Kindergarten - Gateway 3

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

The materials distinguish between problems and exercises within each lesson. Lessons include Spark Your Learning or Step it Out, Turn and Talk, Build Understanding, Check Understanding, and On Your Own, and More Practice/Homework. Spark Your Learning Problems activate prior knowledge and introduce new mathematics to students. Build Understanding includes problems that help students build conceptual understanding of the mathematics topic being taught. Check Understanding and On My Own sections include exercises that ask students to use the newly learned mathematics in each lesson. Additional practice and Homework is available in a separate Student Edition, providing more exercises for students to solve.

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

At the end of the lesson, On Your Own, More Practice/Homework, and Additional Practice 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. Test Prep and Spiral Review also include exercises.

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

Overall, lessons are intentionally sequenced and scaffolded so students develop their 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.

Exercises are given in intentional sequences. In general, lessons are designed to begin with activating prior knowledge and build toward conceptual development and procedural skill. In Spark Your Learning, students use manipulatives and/or visual models to engage with the mathematical content, developing a concrete or representational understanding. This is followed by a Turn and Talk with a partner where students process the connections they have found. Throughout the lessons, students are provided scaffolding with new content in Build Understanding and Step It Out, where the abstract concept is broken down into smaller steps with additional Turn and Talks, and students complete independent exercises to build understanding and mastery. Check Understanding provides a mid-lesson check in and can be used to indicate the need to differentiate learning for students. Students solve and practice concepts in On Your Own, and More Practice/Homework.

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for having a variety in what students are asked to produce.

In Spark Your Learning, Build Understanding, and Step It Out, students use visuals to show their thinking. In Turn and Talks, students frequently construct arguments, and explain why. There are opportunities for students to produce answers and solutions in On Your Own, while also providing opportunities for students to provide written explanations. Throughout the materials, students represent mathematics using equations.

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The Planning and Pacing Guide, Manipulatives and Tools, explains how manipulatives are used in each module.  The materials identify the manipulatives needed at the beginning of each lesson, and on student pages there is a picture of the manipulative they will use. Examples of manipulatives for Kindergarten include: connecting cubes, pattern blocks, and counters.

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

Throughout the Teacher Edition, questions are posted to help support teachers with questions to guide students’ mathematical development. Activate Prior Knowledge, Spark Your Learning, Build Understanding, On Your Own, and Turn & Talk consistently provide questions to drive student discussion. 

• Module 2, Lesson 3, Build Understanding provides the following questions for teachers: “When counting baseballs, how do you know how many baseballs are in the group? How can you check if your answer to how many baseballs are in each group is correct?”
• Module 4, Lesson 4, Learn Together provides the following questions for teachers: “How many different colors of crayons should you use? Which colors do you want to use? After you draw the crayons, how can you find the number of crayons in each category? Do any of the boxes of crayons have the same number of crayons? How can you sort the categories by count?”

The instructional materials reviewed for HMH Into Math Kindergarten 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 I Can Statement, Learning Objective, Language Objective, materials needed, and Mathematical Progressions 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.

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

Each module in the Teacher Edition includes Mathematical Progressions 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 notes “Algebra as a course of study today is integrated around four progressions of elementary and 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 K-5, 6-7, and Grade 8 / Algebra fit into these progressions.

The instructional materials reviewed for HMH Into Math Kindergarten 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. “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 in the Teacher Edition.

The instructional materials reviewed for HMH Into Math Kindergarten 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 Common Errors 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 Fors and question prompts that highlight areas of potential student misconceptions.

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

The Lesson Focus and Coherence page indicates the CCSSM that will be addressed within the Lesson. Throughout the lesson, there are formative assessments in Check for Understanding, On Your Own, and More Practice/Homework. Each lesson has a diagnostic assessment, Are You Ready, correlated to standards.

Each Module has an End of Module Test, and the standards associated with each problem on this test can be found on the Individual Record Form within the Assessment Guide Book. In addition, Assessment Preparation includes Standards-Based Practice for most lessons.

Each Unit has a summative Performance Task that includes the content focus in the teacher pages of the Assessment Guide.

The instructional materials for reviewed HMH Into Math Kindergarten meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Each lesson has a diagnostic assessment, Are You Ready, and the materials state that teachers can use Online Ed, to assign the Digital Are You Ready? to power actionable reports including proficiency by standards item analysis.

The Planning and Pacing Guide notes, “Check Understanding is a quick formative assessment in every lesson. Teachers use data to determine which students need additional small-group support and which students can continue on to independent practice or math center challenges.” 

