Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 3 are aligned to the CCSSM. Most of the assessments are focused on grade-level standards, and the materials spend the majority of the time on the major work of the grade. The materials are also coherent. The materials follow the progression of the standards and connect the mathematics within the grade level although at times off-grade level content is not identified. There is also coherence within units of each grade. The Grade 3 materials include all three aspects of rigor, and there is a balance of the aspects of rigor. The MPs are used to enrich the learning, but additional teacher assistance in engaging students in analyzing the arguments of others is needed. Overall, the materials are aligned to the CCSSM.

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
12
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
16
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
37
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The materials reviewed for Grade 3 meet the expectations for Gateway 1. These materials do not assess above-grade-level content, and they spend the majority of the time on the major clusters of the grade level. Teachers using these materials as designed will use supporting clusters to enhance the major work of the grade. These materials are partially consistent with the mathematical progressions in the standards, and students are offered extensive work with grade-level problems. Connections are made between clusters and domains where appropriate. Overall, the Grade 3 materials are focused and follow a coherent plan.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for assessing grade-level content. Overall, the instructional materials can be modified without substantially affecting the integrity of the materials so that they do not assess content from future grades within the summative assessments provided. Summative assessments considered during the review for this indicator include unit post-assessments and Number Corner assessments that require mastery of a skill.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for focus within assessment. Overall, the majority of summative assessment items reviewed did assess material in alignment with the Grade 3 content standards:

  • In Unit 3, Multi-digit Addition and Subtraction, the standard algorithm is not explicitly assessed, although students could choose to use it. For example, in the post-assessment for the unit, equations are all written horizontally and students are prompted to “Use a strategy that is more efficient than counting on by 1s.”
  • In alignment with the NF domain for Grade 3, within the fractions units (units 4 and 6), all items on the post-assessment use denominators limited to 2, 3, 4, 6 and 8.

Assessment items that assessed above, grade-level content:

  • In the post-assessment for unit 2, question 1 assesses multiplicative comparison which is a Grade 4 expectation, 4.OA.A.1.
  • In the post-assessment for unit 4, question 13b assesses a comparison of fractions that don’t have the same numerator or denominator, which is a Grade 4 expectation, 4.NF.A.2.
  • Although these two items assess content standards from above Grade 3, the omission of these items and any lesson material that accompany the concepts would not substantially affect the underlying structure of the materials for Grade 3.

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for focus on the major clusters of each grade. Students and teachers using the materials as designated will devote the majority of class time to major clusters of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for focus by spending the majority of class time on the major work of the grade. All sessions (lessons), except summative and pre-assessment sessions, were counted and assigned 60 minutes of time. Number Corner activities were counted and assigned 20 minutes of time. When sessions or Number Corner activities focused on supporting clusters and clearly supported major clusters of the grade, they were counted. Reviewers looked individually at each session and Number Corner in order to determine alignment with major clusters and supporting clusters. Standards reported in the teacher materials for sessions and Number Corners were not always found to be accurate or representative of the actual content of the sessions and Number Corners. Reviewers determined standards alignment of the sessions and Number Corner activities based on teacher directions, student activities and work, not standards that the teacher materials claimed. Optional Daily Practice pages and Home Connection pages were not considered for this indicator because they did not appear to be a required component of the sessions.

Some calculations, specifically the number of units and the number of sessions (lessons), equaled less than 65 percent of the time spent on major and supporting clusters of the grade. However, looking at the modules (chapters) and instructional time, when considering both sessions and Number Corners together, the calculations equal more than 65 percent of the time spent on major and supporting clusters of the grade.

  • Units – Five out of eight spend the majority of the time on major work of the grade, which is approximately 63 percent. Units 2, 4 and 7 spend all or most of the instructional time on major work of the grade. Units 1 and 3 do not spend any instructional time on major work of the grade. Units 6 and 8 spend instructional time on major work of the grade about half of the time. Unit 1 is largely a review of the Grade 2 critical areas of addition and subtraction within 100 and application of addition and subtraction through measurement and data standards. Unit 8 provides some application for solving problems involving the four operations through the major cluster standards in measuring mass, area, and perimeter when students are designing and building bridges.
  • Modules (chapters) – 21.5 out of 32 spend the majority of the time on major work of the grade, which is approximately 67 percent. Modules that spend the majority of the time on major work of the grade are: Unit 2, Modules 1, 2, 3, and 4; Unit 4, Modules 1, 2, 3, and 4; Unit 5, Modules 1, 2, 3, and 4; Unit 6, Modules 3 and 4; Unit 7, Modules 1, 2, 3, and 4; Unit 8, Modules 1, 2, and 3 are spent on major work half of the time. There are no modules in Units 1 and 3 that spend the majority of the time on major work of the grade.
  • Bridges Sessions (lessons) – 88 out of 146 spend the majority of the time on major work of the grade, which is approximately 60 percent. Approximately 26 percent of Bridges sessions or 38 out of 146 sessions are spent on multiplication or division, and approximately 15 percent of Bridges sessions or 22 out of 146 sessions are spent on fractions. Some examples of supporting work connected to major clusters are: Unit 2, Module 3, Session 5 has students working with representing and interpreting data, but also has them multiplying during this session which connects to the major work of 3.OA.1 and 3.OA.7 fluently multiplying within 100. Unit 4, Module 4, Session 3 supports the major work of fractions in third grade by using a measurement line plot including fraction units within it. In Unit 6, Module 3, Session 2, the students are working with perimeter, but they are also creating rectangles with different areas which connects to major standard 3.MD.6. Another example is in Unit 6, Module 3, Session 5 where the students are required to rearrange square units to find different areas of tables. While the supporting work here involves mathematics with perimeter and real world problems (3.MD.8), the majority of the work connects to the understanding of area and square units. Unit 6, Module 4, session 1 has the students working with geoboards to explore fractions, supporting the major work of fraction understanding in 3.NF.1 and 3.NF.2.
  • Instructional Time, including Bridges sessions and Number Corner activities – 7,860 instructional minutes out of 11,940 instructional minutes are spent on the major work of the grade, which is approximately 66 percent. It is important to note the significance of The Number Corner activities as imperative to the time spent on the major work of Grade 3. The Bridges sessions alone equaled 5,280/8,760 minutes devoted to major work, which equals 60 percent of instructional time being spent on the major work of Grade 3. However, when the Number Corner activities are included, with 2,580/3,180 (approximately 81 percent) minutes devoted to major or supporting clusters, the combined percentage of time devoted to the major work of the grade is approximately 66 percent, making the Number Corner activities a vital component of the overall percentage of time spent on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for coherence. The materials use supporting content as a way to continue work with the major work of the grade. The materials provide viable content for a school year, including 160 days of lessons and assessments. The materials are partially consistent with the progressions in the standards, with some above, grade-level content unidentified and interfering with grade-level work. All students are given extensive work on grade-level problems, even students who are struggling, and this work progresses in a mathematically logical way. Knowledge from prior grades is related to grade-level standards. Connections are made between domains and clusters within the grade level, however the materials lack visible learning objectives shaped by CCSSM cluster headings. Overall, the Grade 3 materials partially support coherence and consistency with the progressions in the standards.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall the materials engaged students in major clusters of the grade while focusing on supporting clusters. For Grade 3, reviewers focused on the use of data and scaled graphs and area measurement to support major work of multiplication and division, as well as the use of geometry and data to support the major work of fractions.

  • Unit 2, Module 4 "Story Problems with Graphs & Multiple Operations," session 2 connects multiplication (multiples) with scaled graphing. Directions 5-7 (page 9) discuss labeling the scale with multiples of 4, asking the students what they notice, and then how to show quantities that are not multiples of 4.
  • February Number Corner "Solving Problems" involves working with scaled picture and bar graphs that have multiples of 10 represented.
  • March Number Corner "Calendar Grid" involves picture and bar graphs with scales of 3 and 4, working with multiples.
  • Unit 6, Module 4 "Shapes and Fractions," session 1 (Exploring Halves on a Geoboard), session 2 (Fractions on a Geoboard), and session 3 (Geoboard quilt blocks) (3.G.A.2) connect to explaining equivalence of fractions (3.NF.3).
  • Unit 5, Module 4 "Introducing Area," sessions 1-5, integrate area and multiplication (3.MD.C).
  • Unit 6, Module 3 "Perimeter & Area" integrates area with multiplication (3.OA).
  • March Number Corner "Solving Problems" is area and perimeter problems (3.MD.C.7) and connects area and multiplication (3.OA).
  • In Unit 8, Module 2, session 3 "Researching & Building Suspension Bridges," students generate bridge length data to the nearest half and plot it on a line plot. (3.MD.B.4 is connected to 3.NF.A).
  • In Unit 8, Module 3, session 5 "Long Bridge Analysis, Part 1," students generate and plot measurement data to the nearest halves and fourths, involving bridge span lengths and deck thickness. (3.MD.B.4 is connected to 3.NF.A).

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. While reviewers note that there are a minimum of 80 minutes of instruction required daily for all the curriculum components to be completed, including sessions and Number Corner activities, the amount of content, specifically the number of days, is viable for one school year:

  • The materials contain 160 sessions (daily lessons) that are evenly spread across eight units of instruction, including assessments.
  • Most of the sessions are 60 minutes of instruction or assessment, however some sessions, especially in Unit 8, are up to 160 minutes of instruction.
  • In addition to daily sessions, daily Number Corner activities are an essential component of the curriculum.
  • For Number Corners, there are 20 days in September, October, January, February, March, April, May/June; and 15 days in November and December, which equals 170 days of Number Corner activities, including assessments.
  • Number Corner activities are daily 20-minute workouts that introduce, reinforce, and extend skills and concepts related to the critical areas of study at each grade level.
  • While a district, school or teacher would not need to make significant changes to the curriculum scope and sequence, reviewers indicated concerns for the amount of time necessary to complete all required components of each daily requirement, including sessions and Number Corners.
  • The materials are structured so that a teacher could make modifications of days or time if necessary.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
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-
Indicator Rating Details

The instructional materials for Grade 3 partially meet the expectations for the materials being consistent with the progressions in the standards. Content from prior grades is clearly identified and related to grade-level work, however content from future grades is not clearly identified and does not always clearly relate to grade-level work. Materials give all students extensive work with grade-level problems. Materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from prior grades is clearly identified and relates to grade level work, however content from future grades is not always identified and does not always relate to grade-level work:

  • All below, grade-level content is marked with the appropriate Grade 2 standards, including: 2.OA.1, 2.OA.2, 2.OA.9, 2.NBT.2, 2.NBT.5, 2.MD.1, 2.MD.3 and 2.MD.5.
  • Some sessions use previous grade-level content in support of upcoming Grade 3 content with addition and subtraction. For example, in Unit 1, Module 3, sessions 3, 4 and 5, students are working on addition and subtraction of length with a ruler as a tool in order to prepare students for open number line as a strategy for multi-digit addition and subtraction.
  • Some sessions are solely Grade 2 content, such as: Unit 1, Module 1, sessions 4 and 5 “The Addition Table, Part 1" and "The Addition Table, Part 2," and Module 2, sessions 1 and 2, “The Subtraction Table, Part 1” and "The Subtraction Table Part 2," where students are working with addition and subtraction facts within 20.
  • Unit 2, Module 3 is called "Ratio Tables and the Multiplication Table" (6.RP.A). Students are working with above grade-level concepts of unit rate and decimal multiplication. In Session 2, teacher direction 5 (page 14) says, "The rabbit food costs 1.50 per pound. What does that mean?" (6.RP.A.2). There is also an example of a ratio table that shows 1, 2 and 4 in the x column, and 1.50, 3.00, and 6.00 in the y column, with an arrow showing 1.50 x 2 (5.NBT.B.7). The above, grade-level standards are not marked or addressed as above grade level in any way.
  • In Unit 8, Module 3, Session 6, the students are working with a line plot, and they are asked to calculate mean (6.SP.B.5.C). The above grade-level standard is not marked or addressed as above grade level in any way.

Materials give all students extensive work with grade-level problems:

  • 136 out 146 of Bridges Sessions provide an opportunity for students to engage with grade-level problems through a Problem & Investigation or a Problem String.
  • 84 out of 160 Number Corner Sessions provide opportunities for students to engage in problem solving through Calendar Grid and Solving Problems activities.
  • Number Corners is a time for practice with grade level concepts (20 minutes each day). “The five Number Corner workouts are the springboard for whole-group skills practice” (pg. iii).
  • Within the sessions, many of the practice pages related to the lessons are listed as "optional daily practice" and optional "home connections." While there is additional opportunity for extensive practice of grade-level work in these components, they are always listed as optional.
  • In addition to the explicit suggestions for support or challenge contained in the sessions, as identified in the Differentiation Table, the Problem & Investigations and Problem Strings are "open-ended and lend themselves to differentiated instruction by the nature of the task design."
  • Suggestions for SUPPORT or CHALLENGE are embedded in some sessions (not consistent) and noted in the Teacher’s Guide. Students are working with grade-level content, with modifications.

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades:

All grade-level standards are identified at the beginning of each unit in a guide called Skills Across the Grade Levels. It lists the skills that are introduced, developed or mastered within each unit. It also includes whether the concept can be extended to higher levels.

  • Each unit has a section in the introduction titled "Skills Across the Grade Levels." These tables show "the major skills and concepts addressed" in each unit. It provides a quick snapshot of the expectations for learning during the unit, the skills that are introduced, developed or mastered, and the extensions from previous grades.
  • Unit 1 extends or masters standard 2.OA.1 and 2.OA.2 in solving addition and subtraction problems and fluently adding and subtracting within 20. It also includes sums to 100 involving measurement. 2.MD.5.
  • Students were introduced to writing whole numbers as fractions in second grade. In third grade, they now work on recognizing fractions that are equivalent to whole numbers and re-visit it again in Unit 7 as well as in Number Corners (Oct. and May).This particular skill also is reviewed in the Grade 4 lessons.
  • Students are introduced to area of equal parts as fractions of a whole during second grade. They master this concept in Grade 3 during Unit 7, but it is also found in Units 4,6 and 8.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials lack learning objectives that are visibly shaped by CCSSM cluster headings, however the materials do include problems and activities that serve to connect two or more clusters in a domain and two or more domains in a grade.

There are missed opportunities to attend to cluster level headings in Bridges sessions, including:

  • Fractions as Fair Shares and Fractions on a Line Plot; these are the first two fractions modules in Grade 3 and could have attended more closely to the cluster heading, "Develop an understanding of fractions as numbers."
  • The sessions "Rounding and Multi-digit Addition," "Estimating to Add and Subtract," and "Exploring the Algorithms for Addition & Subtraction" could have all attended to the cluster heading "Use place value understanding and the properties of operations to perform multi-digit addition and subtraction."

There are many instances of problems and activities within the materials that serve to connect two or more clusters in a domain and two or more domains in a grade:

  • Unit 4, Module 4: Fractions on a Line Plot includes connections between 3.NF.1, 3.NF.3 and 3.G.2.
  • Unit 6, Module 4: Shapes and Fractions includes connections between 3.NF and 3.G.2.
  • Unit 2, Module 4: Story Problems with Graphs & Multiple Operations includes connections between 3.OA.8 and 3.MD.3.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The materials reviewed for Grade 3 meet the expectations for Gateway 2, Rigor and Mathematical Practices. All three of the aspects of rigor are present and focused on in the materials. There is a balance of the three aspects of rigor within the grade, specifically where the standards set explicit expectations for conceptual understanding, procedural skill and fluency and application. All eight MPs are included in a way that connects logically to the mathematical content. However, the MPs are not always identified correctly and/or the full meaning of the MPs is sometimes missed. The materials set up opportunities for students to engage in mathematical reasoning and somewhat support teachers in assisting students in reasoning, however there are missed opportunities to assist teachers in supporting students to critique the arguments of others. The materials attend to the specialized language of mathematics and provide explicit instruction in how to communicate mathematical reasoning using words, diagrams and symbols. Overall, the materials for Grade 3 meet the expectations for rigor and MPs.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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-
Criterion Rating Details

The materials reviewed for Grade 3 meet the expectation for this criterion by providing a balance of all three aspects of rigor throughout the materials. Within the Bridges sessions and Number Corners, key concepts related to the major work of the grade are developed with a variety of conceptual questions, different concrete and pictorial representations and student explanations. In Grade 3, fluency and procedural work includes 3.OA.C.7 (fluently multiply and divide within 100) and 3.NBT.A.2 (addition and subtraction within 1,000). Application problems occur regularly throughout both the Bridges sessions and the Number Corner activities.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations by attending to conceptual understanding. Overall, the instructional materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

  • Problem strings are used throughout the year to provide a conceptual understanding approach to teaching procedural skills and computational fluency with an emphasis on making connections across representations, including number lines, arrays, and equations.
  • A mathematics forum structure is used throughout the units, which allows students to share their thinking, ask questions, and explore key concepts. For example, Unit 5, Module 2, Session 2 is a forum where students work on their knowledge of the differences between sharing and grouping in division (3.OA.A.2).
  • The Bridges Introduction pages of the Teacher Manual outline a variety of models that students access throughout the school year in order to demonstrate their understanding. In Unit 2, in the teacher directions and the introduction to the unit (pages ii, iii, iv, v, vi, vii and viii), there is information about the conceptual development of multiplication. Information on concepts, the properties of multiplication, strategies and models can be found and are explained for the teacher.
  • Many representations are used throughout the sessions. For example, Unit 2, Module 1, Session 3 has students using arrays of stamps to determine the total cost of the stamps. The materials continue to focus on grouping to solve. In Unit 2, Module 1, session 4, in the Problems & Investigations, the students work with number line puzzles to solidify their efficiency and use of strategy to solve multiplication problems (3.OA.A.1).
  • In Unit 4, Module 3, Session 1, students explore fractions with paper folding. Teacher direction 6 says, “Work with the class to compare non-congruent halves, and help them understand that pieces don’t need to be congruent to be equivalent.” (page 5.)
  • In Unit 4, Module 3, Sessions 1 and 3, students use paper and pattern blocks to explore fractions, and then in sessions 4 and 5, they use a number line to explore “Fractions as Distances.”

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations by attending to procedural skill and fluency. Overall, the instructional materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

  • Problem Strings within the sessions provide fluency practice built from conceptual understanding. In Unit 2, Module 1, Session 2, the assessment is a problem string involving rows/arrays of stamps where students work with doubling strategies to find the totals of the arrays (3.OA.C). In Module 1, Session 3, students work again with groups of stamps to determine the total cost of the stamps. They are laid out in arrays using the digits 4, 5 and 2 (3.OA.C.7). Module 1, session 3 also has a problem string for practice connected to the work during the session (3.OA.C.7).
  • Students build fluency with multiplication facts in Unit 2, Module 3, Sessions 3 and 4, “Multiplication Strategies, Parts 1 and 2.” Students look at the multiplication table and explore strategies such as double facts and double-plus-one facts.
  • Students participate in “Work Place” activities throughout the sessions, which are “engaging, developmentally appropriate math stations that offer ongoing practice with key skills.” (Introduction to Bridges). In Unit 4, Module 3, Session 5, the Work Place activity has students engage with a spinner game called “2D Doubles Help” where they take turns spinning to generate a multiplication problem involving 3 or 4, and then they record the doubles fact that they can use to solve the problem.
  • The Number Corner component of the Bridges curriculum "engages students and contributes to a math-rich classroom environment that promotes both procedural fluency and conceptual understanding." (Bridges Introduction).
    • The Computational Fluency component of Number Corner focuses on "activities, games, and practice pages designed to develop and maintain fluency," (page v, Teacher Manual), like Frog Jump Multiplication in October and Array Race in November. In December through March, students are focusing on multiplication facts starting with zero, one, and two, going to five and ten the next month, and then moving up through the other single-digit numbers.
    • In Number Corners, each month contains a number line component that focuses on procedural skills, for example: Rounding to the Nearest Ten in November, Comparing Fractions in February, and Put it on the Line in April.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations by attending to application. Overall, the instructional materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

  • In the Solving Problems component of the Bridges Number Corner, students spend time working on application problems. "Often the problems connect to another workout in the same month, which enables students to apply skills they learned elsewhere to a problem-solving context." (page vi, Number Corner Volume 1). In Number Corners, each month contains a problem solving component that focuses on application, for example: Multi-Step Problems and Equations in January, Data Problems in February, and Area and Perimeter Problems in March.
  • Teachers pose contextual Problem Strings and Problems & Investigations throughout the Bridges curriculum that are grounded in real-world application in which students model, discuss, reason, and defend their thinking.
    • Within the materials, there are multiple sessions where a problem and investigation of a real-world scenario is paired with a forum for discussion and exploration of the problem solving strategies. For example, Unit 5, Module 3, session 1 has students writing their own story problems for given equations with and unknown quantity (7x5=m). Students are asked to create more than one operation in their problems. Then in Session 2, they have a forum to discuss their work (3.OA.D.8).
  • Unit 4, Module 4 is an application-based exploration of fractions with the context of creating and measuring bean stalks. Students gather data with fractions and create a line plot of their beanstalk data.
  • Unit 8 is a complete project-based application unit around the task of bridge design and construction. Standards involving fractions, measurement and data, and geometry are applied throughout the unit in real-world, problem-solving tasks.
  • Reviewers note that many student pages and sessions throughout the materials contain application problems aligned to major work of the grade, however most of the multi-step, non-routine problems are at the end of the pages and labeled "Challenge."

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for balancing the three aspects of rigor. Overall, within the instructional materials the three aspects of rigor are not always treated together and are not always treated separately.

  • The Problems & Investigations within the sessions call for students to apply procedural skill and fluency and conceptual understanding to solve application problems.
  • Application problems often call for students to model their thinking through the use of area models, number lines, ratio tables, etc.
  • Procedural skill and fluency is often noted side-by-side as students are working in conceptual models.
  • Problem strings target procedural skill and fluency by targeting opportunistic strategies. Teachers represent student thinking with a variety of conceptual models. "Each time, students solve the problem independently using any strategy they like, and then the teacher uses a specific model (an array or a number line, for example) to represent students' strategies." (Teachers Manual Unit 1, Introducing Bridges Mathematics).
  • Application is the focus in Unit 8, when students are designing bridges.
  • Procedural skill and fluency is attended to separately in the Number Corner component "Computational Fluency."

