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Report Overview
Summary of Alignment & Usability: SpringBoard Middle | Math
Math 6-8
The instructional materials reviewed for Grade 6-8 vary in alignment scoring. Grades 6 and 7 do not spend a majority of time on the major work of the grade level. Each of these grades devotes less than 50% of the time to major work. There are some examples of coherence within these grades and some examples of coursework following the progressions of learning throughout the grade levels. In Grade 8, the materials are found to be focused on the major work of the grade level, and they partially meet the criterion for being coherent and consistent with the standards. This grade was reviewed for rigor and MPs. Procedural skills and fluency are found to be strong, but Grade 8 materials support of conceptual understanding and application opportunities are lacking. Grade 8 materials incorporate vocabulary in a meaningful way, but MP 3 is not fully attended to for the teacher nor for the students.
6th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
7th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
8th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 8th Grade
Alignment Summary
The instructional materials reviewed for Grade 8 do not meet the expectations for alignment to the CCSSM. The instructional materials partially meet the expectations for gateway 1 because they meet the expectations for focus on major work and partially meet the expectations for coherence. Since the materials partially meet the expectations for gateway 1, evidence was collected in gateway 2. The instructional materials partially meet the expectations for rigor and balance and do not meet the expectations for practice-content connections. Since the materials partially meet the expectations for gateway 1 and do not meet the expectations for gateway 2, they do not meet the expectations for alignment to the CCSSM.
8th Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The instructional materials reviewed for Course 3 partially meet the expectation for focus and coherence in the CCSSM. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade with 71.4% of the days allocated in the timeline aligning to the major work. For coherence, supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is viable for one school year and will foster coherence between the grades. However, content from prior or future grades is not clearly identified and materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades. The material does lack some consistency for grade-to-grade progressions, and content that is not on grade level, or supports on grade level learning, is not explicit.
Gateway 1
v1.0
Criterion 1.1: Focus
The instructional materials reviewed for Course 3 meet the expectations for focus within the grade. The materials reviewed for Course 3 do assess some above grade-level topics, but if the future grade content was removed, it would not change the underlying structure of the assessments. The instructional materials also meet the expectations for focus within major clusters. Seventy-one percent (71.4%) of the days are suggested for major work of the grade. In addition, there is some support from content in the non-major clusters that directly reinforce the major work. Overall, the instructional materials meet the criteria for grade level assessment as well as spending the majority of time in the major clusters of the grade.
Indicator 1A
The Assessments that are included in the web version of Springboard were reviewed for Course 3 and found to meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades is sometimes introduced, but students should not be held accountable on assessments for those future expectations. If the future grade content was removed, it would not change the underlying structure of the assessments. Overall, the instructional material in the summative assessment items reviewed in Course 3 addressed the major areas of focus for this grade level in a challenging and effective manner with most Units having little or no above grade level standards addressed.
Quality, on grade-level examples are:
- Unit 1, question #8- Asking students to demonstrate their knowledge of 8.EE.A.4 by subtracting numbers in scientific notation and then converting the answer to standard form.
- Unit 4, question- #6. Asking students to demonstrate their knowledge of 8.F.B.4 by creating a function from the given information in the real world problem.
- Unit 4, question- #18. Asking students to demonstrate their knowledge of 8.F.B.5 by analyzing and then describing a graph.
Areas of improvement are:
- Unit 4, Answer key is incorrect on questions 2, 14, and 18.
- Unit 6, This unit address MP standards that do not work on 8th grade content standards. Many questions are aligned to high school compound interest questions.
Criterion 1.2: Coherence
The instructional materials reviewed for Course 3 meet the expectations for focus within the grade. The materials reviewed for Course 3 do assess some above grade-level topics, but if the future grade content was removed, it would not change the underlying structure of the assessments. The instructional materials also meet the expectations for focus within major clusters. Seventy-one percent (71.4%) of the days are suggested for major work of the grade. In addition, there is some support from content in the non-major clusters that directly reinforce the major work. Overall, the instructional materials meet the criteria for grade level assessment as well as spending the majority of time in the major clusters of the grade.
Indicator 1B
The Teacher Edition and Consumable Student Edition reviewed for Course 3 meet the expectations for spending the majority of class time on the major cluster of each grade. To determine this we evaluated three perspectives: 1) the number of ACTIVITIES devoted to major work, 2) the number of LESSONS devoted to major work, and 3) the number of DAYS devoted to major work. The number of DAYS devoted to major work is the most reflective for this indicator because it specifically addresses the amount of class time spent on concepts and our conclusion was drawn through this data.
