8th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 71% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 4 / 8 |
The instructional materials reviewed for Grade 8 Big Ideas partially meet the expectations for Gateway One. Future grade-level standards are rarely assessed and could be easily modified or omitted. The materials devote a majority of the time to the major work of the grade. The instructional materials infrequently connect supporting work with the major work of the grade. Although the materials provide a full program of study that is viable for a school year, students are not always given extensive work with grade-level problems. Connections between grade-levels and domains are missing. Overall, the instructional materials meet the expectations for focusing on the major work of the grade, but the materials are not always consistent and coherent with the standards.
Criterion 1.1: Focus
The materials meet the expectation for not assessing topics before the grade-level in which they should be introduced. The majority of the assessments are on grade-level with a few items that could be easily modified or removed to remain on grade-level.
Indicator 1a
The instructional materials reviewed for Grade 8 meet the expectations for assessing the grade-level content and, if applicable, content from earlier grades. Summative assessments focus on the Grade 8 standards with few occurrences of above grade-level work.
The following assessments were reviewed for this indicator from the print and digital materials: forms A and B of the Chapter Tests, Chapter Quizzes, Standards Assessments, and Alternate Assessments.
The majority of items are within Grade 8, and few above-grade level items were found. There are some items that assess two domains and call for students to explain the meaning behind mathematical concepts and/or reasoning behind their solutions.
- On all Chapter 3 assessments, students are required to explain angle relationships and why triangles are or are not similar. This meets the depth of standards 8.G.5 and 8.EE.5. Similarly, in Chapter 4, several questions have students work with slope and y-intercepts (8.EE.5 and 8.F.4). For example, on the Chapter 4 Alternative Assessment, students must calculate slope, write an equation, explain the meaning of the slope, and use the equation to solve related real-world problems. Similar questions are included on forms A and B.
- On form A (items 25 and 26) and B (items 24 and 25) of the Chapter 7 test, students are required to find the distance between two points. These questions do not prompt students to use the Pythagorean theorem nor are they provided a graph. In Grade 8, students are expected to use the Pythagorean theorem to find distance (8.G.8). In lesson 7.5, examples 2 and 3, the procedure for using the distance formula is explicitly taught after directed exploration found in Activity 3 on page 319.
- On the Chapter 7 Standards Based Assessment, students must identify and use the Pythagorean theorem, and they are asked to find a missing hypotenuse on three different triangles in a composite figure (8.G.7). They must also “show [their] work clearly” and explain how they can identify any irrational numbers (8.NS.A).
- On the alternative assessment in Chapter 7, students must use the Pythagorean theorem to find the missing sides of the given right triangles, and they also identify if the two are similar. In 8.G.4, students are expected to find similarity through transformations and dilations, not by finding proportionality in corresponding sides as noted in the answers on page A13.
It should also be noted that there are items on the Chapter 9 assessments, problems 35-36, and end-of-course tests that do not have connections to any Grade 8 standard (e.g., choosing proper display, explain why the data is misleading).
Criterion 1.2: Coherence
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.
The Grade 8 Big Ideas materials meet expectations for devoting the large majority of class time to the major work of the grade-level. The materials engage students in the major work of the grade more than 65 percent of the time.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Grade 8 meet the expectations for focus on major clusters. The Grade 8 instructional materials do spend the majority of class time on the major clusters of the grade.
The Common Core State Standards to Book Correlation (pages xx-xxvi) and the Book to Common Core State Standards Correlation (page xxvii) were used to identify major work, as well as the first page in each chapter which includes common core progression information, a chapter summary, and a pacing guide (and related online pages). The pacing guide provides the number of days to spend on each chapter opener, activity, lesson, any extensions, and review/assessment days. This guide was used to determine the number of instructional days allotted by the publisher for each standard found in the major work of the grade. Reviewers also examined all lessons with standards identified by the publisher as non-major work to ensure that these lessons did not contain enough material to strengthen major work.
All percentages are greater than 65 percent and were calculated to reflect the chapters, lessons, and instructional time spent on major work:
- The material devoted approximately 80 percent of chapters to major work of the grade. Chapters 8 and 9 were excluded because they only address supporting standards. If over 50 percent of a chapter addressed major work, then the chapter was counted as major work.
- Of the lessons, 86 percent (44 out of 51) were dedicated to major work. One lesson, 7.4, identified as major work did not reach the depth of the standard and was not counted as major work. Lesson 7.4, Approximating Cube Roots, is aligned to 8.EE.2, but students are not required to use square and cube roots to represent solutions to equations.
- Of the instructional days, 85 percent (125 out of 148 ) in the Grade 8 materials are spent focusing on the major clusters of Grade 8. Days were counted based on the recommendation of the pacing guide in the beginning of each chapter for all lessons reviewers found aligned to major work.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 8 do not meet the expectations for coherence. The instructional materials infrequently use supporting content as a way to continue working with the major work of the grade. The materials include a full program of study that is viable content for a school year. Content from prior grades is not clearly identified or connected to grade-level work, and not all students are given extensive work with grade-level problems. Material related to prior, grade-level content is not clearly identified or related to grade-level work. These instructional materials are not shaped by the cluster headings in the standards. Overall, the Grade 8 materials do not support coherence and are not 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.
The instructional materials reviewed for Grade 8 partially meet the expectations for having supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The structure of the chapters and the lessons in the Grade 8 materials do not fully engage students in both supporting and major work to allow natural connections.
Supporting work is identified in Chapters 7, 8, and 9 and shows some connection to major work.
Connections to major work are only identified in Chapter 7 as students move from finding square and cube roots (8.EE.2) in lessons 1 and 2 to using the Pythagorean theorem to find the missing sides of right triangles (8.G.7) in lesson 3, and finally, working with irrational numbers in order to categorize real numbers (8.NS.2) in lesson 4. While an attempt was made to connect these standards by sequencing them in one chapter, they are isolated and addressed in different lessons with one activity and three items found to connect them.
- In Approximating Square Roots, Activity 2 on page 308, students must use the Pythagorean theorem to find the diagonal of a square situated on a number line between 0 and 1 and then estimate the length of the diagonal using the number line in the graphic. Lesson 7.4 has students estimate square roots, compare real numbers, and approximate the value of expressions.
- Items 37-39 in Lesson 7.4 connect 8.G.7 to 8.NS.2 by having students approximate the length of a diagonal of a square or rectangle.
- An opportunity to have students connect approximating square roots and the Pythagorean theorem is missed in Lesson 7.5 when students are not required to estimate an answer while engaging in the practice and problem solving set, and all solutions are expressed in radical form. This connection could be noted in the margin of Laurie’s Notes on page 318 under Previous Learning, and explicit direction requiring students to find approximations could be included in the exercises to strengthen major work.
Connections between 8.G.C and 8.EE.A are found in Chapter 8, Volume and Surface Area of Similar Solids, due to the formulas containing both rational and irrational numbers as well as exponents. 8.EE.2 could be mentioned in the Previous Learning section found in the margin of Laurie’s Notes in each of the following lessons:
- Lessons 8.1, 8.2 and 8.3 are aligned to 8.G.9 and 8.EE.7 where examples use equations to solve problems involving volume.
- In Lesson 8.4, 8.G.9 has connections to 8.G.4 when students use the volumes and surface areas of similar solids to develop understanding of the related formula. While this particular connection is explored in the lesson, this concept regarding three dimensional figures is not addressed until the high school Geometry standards.
- Also, 8.EE.2 is found in Chapters 7 and 8, but then it is isolated from Chapter 10 where the major work with exponents occurs.
Unidentified connections were also found in Chapter 9 in Lesson 2 in which students draw lines of best fit to model a set of data and then use the slope and y-intercept to make predictions about future events. Laurie’s Notes does mention that students “should know how to make scatter plots and write equations in slope-intercept form,” but 8.EE.6 is not explicitly identified.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials reviewed meet the expectation for having an amount of content designated for one grade level that is viable for one school year in order to foster coherence between grade levels. Overall, the instructional materials reviewed for Grade 8 provide a year’s worth of content as written.
In Big Ideas, the length of each class period is 45 minutes, so 149 45-minute class periods would be needed to cover Chapters 1-10. The 149 days of instruction are outlined in the pacing guide on pages xxxii and xxxiii. This pacing includes one day for a scavenger hunt, one day in each chapter for study help and review before the mid-chapter quizzes, and two days for review and assessment at the end of each chapter. In total, ten days are devoted to Study Help/Quizzes and 20 instructional days spent on chapter review assignments and chapter assessments, which leaves 119 days for instructional lessons, activities, and extension lessons. Before each chapter, information is provided for the teacher on how much time to spend on each section including activities, lessons, and any extensions.
The following extension activity found in Chapter 7 is of particular importance and should not be skipped, as this is the place in the material where 8.NS.1 is fully addressed.
- Chapter 7, Extension 7.4 - Writing a repeating decimal in rational form (8.NS.1).
The online lesson plans provided in Chapters at a Glance also include detailed information about when to use the supplemental activities such as extra examples as well as performance tasks for each standard. Any additional days of instruction can be spent implementing these tasks or the additional skills practice found in the online resources.
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.
The instructional materials reviewed for Grade 8 do not meet the expectation for having materials that are consistent with the progressions in the Standards. Materials are not intentionally written to follow the progressions of the grade-level as few lessons are identified as work from prior grade-levels, and there are no lessons identified to connect Grade 8 work to the work of future grades. Materials do not give all students extensive work with grade-level problems although general explanations for how lessons are related to prior knowledge are present.
The materials do not develop according to the grade-by-grade progressions in the standards. Content from prior or future grades is not clearly identified and related to grade-level work.
- Explanations of Common Core Progressions are given at the beginning of each chapter connecting both Grade 6 and Grade 7 work to the Grade 8 work students will encounter in each of the chapters. These connections to below grade-level work are presented as bulleted lists of skills and are not aligned to specific standards.
- Math Background Notes include vocabulary review as well as a general explanation of the most important skills and understandings from the prior grade-level(s) found in the “What You Learned Before” activities on the following page. For the most part, these are procedural in nature and do not add connections or meaning to the mathematics which occurred in prior grade-levels. For example, in Chapter 5, the notes instruct teachers to remind students to use inverse operations to isolate a variable, but there is no mention of the underlying properties of equality that make this possible. Other examples include:
- Chapter 7: Order of operations review cites the “Please Excuse My Dear Aunt Sally” pneumonic before engaging in evaluating expressions with square and cube roots (page T-287).
- Chapter 10: The steps to multiplying decimals are reviewed, and teachers are encouraged to “remind students to count the number of digits in both factors that appear to the right of the decimal point, and then put that many digits to the right of the decimal point in the answer” instead of using estimation or place value, which would further develop the structure of numbers for struggling learners.
- The first page of each chapter is What You Learned Before. The teacher page adjacent to this page identifies the CCSS addressed, which is usually from a previous grade-level, but no explanation of what connects this previous material to the upcoming lessons is included.
- Chapter 1, Section 1 serves as review lesson as students solve one-step equations with rational numbers, but this section is marked as “Learning” 8.EE.7a and 8.EE.7b instead of 6.EE.5 and 7.EE.3.
- Content of future progressions beyond the current grade-level are not identified in the material nor are these lessons accompanied by an explanation of the progressions.
- Students find the distance between two points on the coordinate plane using the distance formula in Chapter 7, but the material does not identify this lesson as high school content.
The materials do not give all students extensive work with grade-level problems. The majority of the problems in the exercises require students to produce an answer or solution. There are open ended, reasoning, and critical thinking items which allow students to engage in grade-level work that meets the depth of the standard in most cases. These opportunities to engage in extensive grade-level problems are provided for all students only if they are given the opportunity to access all of them.
- An assignment guide is provided in each lesson that levels students into basic, average, or advanced. These charts exclude the “basic” learner from the reasoning and critical thinking problems. These problems are critical for all students in order for them to reach the depth of the standard in many of the lessons.
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- For example, in section 4.5, basic learners are excluded from item 23, a critical thinking problem which asks students to reason about the values in the equation in context. Item 22, which requires students to make generalizations about the the graphic representation of all linear equations, is not listed as an opportunity for average or basic learners (8.EE.8).
- Many lessons contain explanations in Laurie’s Notes of a specific homework problem and how Taking Math Deeper can apply to that problem. Usually it is a simple task that can reach the depth of a standard; however, it is rarely part of the Basic Assignment. If students are assigned Basic or Average Level Assignments, they will often not engage with the problems reaching the full depth of the standard.
The materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades.
- Each chapter begins with a What You Learned Before page just before the first lesson. These pages contain problems for students from prior grade-levels and/or chapters found earlier in the material. Connections to specific grade-levels or standards are not identified.
- Laurie’s Notes are found in each lesson. In the margin of these notes for instruction, specific Grade 8 standards that will be addressed are identified. Most of them contain a Previous Learning section that describes prior knowledge students should possess before engaging in the lesson, but again they are not explicit about the particular grade-level or standard tied to the skills or understanding needed. For example, in section 2.6 the Previous Learning states, “Students should know how to plot ordered pairs. Students also need to remember how to solve a proportion.” Neither the specific CCSS standards nor the grade-level is stated.
Overall, explicit connections to prior knowledge are made at a very general level through the chapter and lesson features in this series. Connections are not clearly articulated for teachers and are merely lists of skills without indication of standards, clusters, or domains. There is not a clearly defined progression for teachers to demonstrate how prior knowledge is being extended or developed.
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.
The instructional materials reviewed for Grade 8 partially meet the expectation for fostering coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials do not include learning objectives that are visibly shaped by CCSSM cluster headings, but there are some opportunities to connect clusters and domains.
Examples of the materials not including learning objectives that are visibly shaped by CCSSM cluster headings include:
- Cluster headings were explicitly addressed in the textbook on page xxxv. There is no explanation as to how the lessons are tied together under the cluster heading besides the information found on this page. The language used in the cluster heading was not found.
- Chapter and lesson titles are connected to, but do not appear to be influenced by, cluster headings. They are often descriptive of specific skills or topics but not the overarching idea of the cluster heading. For example, the “Expressions and Equations” domain has the following headings, which are connected to the these chapter titles:
- “Work with radicals and integer exponents” is connected to Chapter 1, “Equations.”
- “Understand the connections between proportional relationships, lines, and linear equations” is connected to Chapter 4, “Graphing and Writing Linear Equations.”
- “Analyze and solve linear equations and pairs of simultaneous equations” is connected to Chapter 5, “Systems of Linear Equations.”
- The lesson goal appears in Laurie’s Notes before the lessons in each section and most closely aligns to an objective. These are descriptions of the parts of the standard that are tackled in the lesson and were not found to describe cluster headings.
- For example, “Today’s lesson is graphing linear equations” is found in section 4.1 and “Today’s lesson is graphing proportional relationships” is found in section 4.3, but neither is shaped by the full meaning of 8.EE.B, which calls for students to understand the connections between proportional relationships, lines, and linear equations.
Examples of the materials providing some opportunities of 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 include the following, but these are not identified for the teacher except in the Chapter 6 example below.
- In Chapter 6, 8.G.A and 8.F.B are connected in the Activity for Lesson 6.4 when students use the perimeters and areas of similar rectangles (8.G.4) to compare linear and nonlinear functions (8.F.3).
- In Chapter 9, 8.SP.A and 8.EE.C are connected in Lesson 9.2 when students draw lines of best fit using slope intercept form to investigate patterns of association in bivariate data.
- The performance tasks could make connections between cluster headings. These tasks present open ended problems with varying ways to represent solutions, but they address one standard at a time with the exception of performance task 8.G.6. Natural connections between 8.G.6 and 8.EE.A occur in this task as students grapple with making connections between the area of the trapezoid and the areas of the embedded right triangles using equivalent expressions and the Pythagorean theorem.
Chapter 7 is the place where the material identifies multiple domains in the same chapter, but the standards are addressed in isolated lessons with few connections across chapters.
Chapter 7 is aligned to the number system, expressions and equations, and geometry domains on page xxxv. An explanation for why these domains were connected was not found in the material. An explanation could be provided in Laurie’s Notes in the “Connect” section where teachers are given a one sentence summary of “yesterday’s learning” and “today’s learning.” It appears in 7.1 and 7.2 when students work with exponents (8.NS) and roots (8.NS), but not in 7.3, which would connect square roots (8.NS) with the Pythagorean Theorem (8.G).