Math Materials Review Committee Reports For. Houghton Mifflin. Expressions. SBCUSD For Internal Use Only

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1 Math Materials Review Committee Reports For Houghton Mifflin Expressions SBCUSD For Internal Use Only

2 Kindergarten Houghton Mifflin Expressions

3 Textbook Review Publisher: Houghton Mifflin Harcourt Expressions Grade: Kindergarten Summary Statement: Houghton Mifflin Harcourt Expressions, a Common Core based program, allows the student to use real world experiences to help them relate to their mathematical world. Hands- on activities that foster growth in mathematics as well as in working with individual, small group, and whole group situations allow the students to explore multiple situations within the units provided. Extensive unit reviews for the teacher will give the instructor various ways to teach concepts to the students, help guide instruction, provided RtI levels to differentiate for all students, and challenges for all students to dig deeper into their learning for each unit presented. The student edition provides materials that are interactive and manipulative so the students can perform tasks with the materials they need to learn successfully. content is aligned Vocabulary is tied to the lessons Content/ to the content standards in a activity not always to the math Alignment clear focused manner standard or math concept with the Content Standards Vocabulary is provided to develop student understanding The student edition lacks a clear overview of the chapter Activities and Questions are open ended and varied allowing for conversations to occur There are concrete representations such as diagrams and images to help with student understanding Provides a variety of ways to teach a concept Methods and algorithms are based on principals and not based on tricks Important mathematical concepts, table of contents and indexes are included Glossary is not included in the student edition

4 Content is aligned to standards None noted Content/ Alignment with the Content Standards are worded through the focus of the lesson Standards - Standards for Mathematical Practice Mathematical Practices are labeled and defined for each lesson There is an activity directly related to the MP (correlates very well) Teaching strategies, questions, notes and activities are available to aid teachers in delivering the MPs and having students practice the MPs MPs are in student edition and teacher edition Digital and online materials are Content/ helpful for teaching math Alignment with concepts the Content Standards - Consistent Progressions Extensive unit overviews per unit are provided to teachers that includes direct instruction strategies, UA, center challenges, RtI, etc. Direct Instruction strategy cards are provided, geared to give students deeper directions into concepts. SMPs and standards are posted in both the TE and the SE. SBAC assessments are provided online. Real world applications are indicated throughout the text. The digital/online offerings are difficult to navigate and would take the average teacher extra time to find and utilize information Pacing of lessons is not intuitively sequential. The TE may be intimidating to some. Intensive study of the TE would be needed. There is a great amount of information that is provided per lesson. This will be a challenge.

5 Universal Access/ Differentiation Every lesson provides differentiated activities Most lessons include Puzzle Penguin to encourage students to do error analysis Materials for English learners are available in every lesson EL materials help student scaffold and access the material There are materials for advanced students in each lesson Reteach materials are difficult to find Materials for at risk students are difficult to find It is difficult to find materials for SPED students Assessment Program has multiple assessments available for each unit Summative assessments are available for each chapter The assessments help students move towards mastery of the content standards and SMPs The assessments take multiple forms to help build rigor The online assessments scaffold and adjust based on students skills Assessments are using multiple methods to access student knowledge Parent reports are available for each unit SBAC preparation is available within this program. None noted

6 Program Print materials are easy to Digital resources are difficult to Resources, navigate navigate Home Communications and Ease of Use There are lesson and unit planning materials available Standards correlation are difficult to find and use All resources are available in digital and print form Concrete and digital manipulative are included in the kit Family letters and home activities are available There are multiple skill level activities available in all lesson

