The materials reviewed in Grade 1 for this indicator meet the expectations by attending to conceptual understanding within the instructional materials.

The instructional materials often develop a deeper understanding of clusters and standards by requiring students to use concrete materials and multiple visual models that correspond to the connections made between mathematical representations. The materials encourage students to communicate and support understanding through open-ended questions that require evidence to show their thinking and reasoning.

The following are examples of attention to conceptual understanding of 1.OA.4:

• In Unit 3, Module 1, Session 5, students use the number rack as a tool to model and solve subtraction word problems. Problem types include Take From-Change Unknown, Take From-Start Unknown, and Compare-Difference Unknown. These varying problem structures provide opportunities for students to develop a deep understanding of the relationship between addition and subtraction.

The following are examples of attention to conceptual understanding of 1.OA.7:

• In Unit 6, Module 1, Session 2, students are provided with equations with a box for the missing addend. They solve various equations and also determine if equations are true.

The following are examples of attention to conceptual understanding of 1.NBT.B:

• In Unit 4, Module 4, Session 2, students build conceptual understanding of bundles of ten within 100 using concrete materials and the structure of a ten-frame.
• In Unit 7, Module 1, Session 2, students count popsicle sticks, grouping 10 ones into groups of 10. Then, two index cards are labeled "10's" and "1's," and students reorganize their sticks so that they can be counted more easily. Students collaborate to model groupings in our base ten number system helping them develop a deep understanding of place value.
• In the February Number Corner Calendar Collector, a ten-strip model is used to build conceptual understanding of place value with tens and ones.

The following are examples of attention to conceptual understanding of 1.NBT.C:

• In Unit 2, Module 2, Session 4, the 100s Number Grid is observed, and students share some things they notice (you can count by 10s in the last column, there are all 0's in that column, there are 1's under 1's and 2's under 2's, etc.). Students use the Number Grid as a scaffold/tool to help solve the "Change Cards" game problems. As students play the game, "Change Cards," they are adding and subtracting multiples of 10 (Cards: 25 and 35 = rule of +10). They then discuss the "rule" and pair-share to make predictions for the next group of cards.
• In Unit 3, Module 3, Sessions 1-4, students are using cube trains of ten and single cubes to represent addition two-digit equations equations.
• In Unit 8, Module 3, Sessions 3-6, students use unifix cube trains

The Grade 1 materials meet the expectations for procedural skill and fluency by giving attention throughout the year to individual standards which set an expectation of procedural skill and fluency.

• Students spend a significant amount of time and have a variety of opportunities to fluently add and subtract throughout Number Corner activities.
  • In the Number Corner September Computational Fluency, in Activity 1, students are using the double 10-frame to solve addition problems by matching the equation with the cards.
  • In the Number Corner October Computational Fluency, in Activity 2, students play Ten-Frame Flash and show, with their fingers, how many dots are on the 10-frame cards.
  • In the December Number Corner Computational Fluency Routine, the routine for this month involves investigating double facts greater than 10 using a double ten-frame.
  • In the March Number Corner Days in School Routine, the hundreds grid is used as a visual model to assist students in explaining their mental reasoning for ten more or ten less.

• Fluency is developed throughout the sessions of the Grade 1 instructional materials.
  • In Unit 1, Module 2, Session 3, students respond to representations of the 10-frame as the teacher flashes the 10-frame cards with totals within 10.
  • In Unit 4, Module 1, Session 5, students solve addition and subtraction combinations such as 3+2 and 5-2. Students are using their fluency to help deepen their understanding about the relationship between addition and subtraction.
  • In Unit 2, Module 2, Session 3, students identify strategies they used in adding numbers represented on a domino. Teacher led discourse elicits student thinking using counting on, doubling, and decomposing strategies.
  • In Unit 1, Module 3, Session 1, students solve missing-addend problems on their number racks. They use 5 as a landmark and find doubles and then count on.
  • In Unit 3, Module 4, Sessions 1 and 2, students use unifix cubes to represent equations up to 10 with various combinations of two or three addends.
  • In Unit 6, Module 2, Session 2, students use ten and double ten frames to represent addition up to twenty in the game "I have, who has" to create the addition equations.

Materials meet the expectations for having engaging applications of mathematics as they 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.

