K-2nd Grade - Gateway 1
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Focus and Coherence
Gateway 1 - Meets Expectations | 90% |
|---|---|
Criterion 1.1: Focus | 11 / 12 |
Criterion 1.2: Coherence | 7 / 8 |
The materials reviewed for Bridges in Mathematics, Kindergarten through Grade 2 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.
Criterion 1.1: Focus
Information on Multilingual Learner (MLL) Supports in This Criterion
For some indicators in this criterion, we also display evidence and scores for pair MLL indicators.
While MLL indicators are scored, these scores are reported separately from core content scores. MLL scores do not currently impact core content scores at any level—whether indicator, criterion, gateway, or series.
To view all MLL evidence and scores for this grade band or grade level, select the "Multilingual Learner Supports" view from the left navigation panel.
Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Bridges in Mathematics, Kindergarten through Grade 2 meet expectations for focus. They assess grade-level content, offer opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series, and provide all students with extensive work on grade-level problems to support mastery of grade-level expectations. The materials partially identify the content standards and mathematical practices assessed in formal assessments.
Indicator 1a
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Bridges in Mathematics Kindergarten through Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.
The Assessment Guide provides an assessment map that identifies when and where each grade-level standard is assessed throughout the school year. The materials are designed to assess skills incrementally, following a typical developmental progression.
The Assessment Guide provides a comprehensive overview of the types and frequency of assessments at each grade level. Kindergarten assessments include a baseline, interim, and closing assessment with both written and interview items for all students. Grades 1 and 2 include a variety of formative and summative assessments, including observational assessments, screeners, Mid-Unit Checkpoints, and End-of-Unit Assessments. There are additional assessments available on the Bridges Educator Site; however, these supplemental items were not considered in the evaluation of grade-level alignment for this indicator. Examples include:
In Kindergarten, Unit 5, Two-Dimensional Geometry, Module 1, Session 4, Sort & Count Checkpoint, students find the number needed to equal ten. The materials read, “Prompt 3: [Point to the student’s group with more pattern blocks.] Ask: How many more blocks would you need to make a total of 10? [Point to the student’s group with fewer pattern blocks.] Ask: How many more blocks would you need to make a total of 10?” (K.OA.4)
In Grade 1, Unit 3, Adding, Subtracting, Counting & Comparing, Module 2, Session 3, Tower Race: Introducing Work Place 3D, Combinations of 10 Checkpoint, Problem 3 states, “Samir rolled a total of 10 when playing Tower Race. One die landed on 6. What number was on the other die?” (1.OA.1)
In Grade 2, Unit 8, Measurement, Data & Multidigit Computation with Marble Rolls, Module 3, Session 5, Unit Assessment, Problems 2 and 3 state, “2. Find the sum. Show your thinking using numbers, labeled sketches, or words. 348+277=___, 3. Find the difference. Show your thinking using numbers, labeled sketches, or words. 653-495=___.” (2.NBT.5, 2.NBT.9)
Indicator 1b
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for Bridges in Mathematics Kindergarten through Grade 2 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.
The Assessment Guide provides an Assessment Map that shows the connection between the formal assessments and the grade-level content standards. In addition, each formal assessment includes a scoring guide that identifies the related standard or standards for each assessed item and the total possible points. These guides are designed to support an asset-based approach to scoring student work, helping teachers identify what students know and can do so they can build on existing understanding. Examples of standard-aligned assessment items include:
In Kindergarten, Unit 2, Numbers to 10, Module 3, Session 2, Craft Stick Tallying Day 2, Interview Interim Assessment 1 Response Sheet, Problem 4 states, “Show the student the demonstration number rack with all the beads pushed to the starting position. a. Say: Show 5 using only the top row of the number rack. b. Prompt the student to show 5 in a different way. Say: Show 5 using both rows of the number rack. If the student successfully shows 5 using both rows of the number rack, prompt them to show 5 using both rows of the number rack in another way.” (K.CC.5, K.OA.3)
In Grade 1, Unit 3, Adding, Subtracting, Counting & Comparing, Module 3, Session 5, Unit 3 Assessment, Problem 5 states, “There are 8 children on the swings, and 1 more joins them. How many children are on the swings? Show your thinking.” (1.OA.1)
In Grade 2, Unit 5, Place Value to 1,000, Module 3, Session 5, Unit 5 Assessment, Problem 7 states, “Lily and Kendra are counting coins from donations to their class’s coin jar. Answer the questions about their coins. Remember to use the ￠ or $ sign. a. How much money does Lily have in her hand? b. How much money does Kendra have in her hand? c. How much money did they count in all? Show your thinking. d. How much more do they need to have 1.00? Show your thinking?” (2.MD.8)
While the content standards are clearly identified for each formal assessment item, the Standards for Mathematical Practice (SMPs) are not consistently or explicitly connected to specific assessment items. The Assessment Guide does describe the importance of the math practices and includes connections to them throughout instruction. For example, in the Assessment Overview section, the guide explains, “The math practice standards reflect the attitudes and ways of thinking and working that characterize successful mathematicians. Though they are broader and less distinct than the math content standards, they are equally — if not more — important. However, they are not a list of discrete skills to be taught. Rather, they are methods for teaching, learning, and doing mathematics at every level. The set of eight practices is identical for each grade level and can be grouped into four categories: habits of mind of a productive mathematical thinker, reasoning and explaining, modeling and using tools, and seeing structure and generalizing (McCallum, 2011).” Despite their instructional presence, the Assessment Guide acknowledges the challenges of linking SMPs to individual assessment items. In the Math Practices in Action section, it states, “The characteristics, habits of mind, and dispositions represented by the math practices don’t easily lend themselves to paper-and-pencil testing, especially in the elementary grades. It’s important for teachers to ask questions, such as the ones in the following table. They must also watch and listen to students during daily instruction, at Work Places, and in individual and small-group settings for evidence that they are demonstrating the desired proficiencies and performances.”
