2nd Grade - Gateway 1

The assessment materials reviewed for Grade 2 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 3 of the assessment overview, the authors state that the post assessments “examine students’ growth over each three- to four-week period of instruction.” Additionally, on page 4, the authors identify the Number Corner Checkups as a long range assessment which “reflects the Common Core Critical Areas of Focus; check for conceptual understanding, procedural fluency and application of coherent and rigorous standards; and provide a snapshot of each student’s skills near the end of each quarter of the school year." Lastly, the Grade 2 Assessment Map found on pages 11–15 indicates when mastery of each standard is expected and where the mastery standard is assessed. Based on these criteria, the following were considered to be the summative assessments and were reviewed for Indicator 1a:

• All Unit Post-Assessments
• Number Corner Checkups 1–4
• Comprehensive Growth Assessment
• Select Unit Checkpoints where mastery is indicated on Assessment Map:
  • Unit 4 M2 S5: Inches, Feet and Yards Checkpoint
  • Unit 5 M1 S5: Three-digit Numbers Checkpoint
  • Unit 7 M2 S5: Metric Measuring and Fractions Checkpoint

The Unit Post-Assessments that contain above-grade level assessment items are noted in the following list:

• In the Unit 4 Post-Assessment on page 82, questions 6a-c are identified by the authors as assessing proportional reasoning and aligned to MP2 and MP4. For example, an envelope pictured on a grid is described as being 2 bricks tall and a dog is 3 bricks tall; question 6a asks, “How many envelopes would you have to stack up to reach the height of two dogs?” Proportional reasoning is not an expectation in the K – 5 grade band. There are three lessons in Unit 4 Module 3 which address this topic and are identified by the authors as “laying the foundation for the kind of multiplicative comparisons and proportional reasoning that will be expected in future grades.” Therefore, it should not be assessed, and its inclusion is not reasonable. Skipping the assessment question and the associated lessons will not impact the integrity of the grade level standards being taught.
• In the Unit 6 Post-Assessment on page 128, question 7a asks students to draw a line to cut a trapezoid in half and color one-half red. This task is aligned to 2.G.3 (Partition circles and rectangles into two, three, or four equal shares...). It is not intended that students partition any shapes other than circles and rectangles when exploring these fractional parts. All other questions in the assessment are grade-level appropriate, and including the trapezoid does not affect the integrity of the grade level standards taught.
• In the Unit 6 Post-Assessment on page 128, question 7b asks students to color half of a rectangle which has been divided into fourths. The authors have aligned this task to 2.G.3 and states that it supports 2.NF; however, there is no NF domain in Grade 2. This task goes beyond the indicated standard and is more appropriately aligned to 3.NF.3.A (Understand that fractions are equivalent if they are the same size…). In the Scoring Guide, it is stated that “Divisions of half other than that suggested by the lines are acceptable.” Therefore, students are permitted to draw a different line to cut the rectangle in half, and because of this, it is reasonable to leave the question in the assessment.
• In the Unit 7 Post-Assessment on page 146, question 4 asks students to color half of an array shown. This is more of an area fraction model, which is not the intent of standard 2.G.3. Since this occurs in the second-to-last unit of the year, the question and any corresponding lessons could be skipped without loss of integrity to the Unit.

The Comprehensive Growth Assessment (CGA) questions that contain above-grade level assessment items are noted in the following list:

• In the Comprehensive Growth Assessment (CGA) written portion on page 10, question 11 is assessing standard 2.OA.4 to total the number of objects arranged in a rectangular array up to 5 rows and 5 columns. This question is an array of 6 columns. The problem could be modified to fit the intent of the standard.

The instructional materials reviewed for Grade 2 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 81 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 equals approximately 88 percent. Unit 6 did not focus on major work of the grade.
• Modules (chapters) – 24 out of 32 modules spend the majority of the time on major clusters of the grade, which equals approximately 75 percent. Units 1, 2 and 3 had three modules that focused on major work of the grade. Units 4 and 7 each had 3.5 modules that focused on major work of the grade. Units 5 and 8 had all four modules focused on major work of the grade.
• Bridges Sessions (lessons) – 123 out of 160 sessions focus on major clusters of the grade, which equals approximately 77 percent. Major work is not the focus of the following sessions:
  • Unit 1, Module 1, Sessions 1-4
  • Unit 1, Module 2, Session 1
  • Unit 2, Module 4, Sessions 1 and 2
  • Unit 3, Module 4, Session 2 and 3
  • Unit 4, Module 3, Session 2
  • Unit 4, Module 4, Sessions 2 and 4
  • Unit 5, Module 2, Session 5
  • Unit 6, Module 1, Sessions 1-5
  • Unit 6, Module 2, Sessions 1-5
  • Unit 6, Module 3, Sessions 1-6
  • Unit 6, Module 4, Sessions 1-4
  • Unit 7, Module 2, Sessions 1-3
  • Unit 8, Module 4, Session 2
• Bridges sessions require 60 minutes. A total of 123 sessions are focused on major work grade work of the grade. Bridges sessions devote 7,380 minutes of 9,600 minutes to major work of the grade. Number Corner activities require 20 minutes. A total of 160 days of Number Corner activities address major work of the grade. Number Corner activities devote 3,200 minutes of 3,400 minutes to major work of the grade. In total 10,580 of 13,000 minutes, approximately 81 percent, is devoted to major work of the grade.