Materials include multiple opportunities for students to engage in application of mathematical skills and knowledge in new contexts. The materials provide single step contextual problems that revolve around real world applications. Major work of the grade level is addressed within most of these contextual problems. The majority of the application problems are done with guiding questions elicited from the teacher through whole group discussions that build conceptual understanding and show multiple representations of strategies. Materials could be supplemented to allow students more independent practice for application and real-world contextual problems that are not teacher guided within discussions.

The instructional materials include problems and activities aligned to 1.OA.1 and 1.OA.2 that provide multiple opportunities for students to engage in application of mathematical skills and knowledge in new contexts. Examples of these applications include the following:

• In Unit 2, Module 2, Session 2, the materials provide story problems to investigate the relationship between addition and subtraction equations. Students write their own story problems and equations as an extension of the learning.
• In Unit 3, Module 1, Session 5, students use the number rack as a tool to model and solve subtraction word problems (problem types - Take From-Change Unknown, Take From-Start Unknown, and Compare-Difference Unknown). These varying problem structures provide opportunities for students to develop a deep understanding of the relationship between addition and subtraction and apply mathematical knowledge and skills in a real-world context.
• In Unit 4, Module 1, Session 3, the teacher provides frog word problem to students and they solve using the number line.
• In Unit 4, Module 2, Session 3, the lesson utilizes a floor number line to investigate the use of addition and subtraction on the number line through contextual story problems.
• In Unit 7, Module 3, Session 2, students solve addition story problems with sums to 20 involving adding to, put together with unknowns in all positions.
• In the Number Corner October Calendar Grid, the teacher provides a word problem (add to, result unknown problem type), and students solve.
• In the Number Corner February Computational Fluency, students began to add to ten in the context of themed story problems and application within the Number Corner computational fluency routine. Thinking within these contextual situations is extended toward building conceptual understanding of subtraction as a missing addend problem.

The materials reviewed in Grade 1 meet the expectations for providing a balance of rigor. The three aspects are not always combined nor are they always separate.

In the Grade 1 materials all three aspects of rigor are present in the instructional materials. All three aspects of rigor are used both in combination and individually throughout the unit sessions and in Number Corner activities. For example, in Unit 3 Module 3 Session 1 and Unit 6 Module 1 Session 4 all aspects of rigor are present. Application problems are seen to utilize procedural skills and require fluency of numbers. Conceptual understanding is enhanced through application of previously explored clusters. Procedural skills and fluency learned in early units are applied in later concepts to improve conceptual understanding.

The instructional materials reviewed for Grade 1 meet the expectations for identifying the MPs and using them to enrich the mathematical content. Although a few entire sessions are aligned to MPs without alignment to grade-level Standards for Mathematical Content, the instructional materials do not over-identify or under-identify the MPs and the MPs are used within and throughout the grade.

The Grade 1 Assessment Guide provides teachers with a Math Practices Observation Chart to record notes about students' use of MPs during Sessions. The chart is broken down into four categories: habits of mind, reasoning and explaining, modeling and using tools, and seeing structure and generalizing. The publishers also provide a detailed, "What Do the Math Practices Look Like in Grade 1?" guide for teachers (AG, page17).

Each session clearly identifies the MPs used in the Skills & Concept section. Some sessions contain a "Math Practice In Action" sidebar that explicitly states where the MP is embedded within the lesson and provides an in-depth explanation of the connection between the indicated MP and the Standards for Mathematical Content for the teacher. Examples of the MPs in the instructional materials include the following:

• Unit 1, Module 4, Session 1 references MP2 and MP5. Unit 1, Module 4, Session 2 references MP5 and MP6. Unit 1, Module 4, Session 3 addresses MP4 and MP6. In Unit 1, Module 4, Sessions 4 and 5 both address MP4 and MP7. There is a "Math Practices In Action" reference in Session 1 and Session 3.
• In Unit 2, Module 1 in the Skills & Concepts section, two sessions (3 and 4) list MP2, Session 4 lists MP3, Session 5 lists MP6, two sessions (1 and 2) list MP7, and Session 2 lists MP8.
• In Unit 6, Module 1, Sessions 1 and 3 reference the MPs within the Problems and Investigations portion of the session as, "Math Practices in Action."
• In Unit 7, Module 2, four of the five sessions address MP7.
• In Unit 7, Module 3, Session 1 references the MPs within the Problems and Investigations portion of the session as, "Math Practices in Action."
• In the September Number Corner, MP4 is addressed in Calendar Grid, Days in School, and Computational Fluency; MP6 is addressed in Calendar Collector, MP7 is addressed in Calendar Grid, Days in School, Computational Fluency, and Number Line, and MP8 is addressed in Number Line.