Indicator 1c
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for Bridges in Mathematics Kindergarten through Grade 2 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.
Formative and summative assessments across Grades K-2 include screeners, checkpoints, unit assessments, interviews, observational tools, and work samples. These assessments measure student progress toward key concepts in individual lessons as well as broader unit goals. They are designed to address grade-level content and practice standards and use a variety of item types, such as one-on-one interviews, written responses, small-group tasks, and student work samples.
In Kindergarten, the two primary types of formal assessments are interim assessments and Checkpoints. Interim assessments include a baseline in Unit 1, three interims in Units 2, 4, and 6, and a closing assessment in Unit 8. These measure skills such as rote counting, numeral recognition and writing, one-to-one correspondence, and early addition and subtraction. Each includes an individual interview and a short written task. Checkpoints, used in Units 3, 5, and 7, vary in format and may include short written tasks or small-group interviews. In Grades 1 and 2, each unit features a variety of assessment opportunities, including work samples and formal paper-and-pencil tasks. These typically include a screener at the beginning of the unit, one or more Mid-Unit Checkpoints, and a Unit-End Assessment. In addition to the embedded unit assessments, optional assessments are available on the Bridges Educator Site to support teachers in monitoring student growth throughout the year.
Examples include:
In Kindergarten, Unit 2, Unit 4 and Unit 6, develop the full intent of K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 with 0 representing a count by no objects). Unit 2, Numbers to 10, Module 4, Session 4, How Many? Checkpoint states, “How Many? Count the dots in each picture. Write a number to show how many dots you counted.” Students count dots and write the corresponding number. Unit 4, Paths to Adding, Subtracting & Measuring, Module 2, Session 3, The Forest Game, Interview Interim Assessment 2 Response Sheet, Problem 3, “On the Interview Interim Assessment 2 record sheet, instruct the student to place their finger in the first space. Ask them to write the numbers from 0 to 15 in the spaces, writing one number in each space. Explain that there are more spaces on the page so they can keep writing the numbers after 15 if they want.” Unit 6, Three-Dimensional Shapes & Numbers Beyond 10, Module 1, Session 2 What is a Sphere?, Interview Interim Assessment 3 Response Sheet, Problem 4 has the student count out five cubes, hide a portion of them, and determine how many are visible and how many are hidden before confirming the total. The process is repeated with varying visible and hidden amounts (including cases with zero) to practice part–whole relationships and basic addition/subtraction..
In Grade 1, Unit 8, Changes, Changes, Module 3, Session 6, Unit 8 Assessment, develops the full intent of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks). Problems 1 & 2 state, “1. Jamar went to soccer practice at 4:00. Circle the clocks that show 4:00. 2. Triya eats dinner at 6:30. Circle the clocks that show 6:30.” Both analog and digital clocks are shown.
In Grade 2, Unit 3, Addition & Subtraction Within 100, Module 2, Session 5, Addition & Subtraction Checkpoint, develops the full intent of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction). Problem 5 states, “Mateo is 36 inches tall. His cousin Jessie is 57 inches tall. How many inches taller is Jessie than Mateo? Show your thinking. (Hint: You can use the number line to help, if you want.)”
