Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 1 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 1 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 constructing viable arguments and 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
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
17
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

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-
Gateway One Details

The materials reviewed for Grade 1 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 each 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 progression 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 1 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 1 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 assessment materials reviewed for Grade 1 meet expectations for focus within assessment. Content from future grades was found to be introduced; however, above grade-level assessment items, and their accompanying lessons, could be modified or omitted without significantly impacting the underlying structure of the instructional materials.

For this indicator, several pieces in the Assessment Overview section of the Assessment Guide were used to identify summative assessments. On page 4 of the assessment overview, the authors note that "The unit assessments are generally longer, more comprehensive in terms of the material covered in the unit, and more summative in nature," and on page 5,"Unit assessments are generally longer, more comprehensive, and summative with respect to the goals of the instruction in the unit." Additionally, on pages 3 and 4, the authors identify the Number Corner Checkups as having a "focus on critical numeracy skills and concepts," and they explain that they are meant to document growth quarterly as compared to a "Baseline" Checkup at the beginning of the year and based on skills and concepts taught in that quarter. Lastly, the Grade 1 Assessment Map found on pages 12-14 in the Assessment Overview section indicates when mastery of each standard is expected and where the mastery standard is assessed. It was found that some of the mastery concepts were assessed on unit checkpoints. Based on these criteria, the following were considered to be the summative assessments and were reviewed for Indicator 1a:

  • All Unit Assessments
  • Number Corner Checkups 1 – 4
  • The Comprehensive Growth Assessment
  • Select Unit Checkpoints where mastery is indicated on Assessment Map:
    • Unit 5 M2 S5: Shapes Checkpoint
    • Unit 6 M2 S5: Combinations and Stories Checkpoint
    • Unit 7 M2 S5: Numbers to 120 Checkpoint
    • Unit 8 M2 S4: Time and Change Checkpoint

Assessments are student observation/interview or written in nature. Most Comprehensive Growth Assessment (CGA) questions are fully aligned to the Grade 1 CCSS. All of the Number Corner Quarterly Checkups are fully aligned to the Grade 1 CCSSM. There are some questions in the Unit Checkpoints that go above Grade 1 assessment expectations.

The Unit Assessment Checkpoints that contain above grade-level or content not specifically required by the standards are noted in the following list:

  • In the Comprehensive Growth Assessment (CGA) (written portion, page 18)
    • question 18 asks the student to create a composite shape. One of the suggestions is to use a rhombus, which is not part of 1.G.1 but is mathematically reasonable to have included.
  • In the Unit 5 Assessment (Module 3, Session 6, p. 54):
    • In Questions 5 and 7, fractional parts are written using symbols (½ and ¾), for example: Draw a line to divide this rectangle in half. Color in one-half (1/2) of the rectangle. Symbolic notation for fractions is a Grade 3 expectation (3.NF.1). However, since the word form is included in the question, it is not necessary for students to have mastered symbolic fraction notation in order to answer the questions. It should be noted that when looking at the sessions leading into this assessment, symbolic notation is included. For example, students play games with fraction cards which show fractional models of shapes and sets with the symbolic fraction form included (Grade 3 expectations).
    • In Question 6, students are required to color in three-fourths of the circle. Coloring in three-fourths of a circle is not mathematically reasonable in Grade 1, and this item would need to be revised or removed from the assessment. The related session, Unit 5, Module 3, Session 5, also includes fractions that are not appropriate for Grade 1 (for example, 2/3).
  • In the Unit 6 Assessment (Module 3, Session 5, p. 66):
    • In Question 2, students are given 14 addition problems (sums up to and including 20). The author aligned the task to 1.OA.6 (add and subtract to 20, demonstrating fluency for addition and subtraction within 10). However, the answer key provided indicates that students score one point for each correct answer recorded during the 3-minute timing. Timing indicates an expectation of fluency with those addition combinations, and six of the problems have sums greater than the limit of 10 as indicated in the standard. This item could be easily modified to be appropriate for Grade 1 by not timing the students.
  • In the Unit 8 Time and Change Checkpoint (Module 2 Session 4) and the Unit 8 Assessment (Module 3 Session 6):
    • Question 2 on both assessments goes beyond the intended “tell time to the hour” to assess elapsed time: soccer practice began at 4:00 and lasted 1 hour; students must identify the clock with shows what it looks like when soccer practice is over.