7 First Grade Houghton Mifflin Expressions

8 Textbook Review Publisher: HM - Expressions Grade: 1 Summary Statement: Overall, the HM Expressions Math series is a well put together comprehensive math program that teaches students the common core standards in math. The lesson planning sections are well organized and in- depth (lots of important and usable information), however, with all this information, it tends to have a lot of words on a page. It would be easier to use if the T.E. wasn t so comprehensive in one volume, but broken down into more easily handled unit T.E.s. The layout of each unit and lessons are uniform, which makes it easy to navigate. The learning progressions are well represented and threaded throughout the entire lessons. There is in depth knowledge of the math background and research related to each unit. The mathematical practices are broken down in the math background before the lessons. Common mathematical errors are addressed throughout the unit and lessons through Puzzled Penguin. Differentiation for all learners is represented: EL, Special Needs, Intervention, On Level, and Challenge. It was easy to locate each in the lesson and the unit planning pages. Component Program Strengths Program Weaknesses Content/ Alignment with the Content Standards The T.E. contains a myriad of content support. It is well organized and easily accessible for the teacher to use from building background to planning and implementing instruction of the content standards on many levels and with tiered and differentiated support. (T.E. Includes in each unit s planning section: a pacing guide, daily routines, CCCS lesson correlations, unit planning guides, universal access built into every lesson in print and online, unit best practices research, common error analysis, Math Talk prompts and stems, The Day at a Glance overview of background, activities, materials and differentiation activities, Digital Resources are also listed on the Day at a Glance.) There are also Cross- curricular connections in each lesson. An optional (?) math literature library has a teacher s guide containing sample discussion questions to use with each selection. In the student edition the math standards are referenced on lesson practice pages and explained comprehensively in a section before the index. The student materials have lists of the curriculum s correlations to the standards in addition to a Table of Contents, Index, and Illustrated Glossary. The student s text/workbook supports rather than guides the instruction. The additional practice book, Homework and Remembering, doesn t have a Table of Contents, but is organized sequentially by lessons. At this time, no weaknesses were found related to the content and alignment with content standards.

9 Content/Alignmen t with the Content Standards - Standards for Mathematical Practice SMP s are explicit in the T.E. in unit planning and in every lesson, but there is also one lesson at the end of every unit that is focused on the direct instruction of specific Standards for Mathematical Practice The math practices are referenced on lesson practice pages in the student edition and explained comprehensively in a section before the index. The SMPs are not referenced in the Homework and Remembering workbook. Content/ Alignment with the Content Standards - Consistent Progressions The Learning Progressions are presented at the beginning of the unit, and are well defined. There were no weaknesses found in the learning progressions at this time. Universal Easy to Access Differentiated Access/ Instruction band in green, provides opportunities for Differentiation students to extend their learning (for all groups: intervention, on level, and challenge). Differentiation Cards support all learners, and have activities available for the ready for more group. Under the green band: differentiation instruction universal access technology is sited for all instructional level groups. It was easy to locate the differentiation sections in the TE. Although each lesson included a page about differentiation and a section in the unit planner, the differentiation strategies listed in the margins of the lesson mostly listed at least one strategy for a specific sub- group of learners. The groups represented were Special Needs, Advanced Learners and Extra Help. Some lessons listed strategies for two subgroups.

10 Universal Access/ Differentiation (Continued) For English Learners there are differentiation notes for the three levels Emerging, Expanding and Bridging on the margin of the lesson. In the planning section of the TE there is a page on differentiation that includes a language objective and strategies for each level of ELD. Differentiation notes for universal access are also noted within lessons for Advanced Learners, Extra Help, and Special Needs. An RtI page breaking down the tiers is also included in the unit overview, planning section. Assessment Houghton- Mifflin Harcourt s Math Expressions has a beginning of the year skills inventory assessment and end of the year skills inventory assessment, but it does not monitor the same skills. Each unit has three quizzes for formative assessment, a unit test and a performance task (with rubric) at the end of the unit. HM boasts a recent partnership with the company creating the SBAC questions, and is planning to have an online practice test for every unit, in the SBAC format, to be taken online on either platform. However, this was not available to evaluate at this time. No SBAC format questions at this time.

11 Program Resources, Home Communications and Ease of Use Materials varied in ease of use. The daily at- a- glance is a good preview, however. There are digital manipulatives available that the teacher can access and project. The company also boasts an electronic personal trainer that will meet the specific needs of every student. However, it was discovered that this feature was not functioning at the time of this evaluation. The materials are unique, and there are concrete materials available for purchase covering all the areas of common core math for first grade. Many chapters had a letter to the parents, explaining what the student is learning. Each lesson has 3- levels of differentiation in the Universal Access portion. The TE pages are very wordy, and not easy to use as a guide while teaching. Standards are referenced on each page, though descriptions are only in TE, not on pages for students or parents.