Lessons are aligned to MPs with no alignment to Standards of Mathematical Content. These sessions that focus entirely on MPs include the following:

• Unit 1, Module 2, Session 1
• Unit 6, Module 4, Session 4
• Unit 8, Module 4, Session 5

The materials meet the expectations for attending to the full meaning of each practice standard. Each Session clearly identifies the MPs used in the Skills & Concept section of the session. Typically there are two MPs listed for each session, so there is not an overabundance of identification.

Some sessions contain a "Math Practice In Action" sidebar that explicitly states where the MP is embedded within the lesson and provides an in-depth explanation for the teacher. Although the MPs are listed at the session level, the MPs are not discussed or listed in unit overviews or introductions (major skills/concepts addressed); however, they are listed in the section 3 of the Assessment Overview. With limited reference in these sections, overarching connections were not explicitly addressed.

In Number Corners, the MPs are listed in the Introduction in the Target Skills section with specific reference to which area of Number Corner in which the MP is addressed (Calendar Grid, Calendar Collector, Days in School, Computational Fluency, Number Line). The MP are also listed in the assessment section of the introduction as well. Although the MPs are listed in these sections, there is no further reference to or discussion of the MPs within Number Corner.

The following are examples of times that the instructional materials attend to the full meaning of the MPs:

• MP7 is addressed in Unit 1 Module 3 Session 2. This session focuses on the pattern and structure of the unit of ten using number lines, 10-frames and the place value relationship between the ones unit and tens unit.
• MP1 is addressed in Unit 3, Module 1, Session 5. Students are presented with very challenging number rack story problems in the Problems & Investigations section of this lesson. The wide range of problem types makes this session cognitively challenging for students in Grade 1. They are supported in their efforts to solve the problems and grow accustomed to devoting significant time and effort to persevere in solving them.
• MP3 is addressed in Unit 6, Module 2, Session 5. Students are working together to play the game "Pick Two to Make Twenty." Students have to pick two cards that total a number closest to 20. Students share their ideas and learn to construct viable arguments and critique the reasoning of others. Playing together as a team against the teacher motivates students to listen carefully to one another so they have the best chance at winning (Math Practices In Action, page 31). Students are invited to make a case for the combination they thinks works best by explaining their thinking to the class, and they can demonstrate on the number rack to help justify their thinking.
• MP5 is addressed in Unit 8, Module 4, Session 2. This session is titled, "How We Have Grown." Students work to compare the lengths of two strings that represent the length of an average baby with the length of an average student in Grade 1. Students are asked what strategies they might used to figure out the difference between the two lengths, and possible strategies are discussed, such as using Unifix cubes to represent lengths and then laying them next to each and count the extras on the big one, a number line, and models. Students are using appropriate tools strategically when they compare the lengths using strings, Unifix cubes, and the number line. They think carefully about how to use Unifix cubes and how to use efficient jumps on the number line. They are making choices about which tools to use and how to use them based on the problem at hand. (Math Practices in Action).

However, at times the materials only partially attend to the meaning of MP4. The intent of this practice standard is to apply mathematics to contextual situations in which the math arises in everyday life. Often when MP4 is labeled students are simply selecting a model to represent a situation. For example, in Unit 3, Module 1, Session 1, MP4 is indicated, but students are simply representing a number on a 10-frame. The Math Practices in Action note states that "Students will use drawings, numbers, expressions, and equations to model with mathematics."

The materials reviewed for Grade 1 meet the expectations of this indicator by attending to the standards' emphasis on mathematical reasoning.

Students are asked to explain their thinking, listen to and verify other's thinking, and justify their reasoning. This is done in interviews, whole group teacher lead conversations, and in student pairs. For the most part, MP3 is addressed in classroom activities and not in Home Connection activities.

• In Unit 2, Module 1, Session 4, students work with the teacher to create a class "Addition Strategies Chart." As they review the Domino Add & Compare game, students discuss some of their strategies they can use to find the total number of dots on a domino. After the chart is created, students are asked to share the advantages and disadvantage of each strategy. Since all of the strategies are written on the chart, students are able to critique and compare the strategies of others in a safe manner.
• In Unit 3, Module 4, Session 2, students are asked to show their thinking about how to decompose the number seven into two addends in multiple ways using addition and subtraction.
• In Unit 4 Module 3 Session 5, students are given a contextual word problem to compare two number sets involving the unit of one with the tool of pennies. They have to show their thinking with a visual representation.
• In Unit 6, Module 2, Session 5, students are introduced to a new game, "Pick Two to Make Twenty." When students share their ideas about how to get as close to 20 as possible, they are learning to construct viable arguments and critique the reasoning of others.
• In Unit 6, Module 4, Session 2, students are asked to show how they solved a contextual problem using pictures, numbers and words to explain their thinking.
• In Unit 7, Module 2, Session 1, students are making trains of Unifix cubes that total 120. Before beginning, students are asked to discuss with their partner about how many groups of 20 cubes will be needed to make the train. Volunteers share and explain their thinking. The next part of the lesson students are asked again to explain their thinking regarding locating a specific cube within the train.

The instructional materials reviewed for Grade 1 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 that is present throughout the materials.

The instructional materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. Students have opportunities to explain their thinking while using mathematical terminology, graphics, and symbols to justify their answers and arguments in small group, whole group teacher directed, and teacher one-to-one settings.

The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them. Examples of this include using geometry terminology such as rhombus, hexagon and trapezoid and using operations and algebraic thinking terminology such as equation, difference, and 10-frame.

• Many sessions include a list of mathematical vocabulary that will be utilized by students in the session.
• The online teacher materials component of Bridges provides teachers with "Word Resources Cards" which are also included in the Number Corner Kit. The Word Resources Cards document includes directions to teachers regarding the use of the mathematics word cards. This includes research and suggestions on how to place the cards in the room. There is also a "Developing Understanding of Mathematics Terminology" included within this document which provides guidance on the following: providing time for students to solve problems and ask students to communicate verbally about how they solved them, modeling how students can express their ideas using mathematically precise language, providing adequate explanation of words and symbols in context, and using graphic organizers to illustrate relationships among vocabulary words
• At the beginning of each section of Number Corner, teachers are provided with "Vocabulary Lists" which lists the vocabulary words for each section.
• Unit 3 Module 4, Session 1 investigates the relationship between numbers with the commutative property of operations. The language within the lesson reinforces and contextually uses the terms equations, equal and strategies to explain the reasoning between visual representations.
• In Unit 5, Module 2, Session 4, during a Problems & Investigations activity with 3-dimensional shapes, the teacher asks students how they identified a cube just by touch. The teacher guide gives specific direction to the teacher: "Model the vocabulary of geometry as you field their responses." The student's response includes the word "corner," and the teacher restates the response by saying, "What do you mean the corners - in math we call them vertices..."
• The Number Corner, October Calendar Collection investigates patterns of geometrical shapes using the terms hexagon, rhombus and trapezoid.

The sessions within the units distinguish the problems and exercises clearly. In general, students are learning new mathematics in the Problems & Investigations portion of each Session. Students are provided the opportunity to apply the mathematics and work toward mastery during the Work Station portion of the session as well as in daily Number Corners.

For example, in Unit 5, Module 1 in Session 3, students initially learn about the trapezoid. They work with the teacher to describe a trapezoid, with a focus on using accurate and precise geometrical language. Students then work with the teacher using pattern blocks to fill in a shape three different ways and discuss the differences, the number of blocks used, and the composition of new shapes. Students are introduced to the Pattern Block Puzzle. They observe a sheet with the puzzle and work together to fill in the shape with various pattern blocks. The teacher uses student input from the class to record the solution to solving the puzzle. Students continue in this manner until they have filled in the pattern three different ways and solutions are recorded. In the Work Places activity, students work independently to complete additional Pattern Block Puzzles.

In the February Calendar Grid, students observe various shapes and report out the number of sides and vertices on each of the shapes. Then, students confirm that these shapes are, in fact, triangles. They fill out the Calendar Grid Observation Chart, adding the triangle and it's attributes to the chart.