The instructional materials reviewed for Grade 2 meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade.

Supporting standard 2.OA.3 is connected to 2.OA.A, 2.OA.B and 2.NBT.B, major work of the grade, throughout the instructional materials. For example, in Unit 3, Module 4, Session 1, standards 2.NBT.6 and 2.NBT.9 support major work of 2.OA.3 by connecting even and odd numbers to place value and addition. Another example is found in the September Calendar Grid. In this Calendar students determine if a group of objects has an even or odd number of members and solve story problems.

Supporting standard 2.OA.4 is connected to 2.OA.B and 2.NBT, major work of the grade, throughout the instructional materials. For example, in Unit 1 Module 2, Session 3 in Workplace 1F "Count and Compare Fives" students are provided cards with various arrays (in rows or columns of 5) and practice counting by 5's with them and compare them to see which is greater; this supports both 2.NBT.2 and 2.NBT.5. Also, in Unit 2 Module 4, Session 1 "Thinking About Twos" and in Unit 4 Module 4, Session 2 "Thinking About Threes," students write equations to match dot arrays. This supports 2.OA.B and 2.NBT.5. The September, October, November, December, and January Number Corner Daily Rectangle activities also connect 2.OA.4 with 2.OA.2 and 2.NBT.5

Supporting standard 2.MD.7 is connected to 2.NBT.2 throughout the instructional materials. For example, these connections can be seen in the September, October, and February Number corner Calendar Collectors and the November Calendar Grid. These activities connect time with skip counting as students are always asked to “count by 5's” whenever determining the time on an analog clock.

Supporting standard 2.MD.8 is connected to 2.OA.1, 2.NBT.2, 2.NBT.5, and 2.NBT.7, major work of the grade, throughout the instructional materials. Work with money strongly supports place value understanding. For example, in the Unit 1 Module 2, Session 3 Workplace 1F "Count and Compare Fives" work with nickels provides a context for practicing counting by 5's. In Unit 5, Module 2, Sessions 1–6 use 5-frames and 10-frames to counting money and build place value understanding. Also, in Unit 7 Module 4, Sessions 1 – 2 students write their own word problems involving money and then solve each other’s problems. This supports 2.OA.1, 2.NBT.5 and 2.NBT.7. Also, the Number Corner March Calendar Collector "Two Quarters a Day" features word problems dealing with money which supports 2.OA.1.

Supporting standard 2.MD.9 strongly supports work with 2.MD.A, major work of the grade. For example, in Unit 8 Module 2, Sessions 4 - 5 in the "Marble Roll Experiment 1 Ramp Height" and in the Module 3, Sessions 1–5 "Marble Roll Experiment 2 Marble Mass," students are involved in an engaging project in which they collect and plot measurement data to see what factors will affect marble rolling distance. These lessons strongly support 2.MD.A as the students practice measuring skills while they measure distances to plot. Another example of the connection between 2.MD.9 and 2.MD.A are the Number Corner April and May Calendar Collector activities "Measuring and Plotting Plant Growth" and "Measuring and Plotting Student Heights."

Supporting standard 2.MD.10 is connected to 2.OA.1 in the instructional materials. Although these connections are seen in the materials, the graphs do not always use a single-unit scale as prescribed by this standard; instead many of the graphs are scaled beyond a single unit. For example, in Unit 3 Module 4, Session 3 a bar graph, not single-unit scale, is used to solve word problems involving addition and subtraction. Also, in the Number Corner December Calendar Collector "Student Surveys," students work with surveys and make pictographs and bar graphs and solve simple put together/take apart word problems.

The instructional materials reviewed for Grade 2 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 were 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, 1 interview and 1 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 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.

The instructional materials reviewed for Grade 2 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:

• Unit 1, "Figure the Facts," is shaped by 2.OA.B.
• Unit 2, Module 1, Session 5 “Base Ten Riddles” connects 2.NBT.1 and 2.NBT.3 (standards within the 2.NBT.A cluster heading) by having students demonstrate an understanding of a 3-digit number and then write those numbers.
• Unit 2, Module 3, "Adding on the Open Number Line," is shaped by 2.MD.6.
• The Unit 5, Module 1 session learning objective "Use strategies based on place value, properties of operations or the relationship between addition and subtraction to add with sums to 1,000 and subtract with minuends to 1,000" is shaped by to 2.NBT.B.
• Unit 6, Module 1, "Attributes of Two-Dimensional Shapes" is shaped by 2.G cluster heading, "Reason with shapes and their attributes."

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

• In Unit 1, Module 4, Session 1 students use bead strings to count by 5's connecting 2.OA to 2.NBT.
• Unit 1, Module 4, Session 2 makes a connection between three clusters, 2.MD, 2.NBT and 2.OA. Students use the number line to count by 5's and solve word problems.
• Unit 2, Module 1, Session 3 “How Many More? How Many Fewer?” connects 2.OA with 2.NBT by having students solving word problems and demonstrate their understanding that 100 can be thought of as a bundle of 10 tens.
• Unit 2, Module 2 "Measuring Jack's Giant Beans with Tens" connects with 2.NBT and 2.MD.
• Activities in Unit 5, Module 2 connect 2.MD with 2.NBT when working with money organized into 10-frames to make connection with place value.
• Activities in Unit 5, Module 3 connect 2.MD measurement with 2.NBT, understanding place value and using place value understanding to add when measuring with paper clips.