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 1 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 1 meet the expectations for focus by spending the majority of class time on the major clusters of the grade. All sessions (lessons), except summative and pre-assessment sessions, were counted as 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. 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.

When looking at the modules (chapters) and instructional time, when considering both sessions and Number Corners together, approximately 86 percent of the time is spent on major work of the grade.

  • Units – Approximately seven out of eight units spend the majority of the unit on major clusters of the grade, which is approximately 88 percent. Much of Unit 5 is not focused on major work of the grade. The other units devote most of the instructional time to major clusters of the grade.
  • Modules (chapters) – Approximately 27 out of 32 modules spend the majority of the time on major clusters of the grade, which equals approximately 84 percent. Units 2, 5, and 8 had modules that were not focused on major work of the grade.
  • Bridges Sessions (lessons) – 137 out of 160 sessions focus on major clusters of the grade, which equals approximately 86 percent. Major work is not the focus of the following sessions:
    • Unit 1, Module 2, Session 1
    • Unit 2, Module 4, Session 1
    • Unit 2, Module 4, Sessions 2 and 3
    • Unit 5, Module 1, Sessions 1-5
    • Unit 5, Module 2, Sessions 1-5
    • Unit 5, Module 3, Sessions 2-5
    • Unit 8, Module 1, Sessions 2 and 3
    • Unit 8, Module 3, Sessions 1 and 6
    • Unit 8, Module 4, Session 5
  • Bridges sessions require 60 minutes. A total of 137 sessions are focused on major work grade work of the grade. Bridges sessions devote 8,220 minutes of 9,600 minutes to major work of the grade. A total of 150 days of Number Corner activities address major work of the grade. Number Corner activities are 20 minutes each adding another 3,000 minutes to this total. In all 11,220 of 13,000 minutes, approximately 86 percent, is devoted to major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
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-
Criterion Rating Details

The instructional materials reviewed for Grade 1 meet the expectations for coherence. The materials use supporting content as a way to continue working with the major work of the grade. For example, students count shapes in categories and then compare the quantities. The materials include a full program of study that is viable content for a school year, including 160 days of lessons and assessment. All students are given extensive work on grade-level problems, even students who are struggling, and this work progresses mathematically. However, future grade-level content is not consistently identified. These instructional materials are visibly shaped by the cluster headings in the standards; for example, one session is called "Sorting & Graphing Shapes." Connections are made between domains and clusters within the grade-level. For instance, materials make connections between operations and algebraic thinking and measurement and data. Overall, the Grade 1 materials support coherence and are consistent 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 1 meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade.

Supporting standard 1.G.2 is connected to 1.NBT.1 throughout the instructional materials. For example, in Unit 5, Module 1, Session 4 when filling outlines of shapes with pattern blocks, students are asked to count and record in a table the number of each type of shape used. Students practice writing numerals as they record information in the table.

Supporting standard 1.MD.4 is connected to major work of the grade throughout the instructional materials. For example, in Unit 1, Module 1, Session 2 students are creating popsicle graphs and then counting to determine the differences between the flavors; sums and differences are primarily within 10. Within Unit 2, Module 3, Session 3, Workplace 2E, 1.MD.4 supports the major work of 1.OA.6 with the game "Spin & Add;" students are spinning two spinners, adding, and recording totals on chart. Another example is Unit 5, Module 4, Session 2; students make a graph after sorting shapes into two categories and then answer questions such as how many more than, fewer than, and in all. This work with 1.MD.4 supports standard 1.OA.1 and practice with standard 1.OA.6. Also, in the September-May Calendar Collector 1.MD.4 is connected to 1.OA.4, 1.NBT.1, and 1.NBT.3. The first few weeks are spent collecting the data. In the fourth week, students compare and order, estimate and count collections from the previous three weeks. Most months also have students applying concepts to story problem contexts.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 1 meet the expectations for this indicator by providing a viable level of content for one school year. Overall, the materials have expectations for teachers and students that are reasonable.

  • Materials provide for 160 days of instruction. Each Unit has 20 sessions = 20 days. There are eight Units. (20x8=160)
  • The prescribed daily instruction includes both Unit session instruction and a Number Corners session. (170 days). There are no additional days built in for re-teaching.
  • Assessments are incorporated into sessions and do not require an additional amount of time. Instead, they are embedded into module sessions one on one as a formative assessment.
  • The Number Corner Assessments/Checkups (a total of 10 assessments, one interview and one written, in each of the following months: September, October, January, March and May) would require additional time to conduct a 7-10 minute interview with each student.
  • A Comprehensive Growth Assessment is completed at the end of the year and will require additional number of days to administer.
  • There are no additional time/days built in for additional support, intervention or enrichment in the pacing guide. The publisher recommends re-teaching of strategies, facts, and skills take place in small groups while the rest of the class is at work places (math stations) or doing some other independent task. There is a concern that if a particular session’s activities take up most of the 60 minutes allotted, there will be no time for the remediation and enrichment to take place.
  • Based on the Bridges Publisher Orientation Video and Guide provided to the reviewers, Unit sessions are approximately 60 minutes of each instructional day.
    • Each Unit session contains: Problems & Investigations (whole group), Work Places (math stations), Assessments (*not found in each session), and Home Connections (homework assignments *not found in each session).
  • Based on the Introduction section in the Number Corners Teacher Guide, as well as the Bridges Publisher Orientation Video, Number Corners sessions are approximately 20 to 25 minutes of each instructional day.
  • Approximately 80-85 minutes is spent on the Bridges and Number Corner activities daily.

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 reviewed for Grade 1 are partially consistent with the progressions in the standards. Although students are given extensive grade-level problems and connections to future work are made, off-grade level content is not always clearly identified to the teacher or student.

At times, the session materials do not concentrate on the mathematics of the grade. Some of the sessions within each module concentrate on below or above-grade level concepts. Examples of this include counting objects one-by-one, growing patterns, rotational symmetry, building shapes from nets, fraction notation, and fractions of a set. The inclusion of off-grade level concepts takes away from the number of sessions that could be spent more fully developing the work on the mathematics of the grade.

In some cases, the below or above-grade level content is identified as such by the publishers, and in other cases it is not. On the first page of every session, the skills and concepts are listed along with the standard to which it has been aligned by the publisher. In some cases, this alerts the user to the inclusion of off-grade level concepts. Examples include:

  • Unit 1, Module 2, Session 1: One of the skills listed is "Count objects one by one, saying the numbers in standard order and pairing each object with only one name." The publisher lists this standard as K.CC.4.A, alerting teachers to the fact that this session involves below-grade level standards.
  • Unit 1, Module 2, Session 1: One of the skills listed is "Count up to 20 objects arranged in a line or array to answer "how many?" questions." This skill is listed as K.CC.5, alerting teachers to the fact that this session involves below-grade level standards.
  • Unit 1, Module 2, Session 3: One of the skills listed is "recognize the number of objects in a collection of 6 or fewer, arranged in any configuration." This skill is listed as "supports K.CC" which alerts the teacher that this is a below-grade level concept.
  • Unit 2, Module 1, Session 1: One of the skills listed is "count up to 20 objects arranged in a line, rectangular array, or circle to answer "how many." This skill is listed as K.CC.5 which alerts the teacher that this is a below-grade level concept.
  • Unit 2, Module 1, Session 1: One of the skills listed is "identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group for groups of up to 10 objects." This standard is listed at K.CC.6 which alerts the teacher that this is a below-grade level standard.
  • Unit 5, Module 3, Session 2: The About This Session note acknowledges that the activity dives into symmetry and that symmetry isn’t formally studied until fourth grade, so this is simply an “exploration.”

In other cases, the below or above-grade level concepts are not identified as such within the sessions in the "Skills and Concepts" listing or at the beginning of the units in the "Skills Across the Grade Levels" sections. Examples of unidentified below or above-grade level content include:

  • Unit 1, Module 1, Session 2: Counting by 5's is a Grade 2 standard (2.NBT.2).
  • Unit 1, Module 1, Session 3: The Work Place focus is on Polydrons, 1.G.2; however, work involves Grade 6 standards constructing triangular prisms and pyramids.
  • Unit 1, Module 1, Session 5: Counting by 2's is the focus of this lesson and is a Grade 2 standard (2.OA.3).
  • Unit 1, Module 3 and Unit 1, Module 4, Session 3: Counting by 5's is a Grade 2 standard.
  • Unit 2, Module 4, Session 1: Students are making triangular quilt pieces to represent the five arms of a sea star. Counting by 5's is a Grade 2 standard.
  • Unit 2, Module 4, Session 1: Students are assembling a quilt making rows of five which is a Grade 2 standard (2.OA.4).
  • Unit 2, Module 4, Session 3: The focus is counting by 5s, a Grade 2 standard.
  • Unit 3, Module 1, Session 2 and Session 5: Counting by 2’s is a skip counting strategy/skill that is not introduced until Grade 2 (2.NBT.2).
  • Unit 4, Module 4, Session 2 and Session 5: Both sessions involve counting by 5’s, which is a skip counting strategy/skill that is not introduced until Grade 2 (2.NBT.2).
  • Unit 6, Module 4, Session 5: The publisher identifies count by twos and number patterns as “supporting 1.NBT” as an indicator that this is not Grade 1 expectation, but it doesn’t specifically call out for which grade level it would be appropriate.

Materials provide students opportunities to work with grade-level problems. The majority of differentiation/support provided is on grade-level. Extension activities are embedded within Sessions and allow students to engage more deeply with grade-level work. Additional Extension activities are also provided online.

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.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 1 meet the expectations for fostering coherence through connections at a single grade, where appropriate and when the standards require. The standards are referred to throughout the materials. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings and include problems and activities that connect two or more clusters in a domain or two or more domains when these connections are natural and important.

Instructional materials shaped by cluster headings include the following examples:

  • The Unit 5 Module titles are loosely informed by the K.G cluster headings.
  • Unit 5, Module 3, “Putting Shapes Together & Taking Them Apart,” is informed by 1.G.A.
  • Unit 5, Module 4, “Sorting & Graphing Shapes,” is similar to 1.G.A.
  • Unit 6 Module titles are informed by the 1.OA cluster heading.
  • Unit 6, Module 1, “Story Problems for Basic Addition & Subtraction,” is shaped by 1.OA.A.
  • Unit 6, Module 3, “Solving for the Unknown in Penguin Stories,” is informed by 1.OA.A.
  • Unit 6, Module 4, “Measuring & Comparing Emperor and Little Blue Penguins,” is informed by 1.MD.A.

Units, Modules, and Sessions that connect two or more clusters in a domain or two or more domains include the following examples:

  • Unit1, Module1, Session 2: "Popsicle Graph" connects 1.MD.C cluster to 1.OA.A as students are adding up popsicles and determining how many more/many fewer/in all.
  • Unit1, Module 2, Session 2: "Making 5 & 10" connects 1.OA.B with 1.OA.C as students are counting on their number racks to make combinations of 5 and 10, then writing the combinations in the form of equations.
  • Unit 1, Module 3, Session 3: "Which Coin Will Win" connects cluster 1.NBT.A with 1.MD.C as students are counting and writing numerals to represent the number of coins on the graph.
  • Unit 1, Module 3, Session 4: "Quick Look!" connects cluster heading 1.OA.C with 1.NBT.A as students are counting and adding beads on the number rack then writing a numeral that represents the number of beads.
  • Unit 1, Module 3, Session 5: "Measuring with Popsicle Sticks" connects cluster 1.MD.A with 1.NBT.A as students measure the length of their hands, use tallies to record the amount on a frequency chart, then write down the numeral that represents the number of tally marks.
  • Unit 1, Module 4, Session 1: "Number Rack Detectives" connects clusters1.OA.B, 1.OA.C, and 1.OA.D as students play a game of building addends on the number rack and then only share one row of the number rack with a partner, who then determines how many beads must be on the bottom rack.
  • Unit 1, Module 4, Session 3- "How Long is the Jump Rope" -connects cluster 1.NBT.A with 1.MD.A as students are measuring a jump rope using steps and then representing the number of steps with a numeral.
  • Unit 1, Module 4, Session 4: "Quick! Look! Plus One, Minus One" connects cluster 1.OA.C with 1.NBT.A as students are shown various quantities of beads on the number rack, record the number of objects with a numeral, and then write down the number that comes before and after it.
  • Unit 2, Module 1, Session 3: "Domino Add & Compare" connects cluster 1.OA.C to 1.NBT.B as students count dominos, compare amounts, and represent with a greater than, less than, or equal to symbol.
  • Unit 2, Module 2 connects cluster-level headings 1.OA.A and 1.OA.C.
  • Unit 2, Module 2, Session 1: "Introducing Double-Flap Dot Cards" connects cluster 1.OA.B with 1.OA.C as students identify number of dots on the dot cards, count on to find the total, and then write an equation to represent the dots shown as fact families.
  • Unit 2, Module 2, Session 2: "Double-Flap Picture Cards" connects cluster 1.OA.A to 1.OA.B as students add objects on picture cards to solve word problems and write equations that represent fact families.
  • Unit 2, Module 2, Session 3, Introducing Work Place 2C: "Sort the Sum" connects cluster 1.OA.C to 1.NBT.C as students find the sum of dots and then compare the totals. *Note - totals are under 10 which is not the full intent of 1.NBT.3 which calls for comparing two two-digit numbers.
  • Unit 2, Module 2, Session 4: "Double Flap Number Cards" connects 1.OA.B to 1.OA.D as students add numbers on the number cards applying strategies to add and subtract as well as determining the unknown whole number in equations.
  • Unit 2, Module 3, Session 3: connects cluster 1.OA.C with 1.MD.4 as students are counting numbers and dots on spinner, counting on to get the sum, and then recording amount on a graph
  • Activities in Unit 5, Module 1, Session 4: "Pattern Block Puzzles: How Many Ways?" connects 1.G.2 with 1.NBT.1 and 1.MD.4. When composing shapes within a shape outline, students count and record the number of each shape in a table and answer questions regarding which shape is fewer or more.
  • Activities in Unit 6, Module 1 connect addition and subtraction story problems 1.OA.A to 1.OA.C.
  • Unit 6, Module 2: “Combinations and Story Problems” connects 1.OA.A and 1.OA.C.
  • Activities in Unit 6, Module 3 connect work in story problems (1.OA.A) to solving for an unknown in an addition equation involving 3 whole numbers (1.OA.D)
  • Activities in Unit 6, Module 4 connect 1.NBT with 1.MD.
  • Unit 6, Module 2: “Combinations and Story Problems” connects 1.OA.A and 1.OA.C.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The materials reviewed for Grade 1 meet the expectations for Gateway 2. The materials include each aspect of rigor: conceptual understanding, fluency and application. These three aspects are balanced within the lessons. The materials meet the expectations for the connections between the MPs and the mathematical content. More teacher guidance about how to support students in analyzing the arguments of others is needed.

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
+
-
Criterion Rating Details

The materials reviewed for Grade 1 meet the expectations for this criterion by providing a balance of all three aspects of rigor throughout the lessons. To build conceptual understanding, the instructional materials include concrete materials, visual models, and open-ended questions. In the instructional materials students have many opportunities to build fluency with adding and subtracting within 20. Application problems occur throughout the materials. The three aspects are balanced within the instructional materials.

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
+
-
Indicator Rating Details

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

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

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

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

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

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

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

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

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

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

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

  • Students spend a significant amount of time and have a variety of opportunities to fluently add and subtract throughout Number Corner activities.
    • In the Number Corner September Computational Fluency, in Activity 1, students are using the double 10-frame to solve addition problems by matching the equation with the cards.
    • In the Number Corner October Computational Fluency, in Activity 2, students play Ten-Frame Flash and show, with their fingers, how many dots are on the 10-frame cards.
    • In the December Number Corner Computational Fluency Routine, the routine for this month involves investigating double facts greater than 10 using a double ten-frame.
    • In the March Number Corner Days in School Routine, the hundreds grid is used as a visual model to assist students in explaining their mental reasoning for ten more or ten less.
  • Fluency is developed throughout the sessions of the Grade 1 instructional materials.
    • In Unit 1, Module 2, Session 3, students respond to representations of the 10-frame as the teacher flashes the 10-frame cards with totals within 10.
    • In Unit 4, Module 1, Session 5, students solve addition and subtraction combinations such as 3+2 and 5-2. Students are using their fluency to help deepen their understanding about the relationship between addition and subtraction.
    • In Unit 2, Module 2, Session 3, students identify strategies they used in adding numbers represented on a domino. Teacher led discourse elicits student thinking using counting on, doubling, and decomposing strategies.
    • In Unit 1, Module 3, Session 1, students solve missing-addend problems on their number racks. They use 5 as a landmark and find doubles and then count on.
    • In Unit 3, Module 4, Sessions 1 and 2, students use unifix cubes to represent equations up to 10 with various combinations of two or three addends.
    • In Unit 6, Module 2, Session 2, students use ten and double ten frames to represent addition up to twenty in the game "I have, who has" to create the addition equations.

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

Materials meet the expectations for having engaging applications of mathematics as they are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

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

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

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

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

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

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The materials reviewed for Grade 1 meet this criterion. The MPs are often identified and often used to enrich mathematics content. There are, however, several sessions that are aligned to MPs with no alignment to Standards of Mathematical Content. The materials usually attend to the full meaning of each practice. The materials reviewed for Grade 1 attend to the standards' emphasis on mathematical reasoning. Students are prompted to explain their thinking, listen to and verify the thinking of others, and justify their own reasoning. Although the materials often assist teachers in engaging students in constructing viable arguments, more guidance about how to guide students in analyzing the arguments of others is needed.

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

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

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

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

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

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

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
2/2
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Indicator Rating Details

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

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

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

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

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

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

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

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

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

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.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 1 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Although the instructional materials often assist teachers in engaging students in constructing viable arguments, there is minimal assistance to teachers in how to guide their students in analyzing the arguments of others.

There are Sessions containing the "Math Practice In Action" sidebars that explicitly states where the MP is embedded within the lesson and provides an in-depth explanation for the teacher. A few of the sessions contain direction to the teacher for prompts and sample questions and problems to pose to students.

  • In Unit 1, Module 2, Session 1, the teacher asks students to share strategies of how they found different combinations of numbers on the number rack to equal the number the teacher gave students to create.
  • In Unit 7, Module 2, Session 1, students construct and share their thinking about units of 20 within a total of 120. A number path with discrete units is used to analyze and explain their thinking.
  • In Unit 7, Module 4, Session 4, the Problems & Investigations lesson involves critiquing the reasoning of others in using place value understanding with units of 5 and 10 with number bonds, equations and coins. Students represent their thinking in multiple ways and make connections between the reasoning of others in comparison to their own chain of reasoning.

Although teachers are provided guidance to help students construct arguments and students are provided many opportunities to share their arguments, more guidance is need to support teachers in guiding their students through the analysis of arguments once they are shared. For example, in Unit 5, Module 4, Session 2, students are introduced to the Work Place "Shape Sorting & Graphing." The teacher ask students to talk with their neighbors about how the two shapes are alike and how they are different. Within the sample dialogue, students are asked, "Can you explain more about that?" and "Can someone tell me more about that?" The teacher is provided with sample dialogue that encourages students to construct viable arguments; however, little direction is provided for students to continue the discourse and analyze the arguments of others. Although this activity allows students to analyze the arguments of classmates, the teacher is not provided enough support to help students with this analysis.

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 1 meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics that is present throughout the materials.

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

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

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

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 Number Corner. Students produce a variety of types of answers including both verbal and written answers. Manipulatives such as 10-frames, craft sticks, and Unifix cubes are used throughout the instructional materials as mathematical representations 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 5, Module 1 in Session 3, students initially learn about the trapezoid. They work with the teacher to describe a trapezoid, with a focus on using accurate and precise geometrical language. Students then work with the teacher using pattern blocks to fill in a shape three different ways and discuss the differences, the number of blocks used, and the composition of new shapes. Students are introduced to the Pattern Block Puzzle. They observe a sheet with the puzzle and work together to fill in the shape with various pattern blocks. The teacher uses student input from the class to record the solution to solving the puzzle. Students continue in this manner until they have filled in the pattern three different ways and solutions are recorded. In the Work Places activity, students work independently to complete additional Pattern Block Puzzles.

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

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 continued to be reviewed, practiced and extended throughout the year.

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

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

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

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

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

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

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 10-frames, number lines, Unifix cubes, number racks, coins, craft sticks and tiles. When appropriate, they are connected to written representations.

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

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

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

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

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 1. The visual design is used to enhance the mathematics 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 the Number Corner April, "Days In School", students are working with two separate hundreds grids to mark and represent the number of days they have been in school. The Day 2, Activity 1 task has students marking another day on the second hundreds grid, and then the teacher represents the total number of days in digit form, word form and expanded form. The charts are easy to see and read using a the familiar hundreds grid and a large, clear chart for expanded notation.

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 conduct discourse that allows student thinking to be visible. Discussion questions provide a context for students to communicate generalizations, find patterns, and draw conclusions.

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

In Unit 1, Module 2, Session 1, the teacher is prompted to ask the following questions:
  • "How many red beads do you see? How many white?"
  • "I heard you counting. Can you come show us on the big rack how you were counting those beads? And can you show us how you knew there were the same number of white as red?""
In Unit 3, Module 1, Session 2, students are working on number lines. The teacher is prompted to ask the following questions:
  • "What if you could choose - you could jump by either a 5 or 10. Would that make the problem any shorter?
  • Could we use fewer jumps to get from 0 to our target of 15?"
  • "How do you know that?"
  • "Does anyone have a different solution?"

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

  • "How long do you think each strip will be when it's cut out? Why?"
  • "Will they stretch out the length of the poster board strip? How do you know?"
  • "Who is likely to use this tool, and when?"
  • "How does a ruler help us measure the length of something?"
In Unit 5, Module 2, Session 1 teachers are prompted to ask the following questions:
  • "Who can tell us what they saw?"
  • "Did anyone else see something different, or have a different way to describe what they saw?"

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

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

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, 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 the notes 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, in Unit 2 the following is provided: "Throughout Unit 2, students explore base ten concepts and models within 1,000. The unit is designed to promote measuring concepts even as students are learning about our base ten number system. As they count, total, and compare units, they are encouraged to think about and apply base ten concepts."

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

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

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 mathematical practices and the characteristics of children in that grade level for each of the MPs. There is an explanation of the Skills Across the Grade Levels chart, the assessments chart, and the differentiation chart to assist teachers with the use of these resources. The same explanations are available on the website. There are explanations in the Assessment Guide that go into the Types of Assessments in Bridges Sessions and Number Corner.

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

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

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).
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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 CCSS 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.
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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 1 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 1 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.
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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. In the Introductory section of Unit 1, there is a reference to the number rack and research as follows: "Research has consistently identified the importance of helping students visualize number quantities. The number rack is instrumental in this endeavor, allowing them to 'see inside' numbers."

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. Checkpoint interviews 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.

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

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

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 these misconceptions that students may have with the skill being taught.

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

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
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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. Ongoing review and practice is often provided through Number Corner routines. Each routine builds upon the previous month’s skills and concepts. For example, in the Number Corner May "Days in School" activity, students get to practice their understanding that the digits in a 2-digit number represent amounts of tens and ones (1.NBT.2).

Indicator 3p

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

Assessments clearly denote which standards are being emphasized.
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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 notes which CCSSM is addressed.

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

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

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

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.

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, encouraging student reflection, exit cards, and comparing work samples from earlier and later in the school year.

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. For example, in Unit 4 “Number Lines,” Module 1 uses a giant number line, Module 2 focuses on jumping by fives and tens on the number line, Module 3 focuses on an open number line with fives and tens, and Module 4 focuses on measurement on the number line.

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

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

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

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

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

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
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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 & Investigations section, students often are given the opportunities to share strategies they used in solving problems that were presented by the teacher. Students are given multiple strategies for solving problems throughout a module. They are then given opportunities to use the strategies they are successful with to solve problems in Work Places, Number Corner, and homework.

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

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

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).
2/2
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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:

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

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

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

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 2, Module 1, Session 1, the teacher introduces a dominoes game to students. They start out as a whole group as she reads-aloud from the book Domino Addition and then models the game. Students then pair up and practice playing the game. In their Work Places, they can either remain in pairs and continue playing dominoes or work individually in a Work Place station.

In the Number Corner February Calendar Collector, students are asked to quietly observe the Cube Collection Data Sheet and then share their observations with a partner and then as a whole group.

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.
0/0
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Criterion Rating Details

All of the instructional materials available in print are also available online. Additionally, the Bridges website offers additional resources such as Whiteboard files, interactive tools, virtual manipulatives, and teacher blogs. Digital resources, however, do not provide additional 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.
0/0
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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.
0/0
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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 MPs.

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, number pieces, number racks, number frames, and mathematics vocabulary;
  • Interactive Whiteboard Files - Whiteboard files that go with each Bridges Session and Number Corner;
  • Online Games- online games such as 100 Hunt using the hundreds grid, 2-D Shape Pictures, Interactive mathematics dictionary, Addition With Manipulatives, and Balloon Pop Comparisons (greater than/less than); and
  • Images - for example, 1,000 M&M candies arranged on hundred grids by students

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 978-1-60262-332-3 null null null
null 978-1-60262-333-0 null null null
null 978-1-60262-334-7 null null null
null 978-1-60262-335-4 null null null
null 978-1-60262-336-1 null null null
null 978-1-60262-337-8 null null null
null 978-1-60262-338-5 null null null
null 978-1-60262-339-2 null null null
null 978-1-60262-340-8 null null null
null 978-1-60262-343-9 null null null
null 978-1-60262-344-6 null null null
null 978-1-60262-345-3 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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