7th Grade - Gateway 3

The instructional materials for EdGems Math Grade 7 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 In Lesson 2.4, Proportional Relationship Equations, Teacher/Lesson Guide, the lesson planning suggestion states, “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. Additional Teacher Gem activities may be used on Day 3 to help students have more experiences with proportional relationships. Day 1:  Choice of warm-up activities from above, Lesson Presentation, Explore! Activity: “Equation Connection”, Exit Card.”

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 In Lesson 6.2, The Distributive Property, Student Lesson, students learn the content by solving problems without context and apply the content in real-world contexts. “Use the Distributive Property to rewrite each expression without parentheses. 4. 8(x + 5)” Near the conclusion of the problems, students evaluate the reasoning of others. “30. Store A put items on sale for 20% off the original price. Later they took an additional 30% off the sale price. Store B first put the same items on sale for 30% off the original price. Later they took an additional 20% off the sale price. Francis says it doesn’t matter which store she purchases a sale item from because now it is the same price at both stores. Do you agree or disagree? Explain your reasoning.”

The instructional materials for EdGems Math Grade 7 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 3.1, Fractions, Decimals, and Percents, 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. Additional time may be given to use Teacher Gem activities or independent student practice.”

Day 1: 

• Explore! Activity: “Fractions and Decimals” 
• Lesson Presentation 
• Focused Assignment or Online Practice 

Day 2: 

• Exit Card as entrance activity
• Choice of Teacher Gem Activity (7.NS.2d Partner Math, MATHO, Categories)
• Leveled worksheet assignment

The instructional materials for EdGems Math Grade 7 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 1.2,  Unit Rates, Exercises, students find unit rates through multiple examples, “Find each unit rate. 1. 70 miles/2 hours”

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

• In Unit 4, Sums and Differences of Rational Numbers, Student Gem from Illustrative Mathematics, students use the difference of rational numbers to work out a problem that has a real-world connection. "Imagine that the temperature has dropped to the freezing point for ocean water. How many degrees more must the temperature drop for the antifreeze to turn solid?”

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

• In Lesson 8.2, Vertical and Adjacent Angles, Teacher Gem: Partner Math, students solve problems to find a missing variable using the properties of vertical and adjacent angles, 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 7 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 7.1, Solving One-step Equations, “‘Introduction to Equation Mats’  is an activity that requires algebra tiles. Algebra tiles can be purchased or made from card stock. In this activity, students use the concept of zero pairs to cancel out positive or negative tiles. Talk to students about the fact that one negative and one positive, when combined, form a zero pair and can be removed from the equation mat as the pair is worth zero together. This activity works best when students work in partner sets with one equation mat between them. One student can be responsible for manipulating the tiles on the board while the other records on the Explore! activity sheet. Have student pairs share out Step 8 with the class to wrap up the activity.”
• 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 7 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 4.3, Subtracting Integers, Communication Prompt, “How is subtracting integers similar to adding integers?”
• In Lesson 8.6, Area of a Circle, Communication Prompt, “What is the same about the formulas for area and circumference of a circle? What is different about the formulas for area and circumference of a circle?”

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

• In Lesson 3.3, Percent of Change, Mathematical Practices - A Closer Look, “MP3: Use the Explore! to lead students to a conjecture about how to find percent of change (that they will need to know the change in values and the original amount). Also, Exercise 15 asks students to critique the work of a student to fix an error that was made.”
• In Lesson 9.2, Surface Area of Prisms, Teaching Tips, “ In sixth grade, students found surface area for the first time in the standards. They may have been introduced to the process using nets or formulas. Ask students about their experiences by introducing the lesson by saying, ‘If I wanted to find the surface area of a prism, how could I do that? What is surface area?’”

The instructional materials for EdGems Math Grade 7 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 6.1, Algebraic Expressions, “In this activity, students will evaluate geometric formulas by substituting values for the variables in the formulas. This activity connects to previous work students have done finding area, surface area and volume. ‘Formula Frenzy’ should be used at the end of Day 1 or the start of Day 2 of this lesson. It could also be sent home as homework at the end of Day 1. If this is done, it would be best to group up students to compare solutions at the beginning of the next class as a warm-up activity”
• Mathematical Practices - A Closer Look, contains information related to each Mathematical Practice contained in the lesson and suggestions for teachers. For example, in Lesson 1.4, Scale Drawings, “MP6: Emphasize paying close attention to units in the problems to understand whether the measurement is an actual measurement or a scaled measurement.”
• 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 9.1, Three Dimensional Figures, Teaching Tip, “You may want to review vocabulary with students by asking them to discuss the difference between parallel and perpendicular prior to starting the lesson.”

The instructional materials for EdGems Math Grade 7 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 5, Products and Quotients of Rational Numbers, the Learning Progressions contains:

“In earlier grades, students have:

• Used positive and negative rational numbers to represent situations. (6.NS.5) 
• Graphed rational numbers on a number line. (6.NS.6) 
• Compared rational numbers. (6.NS.7) 
• Multiplied and divided fractions. (5.NF and 6.NS.1) 
• Multiplied and divided decimals. (6.NS.3) 

In future grades, students will:

• Use rational numbers to solve multi-step equations. (8.EE.7) 
• Simplify expressions with rational exponents. (HS.N-RN)”

The instructional materials for EdGems Math Grade 7 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 7.4, Linear Inequalities, Common Misconceptions, “Students may forget to switch the inequality sign when multiplying or dividing by a negative. Help students by asking them to check answers in their solution sets in the original inequality to see if they satisfy the inequality.”

The instructional materials for EdGems Math Grade 7  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 7 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 7 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 2.4, Proportional Relationship Equations, Proficient Practice for on-level students has questions focusing on the content, “Complete each input-output table and graph each function in Quadrant I. 1. y = 2x”. The Challenge practice, focused on extension of the concept, includes determine if a relationship represents a proportional relationship “Tell whether or not each table shows ordered pairs that model a proportional relationship. If the ordered pairs represent a proportional relationship, write an equation for the table in the form y = rx. If the ordered pairs do not show a proportional relationship, explain how you know.”. The Tiered Practice is geared towards students that need more focused help with the content which is done by providing more scaffolding by providing a partially complete table, “Complete each input-output table and graph each function in Quadrant I. 1. y = 2x”.
• Assessments and Tiered Assessments are located in each Unit.

The instructional materials for EdGems Math Grade 7 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 10.3, Compound Probability, Teacher Guide, “In ‘Three Sports’, students are introduced to three models for finding the total number of possible outcomes of an event happening, as well as being introduced to compound probability. This Explore! activity may take a full class period and the Lesson Presentation may need to be moved to Day 2. In this activity, students make lists, tree diagrams and tables and then get a chance to talk about the model they prefer. It may work best for every student to have his or her own activity sheet during the group work so each student has the opportunity to see first-hand how to create each of the models.”

The instructional materials for EdGems Math Grade 7 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 7 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: Katie, Keisha, Willis, Juan, Seth, Sherry, Mikayla, 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.