7th Grade - Gateway 3

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for having an underlying design that distinguishes between problems and exercises.

• Each Topic includes three sections: Overview, Exploring, and Summary. The Overview section introduces the mathematical concepts that will be addressed in the Topic. The Exploring section includes two to four explorations. In these explorations students learn the mathematical concepts of the Topic through problems that include technology-enhanced animations and full-class activities. The Summary section highlights the most important concepts from the Topic and gives students another opportunity to connect these concepts with each other.
• Each Topic also includes three additional sections: Practice, Assessment, and Activity Sheets. The Practice section includes Guided Practice and More Practice. Guided Practice consists of exercises that students complete during class periods, providing opportunities for students to apply the concepts learned during the explorations. More Practice contains exercises that are completed as homework assignments. The Assessment section includes Automatically Scored and Constructed Response items. These items are exercises to be completed during class periods or as part of homework assignments. They provide more opportunities for students to apply the concepts learned during the explorations. The Activity Sheets also contain exercises, which can be completed during class periods or as part of homework assignments, that are opportunities for students to apply the concepts learned during the explorations.
• Some Topics also include MARS Tasks, which are exercises that present students with opportunities to apply concepts they have learned from the Topic in which the MARS Task resides or to apply and connect concepts from multiple Topics.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for having a design of assignments that is not haphazard with problems and exercises given in intentional sequences.

The sequencing of Topics, and explorations within the Exploring section for each Topic, develops in a way that helps to build students’ mathematical foundations.

• The Topics are comprised of similar content. For example, in Topic 5 Adding and Subtracting Integers the Exploring section includes Modeling with Algebra Tiles, Using the Number Line, and Using the Vertical Number Line.
• Within the explorations for each Topic, problems generally progress from more simple to more complex problems and incorporate knowledge from prior problems or Topics, which offers students opportunities to make connections among mathematical concepts. For example, solving problems related to relationships for different pairs of angles in Topic 12 incorporates and builds upon writing and solving equations from Topic 8.
• As students progress through the Overview, Exploring, and Summary sections, the Practice (Guided and More), Assessment (Automatically Scored and Constructed Response), and Activity Sheets sections are placed intentionally in the sequencing of the materials to help students build their knowledge and understanding of the mathematical concepts addressed in the Topic.
• The MARS Tasks are also placed intentionally in the sequencing of the materials to support the development of the students’ knowledge and understanding of the mathematical concepts that are addressed by the tasks.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for having a variety in what students are asked to produce.

Throughout a Topic, students are asked to produce answers and solutions as well as explain their work, justify their reasoning, and use appropriate models. The Practice section and Automatically Scored items include questions in the following formats: fill-in-the-blank, multiple choice with a single correct answer, and multiple choice with more than one correct answer. Constructed Response items include a variety of ways in which students might respond, i.e. multiple representations of a situation, modeling, or explanation of a process. Also, the types of responses required vary in intentional ways. For example, concrete models or visual representations are expected when a concept is introduced, but as students progress in their knowledge, students are expected to transition to more efficient solution strategies or representations.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models. The materials include a variety of virtual manipulatives, as well as integrate hands-on activities that allow the use of physical manipulatives.

Most of the physical manipulatives used in Agile Mind are commonly available: ruler, patty paper, graph paper, algebra tiles, and graphing calculators. Due to the digital format of the materials, students also have the opportunity to represent proportional relationships virtually with a table and graph and generate random samples to draw inferences. Each Topic has a Prepare Instruction section that lists the materials needed for the Topic. Manipulatives accurately represent the related mathematics. For example, Topic 8, Exploring Modeling and Solving Linear Equations, students use physical Algebra Tiles to model an equation and write a mathematical procedure along with having an interactive, virtual model of the same problem.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. The Deliver Instruction section for each Block of a Topic includes Framing Questions for the start of each lesson. For example, in Topic 6 Block 2, the Framing Questions are: “Can you model the multiplication problems from yesterday? (If students struggle, model a few to get them going.) How do you think we could model division with algebra tiles?” During the lesson, the Deliver Instruction section includes multiple questions that teachers can ask while students are completing the activities. At the the end of each lesson, Deliver Instruction includes Further Questions. For example, in Topic 6 Block 6 “How are the rules for integer multiplication related to the rules for raising integers to powers?”

