8th Grade - Gateway 3

The instructional materials for HMH Into Math Grade 8 meet the expectations that there is a clear distinction between problems and exercises in the materials.

Each Module presents lessons with a consistent structure. During the instructional sections, which include Build Conceptual Understanding and Connect Concepts and Skills, students have opportunities to learn new content through examples and problems for guided instruction, step-by-step procedures, and problem solving.

Additional practice is provided in a separate student journal which allow students to independently show their understanding of the material. Exercises and problems are designed for students to demonstrate understanding and skills in application and non-application settings. Test Prep and Spiral Review also include exercises.

The instructional materials for HMH Into Math Grade 8 meet the expectations that the design of assignments is intentional and not haphazard.

Overall, lessons are intentionally sequenced and scaffolded so students develop understanding of mathematical concepts and skills. The structure of a lesson provides students with the opportunity to activate prior learning, build procedural skills, and engage with multiple activities that utilize concrete and abstract representations and increase in complexity. Examples include:

• Spark Your Learning serves to motivate and set the stage for students to learn new material and persevere through a related mathematical task.
• Build Understanding and Step It Out provide opportunities for students to learn and practice new mathematics, as well as “connect important processes and procedures” according to the Planning and Pacing Guide.
• Check Understanding provides a formative assessment opportunity after instruction.
• On Your Own, More Practice/Homework, Test Prep, and Spiral Review in each lesson support students in developing independent mastery of the current lessons as well as reviewing material from previous lessons.
• Lessons are in a logical order that build coherence throughout the grade level.

The instructional materials for HMH Into Math Grade 8 meet the expectations for having a variety in what students are asked to produce, for example:

• Performance Tasks: Unit 3, Back to the Future states, “Although time travel often occurs in movies and books, it isn’t possible in real life. But if it were possible, companies would probably exist to see trips!” This is followed by five questions which require students to use functions to represent data and find relationships.
• STEM activities: Unit 6 states, “Light travels at a speed of about 186,000 miles per second. How many miles does light travel in one hour? Write your answer in standard form and as a number multiplied by a power of ten.”
• Show written calculations and solutions
• Verbally defend or critique the work of others to show understanding
• Analyze double number lines and bar diagrams
• Build models for a problem by using diagrams and equations
• Use a diagram and a coordinate plane to represent a linear equation
• Compare multiple representations - table, graph, equation, situation - of data
• Use a digital platform to conduct and present their work
• Use manipulatives, especially in small groups, to represent mathematics
• Construct written responses to explain their thinking

The instructional materials reviewed for HMH Into Math Grade 8 present and, when appropriate, are connected to written methods.

• The series does not involve extensive use of manipulatives, however, when they are included, they are consistently aligned to the expectations and concepts in the standards.
• Most hands-on manipulatives are integrated in supplemental, small-group, differentiated instruction activities, and warm-up options.
• Examples of manipulatives include: Two-color counters, calculator, coins, number cubes, playing cards, string, square tiles, unit cubes, colored chips, algebra tiles, grid paper, index cards, anchor charts, ruler, compass, protractor, geometry software, bar diagrams, fraction strips, number lines, decimal grids, x-y tables, and pie charts.

The instructional materials for HMH Into Math Grade 8 meet the expectations for providing quality questions to help guide students’ mathematical development.

There are Guided Student Discussion questions and sample student answers throughout the Teacher Edition including on the Module Opener page, Warm Up Options, Spark Your Learning, Build Understanding, Common Errors, and Step It Out pages that correspond to the tasks or exercises on the page. Each module review also contains suggested questions intended to have students summarize concepts and skills developed within the module.

Each lesson introduction poses an essential question intended to guide student learning. For example, in Lesson 13.4, the Essential Question is “How can you use volume formulas to solve problems involving cylinders, cones, and spheres?”

The Spark Your Learning planning page in the Teacher Edition includes examples of student work which show On Track, Almost There, and Common Errors. Each example has suggested questions for teachers to correct or advance student thinking. For example, in Lesson 11.1, Almost There about Pythagorean Theorem states, “What is the area of each of the smaller squares? What is the area of the larger square? Do you see a relationship among these areas?”