Indicator 1d
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials provide students with extensive work with grade-level problems through the daily structure of Bridges sessions. Each session includes one or more of the following components: Warm-Up, Problems & Investigations, Work Places, and Assessments. A 60-minute instructional block is allocated for these activities, with an additional 20 minutes dedicated to Number Corner routines. Throughout the year, students engage with grade-level standards through scaffolded lessons, repeated practice in Work Places, and fluency development in Number Corner. The Problems & Investigations component emphasizes conceptual understanding and application, while Number Corner reinforces foundational skills. Examples of extensive work with grade-level problems to meet the full intent includes:
In Kindergarten, Unit 8, Computing & Measuring with Frogs & Bugs, Module 2, Session 1, Problems & Investigations, engages students with the full intent of K.MD.2 (Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference). Students compare the lengths of craft sticks and Unifix cubes and determine which is longer/shorter. The materials state, “Briefly discuss the different ways students have made comparisons throughout the school year: comparing quantities, comparing weight, and comparing length. Tell the class that now that they’ve compared the quantities of cubes and sticks, you want to compare the length of the cubes and the sticks. Wonder aloud: If we lay the craft sticks in a line and the cubes in a line, which one would make a longer line? Review the definition for the term length as how long something is. Invite students to predict which line of objects will be longer and to explain their reasoning. Conduct a quick vote, having students show a thumbs-up for the set of objects that they think will make a longer line. Have a few students share their predictions and reasoning with the class. Teacher: Which do you think will make the longer line, the cubes or the craft sticks? Raul: They would be the same because there are 16 of each. Teacher: Show a thumbs-up if you agree with Raul. Who thinks that both lines will be the same?’ Ada: I’m not sure. I think because the sticks are longer than the cubes, the line will be longer. Ask: How can we test our predictions to determine which line will be longer? Encourage students to provide step-by-step instructions for comparing the lengths of the two collections of objects. Connect the cubes into a train and lay it on the ground. Then work with students to lay out the sticks end to end in a straight line next to the cube train. Consider putting a piece of masking or painters’ tape on the floor as a starting line for the two collections. Discuss measurement conventions with students needed. These may include lining up the sticks with no gaps or overlaps, making a straight line, and starting at the same point as the cubes. Ask: Which line is longer? Then briefly discuss the following question: If we had the same number of cubes, why is the cube line so much shorter? Lin: I think it’s because the cubes are shorter. McKenzie: It takes more of them to go the same length. All the cubes are almost the same length as three sticks because the sticks are so much longer than the cubes. Engage students in a brief reflection by inviting them to think-pair-share: If we measured the length of your foot with craft sticks and cubes, would you need more craft sticks or more cubes? How do you know? Emphasize students’ comments about the size of the unit impacting the measurement. Focus especially on the fact that it will take more of a shorter unit than a longer unit to measure the length of a foot.”
In Grade 1, Unit 2, Developing Foundation Facts, Module 2, Session 5, Problems & Investigations, engages students with the full intent of 1.OA.7 (Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false). Students determine the missing number to make an equation true and develop an understanding of the equal sign as representing a relationship between two expressions with the same value. The materials state, “Explain that you have some new double-flap cards to share with them. Hold up the back of the first double-flap number card (numbers 6 and 2) so students can see the numeral you have written: 8. Turn the card over and lift the first flap to show number 6. Tell students there is another number under the other flap, and that when you add the two numbers, their sum is 8. Have students share ideas with a partner about the number under the second flap. Write 6+ __=8 on the board or chart paper, and read it to the class. Discuss what number should go in the square to make the equation true. Teacher: This equation can be read as, ‘Six plus some number has the same value as 8?’ What number can we put in the square to make the equation true? Students: I think it’s 2 because you can go 6, and then 7, 8. It can’t be 1 because 6 plus 1 is only 7. It’s 2 because I know that 6 plus 2 more is 8. Lift the second flap so students can confirm their answers. Write 2 in the square on the board or chart paper, and then read the equation with the class. Ask: Is it true that 6 plus 2 has the same value as 8? Many young children’s understanding of the word ‘equal’ is confined to ‘the answer’ or ‘what you get at the end.’ Therefore, it’s important to use the words ‘has the same value as” in these discussions. As students gain a deeper understanding of equivalence in the years to come, they will begin to use the more mathematically accurate terminology when discussing equivalence. For now, the goal is for students to understand that the equal sign describes a relationship between two quantities that have the same value. Now close the first flap and write __+2=8 on the board or chart paper. Read it to the class, give students a few moments to quietly share their ideas of what number is under the flap, and then call on a few volunteers to explain their thinking. Teacher: This equation can be read as, ‘some number plus 2 has the same value as 8.’ What number can we put in this square to make the equation true? Share your ideas with the person sitting next to you. Students: It has to be 6, because it was 6 the first time. The number didn’t change. But it’s mixed up. The square is first this time. It has to still be 6. You can count on your fingers starting at 2, and then 3, 4, 5, 6, 7, 8. That’s 6 more. Now lift the other flap so students can see both numbers.’ Write 6 in the square on the board or the chart paper, and read the equation with the class. Once more, ask: Is it true that 6 plus 2 has the same value as 8? Explain that you are going to write another equation on the board. They will read it and decide whether it is true or false. If they think it is true, they should move to one side of the room. If they think it is false, they should move to the other side. Alternatively, have students remain in their places and show a thumbs-up for true and a thumbs-down for false. 14 Write 8 = 6 + 2 below the other two equations. Ask students to each think privately, and then move to the side of the room that reflects their thinking about the equation. Lead a debate about whether the equation is true or false. Discuss students’ responses with the class. When sharing their position, students should explain their reasoning. Allow students to switch sides if an argument they hear convinces them to change the way they are thinking about the equation. Teacher: I see students on both sides of the room. Can someone tell us why they think the equation is true or false? Asha: You can’t write the answer first. It’s wrong that way. Teacher: If I understand you correctly, you are saying the equation is backward, and you can’t put the 8 first. Is that what you mean? Can someone from the other side of the room tell us why they think the equation is true? Khairi: I think it’s true because it says, ‘8 has the same value as 6 plus 2’, and that’s true. When my parents write things at home, they start on the right and then go left. You can say the same thing, just write it in a different order. Teacher: Does 8 really have the same value as 6 plus 2? Rosario: Well, if you add 6 and 2, it makes 8, so it’s kind of the same. Reverse the card so students can see the 8 on the back. Then turn it over and lift both flaps so they can see the 6 and 2 as you reiterate that 8 has the same value as 6 plus 2. 16 Write 8–2= on the board. As students watch, lower the flap over the 2 and say: Eight minus 2 is what number? Kylie: You covered up the 2, and only the 6 is left. Eight minus 2 is 6. Write 8– __ =2. Ask: What number do I need to take away, or cover, to leave only the 2? Discuss the answer with the class and then record it in the square. Mato: If you cover up the 6, that will leave just the 2. Teacher: So it sounds like 8 minus 6 (lowers the flap over 6) is 2, so I need to write 6 in the square. Is that right? Show students your other double-flap number card (numbers 5 and 3). Call on students to come up, one at a time, and lower one of the flaps and pose a question to the class. For example, a student might cover the 3 and ask: Five plus what makes 8?”
In Grade 2, Unit 1, Figure the Facts, Module 2, Session 3 and 4, Unit 3, Addition and Subtraction Within 1000, Module 1, Session 1, and Unit 5, Place Value to 1,000, Module 1, Session 3, engages students with the full intent of 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s). Unit 1, Module 2, Session 3, Warm Up, students' choral count by 5s. “Invite students to choral count by 5s from 5 to 60. Record the numbers, and discuss the patterns that emerge. As students count, record the numbers horizontally on the board or on chart paper, with four numbers in each row.” In Session 4, Home Connections, students apply skip-counting by 5s in real-world contexts by determining the total number of fingers on multiple hands and toes on multiple feet, reinforcing multiplication concepts using familiar groupings. In Unit 3, Module 1, Session 1, Home Connections, students count by tens. “Count by 10s to fill in the blanks. Problem 1. 10, 20, , , 50, , 70, , 90, . Problem 2. 14, 24, , , 54, , 74, , 94, , 114, 124.” In Unit 5, Module 1, Session 2, Warm-Up students practice counting by 1, 10, and 100. The materials state, “Problem 1. Invite students to choral count from 1 to 10 by 1s. As students count, record the numbers on the board with five numbers in each row. Leave enough blank space between the two rows for two additional rows to be added later. Problem 2. Invite students to count from 10 to 100 by 10s. As students count, record the numbers on the board beneath the counting-by-1s numbers using a different color. Briefly ask students to share what they notice and to make predictions about what might come next. If students don’t predict it, share with them that they will be counting by 100s next. What do they think that pattern will look like? Problem 3. Invite students to choral count from 100 to 1,000 by 100s. As students count, record the numbers on the board beneath the counting-by-10s numbers using yet another color. Problem 4. Invite students to share what they notice about the numbers. Can they find and describe any patterns? Encourage students to consider patterns with the counting-by-1s and counting-by-10s numbers.”
Indicator 1d.MLL
Materials assess the grade-level content and, if applicable, content from earlier grades.
The instructional materials reviewed for Grades K–2 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide some strategies for MLLs’ participation in grade-level problems, but they do not apply these supports consistently across units and sessions. Also, they are often not tailored to the specific language demands of individual sessions.
The materials provide authentic, real-world contexts that engage students in solving meaningful, language-rich mathematical tasks and encourage them to share their thinking orally and through drawings or models. The materials provide language supports for MLLs’ participation in grade-level problems at two levels: in notes titled, MLL in the sessions and in Work Place guides, and embedded in session facilitation. In the resource titled, Supporting Language Development with Discussion Structures & Routines, the materials describe how math routines and discussion structures embedded in session facilitation support MLLs in using the language needed to participate in grade-level problems. It states, “Math routines and discussion structures are part of students’ everyday experience in the Bridges classroom. Bridges supports multilingual learners in developing the language skills and vocabulary needed to explain and justify their thinking, respond to the thinking of classmates, discover and describe patterns, and make conjectures and generalizations… These practices have been shown to support language development and deepen mathematical understanding.” Then, the resource lists the following discussion structures and math routines embedded within sessions, along with a description of the routine and why it is useful:
Discussion structures: Think-Pair-Share, Noticing & Wondering, Open Strategy Sharing, Gallery Walk, Compare & Connect, What’s Best & Why?, Math Forums
Math Routines: Choral Counting, Quick Images, Dot Talks, Would You Rather?, Same & Different, Which One Doesn’t Belong?, Guess My Rule, What Comes Next?, I Have, You Need, Number Talks, Number Strings, Problem Posing
While math routines and discussion structures provide support for MLLs by providing predictable, language-rich structures, the materials do not include educational teacher guidance to fully and completely support MLLs with accessing the mathematical content discussed in each math routine and discussion structure.
In addition, the introduction to each grade level in the Teacher Edition contains two sections that outline how the materials support MLLs with participation in grade-level problems. The Community of Learners section outlines considerations for successfully developing a community of learners, including suggestions that support MLLs’ full and complete participation such as, “Encourage active engagement from all students. The Think-Pair-Share routine allows students to process ideas individually and rehearse their explanation with a partner before engaging in whole-group discussion.” The Language Supports section provides an explanation of the instructional approaches of the program for MLLs, including general recommendations to support math language development (see the report for 3e.MLL for details). These general recommendations are periodically found in MLL notes at point-of-use within session facilitation and Work Place guides. These notes are repetitive in nature, typically falling into one of these general recommendations: flexibly pairing MLLs to leverage home language usage, encouraging multimodal expression, providing clarifying questions and sentence frames and starters, and referencing the ABCs of Math Talk poster and the Word Resource Cards. The Work Place guides feature similar recommendations for each Work Place game, leaning more heavily on sentence frames and starters that are specific to the game. The teacher guidance for supporting students with authentically using the sentence frames and starters is brief and generic, suggesting that the teacher print the sentence frames and starters and make them available while students play the Work Place games. Across the MLL notes in both the session facilitation and the Work Place guides, the materials infrequently reference the ABCs of Math Talk poster and frequently reference the Word Resource Cards. This does not support MLLs’ full and complete participation. Within sessions, the MLL notes are found infrequently, and often remain general in nature and not specific to the task, which limits their impact on MLLs’ ability to access grade-level problems. Additionally, the placement of the MLL notes within sessions often does not correspond with the section of the session that directly addresses grade-level standards.
As a result, the linguistic access points that MLLs need with grade-level problems, such as intentional scaffolds for productive and receptive language, suggestions for structured academic discourse, amplification of language (such as explicit attention to morphology), and support for language functions, are inconsistently applied. MLLs may successfully play the Work Place games or complete the Problems & Investigations tasks, but the materials do not consistently provide language scaffolds to support MLLs’ ability to use and develop precise mathematical language within grade-level problems.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Bridges in Mathematics, Kindergarten through Grade 2 meet expectations for coherence. They address the major work of the grade, make meaningful connections across clusters and domains, and clearly show how grade-level content builds on knowledge from prior grades and lays the foundation for future learning. The materials partially provide connections between supporting content and the major work of the grade.
Indicator 1e
When implemented as designed, the majority of the materials focus on the major clusters of each grade.
The materials reviewed for Bridges in Mathematics Kindergarten through Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.
According to the Teacher’s Guide, “a Bridges classroom features a combination of whole-group, small-group, and independent problem-centered activities.” Daily instruction “takes the form of a 60-minute Bridges session and a 20-minute Number Corner workout.”
The instructional materials devote at least 75 percent of instructional time to the major clusters of the grade as included in the following grade-level breakdowns:
In Kindergarten:
The approximate number of units devoted to major work of the grade (including assessments and related supporting work) is 8 out of 8, approximately 100%.