12 Second Grade Houghton Mifflin Expressions

13 Textbook Review Publisher: Houghton Mifflin/Expressions Grade: 2 Summary Statement: This adoption is built to teach the math behind the math. This program sets a high expectations for the three foundational components of focus, coherence, and rigor. Methods and algorithms are based on principles of mathematics, not mnemonics or tricks. This will lead students to computational skill and fluency, understanding, and the application of mathematics. H.M. Expressions supports comprehensive teaching of the Standards of Mathematical Practices that are aligned to grade level content. Materials are consistent with the learning progressions outlined in the Common Core State Standards. Instructional materials provide access to the standards- based curriculum for English Learners, advanced Learners, and students below grade level. It helps English Learners access challenging mathematics, learn content, and developing grade- level language. HM Expressions includes a variety of assessments types needed for formative assessment, including end of unit performance tasks. The assessments are designed to provide multiple methods of assessing what students know and are able to do. There are constructed response, real world problems, and open- ended questions. Materials are easy to navigate and things are easily found within the program. Content/Alignment with the Content Standards Mathematic content is correct, factually accurate, and written with precision. Given definitions are used to develop students understanding. Materials feature high- quality conceptual problems and questions that serve as fertile conversation problems. Had concrete models and multiple ways to explain concepts. Methods and algorithms are based on principles of mathematics. Contains an overview of chapters. Clearly identifies mathematical concepts. Includes table of contents, indexes, and glossaries. None noted at this time

14 Content/Alignm ent with the Content Standards - Standards for Mathematical Practice A variety of SMPs are explicitly applied in the outline of each lesson. The lesson pages give teachers an example of what the SMPs look like within the class lesson. The lessons are 'true' to the SMPs listed and allow teachers the flexibility to met all DOK Levels. Standards and SMPs are explicitly stated in teacher's TE and student's edition. SMPs are explicitly applied in the lesson outlines. Standards are explicitly stated in student editions. At the end of each lesson there is a Performance Task that incorporates all eight SMPs. None noted at this time Content/Alignm ent with the Content Standards - Consistent Progressions Digital materials allow navigation across grade level standards and practice for below and above grade level students. Materials are consistent with Common Core Learning Progressions and are aligned with Common Core Standards. Challenge material is available for students who are ready for a deeper understanding Accesses prior knowledge and builds on it. Problems involve real world application of knowledge learned in earlier grades. None noted at this time

15 Component Program Strengths Program Weaknesses Universal Access/ Differentiation A variety of differentiation strategies are available throughout each lesson. Differentiation cards are available to supplement the textbook. EL strategies for each level included in each lesson. Math speak is embedded throughout the lesson which helps develop appropriate grade level language. Opportunity for greater depth of study included throughout each lesson. Common misconceptions not mentioned in each lesson. Although there is tier 3 support mentioned in the catalog, there was none available to view. Differentiation strategies included throughout the lessons, but not clearly defined. "Differentiated Instruction" sections offer behavior management strategies rather than academic strategies. Component Program Strengths Program Weaknesses Assessment There are a variety of assessment options including graphic organizers, student observation, student interviews, journals, logs, self and peer evaluation, tests, quizzes, and performance tasks. Unit reviews and tests are included. Reteach activities and personal math trainer remediate. Summative and formative assessments available. Fluency checks, planning guides, and quick quizzes address rigor. Individual online assessment and intervention systems based on individual needs. Assessments contain multiple choice, yes/no, true/false, & constructed response questions. Embedded online assessment within Think Central and Personal Math Trainer allow teachers to print reports on student progress. SMPs are addressed through all lessons and assessments. Assessment guide contains SBAC formatted test items. TE is easy to read & teacher friendly. Directions are clear & concise. Standards are noted in student workbook. None noted at this time

