6th Grade - Gateway 3

The instructional materials for EdGems Math Grade 6 meet the expectations for distinguishing between problems and exercises. Each Unit presents lessons with a consistent structure. The instructional sections, which vary by day, include: Warm-Up, Introduction to lesson using Lesson Presentation, Explore! Activity, and Focused Assignment or Online Practice. 

Within the Teacher/Lesson Guide, the student work is referred to as exercises, activities, and independent student practice. For example:

• In Lesson 2.1, Adding and Subtracting Decimals, Teacher/Lesson Guide, the lesson planning suggestion states, “This lesson may take 2 class periods (45-60 minutes per period). A suggested order for covering the content in this lesson in two days is below. Additional time may be given to use Tic-Tac-Toe activities or independent student practice. Day 1: Warm-up of choice from above, Lesson Presentation, Teacher Gem Activity (6.NS.3 Relay), Focused Assignment or Online Practice.”

Within the Student Lessons throughout the materials, multiple examples are provided to show the steps to take when working with the content. The students then practice the content out of context before working with the content in story problems within context. For example:

• In Lesson 4.3, Dividing Fractions, Student Lesson, students learn the content by solving problems without context and apply the content in real-world contexts. “Find each quotient. Write your answer in simplest form. 5. 2/3 ÷ 1/3.” Near the conclusion of the problems, students evaluate the reasoning of others. “Two students solved division expressions. In Exercises 30 and 31, determine if the work shown by each student is correct and solve correctly if an error was made. Explain your reasoning.”

The instructional materials for EdGems Math Grade 6 meet the expectations that the design of assignments is intentional and not haphazard. Overall, lessons are sequenced so students develop an understanding of mathematical concepts and skills. The structure of the lessons provides students with the opportunity to activate prior learning, build procedural skills, and engage with multiple activities that increase in complexity, utilizing concrete and abstract representations.

In each Teacher/Lesson Guide, there are Lesson Planning Suggestions. These suggestions sequence the content in an order to help students develop understanding. For example, in Lesson 3.3, Percents of a Number, Lesson Planning Suggestions builds from guided practice to more abstract and contextual work with the content, “This lesson may take 2-3 class periods (45-60 minutes per period). A suggested order for covering the content in this lesson in two days is below.”

Day 1: 

• Explore! Activity: “Double Number Lines” 
• Lesson Presentation 
• Teacher Gem Activity (6.RP.3c Relay) 

Day 2: 

• Exit Card as entrance activity 
• Focused Assignment or Online Practice 
• Communication Prompt

The instructional materials for EdGems Math Grade 6 meet the expectations for having a variety in what students are asked to produce. In the practice pages, students develop concepts and skills by answering multiple questions on the content. For example:

• In Lesson 1.3, Rates and Unit Rates, Exercises, students find unit rates through multiple examples, “Find each unit rate. 1. 60 miles/2 hours”

Students connect content to real-world situations and gain extra practice through the Student Gems, linked resources from Open Educational online sites. For example:

• In Lesson 5.2, Order of Operations, Student Gems from Desmos, students complete extra practice on the order of operations. Summary from the Desmos website, “In this activity, students use sketch to solve "twin puzzles" as a way to practice their order of operations skills. Teachers can use the overlay feature in the teacher dashboard to assess the class at a glance and to facilitate class-wide error analysis discussions, or the response view to identify individual students who need additional support.”

With the Teacher Gems, students create arguments and justify their answers. For example:

• In Lesson 9.5, Volume of Rectangular Prisms, Teacher Gem: Partner Math, students solve problems involving the volume of rectangular prisms, they justify their answers to others to compare work, “4. Once the students have a new partner, they need to compare answers from the previous two tasks. If they agree, they sign their initials in the circle connecting the two task boxes. If students disagree, they work to determine who is correct prior to signing. Once students compare, the teacher should have posted what the next two tasks are and they work with this partner to complete the next two tasks.”

The instructional materials reviewed for EdGems Math Grade 6 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 often incorporate the use of manipulatives, but when they are included, manipulatives are consistently aligned to the content in the standards. For example, In Lesson 4.1, Multiplying Fractions, Explore, ‘Fraction Action’ is an activity that uses paper to help students create conceptual understanding of multiplying fractions. “Step A: First he divided a piece of paper horizontally into as many sections as were shown in the denominator of one of the factors. For 3/4 , divided the paper into 4 horizontal sections.”
• Examples of manipulatives include: Algebra tiles, grid paper, rulers, patty paper/tracing paper, cylinders and cones, protractor, and x-y tables.