The number of modules devoted to major work of the grade (including assessments and related supporting work) is 28 out of 32, approximately 88%.
The number of sessions devoted to major work of the grade (including assessments and related supporting work) is 129 out of 160, approximately 81%.
Bridges sessions require 60 minutes per day, with a total of 129 sessions focused on the major work of the grade. This accounts for 7,740 minutes out of 9,600 total Bridges session minutes. Number Corner, delivered alongside Bridges each day, requires 20 minutes per day and is implemented over 170 instructional days. Of those, 158 days focus on the major work of the grade, contributing 3,160 minutes. Altogether, 10,900 of the program’s 13,000 total instructional minutes, approximately 84%, are devoted to the major work of the grade.
In Grade 1:
The approximate number of units devoted to major work of the grade (including assessments and related supporting work) is 7 out of 8, approximately 88%.
The number of modules devoted to major work of the grade (including assessments and related supporting work) is 26 out of 32, approximately 81%.
The number of sessions devoted to major work of the grade (including assessments and related supporting work) is 130 out of 160, approximately 81%.
Bridges sessions require 60 minutes per day, with a total of 130 sessions focused on the major work of the grade. This accounts for 7,800 minutes out of 9,600 total Bridges session minutes. Number Corner, delivered alongside Bridges each day, requires 20 minutes per day and is implemented over 170 instructional days. Of those, 155 days focus on the major work of the grade, contributing 3,100 minutes. Altogether, 10,900 of the program’s 13,000 total instructional minutes, approximately 84%, are devoted to the major work of the grade.
In Grade 2:
The approximate number of units devoted to major work of the grade (including assessments and related supporting work) is 7 out of 8, approximately 88%.
The number of modules devoted to major work of the grade (including assessments and related supporting work) is 29 out of 32, approximately 91%.
The number of sessions devoted to major work of the grade (including assessments and related supporting work) is 137 out of 160, approximately 86%.
Bridges sessions require 60 minutes per day, with a total of 130 sessions focused on the major work of the grade. This accounts for 8,220 minutes out of 9,600 total Bridges session minutes. Number Corner, delivered alongside Bridges each day, requires 20 minutes per day and is implemented over 170 instructional days. Of those, 123 days focus on the major work of the grade, contributing 2,460 minutes. Altogether, 10,680 of the program’s 13,000 total instructional minutes, approximately 82%, are devoted to the major work of the grade.
An instructional minute analysis is the most representative measure of the materials, as both the Bridges sessions and the Number Corner include major work, supporting work connected to major work, and embedded assessments throughout each unit. As a result, in Kindergarten approximately 84% of the instructional materials focus on major work of the grade. In Grade 1, approximately 84% of the instructional materials focus on major work of the grade. In Grade 2, approximately 82% of the instructional materials focus on major work of the grade.
Indicator 1f
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Bridges in Mathematics Kindergarten through Grade 2 partially meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
While the materials include some instances where supporting standards are connected to the major work of the grade, these connections are not consistently present across all grade levels. In some cases, coherence map opportunities are addressed, while in others, identified connections between supporting and major work are either limited to assessments or entirely absent from instructional materials.
The Teacher’s Guide provides a listing of potential connections between supporting and major work standards. In some cases, these are reflected in sessions; however, several coherence map connections are missing or not explicitly developed within the instructional materials. While some lessons reflect alignment between supporting and major work, several coherence map connections are not addressed in the instructional materials.
In Kindergarten, the materials include explicit examples of supporting work, enhancing major work. An example of a connection in Kindergarten includes:
Unit 4, Paths to Adding, Subtracting & Measuring, Module 4, Session 1, Which Coin Will Win?, connects the supporting work of K.MD.3 (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.) to the major work of K.CC.6 (Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies). Students observe, predict, vote, count, and compare results as they play a coin spinner game and track outcomes using number racks and tally marks. Teacher’s Guide states, “With each spin and recording, discuss which column has more X’s and which has fewer. Once you reach 5 in one column, emphasize counting on from 5. For example, ask: What is 5 and 1 more? Let’s count on from 5 to find out. What is 5 and 2 more? Can you count on from 5 to find out? Continue playing until one of the columns on the record sheet is filled to the top and discuss the final results. With students’ input, record a total for each coin and circle the winning coin on the record sheet.”
In Grade 1, there are coherence map connections that are not addressed. There is no evidence of a connection between the major work of 1.OA.2 (Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem) to the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another). While 1.OA.1 and 1.MD.4 appear together in assessment materials, their connection is not developed within session-level instruction, limiting opportunities for students to engage with the major work through supporting content.