The assignments are intentionally sequenced, moving from introducing a skill to developing that skill and finally mastering the skill. After mastery, the skill is continued to be reviewed, practiced and extended throughout the year.

The "Skills Across Grade Level" table is present at the beginning of each Unit. This table shows the major skills and concepts addressed in the Unit. The table also provides information about how these skills are addressed elsewhere in the grade, including Number Corner, and in the grade that follows. Finally, the table indicates if the skill is introduced (I), developed (D), expected to be mastered (M), or reviewed, practiced or extended to higher levels (R/E).

Concepts are developed and investigated in daily lessons and are reinforced through independent and guided activities in Work Places. Number Corner, which incorporates the same daily routines each month (not all on the same day) has a spiraling component that reinforces and builds on previous learning. Assignments, both in class and for homework, directly correlate to the lesson being investigated within the unit.

The sequence of the assignments is placed in an intentional manner. First, students complete tasks as a whole group in a teacher-directed setting. Then students are given opportunities to share their strategies used in the tasks completed in the Problems & Investigations. The Work Places activities are done in small groups or partners to complete tasks that are based on the problems done as a whole group in the Problems & Investigations. The students then are given tasks that build on the Session skills learned for the Home Connections.

For example, 1.OA.1 and 1.OA.2 are introduced in Unit 2 and continue to be developed in Units 3 and 4. Mastery is expected in Units 6 and 7. The standard is developed further in Number Corners in October, January, and February. Another example is 1.NBT.3. This standard is Introduced in Unit 2 and continues to be developed in Units 4, 6, 7 and 8 and Number Corners in October, November, January and February.

There is variety in what students are asked to produce. Throughout the grade, students are asked to respond and produce in various manners, often by working with concrete and moving to more abstract models as well as verbally explaining their strategies. Students are asked to produce written evidence using drawings, representations of tools or equations along with a verbal explanation to defend and make their thinking visible.

For example, in Unit 5, Module 2, Session 4, students are given many opportunities to work with 3-dimensional shapes concretely, abstractly, verbally, and then back to concrete by actually creating cubes using Polydrons. First, students play the game "Guess My Shape." They initially observe 3-dimensional shape cards and geoblocks, and then they match up the geoblocks with the 3-dimensional shape cards, naming the shapes as they go. Next, the teacher gives a series of clues to students as they listen carefully and act like detectives to guess the teacher's secret shape. The clues are characteristics of the shape. As clues are given, students remove the shapes that don't match the clues, ending up with the last shape which should be the secret shape. The next activity requires students to identify a cube just by touch as they place their hand in a bag and feel for the cube. Students are asked how they identified the cube, and the teacher models the vocabulary of geometry as students share. For example, as student share "There are a lot of corners on the cube," the teacher replies, "In math, we call the corners, vertices." Then students construct cubes using Polydrons. Finally, students work with a worksheet to identify pictures of Polydrons and determine if they can make a cube. They first make a prediction and then use the actual Polydrons to test their predictions.

Also, in Unit 3, Module 3, Session 1, "Ten & Some More," students are working with activities that focus on the teen numbers. They move from concrete to abstract and explain their strategies verbally. Students look at double 10-frame cards with matching equations, build the sum with Unifix cubes, and write their own equations. Next, the teacher presents students with a teen number, and students imagine what it will look like with Unifix cubes and then write an equation to match.

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods. Manipulatives are used and provided to represent mathematical representations and provide opportunities to build conceptual understanding. Some examples are the 10-frames, number lines, Unifix cubes, number racks, coins, craft sticks and tiles. When appropriate, they are connected to written representations.

For example, in Unit 2, Module 3, Session 1, in the Problems & Investigation section, students are using dominoes and number racks to write and solve addition problems. Students begin with having the dominoes flashed at them then use their number racks to represent the number of dots shown. Finally, they write an equation to represent the amounts.

Although manipulatives are faithful representations, there are some that are unusual and difficult to understand representations.

For example, In Unit 7, Module 2 is called "Hansel & Gretel's Path on the Number Line." The symbols/images used are difficult representations of the number line. A picture is used to display pebbles, breadcrumbs, and pinecones on a path. Students are asked to fill in the empty boxes on the path or "Number Line." There is a key that shows the symbols that represent breadcrumbs (every 1 step), pinecones (every 5 steps), and pebbles (every 10 steps). The images may be confusing for students, and this theme continues for all of Module 2.

Also, in Unit 7, Module 3 uses fences, benches, trash cans, and flowerpots to have students write and solve addition equations that represent how long each path section is. As in Module 2, a key is used to show how many steps each image represents. The choice and use of images are difficult to understand and make the connection to a number line difficult to make.

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development. Lessons provide teachers with guiding questions to elicit student understanding and conduct discourse that allows student thinking to be visible. Discussion questions provide a context for students to communicate generalizations, find patterns, and draw conclusions.

Each unit has a Sessions page, which is the Daily Lesson Plan. The materials have quality questions throughout most lessons. Most questions are open-ended and prompt students to higher-level thinking.

• "How many red beads do you see? How many white?"
• "I heard you counting. Can you come show us on the big rack how you were counting those beads? And can you show us how you knew there were the same number of white as red?""

• "What if you could choose - you could jump by either a 5 or 10. Would that make the problem any shorter?
• Could we use fewer jumps to get from 0 to our target of 15?"
• "How do you know that?"
• "Does anyone have a different solution?"

In Unit 4, Module 1, Session 4, students are working on measuring using their "Inchworm Rulers." The teacher asks the following questions:

• "How long do you think each strip will be when it's cut out? Why?"
• "Will they stretch out the length of the poster board strip? How do you know?"
• "Who is likely to use this tool, and when?"
• "How does a ruler help us measure the length of something?"

• "Who can tell us what they saw?"
• "Did anyone else see something different, or have a different way to describe what they saw?"

In Number Corner December Calendar Grid, the following questions are provided to help students as they work with shapes:

• "What shape do you think you'll see on the next marker - why?"
• "If there were 32 days in December, what kind of shape would be on marker 32? How do you know?"
• "What observations can you make about today's shape?"
• "How many sides does it have?"
• "How many vertices?"

Materials contain adult-level explanations of the mathematics concepts contained in each unit. The introduction to each unit provides the mathematical background for the unit concepts, the relevance of the models and representations within the unit, and teaching tips. When applicable to the unit content, the introduction will describe the algebra connection within the unit.

At the beginning of each unit, the teacher's edition contains a "Mathematical Background" section. This includes the mathematics concepts addressed in the unit. For example, in Unit 2 the following is provided: "Throughout Unit 2, students explore base ten concepts and models within 1,000. The unit is designed to promote measuring concepts even as students are learning about our base ten number system. As they count, total, and compare units, they are encouraged to think about and apply base ten concepts."

The mathematical background also includes sample models with diagrams and explanations, strategies, and algebra connections. There is also a Teaching Tips section following the Mathematical Background that give explanations of routines within the sessions such as: "Like any mathematical tool, the more teachers are aware of both the benefits and constraints of the number line, the more likely they are to use it effectively with students..."

In the Implementation section of the Online Resources, there is a "Math Coach" tab that provides the Implementation Guide, Scope & Sequence, Unpacked Content, and CCSS Focus for Grade 1 Mathematics.

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.

In the Unit 1 binder, there is a section called "Introducing Bridges in Mathematics." In this section, there is an overview of the components in a day (Problems & Investigations, Work Places, Assessments, Number Corner). Then there is an explanation of the Mathematical Emphasis in the program. Content, Practices, and Models are explained with pictures, examples and explanations. There is a chart that breaks down the mathematical practices and the characteristics of children in that grade level for each of the MPs. There is an explanation of the Skills Across the Grade Levels chart, the assessments chart, and the differentiation chart to assist teachers with the use of these resources. The same explanations are available on the website. There are explanations in the Assessment Guide that go into the Types of Assessments in Bridges Sessions and Number Corner.

The CCSSM Where to Focus Grade 1 Mathematics document is provided in the Implementation section of the Online Resources. This document lists the progression of the major work in grades K-8.

Each unit introduction outlines the standards within the unit. A “Skills Across the Grade Level” table provides information about the coherence of the mathematics standards that are addressed in the previous grade as well as in the following grade. The "Skills Across the Grade Level" document at the beginning of each Unit is a table that shows the major skills and concepts addressed in the Unit and where that skill and concept is addressed in the curriculum in the previous grade as well as in the following grade.

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The September Number Corner Baseline Assessment is designed to ascertain students' current levels of skills. The Comprehensive Growth Assessment contains interview items and written items and addresses every Common Core standard for Grade 1. The Comprehensive Growth Assessment can be administered as a baseline assessment, an end-of-the-year summative assessment or quarterly assessment to monitor students' progress.

Informal observation is used to gather information. Many of the Sessions and Number Corner workouts open with a question prompt: a chart, visual display, a problem, or even a new game board. Students are asked to share comments and observations, first in pairs and then as a whole class. This gives the teacher an opportunity to check for prior knowledge, address misconceptions, as well as review and practice with teacher feedback. There are daily opportunities for observation of students during whole group and small group work as well as independent work when they work in Work Places.

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

Most Sessions have a Support section and ELL section that suggests common misconceptions and strategies for remediating these misconceptions that students may have with the skill being taught.

Materials provide sample dialogues to identify and address misconceptions. For example, the Unit 4 Module 2 Session 5 “Support” section gives suggestions for struggling students. The materials suggest that teachers draw students' attention to one or both of the large floor number lines on display and use the toy frog to tell an addition and then a subtraction story problem, reviewing how Little Frog hops forward and backward along the line.

Materials provide opportunities for ongoing review and practice, with feedback for students in learning both concepts and skills.

The scope and sequence document identifies the CCSSM that will be addressed in the sessions and in the Number Corner activities. Sessions build toward practicing the concepts and skills within independent Work Places. Opportunities to review and practice are provided throughout the materials. Ongoing review and practice is often provided through Number Corner routines. Each routine builds upon the previous month’s skills and concepts. For example, in the Number Corner May "Days in School" activity, students get to practice their understanding that the digits in a 2-digit number represent amounts of tens and ones (1.NBT.2).

All assessments, both formative and summative, clearly outline the standards that are being assessed. In the assessment guide binder. the assessment map denotes the standards that are emphasized in each assessment throughout the year. Each assessment chart notes which CCSSM is addressed.

For example, the Unit 3, Module 3, Session 5 Unit checkpoint includes a Checkpoint Scoring Guide that lists each prompt, the correct answer, each standard, and the points possible. Another example is Unit 6, Module 3, Session 5; this Unit 6 Assessment includes a Unit Scoring Guide that lists all items, correct answers, standards, and the possible points. Another example is Number Corner Checkup 4; the Interview Response Sheet has a CCSSM correlation for each of the questions at the top of the Response Sheet as well as a Number Corner Checkup 4 Scoring Guide for the written part of the assessment.

Also, each item on the Comprehensive Growth Assessment lists the standards being emphasized on the Skills & Concepts Addressed sheet, the Interview Materials List and the Interview and Written Scoring Guides.

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting students' performance and suggestions for follow-up.

All Checkpoints, Check-ups, the Comprehensive Growth Assessment, and Baseline Assessments are accompanied by a detailed rubric and scoring guideline that provide sufficient guidance to teachers for interpreting student performance. There is a percentage breakdown to indicate Meeting, Approaching, Strategic, and Intensive scores. Section 5 of the Assessments Guide is titled "Using the Results of Assessments to Inform Differentiation and Intervention.” This section provides detailed information on how Bridges supports RTI through teachers' continual use of assessments throughout the school year to guide their decisions about the level of intervention required to ensure the success of each student. There are cut scores and designations assigned to each range to help teacher identify students in need of Tier 2 and Tier 3 instruction. There is also a breakdown of Tier 1, 2 and 3 instruction suggestions.

The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Units and modules are sequenced to support student understanding. Sessions build conceptual understanding with multiple representations that are connected. Procedural skills and fluency are grounded in reasoning that was introduced conceptually, when appropriate. An overview of each unit defines the progression of the four modules within each unit and how they are scaffolded and connected to a big idea. For example, in Unit 4 “Number Lines,” Module 1 uses a giant number line, Module 2 focuses on jumping by fives and tens on the number line, Module 3 focuses on an open number line with fives and tens, and Module 4 focuses on measurement on the number line.

In the Sessions and Number Corner activities, there are ELL strategies, support strategies, and challenge strategies to assist with scaffolding lessons and making content accessible to all learners.