We determined our evidence from the Contents Page, pgs. v - ix and the number of days suggested in "Planning the Unit" found in the the Teacher Edition and written by the publisher.
- Activities – 27 out of 36 activities which is 75% percent of time spent on major work
- Lessons – 62 out of 84 lessons which is 73.8% percent of time spent on major work
- Days – 100 out of 140 days which is 71.4% percent of time spent on major work
Including Embedded Assessment Days:
- Unit 1: 30 days, not all days on major work (15 days on Major Work)
- Unit 2: 28 days, all days on major work
- Unit 3: 43 days, All but Activity 26 (4 days) and one embedded test day (1 day) on major work
- Unit 4: 19 days all on major work
- Unit 5: 16 days, none on major work, of the grade level
- Unit 6: 4 days, none on major work, of the grade level
This allows for 100 days out of 140 which is 71.4% to be spent on major work of 8th grade.
Excluding Embedded Assessment Days:
- 8.EE.A,B,C has 36 instructional days out of 116 total days (31%)
- 8.F.A,B has 16 instructional days out of 116 total days (14%)
- 8.G.A,B, has 31 instructional days out of 116 total days (27%)
This allows for 83 days out of 123 which is 67.5% to be spent on major work of 8th grade.
Areas that need clarification are:
- Unit 1 - Activities 1 and 2 (6 periods) are spent on reviewing. There are no standards indicated for the lessons.
- Unit 2 - Activity 9 goes into geometric sequences allowing students to recognize models and patterns to support the work in 8.EE. There are no standards indicated for the lessons in this activity.
- Unit 3 - Activity 25 is focused on surface area of prisms and cylinders which is standard 7.G but is not indicated. There is only one problem in this activity of two lessons using the Pythagorean Theorem that matches with the standard indicated (page 332 problem 11)
- Unit 6 - There are no standards indicated for the activities in this unit. This is a Financial Literacy Unit that is continued from grades 6 through 8.
Criterion 1.3: Coherence
The instructional materials reviewed for Course 3 partially meet the expectations for being coherent and consistent with the standards. Supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is viable for one school year and will foster coherence between the grades. However, content from prior or future grades is not clearly identified, and materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades. The material does lack some consistency for grade-to-grade progressions, and content that is not on grade level, or supports on grade level learning, is not explicit.
Indicator 1C
The instructional materials reviewed for Course 3 partially meet expectations that supporting content enhances focus and coherence by engaging student in the major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not.
Examples where connections between supporting content and major work are present but are not well explored include the following:
Non-Major Cluster 8.NS.A- Know that there are numbers that are not rational, and approximate them by rational numbers.
- Unit 1- Activity 3, pgs. 33-44 support 8.EE through having students create and solve expressions and equations based on Powers and Roots.
Non-Major Cluster 8.SP.A- Investigate patterns of association in bivariate data.
- Unit 5- Activity 33-2, pages 459-460 support 8.EE through the use of Trend Lines.
Examples where connections are missed or not explicitly stated:
- Unit 2- Activity 10, pages 119-130 is an activity aligning with 7.EE but is not identified as such. This supports the 8th grade major work in 8.EE.
- Unit 5- None of the work in this unit that contains the 8.SP.A standards support any major standards in eighth grade.
Indicator 1D
The instructional materials reviewed for Course 3 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The Teacher’s Guide offers a 'Planning the Unit' section for each of the 6 Units and the pacing provided by the publisher is reasonable for lessons to be completed in the time suggested.
With embedded assessment days not included there are approximately 123 days of lessons in the materials. This team believes that the amount of those days on major work of the 8th grade will ensure a student'sgrasp of all major work at this grade level and will foster coherence between the grades. Overall, the amount of days that are designated as "lesson days" for this grade level is short of the amount of material needed to make it truly viable for one school year, this team believes that when the Embedded assessments and Summative End of Unit tests are included, this material meets expectations.
- According to the pacing guide, each period is 45 minutes in length and there is a suggested 123 days of lessons.
- When Embedded assessments are also included in the pacing guide and if all are given during the course of the year the total would be 140 days.
- Also, if a summative end of the unit test is included and one day per unit is added, this would bring the total to 146 days.