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for containing a teachers edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, the materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The materials contain Professional Support which includes a Plan the Course section and a Scope and Sequence document. The Plan the Course section includes Suggested Lesson-planning Strategies and Planning Resources. Each Topic contains an Advice for Instruction section that is divided into Prepare Instruction and Deliver Instruction. For each Topic, Prepare Instruction includes Goals and Objectives, Topic at a Glance, Prerequisite Skills, Resources, and Language Support, and for each Block within a Topic, Deliver Instruction includes Agile Mind Materials, Opening the Lesson, Framing Questions, Lesson Activities, and Suggested Assignment. In Lesson Activities, teachers are given ample annotations and suggestions as to what parts of the materials should be used when and Classroom Strategies that include questions to ask, connections to mathematical practices, or statements that suggest when to introduce certain mathematical terms or concepts.

Where applicable, the materials include teacher guidance for the use of embedded technology to support and enhance student learning. For example, in Topic 9 Block 1 teachers are directed to, “Show the animation on page 3. Stop the animation on each panel and have students work in pairs to understand the definition of each bolded vocabulary word. Allow students to use previous knowledge or resources to record their definitions and examples. [SAS, question 1]. Show page 4. Have students discuss each profession. Ask for suggestions for other professions that utilize probability.”

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

In Professional Support, Professional Learning, there are four interactive essays entitled “Developing concepts across grades”. There is an Overview that explains the purpose of the four essays, and the topics for these four essays are Functions, Volume, Rate, and Proportionality. Each essay is accessible to teachers and not students, and the Overview states “these essays are available for educators to illustrate connections and deepen understanding around what students may have already learned, and where they are headed on their journey.” Each essay examines the progression of the concept from Grades 6-8 through Algebra I, Geometry, Algebra II, and beyond. By examining the progressions of the concepts beyond Algebra II, teachers have the opportunity to improve their own knowledge of more advanced mathematics concepts that build upon grade-level standards. For example, in Volume, teachers progress from packing a right, rectangular prism with unit cubes to developing the formulas for the volume of cylinders and cones to finding the volume of a figure generated by rotating a two-dimensional shape around a horizontal axis. Also, in Proportionality, teachers explore how proportional relationships are part of the following mathematical concepts: scaling images, linear functions, trigonometric ratios, rational functions, and the derivative.

In addition to “Developing concepts across grades”, the Grade 7 materials also contain a section of interactive essays entitled “Going beyond Grade 7”. There is an Overview that explains the purpose of the three essays, and the Overview states, “These essays are not intended for use with your 7th grade students; rather, they are designed to provide you with important connections and background that will support you as you help your students master 7th grade content.” The topics for these three essays are Rate of Change, Random Variables, and Volume of Solids with Known Cross Sections. Along with having their own section in Professional learning, each of these essays are also referenced in Deliver Instruction for the Blocks where they are appropriate under the title of Teacher Corner. For example, in Topic 3, the essay Rate of Change is referenced for teachers in Block 2 on page 4, and in Topic 9, Random Variables is referenced in Block 4 on page 6. Two of the essays, Rate of Change and Random Variables, connect the Grade 7 content to advanced mathematical concepts through multiple grades and courses, but Volume of Solids with Known Cross Sections progresses quickly from Grade 7 content to content that would be part of a Calculus course. This transition provides few, if any, opportunities for Grade 7 teachers to connect the concept to advanced high school content in Calculus.