16 Program Resources, Home Communications and Ease of Use Resources are well organized and easy to find. The structure is consistent throughout all lesson units. Charts with lessons, prompts and suggestions for differentiation are easy to read and available. Materials are available in all platforms. Manipulatives are included and appropriate. Letters home are included in every unit. Website can be accessed from home with math tutorials, practice, and literature links. Homework is included for all lessons. ExamView included. None noted at this time

17 Third Grade Houghton Mifflin Expressions

18 Textbook Review Publisher: HM Math Expressions Grade: 3rd Summary Statement: Everything that is in written form is available online, but we were unable to review it due to lack of access. The strategies it uses involve multiple approaches that allow students to understand the reasoning, but you have to search for them. The program is designed so it builds upon old knowledge based on conceptual development strategies. The program does incorporate real world application. Program creates its own vocabulary instead of using standard academic language. Program has one author and is based on her own research. Content/Alignment with the Content Standards Aligned with content standards. Does not use a traditional textbook format. So it is difficult to find standards in the student textbook. Content/Alignment with the Content Standards - Standards for Mathematical Practice MP s are in the beginning of the lessons, labeled and explained. The MPs are accurate and explained at this selected grade level. The student book and TE do not consistently line up. Content/Alignment with the Content Standards - Consistent Progressions Everything that is in a written copy is online, but we were unable to look it up. The strategies the program uses involves multiple strategies that allow students to understand the reasoning. The program is designed so that it builds on old knowledge. The program claims both teacher and students can browse progression online, but we were unable to look at it. The strategies provided are limited. The program is designed to build on knowledge that was taught in previous years, but all this conceptual learning is new.

19 Content/Alignment with the Content Standards - Consistent Progressions The program does incorporate real world application. Students, they won t have anything to build upon until students have been introduced for a few years. The real world application was very limited. Universal Access/ Differentiation Uses specialized teaching methods for at risk and intervention level students. Research is solely that of the author s. Cannot be based on current and confirmed research. There are ELL strategies in the lessons but they are not labeled as such. The strategies labeled are rudimentary and do not appear effective. Program uses its own vocabulary. Assessment Performance assessments are available for each unit and include s a rubric. SBAC prep book available, includes variety of question types. Unit assessments also include a variety of question types. Fluency checks available. Rubrics are not in student friendly language. Only unit assessments available in student text, no quizzes or chapter tests. Only available to copy in separate book. Online assessments were not accessible at time of review. Program At least one parent letter in Program says homework is Resources, Home the student tear out book per crucial for the success of the Communications unit. program. Page 8, Unit 1 Teacher and Ease of Use There is accessibility for Edition. various student levels Students do not have a full including ELL, at- risk, and challenge. Fluency practice. textbook. TEs are not user friendly, would require a great deal of professional development. Program would require a great deal of planning outside of contract time. Manipulatives are not durable.

20 Fourth Grade Houghton Mifflin Expressions

21 Publisher: Math Expressions Textbook Review Grade: 4th Summary Statement: Although the program has many conceptual activities, it is lacking in the area of procedural and problem solving practice, and suffers greatly from being poorly organized and confusing. SMPs are identified by the standard numbers and letters only (eg. MP.3 or MP.5), and are not explicitly applied nor stated in the student lesson, and only listed at the top of the TE lesson outline. Everything that is in a written copy is online, but we were unable to look it up. The strategies the program uses involve multiple strategies that allow students to understand the reasoning, but you have to go around looking for them. The program is designed so that it builds on old knowledge based on common core standards and strategies, but students have just started to think critically and they might struggle. The program does incorporate real world application. Math Expressions does not contain as many universal access materials like we have been used to in the past for our tier 2 and tier 3 students. Math Expressions has 8 of the 9 components present. However, it does not provide many examples to assist those students who are struggling with math concepts. We were also unable to preview the RTI Skill and example books for Tiers 2 and 3. Expressions provides a variety of assessments, both formative and summative. Question types and level of rigor are intended to mimic the SBAC by calling for a variety of responses (multiple choice, short answer, etc.) that show students conceptual understanding and mathematical skill/fluency. The program is difficult to navigate, and the TE is unwieldy 36 pages, for example, of preliminary material for the teacher to wade through on the way to the actual lesson. Typical charts correlation standards and units are provided. Everything is available online and is platform- neutral. Manipulatives and concrete Teacher s Manual is hard to follow Content/ representations are present Teacher s Manual poorly organized Alignment with the Content Standards The methods and algorithms are based on principals mathematics Online materials were not presented Very little student practice Program relies on using students as teachers Textbook does not define vocabulary/math terms Relies primarily on concrete, conceptual problems, but offers very little, if anything, in the way of procedural and problem solving practice

