructional materials do not provide opportunities for teachers to collaborate with other teachers or students to collaborate with other 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 Ready Grade 4 instructional materials include Interactive Tutorials that are animated interactive lessons assigned to students in their personalized online instruction plan. These tutorials include integrative technology such as interactive tools and virtual manipulatives/objects to engage students in the Mathematical Practices as they model the mathematical content of the lesson.

## Report Overview

### Summary of Alignment & Usability for Ready | Math

#### Math K-2

The instructional materials for Ready Grades K-2 meet the expectations for focus and coherence in Gateway 1. All grades meet the expectations for focus as they assess grade-level topics and spend the majority of class time on major work of the grade, and all grades meet the expectations for coherence as they have a sequence of topics that is consistent with the logical structure of mathematics. In Gateway 2, all grades meet the expectations for rigor and balance, and all grades meet the expectations for practice-content connections. In Gateway 3, all grades meet the expectations for instructional supports and usability. The instructional materials show strengths by being well designed and taking into account effective lesson structure and pacing, supporting teacher learning and understanding of the Standards, and supporting teachers in differentiating instruction for diverse learners within and across grades.​​

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

#### Math 3-5

The instructional materials for Ready Grades 3-5 meet the expectations for focus and coherence in Gateway 1. All grades meet the expectations for focus as they assess grade-level topics and spend the majority of class time on major work of the grade, and all grades meet the expectations for coherence as they have a sequence of topics that is consistent with the logical structure of mathematics. In Gateway 2, all grades meet the expectations for rigor and balance, and all grades meet the expectations for practice-content connections. In Gateway 3, all grades meet the expectations for instructional supports and usability. The instructional materials show strengths by being well designed and taking into account effective lesson structure and pacing, supporting teacher learning and understanding of the Standards, and supporting teachers in differentiating instruction for diverse learners within and across grades.​​

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

#### Math 6-8

The instructional materials for Ready Grades 6-8 meet the expectation for focus by assessing grade-level topics and spending the majority of class time on major work of the grade. All grades meet the expectations for coherence in Gateway 1 as they have a sequence of topics that is consistent with the logical structure of mathematics. In Gateway 2, the materials for all grades meet the expectations for rigor and balance, and they meet the expectations for practice-content connections. The materials for all grades were reviewed for Gateway 3 and meet the expectations for instructional supports and usability. The instructional materials show strengths by being well designed and taking into account effective lesson structure and pacing, supporting teacher learning and understanding of the CCSSM Standards, and supporting teachers in differentiating instruction for diverse learners within and across grades.

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

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### Overall Summary

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###### Alignment
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###### Usability
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