The guiding focus taken for this indicator for our team was, "Will this material be enough to prepare a student for the next grade level?" With the amount of days and those days that are focusing on major work, it will prepare the student for the next grade level and supports this indicator receiving a 'meets' rating.
Indicator 1E
The Teacher Edition, Consumable Student Edition, and Summative end of Unit Assessments reviewed for Course 3 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from lower/above grade standards is not clearly identified, and a teacher will have to spend much time unpacking the Activities to identify the non-grade level material. Also, materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades within each lesson. Connections are not explicitly made to content in future grades. However, in general, the progression of standards are followed throughout this course.
Some examples of areas where identification of standards from lower/upper grades would be beneficial are:
- Unit I, Activity 1 Investigating Patterns uses sequences to describe patterns. The work from this activity aligns to F.IF.A.3, which is a high school standard. One could argue that this activity addresses linear relationships, but since the book does not adequately describe this in the teachers edition, it just appears to be off grade level.
- Unit I, Activity 2 Operations with Fractions adds to work from 5th grade. As with the other books from the series, it does not list the standards addressed and how it relates to grade level work. The majority of the practice problems were procedural in nature and did not address any extensions to challenge students.
- Unit 3 Activity 25 works with surface area and volume. (7.G.B.6) The book does not discuss the relationship of the work completed in this activity and the prior and future activities of the unit. Some of the work in this unit is prior or supporting work and could claim that is was necessary to support the overall unit, however without them being specifically mentioned, it appears to just be off grade level.
The instructional materials reviewed for Course 3 partially meets the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.
For each activity, there are 0 to 6 standards attached and there are at least 1 to 4 lessons based on that activity to extend and develop the understanding of the standards included in the activity. For struggling learners or those that need enrichment, the book does provide pointers interspersed throughout the units with ideas on how to differentiate or teach the topic in a different way.
Examples of this are:
- Unit 3, Activity 16- page 211, has general pointers for differentiating instruction to assist the teacher with teaching the concept.
- Unit 4, Activity 28- page 380, has ELL Support and Teacher to Teacher suggestions on how to assist and present the work needed for this activity.
Examples that are not at the depth of knowledge needed to prepare a student for the next grade are:
- The summative assessments reviewed for this course were limited in nature, containing multiple-choice responses and no significant performance tasks found.
- Unit 1, Activity 3, Lesson 3-3 on Exponents, Roots, and Order of Operations is an example of low depth of knowledge and procedural in nature lesson.
- Unit 1, Activity 6, Lesson 6-2 on Negative Exponents is also very procedural and not at the level needed to prepare a student for the next grade level.
Examples of lessons that do give a student extensive work at the grade level and are real world application problems covering the major work of the grade are:
- Unit 4, Activity 31, Lesson 31-1 on Linear and Non-Linear Functions has the student often justifying their answers and working with real-world problems.
- Unit 5, Activity 33, Lesson 33-3 on Scatter Plots and Trend Lines has students working with prior knowledge of creating equations, justifying answers with that prior knowledge and on grade level work and making predictions that are all beneficial in preparing a student for the upcoming grades.
The instructional materials reviewed for Course 3 partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials only generally relate grade-level concepts explicitly to prior knowledge from earlier grades and most often only make connections within grade level standards.
Most units, in the Teacher's Edition, begin with an "Activity Standards Focus" section that will explain the connections between the previous Activity and the current one or a previous grades learning and the new learning. This is rather a general overview and is never specific as to where the connections are actually happening and between which grades.
Example of the general overview:
- Unit 2, Activity 9- page 105 begins with the "Activity Standards Focus" saying- "Unit 2 focuses on linear equations. Activity 9 introduces some of the ideas that will be needed when analyzing equations by first looking at those ideas in the context of patterns. Before they see algebraic equations, students will be introduced to algebraic expressions as they use them to identify and represent patterns. They will write and evaluate algebraic expressions that represent patterns-some with constant differences and some without."
- Unit 3, Activity 22, page 297 begins with "In this activity, students investigate one of the most important theorems in mathematics, the Pythagorean Theorem. Students explore a proof of the theorem and then use the theorem to find unknown side lengths in right triangles. Note that additional applications of the theorem are covered in Activity 23, and students explore the converse of the theorem in Activity 24."
Indicator 1F
The instructional materials reviewed for Course 3 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.