The instructional materials for EdGems Math Grade 6 meet the expectations for providing quality questions to help guide students’ mathematical development. There is a Communication Prompt in every lesson that provides questions to help guide students’ mathematical development. For example:

• In Lesson 3.2, Percents, Decimals, and Fractions, Communication Prompt, “Explain how you would write 2/5 as a percent.”
• In Lesson 10.3, Dot Plots, Communication Prompt, “Describe the process for creating a dot plot. Include at least 3 steps in your description”

Questions are also located in the Mathematical Practice section, but these questions are not located in every lesson. 

• In Lesson 2.1, Adding and Subtracting Decimals - A Closer Look, “MP2: Students will need to choose the correct operation for each word problem. Brainstorm key words they might see that will give clues about whether they should add or subtract when doing the exercises”
• In Lesson 8.2, Writing Two-Step Equations - A Closer Look, “MP3: Give students an input-output table and ask them to find the equation. Have students construct a viable argument for why their equation is correct.”

The instructional materials for EdGems Math Grade 6 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 Unit Overview, there is information provided to help teachers understand the materials in order to present the content. The Unit Overview provides a brief overview of the content contained within the unit. It also includes standards, learning progression, pacing, and assessments contained within the unit.
• The Student Gems contain links to outside technology-enhanced activities. These contain instructions for students, but there is no guidance for the teacher as to when to use these activities to enhance student learning.
• Explore! Summary and Suggestions provides details about the Explore! Activity and suggestions for how it can be implemented. For example, in Lesson 6.3, Solving Multiplication and Division Equations, “Students have another opportunity to model with equation mats and algebra tiles in “Multiplication Equations”. Students use the tiles to model multiplication equations and then balance their mats. The Explore! activity ends with students summarizing how to use the mats and tiles to model and solve multiplication equations. You may choose to discuss with students what it might look like to solve a division equation on a mat and what the model’s limitations are for this operation.”
• Mathematical Practices - A Closer Look, contains information related to each Mathematical Practice contained in the lesson and suggestions for teachers. For example, in Lesson 1.5, Measurement Conversions, “MP6: Physically show students objects that represent different measurements so they understand better how one relates to another. Focus on the meaning of the prefixes used with metric measurements in the table at the beginning of the lesson. Encourage students to think of other words with these prefixes (e.g., decade for deca-).”
• There are Extra Examples found in each of the lessons for teachers to present if needed.
• Teaching Tips provide teachers with suggestions for teaching the content within the lesson. For example, in Lesson 9.4, Nets and Surface Area, Teaching Tip, “Encourage and point out different nets for the same solid. Having students show different nets for the same solid will reinforce that there are many ways to draw a net. On a wall have students tape up different nets for the same solid.”

The instructional materials for EdGems Math Grade 6 meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

The materials provide information that explains the progression of the content across multiple grades and within the series itself. Each Unit Overview includes Learning Progression which includes concepts and skills that students have experienced in the past and ones that they will experience in the future. For example in Unit 7, Rational Numbers and the Coordinate Plane, the Learning Progressions contains:

“In earlier grades, students have: 

• Compared whole numbers and positive rational numbers. (K.CC-5.NBT) 
• Graphed points in the first quadrant of the coordinate plane. (5.G.1-2) 
• Named shapes based on their properties. (3.G, 4.G and 5.G) 

In future grades, students will:

• Add, subtract, multiply and divide rational numbers. (7.NS)
• Graph proportional relationships and functions on a coordinate plane. (7.RP.2 and 8.F)”

The instructional materials for EdGems Math Grade 6 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions. Each Unit contains a Common Misconceptions document that discusses the common misconceptions for each lesson. This document also provides mathematically sound strategies for the teacher to address student errors. For example:

• In Lesson 4.2, Dividing Fractions with Models, Common Misconceptions, “ The concepts of dividing by 1/2 and dividing in half may confuse some students. Division by 1/2 equates to finding how many one-halves there are in a quantity; division in half yields two equal parts of the original quantity. When teaching fraction division with models, have students show two similar examples (i.e., one for dividing by half, one for dividing in half).”