In Professional Support, there is a section of Professional Essays which are in either Print or Video format. The Print essays are divided as either Curriculum or Course Management Topics, and although some of the Curriculum Essays are content specific, they do not address mathematical concepts that extend beyond the current grade. The Video Essays - categorized into Teaching with Agile Mind, More Teaching with Agile Mind, and Dimensions of Mathematics Instruction - do not directly provide adult-level explanations or examples of advanced mathematics concepts.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. The materials provide opportunities for ongoing review and practice, and feedback occurs in various forms. Within interactive animations, students submit answers to questions or problems, and feedback is provided by the materials. Practice problems and Automatically Scored Assessment items are submitted by the students. Immediate feedback is provided letting students know whether or not they are correct, and if incorrect, suggestions are given as to how the answer can be improved. The Lesson Activities in Deliver Instruction provide some suggestions for feedback that teachers can give while students are completing the lessons.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Each Topic consists of three main sections- Overview, Exploring, and Summary, and these three sections are divided into Blocks. Each Block contains lesson activities, materials for Practice, Assessment, and Activity Sheets, along with a MARS Tasks if applicable for the Topic. In each Topic, the Blocks and lesson activities are sequenced for the teacher. In the Advice for Instruction for each Topic, Deliver Instruction for each Block contains instructional notes and classroom strategies that provide teachers with key math concepts to develop, sample questions to ask, ways in which to share student answers, and other similar instructional supports.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation that materials embed tasks with multiple entry­-points that can be solved using a variety of solution strategies or representations. Overall, tasks that meet the expectations for this indicator are found in some of the Constructed Response Assessment items and Student Activity Sheets that are a part of all Topics. MARS Tasks embedded in some of the Topics have multiple entry-points and can be solved using a variety of solution strategies or representations. For example, in Topic 4 Constructed Response 1 students determine if two fictitious people are correct in their assumption about mixing two types of popcorn together. Students have a choice in the different representations or strategies they can use to correctly analyze the assumption. Another example is Topic 13 Student Activity Sheet 6 Problem 5; students find the area of irregular shapes which can be decomposed in different ways into shapes with which students are more familiar, such as triangles, parallelograms, and trapezoids.

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation that the materials suggest accommodations and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

The materials provide suggestions for English Language Learners and other special populations in regards to vocabulary and instructional practices. In Prepare Instruction for Topic 1, Teaching Special Populations of Students refers teachers to the Print Essay entitled “Teaching English Language Learners” in Professional Support, which describes general strategies that are used across the series such as a vocabulary notebook, word walls, and concept maps. Teaching Special Populations of Students also describes general strategies that are used across the series for other special populations, including progressing from concrete stage to representational stage to abstract stage and explicitly teaching metacognitive strategies through think alouds, graphic organizers, and other visual representations of concepts and problems.

In addition to the general strategies mentioned in Teaching Special Populations of Students, there are also many specific strategies listed across each course of the series in Deliver Instruction. In Deliver Instruction, Support for ELL/other special populations includes strategies that can be used with both English Language Learners and students from other special populations. Strategies specific to other special populations can also be found in Classroom strategy or Language strategy. An example of Support for ELL/other special populations from Topic 2, Block 1, Page 2 is “The Latin prefix uni is common in many languages; connect it to unit for ELL students. Directly proportional is a new idea and ELL students as well as students with learning differences may need a physical connection to the concept. Consider using a choral chant to help students begin to internalize what this means. Have students stand up and say “x and y are directly proportional means x times a number equals y. They are always related only through multiplication.”” An example of a strategy for other special populations from Topic 12, Block 5, Page 3 is “Classroom strategy. Students can also build the triangles with straws or other tools. The use of various tools, including technology, to explore forming triangles helps develop conceptual understanding of the conditions needed and is particularly important for students with certain learning differences.”

The instructional materials reviewed for Agile Mind Grade 7 meet the expectation for providing a balanced portrayal of various demographic and personal characteristics. The activities are diverse, meeting the interests of a demographically, diverse student population. The names, contexts, videos, and images presented display a balanced portrayal of various demographic and personal characteristics.