The Unit titles are clearly labeled and aligned to the standards without a need for much interpretation.
- Unit 1 - Numerical Relationships (8.NS)
- Unit 2 - Equations (8.EE)
- Unit 3 - Geometry (8.G)
- Unit 4 - Functions (8.F)
- Unit 5 - Probability & Statistics (8.SP)
The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. They include a few problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. However, overall the materials only partially foster coherence through connections in Course 3.
- For the majority of the work, most standards were taught and covered within one lesson out of the entire series and not aligned with any other concept throughout the year.
Examples of not fully developed connections are:
- Unit 3 on Geometry never brings in the 8.EE.B.6, "Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b" standard which is a missed opportunity to show coherence through connections. Equations and defining slope are addressed in Unit 2, so it would be a natural fit to address this standard in the Geometry unit.
- Unit 2 covering Equations, standard 8.EE.A.2, "Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number" has a natural connection to 8.NS.A, "Know that there are numbers that are not rational, and approximate them by rational numbers." However, there is no connection to these standards in Course 3.
Some examples of where connections were made are:
8.EE.B.5
- This standard is taught in Unit 2, Activity 11.
- It is reviewed frequently through the unit in Activities 12 and 13.
8.G.B.6 and 8.G.B.8
- These standards are taught in Unit 3, Activity 22.
- They are reviewed throughout the remainder of the unit in Activities 23 and 24.
8.F.A.3
- This standard is taught in Unit 4, Activity 29
- It is reviewed in Unit 4, Activity 31.
Overview of Gateway 2
Rigor & Mathematical Practices
The materials reviewed for Course 3 do not meet the expectations for rigor and MPs. The materials reviewed for Course 3 partially meet the criterion of rigor and balance within each grade. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. Students are provided with multiple opportunities to develop procedural skill and fluency throughout the materials. Students work with applications, although at times scaffolded and routine, and use real-world situations and visuals to develop conceptual understanding. Overall, the majority of lessons focus on procedural skills and fluency with fewer opportunities for students to discover and apply procedures themselves.
The materials reviewed for Course 3 do not meet the expectations for practice-content connections. The instructional materials identify all mathematical practices within the course, but the mathematical practices do not always enrich the mathematical content of the grade. Although practice problems are aligned to the mathematical practices, more teacher guidance to develop these mathematical practices would be beneficial. In the instructional materials students are asked to construct viable arguments and analyze the arguments of others, with limited opportunities to engage in both simultaneously. Mathematical language is introduced and reinforced throughout the instructional materials. Overall, the materials do not meet the expectations for rigor and MPs.
Gateway 2
v1.0
Criterion 2.1: Rigor
The materials reviewed for Course 3 partially meet the criterion of rigor and balance within each grade. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. Students are provided with multiple opportunities to develop procedural skill and fluency throughout the materials. Students work with applications, although at times scaffolded and routine, and use real-world situations and visuals to develop conceptual understanding. Overall, the majority of lessons focus on procedural skills and fluency with fewer opportunities for students to discover and apply procedures themselves.
Indicator 2A
The instructional Materials for Course 3 partially meet the expectations to develop conceptual understanding of key mathematical concepts, especially when called for in specific content standards or cluster headings. Overall the instructional materials present real-world situations and multiple visual examples as a way to develop conceptual understanding, however, the materials lack a fully developed conceptual understanding in some areas that are called for in the common core standards.
- In general, the activities were procedural in nature and did not enhance the student's ability to form a conceptual understanding of major work within the grade. There is a lack of concrete and/or visual representations when developing conceptual understanding and more of a reliance on algorithmic understanding. Students have ample opportunities for independent practice but it is not specifically indicated in the textbook if problems would be best completed within a group to encourage discussion and the ability to have to justify one’s answers. Looking at standards 8.EE.B, 8.F.A and 8.G.A, there are minimal opportunities for hands-on activities.
Each Unit contains activities and then each activity contains lessons. Within these there are essential questions at the beginning of every unit that a teacher could continue to refer back to in order to assist in developing conceptual understanding, and there is a "Teach" section on the wrap around teacher addition that has question numbers and is labeled 'Use Manipulatives, Visualization, Predict and Confirm, Think-Pair-Share, Look for a Pattern, Discussion Groups'. However, there ar no specific questions or statements that will guide a teacher towards building conceptual understanding in these sections and those suggestions are never fully developed or explained.
Examples where the material specifically relate to conceptual understanding and meet the requirements asked for in the Evidence Collection to support a partial rating include:
- 8.EE.B is taught in Unit 2, specifically activities 11-13 and is about understanding connections between proportional relationships, lines, and linear equations. .
- Activity 11 builds on the concept of slope as the rate of change by creating tables, writing linear equations and plotting a linear graph. Also, by graphing proportional relationships, the slope and y-intercept are determined.
- Continued development and practice can be found in Activities 12 and 13.
- However, activity 11, page 136 problem 12 is the only opportunity for students to use similar triangles to explain why the slope is the same between any two distinct points.
- 8.F.A is taught in Unit 4, specifically activities 27-29 and is the introduction to functions.
- Activity 27
- Students are given a specific way, written in steps, to write ordered pairs
- Problem 14 on page 261 asks students to justify their work which requires a higher depth of knowledge.
- There are many problems that require the students to explain their thinking which can lead to having to defend their answers.
- Activity 28
- In this activity, there is a matching portion that can easily be completed in a group setting. This activity would really help students to understand tables, functions, and graphs because they have to match the three.
- Activity 27
- 8.G.A is taught in Unit 3 and focuses on angles, transformations, reflections, rotations, and similar figures
- There is ample practice with angles interspersed throughout the unit
- This unit provides many opportunities to justify their argument/answer.
Indicator 2B
The Instructional Materials for Course 3 meet the expectations to give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Overall, there are multiple opportunities for students to develop procedural skills and fluency which include various questioning strategies for students to explain procedural skills, and chances for students to apply procedural skills to new situations. Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency meeting the expectations for this indicator.
- Based on where the lesson is in the time line of the unit, the level of rigor varies. As expected, it starts off with a low level of rigor and as the students gain more practice, the rigor increases as the unit progresses.
- Activity 10 provides two lessons with a total of 34 problems and 22 practice problems to work toward fluency of solving linear equations in one variable. (8.EE.7)
- Activity 14, pgs. 177-188 addresses the fluency of solving systems of equations through inspection. Questions 3 and 4 on pg. 184 are quality examples of practice needed by students to obtain this fluency.
- Activity 26 provides three lessons with a total of 31 problems and 24 practice problems to work toward fluency of solving real-world & mathematical problems involving volume of cylinders, cones, and spheres. (8.G.9)
- Activity 25 provides two lessons that are below grade level standards (7.G) that support the development of conceptual understanding of problems relating to volume. The two lessons provide 27 problems and 19 practice problems to work toward fluency.
8.EE.C.8b, 8.EE.C.7 and 8.G.C.9 are standards that students will benefit in becoming fluent in and materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
Indicator 2C
The instructional materials for Course 3 partially meet the expectation 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. Overall, the materials have multiple opportunities for application, but in many of the application-based activity problems, the activities are scaffolded in a manner that leads students to the desired outcome and contexts are often very similar, with few of them being non-routine.
- Materials for the major work of the grade did not adequately address the application portion of rigor. Many of the practice problems were procedural in nature and were not designed so that teachers and students spend time working with engaging applications, and did not require students to access their prior knowledge and think critically about the mathematics.
- Many activities have real-world application type problems included in them. However, most of these end up layered in a manner that the student is following given steps to lead them to the outcome wanted.
Examples where the material does not fully develop the student in engaging application of the mathematics include:
- 8.F.B - activity 11, lesson 11-1, page 13. The launching activity was layered in a way that significantly reduces the rigor of the problem. Application problems should be written in a manner that encourages multiple approaches. These multiple approaches will encourage students to think critically.
- 8.EE.C.8.C - activity 15, lesson 15-2, page 194. The subsequent activities do not lend to what one would consider being an application of mathematical concepts. The practice problems for this lesson were at a basic level and do not enhance the critical thinking skills of students. An application problem should encourage students to view the situation from multiple access points and students should be able to solve it using various methods.
Indicator 2D
The instructional materials reviewed for Course 3 partially meet the expectation that the materials balance all three aspects of rigor with the three aspects not always combined together nor are they always separate. Overall, the majority of the lessons focus on procedural skills and fluency with very few opportunities for students to discover and apply procedures for themselves.
The three aspects of rigor are not always treated together and are not always treated separately, meeting the expectations for this indicator. However, there is not a balance of the three aspects of rigor within the grade.
- All three aspects of rigor are present in the program material, but there is some under-emphasis on the conceptual understanding and application parts. Each leg of rigor was not adequately addressed in these materials because conceptual understanding was not enhanced during the early parts of each unit, many of the activities were procedural in nature and the application leg of rigor did not adequately challenge the students nor did it contain situations that encourage students to think critically about the mathematics.
- There isn't enough opportunities for students to make their own connections. Occasionally, they will ask students to make a reflection, but a majority of the lessons require memorized tasks and procedures without meaningful connections. There are several missed opportunities to challenge students to explore their own strategies and create opportunities for multiple solution pathways.
- The materials provide mostly procedural skills and this is the strongest aspect of the indicator. The application type problems are scaffolded in such a way to be more procedural in nature, however their use of real world helps with the balance between procedural skill and application.
- There is very little opportunity for the students to dig deep into the standards with application problems and the lack of opportunity for students to engage in applications and deep problem-solving with these real world situations was significantly noticeable.
- There were many missed opportunities to build from the fluency/procedural problems to move to having the students apply their knowledge.
Criterion 2.2: Math Practices
The materials reviewed for Course 3 do not meet the expectations for practice-content connections. The instructional materials identify all mathematical practices within the course, but the mathematical practices do not always enrich the mathematical content of the grade. Although practice problems are aligned to the mathematical practices, more teacher guidance to develop these mathematical practices would be beneficial. In the instructional materials students are asked to construct viable arguments and analyze the arguments of others, with limited opportunities to engage in both simultaneously. Mathematical language is introduced and reinforced throughout the instructional materials.
Indicator 2E
The Instructional materials reviewed for Course 3 partially meet the expectation for identifying and using MPs to enrich mathematics content within and throughout each grade. While each practice is represented in this book, they are not often used in a way that would promote or enrich the mathematics content and are over identified in most of the units.
- All 8 MPs are evident throughout the materials, however, it was confusing when in some of the problems the MPs are bolded but there is no evident reason why they are bolded and others are not.
- The MPs could be used to enrich the mathematical content, however, there is no guide in the teachers edition as to how to use the problems to enrich the MPs.
- The only guidance that is given to teachers is found on page xii, with a paragraph discussing the integration of the practices.
- The MPs used are only found in the student text and are embedded within the questions asked in each lesson.
- As a whole, the MPs were identified the least in unit 5 with only being addressed 32 times. They were identified the most in unit 4 with being addressed 79 times.
- The summative assessments do test the MPs specifically and most often with above grade-level standards.
Examples where the material does meet the expectation for identifying and using MPs to enrich mathematics content include:
- Unit 1 - activity 4, page 56, question 7 asks students to "Critique the reasoning of others" and then poses a situation where a student incorrectly determines a calculator display.
- Unit 1 - activity 5, page 65, question 4 asks students to "Reason quantitatively" and asks students how to compare without using rational number approximations.
- Unit 3 - activity 18, page 241, question 1c asks student to "Reason abstractly" and then has students describe in their own words why the origin is the center of rotation for a specific rotation transformation.
Examples where the material does not meet the expectation for identifying and using MPs to enrich mathematics content include:
- Unit 1 - activity 5, page 61, question 4 asks student to "Use appropriate tools strategically" and then tells them to use a calculator to determine the values of the square roots, rounding to the nearest tenth.
- Unit 2 - activity 11, page 139, question 24 asks student to "Attend to precision" and then has students calculate the amount of money a student would earn in 52 weeks.
- Unit 3 - activity 21, page 281, question 3 asks student to "Use appropriate tools strategically" and then tells them to use a ruler to draw a dilated image.
Indicator 2F
The instructional materials reviewed for Course 3 do not meet the expectations for carefully attending to the full meaning of each practice standard. The publisher very rarely addresses the MPs in a meaningful way. The only representation of these standards are as practice problems in the book. The publishers missed multiple opportunities to develop activities that could have brought the MPs to the forefront. Overall, the materials identify only part of the MPs during each question and this does not allow for a teacher to reliably use the materials and know when an MP is being carefully attended to.
Examples where the material does not meet the expectation for the full meaning of the identified MP being attended to include:
- MP 1 in unit 1 - activity 1, lesson 1, page 3. Question 1 appears as a task embedded in the activity and states observe, analyze, and search for clues in the diagram to come up with a guess about why the numbers were first written this way. This is not a question that will allow students to make sense of a problem and persevere in solving it.