The instructional materials for HMH Into Math Grade 8 meet the expectations for containing ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

In the Module planning pages, there is a variety of information that can help teachers understand the materials in order to present the content. Each lesson identifies the relevant content standards and Mathematical Practices, an Essential Question, Learning Objective, Language Objective, materials needed, and Mathematical Progressions Across Grades that contain prior learning, current development, and future connections. Unpacking the Standards provides further explanations of the standards’ connections. This section gives an explanation of the content standard contained in the lesson and Professional Learning, which sometimes contains information about the practice standard contained in that lesson. Teaching for Depth provides teachers with information regarding the content and how this relates to student learning.There are additional suggestions about activating prior knowledge or identifying skills in Warm-up Options, activities to Sharpen Skills, Small-Group Options, and Math Centers for differentiation.

There are two prompts in each module related to Online Ed: “Assign the auto-scored Are You Ready for immediate access to data and grouping recommendations” and “Assign the auto-scored Module Test for immediate access to data.” Within lessons, there are multiple prompts. Warm-Up Options and Step It Out both have an icon “Printable & projectible” which states “More print and digital resources for differentiation are available in the Math Activities Center” and “Assign the auto-scored Check Understanding for immediate access to the data and recommendations for differentiation.”

The instructional materials for HMH Into Math Grade 8 meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

Each module in the Teacher Edition includes Mathematical Progressions Across the Grades which lists prior learning, current development, and future connections. Similarly, the beginning of each lesson in the Teacher Edition includes Mathematical Progressions that show connections to prior and future grades’ standards, as well as other lessons within the program.

In the Planning and Pacing Guide, Progressions and Algebra Readiness discusses the “four progressions of middle school content leading to the Algebra course: Number and Operations, Operations and Algebraic Thinking, Statistics and Probability, and Functions” and includes a table that shows how the domains in Grades 3-5, 6-7, and Grade 8/Algebra fit into these progressions.

The instructional materials for HMH Into Math Grade 8 meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

• At the beginning of the year, students’ prior knowledge is gathered through a Prerequisite Skills Inventory, which states, “This short-answer test assesses core precursor skills that are most associated with on-grade success.” (Assessment Guide)
• Each module begins with Are You Ready?, a diagnostic assessment of prior learning related to the current grade-level standards. Intervention materials are provided to assist students not able to demonstrate the necessary skills. Commentary for each standard explains how the prior learning is relevant to the current module’s content.
• Prior learning is identified in the Mathematical Progressions section at the beginning of each module and lesson of the Teacher Edition.

The instructional materials for HMH Into Math Grade 8 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• The module overview in the Teacher Edition contains “Common Errors” as students engage in an introductory task and provides questioning strategies intended to build student understanding.
• The Spark Your Learning planning page for each lesson in the Teacher Edition includes a Common Error section related to the content of the lesson that identifies where students may make a mistake or exhibit misunderstanding. There is a rationale that explains the likely misunderstanding and suggests instructional adjustments or steps to help address the misconceptions.
• There are also “Watch For” boxes and question prompts that highlight areas of potential student misconceptions.

The instructional materials for HMH Into Math Grade 8 meet the expectations that assessments clearly denote which standards are being emphasized.

The standards alignment for each item on the Prerequisite Skills Inventory, Beginning-of-Year, Middle-of-Year, End-of-Year, and Module Tests are listed in the Assessment Guide on Individual Record Forms. Each Performance Task includes the standards in the teacher pages of the Assessment Guide, although the individual questions do not indicate which standards are being assessed.

The instructional materials for HMH Into Math Grade 8 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• At the beginning of each module, Teaching for Depth provides information on strategies to use when teaching the concept, including Represent and Explain, which focuses on ways for students to describe and picture a concept, or Make Connections, which helps students understand a new idea by connecting it to previous knowledge.
• At the beginning of each module, Mathematical Progression Across the Grades makes connections to both prior and future skills and standards to scaffold instruction.
• At the beginning of each module, Diagnostic Assessment, Are You Ready? allows teachers to “diagnose prerequisite mastery, identify intervention needs, and modify or set up leveled groups.”
• Each lesson provides Warm-up Options to activate prior knowledge such as Problem of the Day, Quick Check for Homework, and Make Connections.
• Throughout the lessons, there are notes, strategies, sample guided discussion questions, and possible misconceptions that provide teachers structure in making content accessible to all learners.
• Student practice starts with up to four Check Understanding exercises to complete with guidance before moving to independent work in On My Own or More Practice/Homework.

