5th Grade - Gateway 3

The instructional materials for HMH Into Math Grade 5 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.

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 sections. 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. Step It Out sections help students develop procedural skill and fluency. 

Check Understanding and On Your Own sections include exercises that ask students to use the newly learned mathematics in each lesson. Additional Practice and Homework is available in separate student journal, providing more exercises for students to solve.

For example in Lesson 6.4, Spark Your Learning, students experiment with the following problem: “TV show hosts, Ben and Isa, are preparing small pieces of French toast from slices of bread. Ben cuts his slice into two equal sections. Isa cuts her slice into three equal sections. They were supposed to all be cut into the same-size pieces. Draw a visual model to show what Ben and Isa should do to correct the sizes of their sections of French toast.” Students develop their understanding in the Build Understanding and Step It Out where they write common multiples and equivalent fractions with a common denominator. Then in the On Your Own section students use common denominators to practice writing equivalent fractions. 

The instructional materials for HMH Into Math Grade 4 meet the expectations that the design of assignments is intentional.

Overall, lessons are sequenced and scaffolded so students develop understanding of mathematical concepts and skills. The lesson structure 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 the Spark Your Learning, students use manipulatives and/or visual models to experiment with mathematics thus developing a concrete or representational understanding. This is followed by a Turn and Talk with a partner allowing students to process the connections they have found. Throughout the lessons, students are provided scaffolding with new content in the Build Understanding and Step It Out sections, where the abstract concept is broken down into smaller steps with additional Turn and Talk opportunities, and provided with independent exercises to build understanding and mastery. The Check Understanding section provides a mid-lesson check in and can be used to indicate the need to differentiate learning for students. Students practice the abstract concept in the On Your Own.

For example, in Lesson 1.2, students begin by using manipulatives or a visual model to solve the following problem: “Aaron’s school has set up a website to raise money for a new playground. Each donation is $10. For the first 10 days, the school receives 10 donations each day. How much does the school received the first day? How much does the school receive after 10 days? Explain your thinking.” Students then look for patterns in Step it Out first by multiplying 7 x 10 then 7 x 10 x 10 etc. In On Your Own, they progress to the abstract concept of 5 x $$10^3$$.

Concepts are developed throughout the modules such as 5.NBT.2.7 which is introduced in Module 14, Add and Subtract Decimals. Students continue work with decimals in Module 15, Multiply Decimals and Whole Number, Module 16 Multiply Decimals, and Module 17 Divide Decimals.

The instructional materials for Into Math Grade 5 meet the expectations for having a variety in what students are asked to produce. For example:

There is variety in how students are asked to present mathematics. In the Spark your Learning, Build Understanding, and Step It Out sections, students are often asked to use visuals to show their thinking. Turn and Talk questions frequently ask students to construct arguments and give explanations. There are opportunities for students to produce answers and solutions in the On Your Own sections, while also providing opportunities for students to provide written explanations. Throughout the materials, students are asked to represent mathematics using equations.

Homework assignments ask for a variety of responses from fluency to higher-level thinking. For example, Lesson 4.4, Homework has seven problems. One problem is a multi step word problem. One asks students to describe how they would solve {[24 / (6 - 2)] - 4} x 3. Four problems ask students to use parentheses to make an expression equal to a given value and the last problem asks students to critique the reasoning of another students work that is provided. 

The instructional materials reviewed for HMH Into Math Grade 5 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

At the beginning of the lesson they indicate what materials/manipulatives will be needed. The lesson on the student pages provide a picture of the manipulative that they will use. For example, in Lesson 4.1, students are asked to model a situation with two color counters “Al drum line is made up of 14 fourth-grade drummers and 12 fifth-grade drummers. The fourth-grade drummers stand in a line, and the firth grade-drummers stand in a line behind them.” Students use two color counters or a visual model to create a representation. The manipulatives provide opportunities for students to develop a conceptual model of problems that they will then represent in pictorial form in their student workbook. 

Lesson 6.3, Spark Your Learning, students are encouraged to use a visual representation to show $$\frac{3}{4}$$ and $$\frac{1}{2}$$. They use fractions tiles to make equivalent fractions in order to subtract the fractions. The work with fraction tiles is connected to the written method for making equivalent fractions and subtracting fractions.

Examples of manipulatives for Grade 5 include: base ten blocks, connecting cubes, fraction strips, grid paper, ruler, number line, square tiles, and two color counters

The materials rely heavily on pictures of manipulatives. When physical manipulatives are called for in the lesson materials in the Teacher Edition, it is not always clear how they are to be used. There is sometimes direction for how they can be used in the differentiation section.

The instructional materials for HMH Into Math Grade 5 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. Sections titled, Activate Prior Knowledge, Spark Your Learning, Build Understanding, Learn Together, and Turn & Talk, consistently provide questions to drive student discussion. For example:

• Lesson 4.2, Activate Prior Knowledge, provides teachers with following questions: “Where did you put the parentheses? Why? Which operation will you do first to evaluate the expression? What should happen in your word problem when the expression shows addition? What should happen in your word problem when the expression shows division?” 
• Lesson 19.4, Step it Out, includes questions for teachers to ask students: “How will you complete Antonia’s row in the table? How will you complete Connor’s row in the table? ” “How does writing the numbers as ordered pairs help you analyze their relationship?” 
• Lesson 13.3, Spark Your Learning, includes four questions: “How do you round a whole number, like 853, to the nearest ten?” “How does the value of the number 15.04 compare to the value of the number 15.040?” ”Which digits in the numbers 15.042 and 15.046 have the place value of hundredths?” 

The instructional materials for HMH Into Math Grade 5 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.

Throughout the teacher edition there are ample and useful annotations and suggestions on how to present the content in the student edition to all levels of math learners in the classroom. Specifically, the teacher edition includes sections titled, Lesson Focus and Coherence, Plan for Differentiated Instruction, Spark Your Learning, Motivate, Persevere, and Leveled Questions, designed to assist the teacher in the mathematical standards and concepts that are present in the lesson. For example: 

• Lesson 2.2, Spark Your Learning, includes margin notes for the teacher that  describes possible strategies the teacher can take based on the needs of the students.  
• Lesson 7.1, Activate Prior Knowledge, include the following guidance for teachers:  “Based on the students’ responses to the Problem of the Day, choose one of the following: Project interactive Reteach, Grade 4, Lesson 11.2 or Complete the Prerequisite Skills Activity.”

The instructional materials for HMH Into Math Grade 5 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 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 for HMH Into Math Grade 5 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 of the Teacher Edition.

The instructional materials for HMH Into Math Grade 5 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 5 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 then formative assessments in the Check for Understanding, On Your Own and More Practice/Homework. Each module has an End of Module Test, the standards associated with each problem on this test can be found on the Individual Record Form within the Assessment Guide Book.

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

The instructional materials for HMH Into Math Grade 5 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 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 Your Own or More Practice/Homework.

The instructional materials for HMH Into Math Grade 5 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, 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 four 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.” 3) “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy. And 4) “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 for HMH Into Math Grade 5 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:

There is Language Development to support English Learners 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….”, 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 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.
• There are Reteach, and RtI worksheets that can be assigned online or printed.
• There are 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 for HMH Into Math Grade 5 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:

• 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 Edition provides ideas for extending the task.

The instructional materials for HMH Into Math Grade 5 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

The materials provide various demographic and personal characteristics. The instructional materials reviewed for this series meet the expectation for providing a balanced portrayal of various demographic and personal characteristics. Pictures of adults and children in the text show a variety of demographics and personal characteristics

There are a variety of names used in word problems throughout the text. 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.