In the Unit 3, Module 3, Session 4 Work Place 3F "Fifty or Bust!," the following suggestions are provided:

• "Support" - If students are struggling with making teen numbers from a 10 and some 1s... Gather students in a small group and play the game together. Each time a card is drawn, discuss the 10 and the 1s and the matching teen word.
• "ELL" - Emphasize the vocabulary of the teen numbers: If they have 10 plus 4, for example, point to the four dots or colored cubes and say "four" then to the ten dots or cubes and say "teen," and then "fourteen."

In the February Number Corners Number Line, as students are working with the number line activity of rolling the dice and moving ahead or back the number and the direction shown on the dice, several of the numbers on the number line are covered up. The following "Support" suggestion is provided:

• If students have difficulties, line up more cards to provide additional counting support.

The instructional materials provide teachers with strategies for meeting the needs of a range of learners.

A chart at the beginning of each unit indicates which sessions contain explicit suggestions for differentiating instruction to support or challenge students. Suggestions to make instruction accessible to ELL students is also included in the chart. The same information is included within each session as it occurs within the teacher guided part of the lesson. Each Work Place Guide offers suggestions for differentiating the game or activity. The majority of activities are open-ended to allow opportunities for differentiation. Support and intervention materials are provided online and include practice pages, small-group activities and partner games.

The instructional materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations. Tasks are typically open ended and allow for multiple entry-points in which students are representing their thinking with various strategies and representations (concrete tools as well as equations).

In the Problems & Investigations section, students often are given the opportunities to share strategies they used in solving problems that were presented by the teacher. Students are given multiple strategies for solving problems throughout a module. They are then given opportunities to use the strategies they are successful with to solve problems in Work Places, Number Corner, and homework.

For example, in Unit 3, Module 2, Session 5, students are engaged in Work Place, "Cats & Mice." They are rolling dice and adding the numbers to get their score. The students play the game initially as a whole class, with one student from each team (Cats or Mice) coming up to role the dice for their team. Students share their different strategies for solving. All strategies are accepted and allow students at various levels to all have an entry point into solving the problem using a variety of strategies.

Another example is found in the Number Corner December Days in School. Students are writing equations to represent the number of days in school, which is 58. Students are invited to share how they notice the number on the hundreds grid. Then, they write the equation on the chart. Students are asked for other ways to write the day's number. Students are encouraged to share their different strategies and representations of the number 58.

The instructional materials suggest supports, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

Online materials support students whose primary language is Spanish. The student book, home connections and component masters are all available online in Spanish. Materials have built in support in some of the lessons in which suggestions are given to make the content accessible to ELL students of any language.

There are ELL, Support, and Challenge accommodations throughout the sessions and Number Corner activities to assist teachers with scaffolding instructions. Examples of these supports, accommodations, and modifications include the following:

• In the Unit 4, Module 1, Session 4 Work Place, "The Jump Frog Game," students are making up story problems. The ELL suggestion is to help students learning to speak English formulate simple stories if needed or pair students who speak the same language and invite them to tell stories in their shared language. Teachers are told to challenge them to translate their stories into English for you or another student if it seems appropriate.
• In Unit 6, Module 3, Session 5, the Unit 6 Assessment includes some true and false questions regarding equations. The ELL Support suggested is to write the words true and false on the board and draw a thumbs-up beside the word true and a thumbs-down sign beside the world false.

The instructional materials provide opportunities for advanced students to investigate mathematics content at greater depth. The sessions, Work Places, and Number Corners include "Challenge" activities for students who are ready to engage deeper in the content.

Challenge activities found throughout the instructional materials include the following:

• In Unit 2, Module 2, Session 3, the challenge part of this session extends the target of discovering "how many to ten" by looking at the relationship of tens and discovering patterns for "how many to 20."
• In Unit 7, Module 1, Session 4, students are representing numbers with sticks and bundles in the game "Two Turns to Build." The following Challenge suggestion is provided: Have students who are ready to work with just the numbers without the manipulatives, explain their reasoning to the group and then allow them to play the game using numbers only.

The materials provide a balanced portrayal of demographic and personal characteristics. Most of the contexts of problem solving involve objects and animals, such as frogs and penguins. When students are shown performing tasks, they are cartoons that appear to show a balance of demographic and personal characteristics.