1st Grade - Gateway 3

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.