In Grade 2, there are coherence map connections that are not addressed. There is no evidence of a connection between the major work of 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s) and to the supporting work of 2.OA.3 (Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends). There are no connections that are not developed within session-level instruction, limiting opportunities for students to engage with the major work through supporting content.
Indicator 1g
Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
The instructional materials for Bridges in Mathematics Kindergarten through Grade 2 meet expectations for including problems and activities that connect two or more clusters in a domain, or two or more domains in a grade.
Connections among the major work of the grade are present throughout the materials where appropriate. These connections are listed for teachers in the Teacher’s Guide within each Module Concepts, Skills & Practices chart, and may appear in one or more phases of a typical lesson: Warm-Up, Problem & Investigation, Assessments, or Home Connections.
In Kindergarten, an example of a connection includes:
Unit 4, Numbers to 5 & 10, Module 2, Session 4 connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.CC.B (Count to tell the number of objects). During the Problem & Investigation, students count the number of dots on structured dot cards and then match each card to the corresponding numeral card. They explain how they counted and may recount to confirm their total. Students compare their answers with a partner and discuss different counting strategies. Throughout the activity, they respond to teacher prompts such as “How do you know?” to build reasoning and communication skills while reinforcing accurate counting and number recognition.
In Grade 1, an example of a connection includes:
Unit 1, Numbers All Around Us, Module 2, Session 4 connects the major work of 1.NBT.A (Extend the counting sequence) to the major work of 1.NBT.B (Understand place value). Students learn how to use a spinner and a record sheet to practice writing numerals and recognizing numbers in the ones family. Students spin a 0–9 spinner and then write the numeral they land on in the matching column on the record sheet, beginning at the bottom and continuing until a column is filled. As they record, they trace over dotted numerals that gradually become less scaffolded, promoting independent numeral formation. Problems & Investigation states, “Students spin the spinner, then write the number spun in the matching column of their record sheet. They start at the bottom of the sheet and continue until they have filled a column to the top.”
In Grade 2, an example of a connection includes:
Unit 3, Addition & Subtraction Within 100, Module 1, Session 4 connects the major work of 2.NBT.A (Understand Place Value) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract). Students estimate the total number of craft sticks in a container, then discuss strategies for counting them. Problem & Investigations states, “Jackie: First I added the tens: 40 plus 20 is 60. Then I added the ones: 2 plus 5 is 7. Then I put it all together: 60 plus 7 is 67.” Students bundle their sticks into groups of ten, count their total using tens and ones, and revise their estimates based on new information. They add their bundles to a communal collection and count together, developing strategies to add off-decade numbers. Students engage in a partner activity called Sticks & Bundles where they solve problems like 42 + 25 using concrete representations and place value strategies. They share their answers before explaining their thinking, compare different methods, and build connections across strategies.
Indicator 1h
Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for Bridges in Mathematics Kindergarten through Grade 2 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The Teacher’s Guide includes an introduction that explains the connections to content standards. Prior and future standard connections are identified throughout the Teacher’s Guide, Unit Overview, and the Skills & Concepts Across the Grade Levels section, which states that it “provides a quick snapshot of the expectations for students’ learning during this unit, as well as information about how these skills are addressed in Bridges.” Each Unit Overview outlines the progression of standards related to the concept being taught and shows how they are addressed through Warm-Ups, Problems & Investigations, Home Connections, and Assessments. These standards are identified at the session or workplace level within each unit and module. The Skills & Concepts Across the Grade Levels section also indicates whether a skill is introduced, developing, proficient, reviewed and extended, or supported.
An example of a connection to future grades in Kindergarten includes:
Unit 7, Measurement & Teen Numbers, Overview, connects the work of K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones) to early place value concepts in Grade 1, where students begin to understand 10 as a unit and extend their ability to represent and reason about numbers using tens and ones. Mathematical Background, Place Value states, “In Unit 6, students composed and decomposed numbers from 11 to 19 into 10 ones and some more ones. In the process, they began to see that 11 is 10 ones and 1 more, 12 is 10 ones and 2 more, and so on. Some of them may also have started to understand 10 ones as a new unit called a ten. The work in Module 4 of this unit reinforces these concepts as students count the dots on double 10-frame cards, show the same quantities on their number racks, and record equations to match. Some of the activities in the module involve quantities greater than 20, as students are invited to grab handfuls of craft sticks, organize them into bundles of 10, and count by 10s and 1s to find the total. While this anticipates work they’ll do in first grade, many kindergarten students are ready to apply their counting- by-10 skills to estimating and counting quantities up to 100, and eager to find the matching numerals on a 100 chart.”