- MP 2 in unit 3 - activity 18, lesson 1, page 233. Question 14 appears as a practice question that states to reason abstractly about the three transformations that you most commonly see in the world around you and give examples to support your answer. For this grade level, this is not taking this standard to the level it needs to be for full meaning of the standard.
- MP 3 in unit 1 - activity 1, lesson 1, page 5. Question 6 states that students will construct viable arguments and that is all that is done. The problem only has students creating arguments and they do not need to critique the reasoning of others at the same time. However, if there was guidance on how to develop these standards in the teacher Wrap Around Book, the teacher could pose this problem as group work and students would have to critique others reasoning and defend their own.
- MP 4 in unit 1 - activity 4, lesson 1, page 49. Question 12 appears as a practice problem that states to model with mathematics by describing how you could use paper folding to illustrate a given fraction. This is not a problem that would naturally occur in everyday life, society, or workplace.
- MP 5 in unit 5 - activity 33, lesson 2, page 459. Question 1 is embedded in the activity and states use appropriate tools strategically, then tells the student to place a straightedge like a piece of cardboard or a ruler on the scatter plot in a position that would seem to indicate the general trend of the data and serve as a good, representative linear model. Telling the student the tool to use for the problem does not develop this practice. MP 5 states that a student needs to make sound decisions about which tools and when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.
Indicator 2G
Indicator 2G.i
The materials reviewed for Course 3 partially meet the expectation for appropriately prompting students to construct viable arguments and analyze the arguments of others. Materials occasionally prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. However, there are very few opportunities for students to both construct arguments and analyze the arguments of others together.
- The problems are identified directly with a title of 'Construct Viable Arguments' and 'Analyze the Arguments of Others'.
- There are numerous examples throughout the text addressing this indicator. However, activities could have been embedded to elicit this behavior in a more meaningful way. When one considers MP 4, they think of how students used mathematical discourse with one another, not just looking at scenarios in the text.
- Students are asked to “explain” often, however that frequently falls short of the full meaning of the practice.
Examples of students having to justify, explain, or show their thinking:
- Activity 10, question 18, page 128 – students are asked to explain how equations can have no or many solutions.
- Activity 11, question 11, page 143 – students have to justify their thinking by writing a letter to explain which package Misty should use.
- Activity 12, question 8, page 153 – students have to justify their thinking as to which problem has the greatest rate of change.
- Activity 12, question 15, page 154 – students have to justify their reasoning as to which line is the steepest.
Examples of students having to evaluate someone else’s explanation, work or thinking:
- Activity 3, question 7, page 42 – students have to determine who solved the problem correctly and why.
- Activity 6, question 15, page 74 – students have to determine the mistake that Sebastian made.
Indicator 2G.ii
The materials reviewed for Course 3 do not meet the expectation of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Overall, there is no guidance in the teacher materials to direct teachers on questioning strategies, setting up scenarios where students experiment with mathematics and based on those experiments construct and present ideas, examples of higher level questions and suggested activities that lead students to construct viable arguments and analyze the arguments of others.
The wrap around teachers edition did not specifically address potential teacher moves regarding constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics. The vast majority of the time, the areas that addressed MPs were merely questions added to the practice section of the lessons. Teachers are not given any specific examples on how to address this practice in their daily lessons.
Indicator 2G.iii
The materials reviewed for Course 3 meet the expectation for attending to the specialized language of mathematics. Overall, there are several examples of the mathematical language being introduced and appropriately reinforced throughout the unit.
- There is a Spanish and English Glossary provided at the back of the materials.
- There is a Verbal and Visual Word Association graphic organizer provided in the Resources section of the teacher edition.
- There is a Word Map graphic organizer provided in the Resources section of the teacher edition
- At the beginning of each unit, Academic Vocabulary and Math Terms are identified in the teacher and student editions
- When a new vocabulary term is introduced, a “math terms” box is given with the term blocked out in the right/left margins and italicized in the text.
- The new vocabulary term is then used often throughout the remainder of the unit to reinforce comprehension
- For example, the terms scientific notation and standard form are introduced on page 84 and used extensively throughout the rest of that unit.
- The new vocabulary term is then used often throughout the remainder of the unit to reinforce comprehension
- Teachers are offered assists with the mathematical language through a 'Developing Math Language' section that is periodically offered throughout the units.