The instructional materials for HMH Into Math Grade 8 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• There are Reteach and Challenge activities for each lesson.
• Each module includes Plan for Differentiated Instruction that provides teachers with teacher-guided, Small-Group Options and self-directed Math Center Options based on student need: “On Track/Mixed Ability, Almost There (RtI), and Ready for More.”
• Each lesson provides Leveled Questions in the teacher’s edition identified as DOK 1, 2, and 3 with an explanation of the knowledge those questions uncover about student understanding.
• There are three “Language Routines to Develop Understanding” used throughout the materials: 1) “Three Reads: Students read a problem three times with a specific focus each time.” 2) “Stronger and Clearer Each Time: Students write their reasoning to a problem, share, explain their reasoning, listen to and respond to feedback, and then write again to refine their reasoning.” and 3) “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy.”

The instructional materials for HMH Into Math Grade 8 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

• Each unit includes a STEM Task and a Unit Project which include multiple entry-points and a variety of solution strategies. Teachers are provided with possible answers as well as What to Watch For tips, which include “Watch for students who become discouraged by a task and quickly give up. Strategies that may help these students include: working with a supportive partner, dividing the task into smaller steps, and reminding themselves that working at a difficult task is valuable, even if the task is not completed. Taking on new challenges is how we learn” and “Watch for students who are reluctant to stretch themselves on a challenging task. Encourage these students to: identify similarities between the current task and tasks they have completed successfully in the past, identify one or more promising strategies or approaches, and try one of the strategies.”
• Each lesson begins with Spark Your Learning, which is an open-ended problem that allows students to choose their entry-point for applying mathematics and can be solved in a variety of ways. There are suggestions in the teacher’s edition to help students access the context of the problem. For example, in the side margin of the teacher’s edition, Motivate provides prompts. Grade 6, Lesson 9.1 states, “Introduce the problem. Point out that the problem does not state the amounts of money that Bella and Tia have, only that the two amounts are equal. Nevertheless, this information is enough to find a solution.” Grade 7, Lesson 1.1 states, “Introduce the problem. Ask them if they have ever used a recipe. Tell students to discuss and share with their team members in a small group.” Grade 8, Lesson 5.2 states, “Introduce the problem. Ask students if they have ever set daily goals in reading or running or some other activity. Invite students to discuss and share with their partner or team members in a small group.”
• Support for Turn and Talk in the teacher’s edition provides suggestions to help students using a variety of strategies. Teachers are often prompted to “Select students who used various strategies and have them share how they solved the problem with the class.”

The instructional materials for HMH Into Math Grade 8 meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

In addition to the strategies for meeting the needs of a range of learners described in Indicator 3s, there is further support in place for English Language Learners (ELLs) and other special populations. Examples include:

• For ELLs, there is Language Development in each module which includes linguistic notes that provide strategies intended to help students struggling with key academic vocabulary, such as “Speak with students about words that can have multiple meanings,” “Listen for students who do not distinguish between minus...and the negative sign,” and “Visual cues help students…”
• Language Objectives are included in every lesson.
• There are Teacher Tabletop Flipchart Activities referenced in the teacher’s edition for RtI support.
• There are Reteach, RtI Tier 2, and RtI Tier 3 worksheets that can be assigned online or printed.
• There are Turn and Talk prompts designed to support students in other special populations, such as “go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”

The instructional materials for HMH Into Math Grade 8 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

In addition to the strategies for meeting the needs of a range of learners described in Indicator 3s, there is further support in place for advanced students. Examples include:

• There are optional lessons provided online that teachers may choose to utilize with advanced students.
• Each lesson has a corresponding Challenge page, provided in print or online, addressing the same concepts and standards where students further extend their understanding and often use more complex values in their calculations.
• On the module opener page, Extend the Task in the margin of the teacher’s edition provides ideas for extending the task.

The instructional materials for HMH Into Math Grade 8 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics. Examples include:

• Lessons contain a variety of tasks that interest students of various demographic and personal characteristics.
• Names and wording are chosen with diversity in mind. The materials include various names throughout the problems (e.g., Jayson, Suyin, Malik, Tressa, Anton, Jasmine, Yu, Felice, Sonia, Roselyn, Tracy, Tran, Arie, Miguel, Maria) that are used in ways that do not stereotype characters by gender, race, or ethnicity.
• When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways that do not express gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies.
• When people are shown, there is a balance of demographic and personal characteristics.