Each performance task includes a task-specific rubric indicating a level 0 response through a level 3 response. The structure of the rubrics is the same, but specific words are changed to reflect the mathematical content of the module. Level 3 indicates that the student made sense of the task, has complete and correct answers, and checked their work or provided full explanations. Level 2 indicates that the student made sense of the problem, made minor errors in computation or didn’t fully explain answers. Level 1 indicates that the students made sense of some components of the task but had significant errors in their solution strategies. Level 0 shows little evidence that the student has made sense of the task, addressed specific components,and does not complete the problem. The Planning and Pacing Guide indicates a content focus for each of the items on the Unit Performance Tasks.  Each content area is identified with a depth of knowledge as well as one or more Reteach pages for follow-up with students. 

The Individual Record Forms in the Assessment Guide suggest Reteach Lessons that teachers can use for follow-up based on the Module assessments and Performance Assessments.

The Individual Record Forms for the Prerequisite Skills Inventory, Beginning-of-Year, Middle-of-Year Test, and End-of-Year Tests do not suggest Reteach Lessons or provide other guidance that teachers can use for follow-up with students.

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

Throughout the materials, strategies are present, with guidance in the beginning of each module and lesson for both teachers and students. Examples include: 

• Teaching for Depth provides information on strategies to use when teaching the concept. Represent and Explain focuses on ways for students to describe and picture a concept. Make Connections helps students understand a new idea by connecting it to previous knowledge.
• Mathematical Progressions make connections to both prior and future skills and standards to scaffold instruction.
• 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 Math Routines 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.
• In each lesson, Check for Understanding problems provide information on student understanding of the lesson content, before they begin independent work during On Your Own.

The instructional materials reviewed for HMH Into Math Kindergarten 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 lesson 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, Almost There (RtI), and Ready for More.”
• Each lesson provides Leveled Questions identified as DOK 1, 2, and 3 with an explanation of the knowledge those questions uncover about student understanding.
• In the Teacher Edition, Spark Your Learning provides two possible strategies and a common error. Each section describes student actions and has teachers either describe and practice or remind them of important strategies to support learning and how to intervene..

There are four “Language Routines to Develop Understanding” used throughout the materials: 

• “Three Reads: Students read a problem three times with a specific focus each time.” 
• “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.”  
• “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy.” 
• “Critique, Correct and Clarify: Students correct work that is not their own with a flawed explanation, argument, or solution method and share with a partner to reflect and then refine the sample work.”

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

STEM Tasks are provided at the beginning of every instructional unit and include cross-curricular tasks which allow multiple entry-points and various solution strategies or representations. For example:

• In Unit 4, STEM Task: “Have children work in a group. Give each group three pieces of construction paper. Ask them to use their senses as they think about physical education class. On one piece of paper, have them draw things they might see in a gym. On another piece of paper, have them draw things they might hear in the gym. On the last piece of paper, have them draw things they might feel or touch in the gym. Have the groups share and discuss their work.”

Turn and Talks throughout each lesson provide opportunities for students to share a variety of ways to solve the problem, for example:

• In Module 6, Lesson 1, Turn and Talk: “Have partners tell each other their word problems and compare them. Guide children to discuss how, even though their problems might not be the same, they all should have added one cat and three dogs to get a total of four pets because those are the numbers in the picture..”

In the Planning and Pacing Guide, Spark Your Learning tasks are “designed as ‘low-floor/high ceiling’ tasks that all students can access but that can also be extended to provide challenge.” Teachers are provided guidance on how to assist various levels of learners, depending on how they respond to the problem.

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

In each module, Language Development provides support for ELLs including 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….”, and “Visual cues help students…” Language Development also includes information about the Language Routines embedded in the instructional materials: Three Reads; Stronger and Clearer Each Time; Compare and Contrast; Critique, Correct, and Clarify. These are identified by a pink box throughout lessons with a speech bubble that identifies the Language Routine to be used. In addition, there are supports for special populations including:

• Language Objectives are included in every lesson.
• Reteach and RtI worksheets can be assigned online or printed.
• Turn and Talk prompts designed to support students, for example, “Go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”
• A multilingual glossary is available online.

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

Supports for advanced students include:

• Each lesson has a corresponding Challenge page, provided in print or online, addressing the same concepts and standards where students further extend their understanding. 
• In the beginning of each module, Extend the Task provides suggestions for deeper exploration of the tasks.

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

Pictures of adults and children in the materials show a variety of demographics and personal characteristics. There are a variety of names used in word problems throughout the materials. The lessons contain a variety of tasks and situations in the story problems that interest students of various demographic and personal characteristics. There is a balanced approach to the use of gender identification. Examples include:

• The materials reference roles instead of pronouns (e.g., the players, book fair, sailboats, collection of toy cars, piggy banks, carton of eggs).
• The materials include a set number of names used throughout the problems and examples (e.g., Janette, Anton, Zed, Ari, Tai, Nick, Sam). These names are presented in a way that does not stereotype characters by gender, race, or ethnicity.