High School - Gateway 3

The instructional materials reviewed for HMH Into AGA meet 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 Spark Your Learning, Build Understanding, and Step It Out, students have opportunities to learn new content through examples and problems for guided instruction, step-by step procedures, and problem solving.

At the end of the lesson, Check Understanding and On Your Own provides a variety of exercises which allow students to independently show their understanding of the material. Exercises are designed for students to demonstrate understanding and skills in application and non-application settings. Assessment Readiness and Spiral Review also include exercises.

The instructional materials reviewed for HMH Into AGA meet 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, Exit Ticket, Assessment Readiness, and Spiral Review sections in each lesson support students in developing independent mastery of the current lessons as well as reviewing material from previous lessons.

The instructional materials reviewed for HMH Into AGA meet expectations for having a variety in what students are asked to produce, and examples include:

• Performance Tasks: Algebra 1, Module 15, Packaging Science states, “A team of designers wants to produce a package that can hold the largest possible volume while keeping the cost of production low. As illustrated below, the team can program a machine to cut out a square from each corner of a large sheet of construction material to form the framework of the package.” Students use polynomial multiplication to write and solve an equation for the surface area and volume of the packaging. Geometry, Module 18, On the Spot states, “How can you describe the area of a sunspot?” The Overview on the side provides, “ This problem requires students to ask questions in order to make decisions about how to approach the problem. Examples of questions: How do you measure the dimensions of the irregularly shaped sunspot? Do you only include the larger section, or do you include the smaller dots next to the larger section?”
• STEM activities: Geometry, Unit 2 states, “A triaxial woven carbon fiber provides a lot of strength while remaining lightweight. The fiber has an area density of only75 kg/m2. The frame of a drone is made from the fiber. One section of the frame is 150 mm × 20 mm. What mass does the section add to the drone?” Algebra 2,  Unit 8, states, “An archaeologist allocates an effective sweep width while searching a site for artifacts.” The activity provides a diagram of the effective sweep area. Materials further state, “How successful was the sweep?”
• Show written calculations and solutions
• Verbally defend or critique the work of others to show understanding
• Build models for a problem by using diagrams and equations
• 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 AGA meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent 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.

The instructional materials reviewed for HMH Into AGA meet 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, Spark Your Learning, Build Understanding, 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.

The Spark Your Learning planning page in the Teacher Edition includes examples of student work which show two different strategies and Common Errors. Each example has suggested questions for teachers to correct or advance student thinking. For example, in Algebra 1, Lesson 13.1, Common Error about linear relationships states, “Now find the ratios of consecutive values of the stamp collection. What do you observe? How can you use this observation to solve the problem?”

The instructional materials reviewed for HMH Into AGA meet 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 “I Can” Objective, Learning Objective, Language Objective, and Mathematical Progressions Across the grade 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  prompts in each module related to Online Ed: “Assign the Digital Module Review for built-in student supports, Actionable Item Reports, Standards Analysis Reports” and “Assign the Digital Module Test to power actionable reports including proficiency by standards item analysis.” 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”.

The instructional materials reviewed for HMH Into AGA meet 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.

The instructional materials reviewed for HMH Into AGA meet 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 reviewed for HMH Into AGA meet 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 reviewed for HMH Into AGA meet 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 reviewed for HMH Into AGA meet 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 reviewed for HMH Into AGA meet 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 reviewed for HMH Into AGA meet 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 are struggling with learning mathematics despite their best efforts and hard work. Help them become more responsive to feedback by asking: How can you assert your own needs and viewpoints in non aggressive or defensive ways?” and “Watch for students who resist receiving feedback about their own work or who are reluctant to provide feedback to others by asking them these questions.” (Geometry, Unit 4)
• 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. Algebra 1, Lesson 8.2 states, “Select groups of students who used various strategies and tools to share with the class how they solved the problem. As they present their solutions, have each group discuss why they chose a specific strategy and tool.” Geometry, Lesson 11.1 states, “Have students look at the photo in their books and read the information contained in the photo. Then complete Part A as a whole-class discussion. Give the class the additional information they need to solve the problem. This information is available online as a printable and projectable page in the Teacher Resources.” Algebra 2, Lesson 15.2 states, “Turn and Talk Ask students to draw a Ferris wheel that meets these conditions to help them visualize the situation.”
• 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 reviewed for HMH Into AGA meet 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 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 reviewed for HMH Into AGA meet 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.