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/10
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Criterion Rating Details

The materials reviewed for Grade 3 partially meet the criteria for practice-content connections. The MPs are identified and used to enrich mathematics content. However, the MPs are misidentified in some instances. The materials often attend to the full meaning of each practice; however, there are instances where the students are not using the practices as written. The materials reviewed for Grade 3 partially attend to the standards' emphasis on mathematical reasoning. Overall, students are prompted to construct viable arguments and analyze the arguments of others. However, there are missed opportunities to assist teachers in helping students to critique the arguments of others. The materials attend to the specialized language of mathematics and provide explicit instruction in how to communicate mathematical reasoning using words, diagrams and symbols. Overall, the materials partially meet the criteria for practice-content connections.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for the MPs being identified and used to enrich the mathematics content within and throughout the grade. The instructional materials identify two to four MPs for each Bridges session and Number Corner activity. There are a few Bridges sessions that only identify MPs and no content Standards within those sessions. However, students using the materials as intended will engage in the MPs along with the content standards for the grade.

  • The Introduction to Bridges Grade 3 includes a table describing what the MPs look like for students in Grade 3 for each practice.
  • All eight MPs are identified throughout the curricular materials.
  • The Bridges overall Scope & Sequence for Units does not note the practice standards, however, between two and four MPs are identified in the “Skills and Concepts” section at the beginning of every Bridges session.
  • There are several Bridges sessions that identify only MPs and no content standards:
    • Unit 1, Module 1, Sessions 1 and 2 list 4 MPs in each session, with no content Standards.
    • Unit 8, Module 1, Session 1 lists 4 MPs, with no content Standards.
    • Unit 8, Module 1, Session 3 lists 2 MPs with no content Standards.
    • Unit 8, Module 4, Session 1 lists 4 MPs, with no content Standards.
  • "Math Practices in Action" is located in the margin of the teacher notes within the Bridges sessions. They identify how the students engage with the MPs along with the content standards. For example:
    • In Unit 2, Module 1, Session 6, "Math Practices in Action" explains that teachers facilitate students engaging in MP2: "During this forum, you'll connect the symbolic notation (abstract) to the context of the problems (quantitative)."
    • In Unit 4, Module 3, Session 2, "Math Practices in Action" explains that students engage in MP8, "While repeating the process of dividing the rectangle into equal pieces and removing one of them, students will make use of the regularity they see in their reasoning to make sense of unit fractions. The repetition, and the patterns that emerge, help them develop a stronger understanding of unit fractions."
  • The MPs are identified in the “Target Skills” section at the beginning of every Number Corner month and within the "Skills and Concepts" section at the beginning of the Number Corner activity types. There is a "Math Practices & the Number Corner Learning Community" section at the beginning of the first Number Corner binder, which describes how students engage with the MPs during Number Corners.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
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Indicator Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for carefully attending to the full meaning of each MP. Overall, the materials often attend to the full meaning of each MP, but there are instances where the students are not using the MPs as written.

  • "Math Practices in Action" is located in the margin of the teacher notes within the Bridges sessions. They call the teacher’s attention to how the activities within the Bridges sessions engage students with a particular MP.
  • In many cases, the materials attend to the full meaning of the MPs:
    • In Unit 5, Module 2, Session 4, "Math Practices in Action" explains how students engage in MP3, "Students construct viable arguments and critique the reasoning of others when they discuss whether or not each equation is true."
    • In Unit 6, Module 2, Session 3, "Math Practices in Action" explains MP7 as, "Students look for and make use of structure within and among the quadrilaterals as they sort them. During this process, they are taking into consideration the different attributes of the figures and categorizing them accordingly."
    • In Unit 8, Module 3, Session 3, "Math Practices in Action" explains how students engage in MP4, "As they explore different ways to graph similar data, students are modeling the situations with mathematics."
  • There is ambiguity over whether "model" means to draw a picture representing the problem or whether "model" means to create a mathematical representation. For example, in Unit 7, Module 3, session 3, the "Math Practices in Action" states, "In this module, students model with mathematics using the number line and egg cartons. These models, and the connections between them, deepen students' understanding of equivalent fractions." Within this lesson, and other lessons in the module, students are representing fractions on number lines and in egg carton drawings, and there is not a contextual situation involved.
  • In some cases, when MP1 is identified, students are not engaging in the full meaning of the MP. For example, "Math Practices in Action" in Unit 3, Module 3, Session 1 explains, "Games can be a rich opportunity for students to make sense of problems and persevere in solving them. Students have many chances to play the game, which gives them the opportunity to persist in their efforts and further develop their rounding and computation skills." This does not attend to the full meaning of MP1.
  • The use of the "Math Forum" structure throughout the Bridges program is a missed opportunity to fully attend to MP3. Although there are many opportunities for students to share their strategies for how they got their answers, there is often no mention of students justifying their thinking or questioning their peers. All of the questions are posed by the teacher. Opportunities are missed in that the teacher notes do not provide information on how to facilitate a discussion in which students justify their thinking and critique the reasoning of each other.
  • Taken as a whole, "Math Practices in Action" that explain MP6 only attend to a portion of the MP. The "Math Practices in Action" on MP6 explain precision and accuracy with measurement and calculation, however they do not address precise communication. For example, "Math Practices in Action" in Unit 4, Module 1, Session 6, says, "When measuring the mass of these objects, students must attend to precision because any imprecision will be magnified later when students use these objects to measure more massive objects." and the "Math Practices in Action" in Unit 6, Module 1, Session 4, says "They must make those folds carefully, because they will use the tangrams to explore relationships among figures, and those relationships depend upon precision."

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for prompting students to reason by constructing viable arguments and analyzing the arguments of others. The students’ materials in both Bridges and Number Corner provided opportunities throughout the year for students to reason by both constructing viable arguments and analyzing the reasoning of others, however, while the students materials often prompt students to reason by constructing viable arguments, there is less consistency and opportunities for students to analyze the arguments of others, which leads to a lack of balance. More opportunities could be provided in the student materials, other than formative and summative assessments, to engage in analyzing the arguments of others.

  • In Unit 1, Module 1, Session 2, question 4 says, "How many people did Sophia and Samir survey? How do you know?"
  • In Unit 1, Module 1, Session 4, question 5 says, "Is the sum of 0 and any number always even, always odd, or sometimes even and sometimes odd? Explain."
  • In the Unit 1 Post-Assessment, question 11 says, "Josh says that all the Doubles facts (6 + 6) have even sums. Do you agree with Josh? Why or why not?" Question 12 says "Explain how you can use a Make Ten Fact to solve 9 + 6. Include the answer to 9 + 6 in your explanation."
  • In the Unit 4 Post-Assessment, question 13 says, "Is the statement true or false? Make a sketch to prove you're correct. You can use your pattern blocks to help if you like."
  • In the Unit 6, Polygons & Quadrilaterals Checkpoint, question 4 says, "Damon says that this figure is not a polygon. Do you agree with him? Why or why not? Give two different reasons."
  • "Math Forums, which occur a few times in most units, are a more formal and structured time for students to share and discuss their work. Students who are not sharing their own work are expected to listen carefully, compare their classmates’ work to their own, and ask questions to better understand each students’ ideas.” For example, in Unit 3, Module 2, Session 5, “Subtraction Strategies Forum,” the teacher directions say, “Invite students to present their work one student or student pair at a time. After each presentation, invite the rest of the class to ask questions, and have the presenters respond to those questions. After each student or student pair finishes, ask the students if they understood what the students did and whether anyone else used the same or similar approach. If a student shares something similar that elevates the level of discussion, model what that student did with sketches, numbers, and words." The focus in the forum seems to be on the strategies used, however that misses an opportunity to justify the strategy or even critique each others' reasoning.
  • Within Bridges sessions, there are many prompts for students to explain how they got their answers or show their work, but there are missed opportunities to evaluate the thinking of others. In most of the problems or assignments, the directions say, "Show your work" or "Use numbers, labels, models or words to show your thinking." For example:
    • In Unit 2, Module 3, Session 2, question 2, says "If you paid $16.50 for rabbit food, how many pounds did you buy? Show your thinking."
    • In Unit 5, Module 1, Session 4, questions 1, 2, and 3 say, "Show all your work."
    • In Unit 1, Module 2, Session 1, question 5 says, "Show all your work using numbers, words, or labeled sketches."
    • In Unit 1, Module 2, Session 2, student page question 4 says, "Show all your work using numbers, words, or labeled sketches."
  • In Number Corner activities, students are asked to "Use the space to solve the problem and record your thinking with numbers, words, equations, or models."

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Overall, there is assistance for teachers in engaging students in constructing viable arguments, however there is minimal assistance for teachers in supporting their students in analyzing the arguments of others.

  • Throughout the Bridges curriculum, sample dialogue and teacher directions are provided to assist the teacher in engaging students in constructing viable arguments. For example:
    • In Unit 2, Module 1,Session 1, teacher direction 11 says, "Invite the first pair to share. Have them show their work where everyone can see it." "After the first pair has presented their work, ask the audience to raise their hands if they understand the strategy presented." "Then, ask the students if they have any questions and have the presenters answer them."
    • In Unit 4, Module 3, Session 3, teacher direction 5 says, "Invite volunteers to the front of the class to share their solutions and explain their reasoning."
    • In Unit 3, Module 4, Session 2, teacher direction 7 says, "Encourage students to debate and discuss the strategies they're choosing." Teacher direction 12 says, " When they are done, have them share and compare their work with the people sitting next to them to be sure they have the correct answers." Teacher direction 13 says, "Then talk with the class about their strategies. Which seemed easier? Which seemed more efficient? Why? As students share their strategies, record their work where everyone can see."
  • In the Bridges Number Corner, the September Solving Problems (Adding Two & Three Digit Numbers) has a “Math Practice in Action” on the side of the teacher directions explaining that “when students evaluate other answers and think about whether their answer is correct, you are setting the stage for authentic communication.” The April Number Line (Put it on the Line) has a game where students use the “thumbs up/thumbs down” method to evaluate each other during the game. In the March Solving Problems (Area and Perimeter Puzzles) in Activity 1, direction 5 says, “Share with the whole class, turn and talk,” in which more assistance is needed to support teachers in guiding their students through critiquing the reasoning of others.
  • MP3 is mentioned specifically seven times throughout the Bridges sessions in the "Math Practices in Action," which support teachers in understanding how the MP is applied in the sessions. Despite the "Math Practices in Action," more assistance is needed to support teachers in guiding their students through critiquing the reasoning of others. For example, the Unit 1, Module 4, Session 2, "Math Practices in Action" says, "By creating a chart of strategies, you invite students to make sense of and critique the reasoning of others. When students closely examine a variety of approaches to the same problem and draw connections among them, they build a strong sense of numbers and expand their repertoire of computational strategies." This is vague guidance about how the teacher is to facilitate student reasoning.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The instructional materials reviewed for Grade 3 meets the expectations for the materials explicitly attending to the specialized language of mathematics. Overall, the materials provide some instruction in how to communicate mathematical reasoning using words, diagrams and symbols, however more explicit instruction related to precise communication is needed. There are instances in the materials that introduce vocabulary that is not grade appropriate and in basic, incomplete ways.

  • In the introduction to the series, “The curriculum includes a set of Word Resource Cards for every classroom. Each card features a mathematical term accompanied by illustrations, with a definition on the back. The cards are integrated into lessons and displayed in the classroom to support students’ acquisition and use of precise mathematical language.”
  • In Section 3 of the Assessment Guide, Assessing Math Practices, an app called Math Vocabulary Cards, which included the same illustrated terms and illustrations as the Word Resource Cards, is also available to serve as a compact and convenient math dictionary.
  • At the beginning of the sessions, a sidebar lists the vocabulary for the lesson, with an asterisk that identifies "those terms for which Word Resource Cards are available." Sessions contain directions for use of the cards. For example, in Unit 6, Module 4, Session 3, teacher direction 6 says, "Display the Word Resource Card for equivalent fractions, and review the meaning of fraction equivalency."
  • Students are often supported to show their mathematical reasoning using words, diagrams and symbols. For example:
    • Unit 3, Module 1, Session 5, in the Problems & Investigations, the teacher directions say, "Remind students that they will have a chance to use some of the strategies that they generated a couple of months ago, or come up with new ideas, as they work with a partner on a new collection of story problem." and "Remind students to check the reasonableness of their work; ask them to make sure their strategies and their answers make sense." Also, the teacher directions say, "Make sure students have access to base ten pieces or other manipulatives, but don't suggest their use as sometimes students will employ a less sophisticated method if they think that is what you want." and "Let students know that both students in each partnership need to show their work in their journals."
    • In Unit 1, Module 2, Session 3, the student page, problems 2a and 2b, says, "Show all your work using numbers, words, or labeled sketches." Also, the student page, problem 3, says, "Record your work in your math journal, using numbers, words, or labeled sketches."
    • In the December Number Corner Problem String, the Key Questions in the sidebar prompt teachers to ask, "What strategy could you use?" "How can you show your thinking?" and "What model could you use to show your thinking?" Also, the "Big Idea" listed in the first string is, "When multiplying, you can think about equal groups or repeated jumps on a number line."
  • "Math Practices in Action" that identify MP6 nearly all give direction to the teacher about accuracy with calculation or measurement, not precise communication. For example, in Unit 3, Module 3, session 3, the "Math Practices in Action - MP6" says, "It is important for students to decide when they need to attend to precision and when a mathematical question can be answered without an exact calculation. In this case, an exact answer is necessary, but the inexact estimates students have made can help them confirm whether their calculations make good sense."
  • Unit 2, Module 3, Session 2 lists "ratio table" as a vocabulary word, and there is a Word Resource Card for it. Within the lesson, the teacher directions only refer to them as "tables". Teacher direction 1 says, "and letting them know they will be doing more work with tables." However, providing a word resource card for a concept beyond Grade 3 content may prompt teachers to teach this word to students.
  • Unit 6, Module 4, Session 1 lists the vocabulary word "congruent", and there is a Word Resource Card for it. Teacher direction 7 says, "Work with the class to compare non-congruent halves, and help them understand that pieces do not need to be congruent (exactly the same shape and size) to be equivalent (the same amount)." This concept is beyond Grade 3 and a an imprecise definition.

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

Materials are well-designed, and lessons are intentionally sequenced. Typically students learn new mathematics in the Problems & Investigations portion of Sessions while they apply the mathematics and work towards mastery during the Work Station portion of Sessions and during Number Corner. Students produce a variety of types of answers including both verbal and written answers. Manipulatives such as number lines, geoboards, pattern blocks, pan balance scales, and fraction tiles are used throughout the instructional materials as mathematical representation and to build conceptual understanding.

 

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
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Indicator Rating Details

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 4, Module 3, Session 3 “Pattern Block Fractions,” students are investigating the fractions represented by several pattern blocks and then by combinations of pattern blocks when the hexagon is assigned a value of 1 in order to develop their understanding of a unit fraction and equivalency. During the Problem & Investigation section of the lesson students are given a problem, such as “if this (trapezoid) is ½ of the shape, what does the whole shape look like?” They work together to build what they believe the whole shape would be, then share their solutions and explain their reasoning, and discuss as a whole class. In the Student Book page, students are given a hexagon as the whole, or 1, and have to decide what the fraction of the whole is the shape given (trapezoid, rhombus, triangle). In the Work Place, “4D Hexagon Spin & Fill,” students play a game where they spin to determine a fractional amount, then take the correct pattern block or blocks and set them on the hexagon recording sheet until three hexagons are complete. They must always make trades to ensure that they have the fewest number of pattern blocks possible.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The assignments are intentionally sequenced, moving from introducing a skill to developing that skill and finally mastering the skill. After mastery, the skill is 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 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 with partners to complete tasks that are based on the problems done in whole group during the Problems & Investigations. The students then are given tasks that build on the session skills learned for the home connections.

For example, standard 3.OA.1 (interpret products of whole numbers) is introduced in Unit 2, developed in Units 2 and 5, mastered in Unit 5, and reviewed/practiced/extended in Unit 7. The standard continues to be developed in Number Corners from September through December and continues on in Grade 4. Another example is 3.NF.1 (develop and understanding of a unit fraction). This standard is introduced in Unit 4, developed in Units 4 and 7, and mastered in Units 7 and 8. It is also in Number Corners from October through the end of May, except for the month of March.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

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 6, Module 2, Session 1, students are tasked with creating a series of polygons out of toothpicks by exploring the attributes of a progression of polygons. They are building their understanding of quadrilaterals, identifying shared attributes, and grouping them into different categories accordingly. They first build the polygons with given instructions. Then they record and label their polygons in their math journals, and they sketch the polygons and write their attributes. They, then have a discussion about the definition of a rhombus with the class. They further their understanding by identifying irregular polygons, using Word Resource Cards for definitions to make meaning, and then build their own pentagons and hexagons with irregular sides.

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

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 number lines, geoboards, pattern blocks, pan balance scales, and fraction tiles. When appropriate, they are connected to written representations.

For example, in Unit 4, Module 1, Session 5, students are learning about the difference between mass and weight by using pan balance scales to estimate, measure and solve problems about mass. They investigate and measure several items (paperclips, clay) using gram cubes with the balances and finally discuss how they can make each student’s clay have equal mass.

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
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Indicator Rating Details

The material is not distracting and does support the students in engaging thoughtfully with the mathematical concepts presented. The visual design of the materials is organized and enables students to make sense of the task at hand. The font, size of print, amount of written directions and language used on student pages is appropriate for Grade 3. The visual design is used to enhance the math problems and skills demonstrated on each page. The pictures match the concepts addressed such as having the characters that are in the story problems placed in picture format on the page as well. Some problems may even require students to use the pictures to solve the story problems.

For example, in Unit 7, Module 3, Session 5, in the Work Place the design of the students’ recording sheet supports students in engaging in thoughtful work with fractions. Based on the card drawn, students are building a model of the fraction using “egg cartons.” They fill out the carton and record their findings in the space provided. Each portion of the sheet is clearly marked with spaces to work. The pictures of the cartons are clear and marked for easy use by the students. There is also work space marked, if the student is able to model their fraction without the use of the carton picture.

Also, in the Number Corner February Calendar Collector “Fractions of a Dollar,” students are showing each fraction on a dollar grid. The grids are marked with darker lines to show where the quadrants are located along with lighter lines to show all 100 spaces. These graphs are clear and provide appropriate scaffolding to support students in Grade 3 in their understanding of fractions.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
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Criterion Rating Details

The instructional materials support teacher learning and understanding of the standards. The instructional materials provide questions and discourse that support teachers in providing quality instruction. The teacher's edition is easy to use and consistently organized and annotated. The teacher's edition explains the mathematics in each unit as well as the role of the grade-level mathematics within the program as a whole. The instructional materials are all aligned to the standards, and the instructional approaches and philosophy of the program are clearly explained.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

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 discourse to allow 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.

In Unit 2, Module 2, Session 1, before students do a "count-around" with 9s after completing a "count-around" with 6s, teachers are prompted to ask the following questions:

  • "Will there be more multiplies or fewer multiples of 9? Why?"
  • "Will everyone get to call out a number? Why or why not?"
  • "Can you estimate how many people will get to call out a number? Tell us more about your estimate."
  • "What happens as the numbers we are counting get bigger?"

In Unit 4, Module 3, Session 2, "Comparing and Ordering Unit Fractions" teachers are prompted to ask the following questions:

  • "If you like cookies, would you rather be in a group of 2 people sharing one cookie or 3 people sharing one cookie? Why?"
  • "Would you rather be in a group of 2 people sharing 1 cookie or a group of 6 people sharing two cookies? Why?"
  • "Would you rather be in a group of 50 people sharing or 25 people sharing? Why?"

In Unit 7, Module 3, Session 5, as students are playing a game called "Dozens of Eggs" which gives them practice building and recording egg carton (equivalent) fractions, the teacher is prompted to ask the following questions:

  • "Can you tell how many twelfths there will be in the fraction on the card your classmate just drew for your team?"
  • "How many more twelfths do you need to fill this egg carton? Is there a single fraction you could draw that would give you that many twelfths? How do you know?"
  • "Which team is ahead, and by how much?"

In the November Number Corner Computational Fluency activity, "Array Race," the following questions are provided in the "Key Questions" section in the margin:

  • "If you rolled an 8 and a 6, what would you shade in on the 10-by-10 array?"
  • "Can you imagine how your array will look, and how many squares it will include before you shade it in?"
  • "Now that your array is filled in, how many squares are there in each row? How many are there in each column?"
  • "Can you find out how many squares are in this array without counting them one by one? How?"
  • "How does the array model help you find the answers to multiplication problems?"
  • "What is an efficient way to find your score?"

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
1/2
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Indicator Rating Details

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials; however, additional teacher guidance for the use of embedded technology to support and enhance student learning is needed.

There is ample support within the Bridges material to assist teachers in presenting the materials. Teacher editions provide directions and sample scripts to guide conversations. Annotations in the margins offer connections to the MPs and additional information to build teacher understanding of the mathematical relevance of the lesson.

Each of the eight units also have an introductory section that describes the mathematical content of the unit and includes charts for teacher planning. Teachers are given an overview of mathematical background, instructional sequence, and the ways that the materials relate to what the students have already learned and what they will learn in the future units and grade levels. There is a Unit Planner, Skills Across the Grade Levels Chart, Assessment Chart, Differentiation Chart, Module Planner, and Materials Preparation Chart. Each unit has a sessions page, which is the Daily Lesson Plan.

The Sessions contain:

  • Sample Teacher/Student dialogue.
  • Math Practices In Action icons as a sidebar within the sessions. These sidebars provide information on what MP is connected to the activity.
  • A Literature Connection sidebar. These sidebars list suggested read-alouds that go with each session.
  • ELL/Challenge/Support notations where applicable throughout the sessions.
  • A vocabulary section within each session. This section contains vocabulary that is pertinent to the lesson and indicators showing which words have available vocabulary cards online.

Technology is referenced in the margin notes within lessons and suggests teachers go to the online resource. Although there are no embedded technology links within the lessons, there are technology resources available on the Bridges Online Resource page such as videos, whiteboard files, apps, blogs, and online resource links (virtual manipulatives, images, teacher tip articles, games, references). However, teacher guidance on how to incorporate these resources is lacking within the materials. It would be very beneficial if the technology links were embedded within each session, where applicable, instead of only in the online teacher resource. For instance, the teacher materials would be enhanced if a teacher could click on the embedded link (if using the online teacher manual) and get to the Whiteboard flipchart and/or the virtual manipulatives.

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
2/2
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Indicator Rating Details

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, Unit 2 states, "Unit 2 focuses on helping students develop a conceptual understanding of multiplication. Investigations begin with contexts and problems that invite them to multiply, to think about equal groups and multiplicative comparisons. Story problems are not reserved as a culminating activity after students have explored multiplication. Instead, through the process of solving problems in context, students begin to make the transition from additive to multiplicative reasoning…”

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 think-pair-share, craft sticks, and choral counting. There are also explanations and samples of the various models used within the unit such as frames, number racks, tallies/bundles/sticks, and number line.

In the Implementation section of the Online Resources, there is a "Math Coach" tab that provides the Implementation Guide, Scope & Sequence, Unpacked Content, and CCSSM Focus for Grade 3 Mathematics.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
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Indicator Rating Details

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 MPs 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 3 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 math 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.

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
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Indicator Rating Details

The materials provide a list of lessons in the teacher's edition cross-referencing the standards covered and providing an estimated instructional time for each lesson and unit. The "Scope and Sequence" chart lists all modules and units, the CCSSM standards covered in each unit, and a time frame for each unit. There is a separate "Scope and Sequence" chart for Number Corners.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
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Indicator Rating Details

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Home connection materials and games sometimes include a “Note to Families” to inform them of the mathematics being learned within the unit of study.

Additional Family Resources are found at the Bridges Educator's Site.

  • Grade 3 Family Welcome letter in English and Spanish- This letter introduces families to Bridges in Mathematics, welcomes them back to school, and contains a broad overview of the year's mathematical study.
  • Grade 3 Unit Overviews for Units 1-8, in English and Spanish.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
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Indicator Rating Details

Materials contain explanations of the instructional approaches of the program. In the beginning of the Unit 1 binder, there is an overview of the philosophy of this curriculum and the components included in the curriculum. There is a correlation of the CCSSM and MPs as the core of the curriculum in the Mathematical Emphasis section. The assessment philosophy is given in the beginning of the Assessment binder. The types of assessments and their purpose is laid out for teachers. For example, informal observation is explained as "one of the best but perhaps undervalued methods of assessing students...Teachers develop intuitive understandings of students through careful observation, but not the sort where they carry a clipboard and sticky notes. These understandings develop over a period of months and involve many layers of relaxed attention and interaction."

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
10/10
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Criterion Rating Details

The instructional materials offer teachers resources and tools to collect ongoing data about student progress. The September Number Corner Baseline Assessment allows teachers to gather information on student's prior knowledge, and the Comprehensive Growth Assessment can be used as a baseline, quarterly and summative assessment. Checkpoints and informal observation are included throughout the instructional materials. Throughout the materials, Support sections provide common misconceptions and strategies for addressing common errors and misconceptions. Opportunities to review and practice are provided in both the Sessions and Number Corner routines. Checkpoints, Check-ups, Comprehensive Growth Assessment and Baseline Assessments clearly indicate the standards being assessed and include rubrics and scoring guidelines. There are, however, limited opportunities for students to monitor their own progress on a daily basis.

Indicator 3m

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

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

The September Number Corner Baseline Assessment is a 5-page, written baseline assessment that is designed to ascertain students' current levels of key number skills and concepts targeted for mastery in second grade – addition and subtraction story problems within 100; add single-digit numbers fluently; add and subtract 2- and 3-digit numbers; estimate, compare, and measure length in centimeters; and work with arrays with early fractions. The Comprehensive Growth Assessment contains 42 written items, addressing every Common Core standard for Grade 3. This can be administered as a baseline assessment as well as an end of the year summative or quarterly 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 as they work in Work Places.

Indicator 3n

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

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 the 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 3 Session 3 “Support” section gives suggestions for struggling students. The materials suggest that although most students will likely have had several years of experience with the pattern blocks, the urge to play with these manipulatives never quite goes away. The materials suggest that teachers may find that students are more focused on the problems they are about to pose if you give them a couple of minutes to make designs or structures with their small collection of blocks.

Indicator 3o

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

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. For example, in Unit 5, Module 1, Session 2, students are applying what they already know about multiplication and division in order to solve story problems with products and dividends to 100 involving situations of measurement quantities (3.OA.3). 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 February Number Line as students create their own number lines marked with fractions (halves, fourths, eights, thirds, and sixths), students review and practice using the 0-1 number lines from the previous month (3.NF.2).

Indicator 3p

Materials offer ongoing formative and summative assessments:
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Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
2/2
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Indicator Rating Details

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 details the CCSS that is addressed.

For example, the Unit 3, Module 2, Session 1, Rounding & Multi-Digit Addition Checkpoint includes a Checkpoint Scoring Guide that lists each prompt, the correct answer, the standard, and the points possible. The Unit 5, Module 4, Session 6 Post-Assessment includes a Post-Assessment Scoring Guide that lists all items, correct answers, standards and the possible points, as well as a Student Reflection Sheet. The Unit 6, Module 4, Session 4, Unit 6 Post-Assessment includes a Scoring Guide that lists all items, correct answers, standards, and the possible points, as well as a Student Reflection Sheet. The October Number Corner Checkup 1 includes a Scoring Guide that contains the item, the CCSSM, and the possible points. The May Number Corner Checkup 4 includes a Scoring Guide that contains the item, the CCSSM, and the possible points.

Also, each item on the Comprehensive Growth Assessment lists the standard emphasized in the Skills & Concepts Addressed chart as well as on the Comprehensive Growth Assessment Scoring Guide.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
2/2
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Indicator Rating Details

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, 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 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.

Indicator 3q

Materials encourage students to monitor their own progress.
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Indicator Rating Details

There is limited evidence in the instructional materials that students are self-monitoring their own progress on a frequent basis. The materials do not provide daily exit tickets (other then three generalized writing prompts) or daily formative checks. Bridges Units 1-6 do each include a Student Reflection sheet for both pre and post unit assessments. Each skill is listed in a graphic organizer, along with the problem number. Students reflect upon their work utilizing the following criteria: I can do this well already, I can do this sometimes, and I need to learn to do this. After the Pre-Assessment, each student is asked to make a star next to the two skills that he/she needs to work on the most during the unit. After the Post-Assessment, students are asked to reflect upon 1-2 things that they improved upon, as well as areas still in need of work.

Section 4 of the Assessment Guide is titled, "Assessment as a Learning Opportunity." This section provides information to teachers guiding them in setting learning targets, communicating learning targets, bringing sessions to closure and facilitating student reflection based upon the results of pre and post assessments.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
12/12
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Criterion Rating Details

Session and Number Corner activities provide ELL strategies, support strategies, challenge strategies, and grouping strategies to assist with differentiating instruction. A chart at the beginning of each unit indicates places in the instructional materials where suggestions for differentiating instruction can be found. Most activities allow opportunities for differentiation. The Bridges and Number Corner materials provide many grouping strategies and opportunities. Support and intervention materials are also available online.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
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Indicator Rating Details

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.

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.

For example, in Unit 3, Module 2, Session 4, students are works on "Book & Books & Books." Support is offered: "...give them additional time." Challenge is offered: "ask them to write and solve a story problem with more than one step and more than one operation."

In the Unit 1, Module 3, Session 2 "Adding Lengths" activity, the following suggestions are provided:

  • Support: "Help students model their thinking. Sometimes students can think of a strategy but do not know how to put their thinking on paper. Help them by listening carefully and modeling their work."
  • ELL: "Help the student understand the meaning of the questions. Use objects or pictures of objects to represent the objects in the problems. Use gestures or line up the actual objects."
  • Challenge: "Encourage students to use he most efficient and sophisticated strategies. Ask them if they can make bigger jumps. Ask students to describe their strategies."

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
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Indicator Rating Details

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.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

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 and 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 2, Module 1, Session 1, students are working on "The Pet Store." This session is about seeing, identifying and marking groups to lay the foundation for multiplication. As students share out their representations, the teacher continues to ask "So how many chew toys can you see?" "So there are 4 groups of 3?" "Two dogs. I wonder how many feet they have?" "How can I write that?" During the session, any correct representation is accepted, and students are encouraged to solve using different representations.

Another example is found in the Number Corner February Computational Fluency. Students are working on multiplying by 3, 4, and 8. Each student has a different multiplication table where they are coloring in the facts that they've mastered, with non-mastered facts easily identified. The table also has a sidebar with various facts for example: Zero Facts, Doubles Facts, and Ten Facts.

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
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Indicator Rating Details

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:

  • Unit 2, Module 2, Session 2 provides a Support/ELL suggestion. The suggestion reads as follows: "As you work through the rest of the session, point to the groups of cubes on the train. Use the physical models to help clarify student comments and your questions."
  • In Unit 5, Module 1, Session 5, students are working on Game Store Problems. The following ELL suggestion is provided: "Encourage students to write problems in their own language, using illustrations to make the problems more accessible to classmates who don't speak that language." The following Support suggestion is provided: "Tape copies of Game Store Problems 1, 2, 3 and 4 to the whiteboard, and let students know that these are examples that might give them ideas for their own problems."
  • In the Number Corner April Calendar Collector, students are working with fractions of an hour. The ELL suggestion is: "As always, take time to emphasize important vocabulary through labels, sketches, and examples. Help ELL students connect terms in English to terms in their native language. Try to figure out what students already know in their native language and how that can help them understand the material in this workout."

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
2/2
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Indicator Rating Details

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 1, Module 2, Session 2, the challenge part of this session provides extra questions and asks how each problem relates to the half facts on the Subtraction Table.
  • In Unit 3, Module 1, Session 3, in the Problem String section, students are solving 2-digit and 3-digit addition problems. The "Challenge" suggestion is as follows: "Invite students who understand the give & take strategy to come up with problems that would work well with it. Have them also consider what numbers do not lend themselves to this strategy."
  • In the Number Corner April Number line, students are working with fractions in a game called" Put It on the Line." The Challenge suggestions are as follows: "For student who can solve problems efficiently and easily, you may want to have a few challenge questions posted for them to work on as they finish the problems for the game," and "Challenge students to consider what the total sum must be for all of the answers (the sum of their score and your score)."

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

The materials provide a balanced portrayal of demographic and personal characteristics. Many of the contexts of problem solving involve objects and animals, such as cats and dogs. When people are shown, they are cartoons that appear to show a balance of demographic and personal characteristics.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
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Indicator Rating Details

The instructional materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials offer flexible grouping and pairing options. Throughout the Units, Work Places, and Number Corners, there are opportunities to group students in various ways such as whole group on the carpet, partners during pair-share, and small groups during Problem & Investigations and Work Places.

In Unit 1, Module 4, Session 2, students are grouped in pairs to work a two-digit addition story problem. After, four or five students share their strategies with the whole class. Next students work a story problem independently. After the Problems & Investigations session, they move into Work Places where they work either independently or in small groups with the Work Place centers.

In the Number Corner February Number Line, the class plays "Find the Fraction." The students play the games in teams and then discuss the game, first in pairs and then as a whole class.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
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Indicator Rating Details

There is limited evidence of the instructional materials encouraging teachers to draw upon home language and culture to facilitate learning. The materials provide parent welcome letters and unit overview letters that are available in English and Spanish.

Criterion 3aa - 3z

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

All of the instructional materials available in print are also available online. Additionally, the Bridges website offers resources such as Whiteboard files, interactive tools, virtual manipulatives, and teacher blogs. Digital resources, however, do not provide technology-based assessment opportunities, and the digital resources are not easily customized for individual learners.

Indicator 3aa

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

The digital materials are web-based and compatible with multiple internet browsers. They appear to be platform neutral and can be accessed on tablets and mobile devices.

All grade-level Teacher Editions are available online at bridges.mathlearningcenter.org. Within the Resources link (bridges.mathlearningcenter.org/resources) there is a sidebar that links teachers to the MLC, Math Learning Center Virtual Manipulatives. These include games, Geoboards, Number Line, Number Pieces, Number Rack, Number Frames and Math Vocabulary. The resources are all free and available in platform neutral formats: Apple iOS, Microsoft and Apps from Apple App Store, Window Store, and Chrome Store. The apps can be used on iPhones and iPads. The Interactive Whiteboard files come in two different formats: SMART Notebook Files and IWB-Common Format. From the Resource page there are also many links to external sites such as ABCYA, Sheppard Software, Illuminations, Topmarks, and Youtube.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
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Indicator Rating Details

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

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
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Indicator Rating Details

The instructional materials are not easily customizable for individual learners or users. Suggestions and methods of customization are not provided.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

The instructional materials provide opportunities for teachers to collaborate with other teachers and with students, but opportunities for students to collaborate with each other are not provided. For example, a Bridges Blog offers teacher resources and tools to develop and facilitate classroom implementation.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
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Indicator Rating Details

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Each session within a module offers online resources that are in alignment with the session learning goals. Online materials offer an interactive whiteboard file as a tool for group discussion to facilitate discourse in the MPs. Resources online also include virtual manipulatives and games to reinforce skills that can be used at school and home.

In the Bridges Online Resources there are links to the following:

  • Virtual Manipulatives - a link to virtual manipulatives such as number lines, geoboard, arrays, number pieces, number racks, number frames, and math vocabulary.
  • Interactive Whiteboard Files - whiteboard files that go with each Bridges Session and Number Corner.
  • Online Games - online games such as Drag Race Division, Stop the Clock 3, Battleship Numberline: Fractions, Melvin’s Make a Match (equivalent fractions), and an interactive math dictionary.

Within the Teacher's Edition, there is no direct reference to online resources. If embedded within the Teacher's Edition, the resources would be more explicit and readily available to the teacher.

Additional Publication Details

Report Published Date: Thu Mar 31 00:00:00 UTC 2016

Report Edition: 2015

Title ISBN Edition Publisher Year
null 978-1-60262-464-1 null null null
null 978-1-60262-465-8 null null null
null 978-1-60262-466-5 null null null
null 978-1-60262-468-9 null null null
null 978-1-60262-469-6 null null null
null 978-1-60262-470-2 null null null
null 978-1-60262-471-9 null null null
null 978-1-60262-472-6 null null null
null 978-1-60262-473-3 null null null
null 978-1-60262-474-0 null null null
null 978-1-60262-475-7 null null null
null 978-1-60262-505-1 null null null
null 9781886131736 null null null

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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