22 Content/ Alignment with the Content Standards - Standards for Mathematical Practice None SMP numbers are listed at the top of student practice pages, but not explicitly labeled, nor applied, anywhere in the lesson itself. SMP numbers are only listed in the TE lesson outline, but are not discussed in detail anywhere in the lesson outline. Content/ Alignment with the Content Standards - Consistent Progressions Everything that is in a written copy is online, but we were unable to look it up. The strategies the program uses involves multiple strategies that allow students to understand the reasoning. The program is designed so that it builds on old knowledge. The program does incorporate real world application. The program claims both teacher and students can browse progression online, but we were unable to look at it. The strategies provided are limited. The program is designed to build on knowledge on what was taught in previous years, but all this conceptual learning is new to our students, they won t have anything to build upon until students have been introduced for a few years. The real world application was very limited. Universal Access/ Differentiation Before each unit there is a Putting Research into Practice section. This section explains which errors students tend to create and how to fix that error and help them master the standard and the research to support it. It also provides a list of books to read to help with the topic. No examples Teacher must prep everything and plan ahead of time Can only determine if they don t understand in the Unit test after everything has been taught

23 Universal Getting Ready to Teach the unit The intervention suggestions is Access/ goes over each MP and gives online practice. examples from the unit and how to Differentiation help them reach success in that MP Beginning of unit Called Putting Research into Practice Also found in section called Getting Ready to Teach Unit Has a section called Help Students Avoid Common Errors There is a penguin with a question bubble over his head that also points out that it may be a common error students make. After the unit test is given there is a Common Errors and Prescriptions for Selected Items that explains what the error could be for getting the incorrect answer and how teacher may help students master those items. At the beginning of the Unit it offers Differentiated Instruction for English Learners and suggestions of materials to use for EL students Math Center Challenges, Math Writing Prompts, and Differentiated Instruction cards. Ready Made Math Center Challenges are for Below Level, On Level and Challenge students There is also a RTI suggestion page in the planning section of the unit for On- Level intervention (Tier 1), Strategic Intervention (Tier 2) and Intensive Intervention (Tier 3) At the beginning or the end of the lesson is a blue box called Differentiated Instruction Universal Access Special Needs. It contains a suggestion for special needs students Beginning of Unit Planning for RTI suggestions are only online Personal Math Trainer, and Differentiation Instruction Card for each lesson may be too difficult for below level students. A Response to Intervention Skill/Lesson/Example is mentioned however we were unable to view these materials Some suggestions may need to be prepped before lesson. Does not suggest when you should use the EL lesson in the green box. There is no examples on the Work book pages The suggestions for the EL in the lessons do not challenge the EL s Not very detailed or challenging. Just to get them to understand the concept. The materials do not specify if it will help a visual, cognitive or ADHD student. We were not able to review the UA materials that also comes with the curriculum. Not enough materials for challenge students. Just one task card with one question per lesson.

24 Universal Access/ Differentiation Beginning of every unit there is a Spanish family letter that can be sent home. In every lesson there is an English Learner suggestion mini- lesson for questions to give the EL s in the 3 levels Only intervention that we were able to view was the Differentiated Instruction Cards (Task Cards) for each lesson. It has them work individually or in pairs to accomplish a task. Which may require them to draw or write. Refers to an online Personal Math Trainer, Mega Math or Destination Math depending on the Tier Level they are. Offers an opportunity to write in each lesson with the Math Writing Prompt that can be found in the Differentiation Instruction Universal Access page. The Students book is nicely organized and may appeal to easily distractible students. Challenge students will find the Differentiated Instruction Cards challenging. Teachers will like the MP questions found in the teacher book that they will be asking students. Math talk section of the lesson Online Destination Math

25 Assessment 50- question Inventory Test that We were unable to find covers all domains. evidence of support in informing parents of student Quick Quiz after each Big Idea per progress beyond what is Unit (2-4 Quick Quizzes per unit). available to students online Fluency Checks for each Big Idea. (homework, Personal Trainer, Fluency Checks appear to be etc.) provided with each unit for example, 24 Fluency Checks with Unit 3 (addition & subtraction), 15 add/subtract problems in each Fluency Check. Getting Ready for CCSS Check for Understanding formative assessment: Student explains the math (SMP Communication) Performance Task at the end of each unit Math Talk throughout each lesson End- of- year Performance Assessment Unit tests and Performance Task at the end of each unit. Personal Math Trainer: Adaptive Assessment & Intervention that provides students with feedback and teachers with information on student progress. Assessments are adequate in measuring conceptual understanding and procedural skill/fluency; they seem weaker when it comes to application. Students are required to respond to questions with short- answer, yes/no, true/false, and multiple- choice kinds of answers. Questions often come with a Part A and a Part B (SBAC- style). Questions and tasks can also require the use of math tools and manipulatives. Student consumable has Unit Review/Tests in a form similar to what students will see in SBAC.

26 Program Resources, Home Communications, and Ease of Use Correlates CCSS standards with the units in the adoption. Family Letter at the beginning of each unit. Looking in one chapter alone, there are 36 pages in the TE labeled with a single page number followed by the entire alphabet and beyond into double letters (JJ) not an easy way to find what s needed. Non- tradition style of TE that requires a lot of hunting to find the components needed, etc. Strategies and content are provided for differentiation but don t really aim for acceleration/deceleration.

27 Fifth Grade Houghton Mifflin Expressions

28 Textbook Review Publisher: Houghton Mifflin Harcourt Math Expressions Grade: 5 Summary Statement: Math Expressions was written entirely by researcher Dr. Karen Fuson. Alignment with the Content Standards Content reviewed is correct. All CCSS and CA content standards are addressed to some degree. Lessons are inquiry- driven, requiring math conversations at higher rigor and thinking levels. Lessons are scripted and gradually release responsibility to students. Teacher and student books are text- heavy with few illustrations and diagrams. UA/Differentiation Addresses differentiation using a 3- tier model for intervention, On- Level, Below Level and Challenge. The 3 ELL levels are also addressed in each lesson. Personalized online work is available, however could not be reviewed. Lessons are scripted in TE and would be difficult to teach not following the script. Assessments Formative assessments offered after each lesson. Most unit assessments average 5-6 pages of open- response questions in SBAC form. Online assessment available to customize. Program Resources, Home Communications and Ease of Use Expressions is a curriculum that meets the letter of the CA Common Core standards and also the spirit. It provides the resources teachers need to setup learning communities where students collaborate, model, and explain their work. Assessments might take a little longer to score but assess students deeper understanding of math and not just their ability to get a correct answer. Parents are informed throughout the year via tear out letters from the workbook. Content/ Alignment with the Content Standards CCSS correlation is listed by standard in both volumes of the TE Additional CA standards are addressed and included in CCSS correlation Lessons are inquiry- driven using non- routine problems and alternate algorithms Routinely promotes math talk and reasoning at higher Bloom s and DOK levels. CCSS correlation gives lesson and unit number, but does not refer to page or volume numbers. Some teachers may be unfamiliar with alternate algorithms given. Could be a problem for new teachers or teachers new to a grade level Lessons scripted Fraction +- lessons use fraction bars, however algorithms used may be unfamiliar to some teachers.

29 Takes algebraic approach to problem solving Lessons leading to addition/subtraction of fractions build logically Lessons are very scripted, but gradually release work from teacher to students. All CCSS standards addressed to some degree Glossary is illustrated Glossary and index included in both volumes in TE and student copy Methods and algorithms are not based on mnemonics or tricks Lessons are text heavy with few illustrations or diagrams Student book does not give sample problems or examples. Other than in the glossary, the student text does not include definitions to help develop student understanding Lessons on order of operations do not include exponents/squares, brackets or braces Content/Alignm ent with the Content Standards - Standards for Mathematical Practice The Overview has thorough core standard and SMP explanations, as well as, math content for the teachers. Each lesson and activity has core standards and SMPs listed. Easy to find connections to CCSS and SMPs Formal Math Talk and Math Drawing routines are an integrated part of the lessons and the program. Exploration of math provided through use of mathboards, textbook lessons, manipulatives that are provided, and online exploration in school and at home CGI strategies embedded in the program Quick Practice is inquiry and exploration based Last lesson in each chapter uses all eight SMPs SMPs are listed in red in every lesson and practice item Textbook structure and spiral layout makes it more difficult for teachers to incorporate standards into district units Programs work best with lots of current technology in the classrooms and student homes. Will require tech support for teachers Requires Professional Development on multiple topics for best implementation Child- friendly vocabulary used in lower grades. It will later evolve into traditional vocabulary

30 Content/Alignm ent with the Content Standards - Consistent Progressions Based on California Common Core Standards Routines and vocabulary progress from Kinder through 6 th grades. Progressions for fluency of basic skills and operations with multi- digit numbers. Beginning of each unit has learning progressions for grade before, grade taught, and grade after. Universal Access / Differentiation RtI program is 3- tiered; Tier 1 grade level content, Tier 2 prerequisite skills, Tier 3 scaffolded activities Online Person Math trainer provides students with personalized learning based on assessment results Every lesson includes intervention, on level, and challenge lesson options. ELL lessons are broken into beginning, intermediate, and advanced tasks. Differentiated instruction cards (task cards) make intervention easy Assessment Performance tasks seem comparable to SBAC with rubric. Culminating assessment available at the end of each unit of study. Unit assessments average length is 5-6 pages open response, but is similar to SBAC in style. No multiple choice questions observed. Unable to evaluate online assessments.

31 Program Resources, Home Communications and Ease of Use Resources: Resources are very aligned to spirit of Common Core. Not every lesson is presented from workbook. Some are instead based on modeling or group collaboration Resources include whiteboard cards for each student. New set each year. Instead of textbooks there are two workbooks for students. There is a pacing guide for the year as well as suggested times for each part of the lesson. Online resources have a quickstart guide for teachers. Online planner, assessments, assignments Home Communication: Family letter with activity in Spanish and English are tear outs from workbook. Ease of Use: Online lesson plans break down each part of lesson. Individual SMOs are listed throughout the lesson as students work on them. Can easily open online student textbook while in lesson planner Student resources on designed for computer will also play on ipad The amount of open- ended questions may require a lot of teacher grading time.

32 Sixth Grade Houghton Mifflin Expressions

33 Textbook Review Publisher: McGraw Hill Grade: 6 Summary Statement: This curriculum contains less bells and whistles than other math curriculums. Although it seems to be a bare bones curriculum, it is actually full of strategies and methods for teachers to choose from when designing lessons. The assessment component is strong with timely formative quizzes, unit tests, and performance tasks. Teachers have the opportunity to use their discretion when choosing assessments, and the assessments are targeted towards the concepts that are taught. At first glance, the TE appears word heavy, however, lessons and explanations are clearly laid out along with examples of what the Math Practices should look like for the lesson, and how the Math Discourse should take place. Students are taught how to present various methods for solving problems in front of the class, and are given the option of multiple methods for solving problems. It is the only curriculum we have seen that differentiates EL instruction at the 6 th grade level. Differentiated Activity cards incorporate writing in math. Manipulatives and lesson posters are carefully thought out to enhance student understanding. All resources are available online in a neutral platform for teachers who have access to technology in their classrooms. Each lesson is aligned to the None Noted Content/ common core standards Alignment with Unit Introduction pages list the the Content Standards standards taught and what lessons apply to each standard. Key standards are given more lessons to enable mastery of the standard Putting Research into Practice pages provide research based strategies and understandings for teaching the standards. Error analysis questions are incorporated throughout the units.

34 None Noted Content/ Alignment with the Content Standards - Standards for Mathematical Practice There is a major focus on the SMP's throughout the program with many activities allowing for ample student practice. In the TE, the unit overview explicitly states the SMP's and gives examples and pages numbers to where the particular standards are being addressed. It shows how each SMP is integrated into each unit. In addition, the SMP's are clearly stated throughout each lesson. The student s edition has both SMP's and CCSS stated at the beginning of each lesson. Content/Alignme nt with the Content Standards - Consistent Progressions Universal Access/ Each lesson contains a page for Differentiated Instruction and None Noted Differentiation Universal Access options. They include activities for Intervention, On Level, and Challenge students. There is also a section within each lesson that addresses English Learners at each level (Emerging, Expanding and Bridging). Common Misconceptions found at

35 the end of each unit under differentiated instruction and Universal Access. Includes common errors and a prescription for fixing them. There are 4 different instructional activities for lower level students. There are also differentiated instruction cards and math writing prompts for extra support. Lessons include a section for English Learners; it addresses each level of language development. There are vocabulary words highlighted at the beginning of each lesson. There are also suggestions for teachers to use for mathematical language. Math drawings are also used to help students understand concepts. In the student edition there are activities such as word reviews and crossword puzzles that also help with the understanding of vocabulary. All English Learner levels are addressed in the English Learner section in TE. These consist of the activities that have been provided for below level students, as well as a separate Response to Intervention book with strategies for Tiers 1, 2, & 3. Online Adaptive Assessment System and Intervention program that customizes Math intervention for each student. The Math Center Challenges in each unit are designed to challenge more advanced students. The concepts and activities are more rigorous

36 Assessment The overall assessment piece of Math Expressions is great! It is very extensive and gives the teacher several options for testing. Each of the 9 units includes two to four quick skills quiz, which consists of five questions. Followed by a unit test and a Performance Task. The skills quizzes seem to cover each individual skill very well and would give the teacher enough information to decide whether or not to reteach a skill. The unit test is complete with each skill and a synthesis of the skills. It also uses all of the Smarter Balance question types, more than one right answer, matching, etc. The Performance Task is well written, but not overly long and complicated. It wouldn t be too hard to grade the Performance Task. There are also beginning of the year tests, and end of the year tests. There are also whole book of Smarter Balance assessments. Each of the new common core standards has got a separate test using the smarter balance type questions. The evaluator s web site made it very hard to find the assessment piece. Hopefully the full web access would be easier.

37 Component Program Strengths Program Weaknesses Program Resources, Home Communications and Ease of Use Teacher Edition has a table of contents for each unit that lists each lesson, and the lesson goal. Standards are clearly listed. TE includes detailed scripted examples of Math Discourse. TE includes easy to read alternative strategies for solving problems. Each lesson begins with a Day at a Glance page that outlines lesson, goals, materials, differentiation materials, and daily quick practice or anytime problems. Units broken down into Big Ideas. Ready- made Independent Learning Activities to challenge and extend student learning included in a Math Challenge center and in the TE. Differentiated instruction cards for Intervention, On Level, and Challenge levels w/ an activity and Math Writing Prompt. Four levels of differentiated instructions. Three levels of Differentiation for English Learners. Virtual Manipulatives (itools) Online Interactive Student Activity Book Online Lesson Planner and assessments Connections to Art, Literature, Science, & Social Studies built in. Real World Applications Family Letters in English and Spanish in every unit. Math Models provide multiple methods for learning a skill. Manipulative kits and Teacher Modeling Manipulatives (Larger) Student Mathboards (write on board) that are replaced each year during the length of the adoption. PD Videos for teachers available online None Noted

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