An example of a connection to prior knowledge in Kindergarten includes:
Unit 3, Bikes & Bugs: Double, Add & Subtract, Overview, connects K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations) to the development of operational thinking in Grades 1 and 2, where students build on concrete representations to solve more complex problems using symbolic notation and mental strategies. Mathematical Background, Making Sense of Operations, Properties & Patterns states, ”Young children have a natural sense of addition and subtraction long before they enter school. They know if they have 3 blocks in their toy boat and they put 2 more in, there are more blocks in the boat. If they have 4 orange slices, and they eat 1 of them, they have fewer orange slices. These joining and separating experiences provide intuitions that serve as the foundation for problem solving. When kindergartners approach a contextual problem, they attend to what is happening in the story, often acting it out with counters or their fingers. Contextual problems help students access and better understand the operations of addition and subtraction. Problems with explicit actions and familiar contexts are the most accessible for all students.”
An example of a connection to future grades in Grade 1 includes:
Unit 7, One Hundred & Beyond, Overview, connects the work of 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used) to the work of adding and subtracting multi-digit numbers using place value understanding and properties of operations in Grades 2, 3, 4, and 5. Mathematical Background, Place Value Operations states, “Second graders build upon the skills learned in first grade to become fluent with adding and subtracting 2-digit numbers. They also use concrete models or drawings and strategies based on place value and properties of operations to add and subtract within 1,000. Third graders continue to develop effective and efficient strategies for adding and subtracting 3-digit numbers, with full proficiency expected before midyear. In grade 4, students finalize their work with multidigit addition and subtraction with whole numbers. This develops their proficiency with the standard algorithm for both operations while choosing their strategies mindfully based on the numbers involved in the problems. In grade 5, students extend these strategies to their work with decimals and fractions. They come to understand that properties of addition, unitizing concepts, and patterns in repeated reasoning apply to rational numbers as well.”
An example of a connection to prior knowledge in Grade 1 includes:
Unit 2, Developing Foundational Facts, Overview, connects 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums) to Kindergarten concepts such as composing and decomposing numbers within 10, fluency with facts within 5, understanding part-part-whole relationships, and identifying combinations that make 10. Mathematical Background, Making Sense of Operations, Properties & Patterns state, ”In Unit 1, students worked with several sets of foundational facts, including +0, +1, −0, −1, combinations of 10, and 10 and more, extending concepts and relationships they explored in kindergarten. The development of fluency with foundational facts, including doubles and related subtraction facts, as well as + 2 and − 2, continues to be a significant focus of instruction in Unit 2. Many of the activities and Work Places in Unit 2 are designed to nudge first graders toward counting on, counting back, and using the facts they already know to help solve others that are less familiar.”
An example of a connection to future grades in Grade 2 includes:
Unit 4, Measurement, Overview, connects the work of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction) to the work with place value operation concepts in Grades 3, 4, and 5. Mathematical Background, Place Value Operations states, “Proficiency with adding and subtracting 2-digit numbers is expected by the end of this unit. In future units and months of Number Corner, second graders extend their use of concrete models or drawings and strategies based on place value and properties of operations to add and subtract within 1,000. Third graders continue to develop proficiency with 3-digit addition and subtraction; they also use rounding to estimate and assess the reasonableness of their results. Fourth graders finalize the trajectory with adding and subtracting whole numbers when they connect the standard algorithms for addition and subtraction to prior strategies and apply these strategies flexibly with multidigit whole numbers of any magnitude. In fifth grade, students extend strategies learned in earlier grades to adding and subtracting decimals.”
An example of a connection to prior knowledge in Grade 2 includes:
Unit 1, Figure the Facts, Overview, connects 2.OA.2 (Fluently add and subtract within 20 using mental strategies) to foundational number relationships, early addition and subtraction strategies, and combinations within 5 and 10 in Kindergarten, and facts within 10, doubles, making 10, and the beginnings of derived fact strategies in Grade 1. Mathematical Background, Making Sense of Operations, Properties & Patterns state, ”Demonstrating fluency with addition and subtraction within 20 is an important goal for second graders. However, the development of fact fluency — the ability to solve addition and subtraction combinations to 20 with flexibility, accuracy, and efficiency — is the work of several years. Kindergartners develop understandings of both operations, as well as comfort and confidence with facts to 5 and combinations of 10. First graders develop proficiency with foundational facts to 10, and to 20 in some cases. These include +0, +1, +2; −0, −1, −2; combinations of 10; doubles; the 10 and more facts; and the related subtraction combinations. First graders also begin to develop derived fact strategies for addition, such as near doubles, compensation, and making 10. Second graders solidify their fluency with facts to 20, gaining automaticity with addition facts and strategies, and developing the following derived fact strategies for subtraction: up over 10, down under 10, and think addition.”