The instructional materials for EdGems Math Grade 6 meet the expectations that assessments clearly denote which standards are being emphasized.

Standards for the unit are denoted at the unit level in the Unit Overview in the Standards and Recommended Pacing. The unit standards are also noted on the Pacing Guide for each lesson in the unit. The assessments, tiered assessments, and performance tasks indicate which standards are being assessed at the question level. Standards are provided on the Teacher Unit Page with a blue “i” icon for the assessments, tiered assessments, and performance tasks. Standards are noted using the blue “i” icon for Exit Cards on the Lesson pages. The standards are noted on the Unit Overview in the Assessment section for the Gem Challenges.

The instructional materials for EdGems Math Grade 6 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Every lesson in the Teacher/Lesson Guide has Teaching Tips which provide information on strategies to use when teaching the concept, manipulatives that might be useful, questions to focus on, and other tips depending on the lesson.
• At the beginning of each Unit, Learning Progressions makes connections to both prior and future skills and standards to scaffold instruction.
• Each lesson provides a Warm-up to activate prior knowledge.
• The materials provide three different levels of practice for each lesson (Tiered, Proficient, and Challenge Practice) as well as tiered assessments, however, there are no strategies or instructions for teachers on how to sequence or scaffold these items.

The instructional materials for EdGems Math Grade 6 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

Within the materials there are three levels of practice pages: Proficient (on level), Tiered (more focused development), and Challenge (extension). These pages allow for more development of the content knowledge regardless of the level of the students. The material presents different types of questions all related to the content from the lesson. For example:

• In Lesson 6.1, Equations and Solutions, Proficient Practice for on-level students has questions focusing on the content, “Determine if the number given is the solution of the equation. 1. ???? + 5 = 12 Is 7 the solution? ”. The Challenge practice, focused on extension of the concept, includes solving equations and finding the solutions, “Match each equation on the left with its solution on the right. 1. ???? + 5 = 17 ”. The Tiered Practice is geared towards students that need more focused help with the content which is done by providing the steps to determine if a number is a solution, “Determine if the number given is the solution of the equation. Shade in the correct answer. 1. ???? − 2 = 11 Is 9 the solution?”.
• Assessments and Tiered Assessments are located in each Unit.

The instructional materials for EdGems Math Grade 6 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations. The materials have Performance Tasks embedded into each Unit, and teacher guidance on how to help students solve these problems is limited.

• Each Unit includes Performance Tasks, some of which include multiple entry-points. Within the Unit Overview, Assessment section, the Performance Tasks (Formative or Summative) for each unit are identified. 
• Each Lesson has an Explore! task which does include instructions on its use. For example: Lesson 8.2, Writing two-variable equations, Teacher Guide, “In this Explore! students will write an equation that models the relationship between the number of weeks of school and the number of homework assignments completed. Students work through the development of a linear equation by creating an input-output table of values, looking for the pattern in the table and then writing the equation for the relationship. Students develop the equation by looking for the start value, which corresponds to an input value of 0, and the rate of change, which is the amount the output values increase or decrease by for each increase of 1 in the input column. This Explore! activity helps set the stage for the lesson presentation. You may choose to have students work in partner sets or work through this Explore! activity as a full class.”

The instructional materials for EdGems Math Grade 6 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. The materials provide some opportunities for advanced students to investigate the course-level mathematics at a greater depth. Each lesson includes Tiered Practice, Proficient Practice, and Challenge Practice sheets. The Challenge Practice sheets include more complex problems than the Tiered and Proficient Practice sheets, and the number of problems is comparable. 

The instructional materials for EdGems Math Grade 6 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics. Lessons contain a variety of demographic and personal characteristics.

• Names and wording are chosen with diversity in mind. The materials include various names throughout the problems for example: Mikayla, Shawna, Juan, Seth, Sherry, Dalexis, Julio, Jaylynn, Kobe, Ebizah, Ginger, Gracin, Kitts, Vadek. The names are used in ways that do not stereotype characters by gender, race, or ethnicity. 
• Images portrayed of students throughout the lessons show a wide range of students according to gender, race, and ethnicity. 
• When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways not expressing gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies.