The instructional materials for Into Math Florida Grade 8 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions designed to develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Build Understanding and Step it Out introduce mathematical concepts, and students independently demonstrate their understanding of the concepts in Check Understanding and On My Own problems at the end of each lesson.

• In Lesson 6.1, students determine if tables show a functional relationship between two variables and provide an explanation. (8.F.1.1)
• In Lesson 6.5, students conclude that a table, graph, and description represent the same information, interpret the slope and y-intercept, and use the information to analyze the situation. (8.F.2.4)
• In Lesson 6.6, students extend their understanding of linear relationships by matching nonlinear graphs with various contexts, sketching nonlinear graphs based on context, and explaining contexts based on provided graphs. In On My Own, Question 3, students answer, “The graph represents the speed of a swimmer during a race. Describe the swimmer’s speed during the course of the race.” (8.F.2.5)
• In Lesson 1.5, Build Understanding, Question 1, students use fabric shapes to experiment with transformations by moving the shapes on top of another given figure and “explain how the figures are the same and how they are different regarding size, shape, and orientation.” (8.G.1)
• In Lesson 2.2, students manipulate two-dimensional figures on a coordinate plane to understand dilations. In Step It Out, Question 2, teachers use discussion questions to develop understanding such as, “How does a scale factor greater than 1 affect the dilation?” Between 0 and 1? Equal to 1?” (8.G.1.3)
• In Lesson 5.1, Build Understanding, students develop the concept of slope by examining two similar right triangles with hypotenuses on a line including calculating the rate of change. In Step It Out, students continue to investigate similar triangles. Part E asks, “How does the rise over run ratio from the origin to point P compare to the corresponding ratio from the origin to point R? Explain.” Part F relates that ratio to slope. In Lesson 5.4, students compare proportional relationships by calculating and comparing rates to determine the fastest runner. (8.EE.2)

The instructional materials for Into Math Florida Grade 8 meet expectations for attending to those standards that set an expectation of procedural skills.

The materials include problems and questions designed to develop procedural skills and provide opportunities for students to independently demonstrate procedural skills throughout the grade. The materials develop procedural skills in On Your Own, and students demonstrate procedural skills in More Practice/Homework.

• In Lesson 3.1, students solve multi-step equations such as 2(11t+1.5t) = 12-5t. Equations include all operations and various forms of rational numbers, including fractions and decimals. (8.EE.3.7)
• In Lesson 3.2, students solve linear equations with no solution or infinitely many solutions. They complete partial equations that would have infinitely many or no solutions such as More Practice/Homework, Question 16, “Complete the equation so that it has no solution: 10.5x − 4 = 5 + _______” (8.EE.3.7)
• In Module 7, students solve systems of linear equations in multiple ways including graphing, elimination, and substitution. For example, in Lesson 7.3, More Practice/Homework, Question 3 states, “Flex Gym charges a membership fee of $150.00 plus $40.50 per month to join the gym. A rival gym, Able Gym, charges a membership fee of $120.00 plus $46.75 per month. Find the number of months for which you would pay the same total fee to either gym.” (8.EE.3.8b)
• In Lesson 10.1, students convert decimal expansions that repeat into rational numbers. For example, in More Practice/Homework, Questions 6-11 state, Given a repeating decimal, “Write the number as a fraction or mixed number in simplest form.” (8.NS.1.1)

The instructional materials for Into Math Florida Grade 8 meet expectations for teachers and students spending sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and concepts of the grade-level, and students independently demonstrate the use of mathematics flexibly in a variety of contexts. During Independent Practice and On My Own, students often engage with problems including real-world contexts and present opportunities for application. More Practice and Homework contains additional application problems.

• In Lesson 6.5, On My Own, students compare properties of two functions where one is represented by a graph and the other by a table. For example, “Peter and Robyn decide to program their drone to deliver boxes of flowers to neighbors. With Peter’s program, he must manually attach the box to the drone. With Robyn’s program, the drone can pick up one box at a time from a pile. How much time does it take Peter to attach a box? How much time does Robyn’s drone take to pick up a box? Which program has the drone traveling faster? How do you know?” (8.F.1.2)
• In Lesson 7.6, More Practice/Homework, Question 3, students find the time needed for one horse to catch a second horse as each moves at a different rate. In Check Understanding, Question 1 states, “The Spartan basketball team scored 108 points in last night’s game. They scored 48 baskets in all, making a combination of two-point and three-point baskets. There were not points due to free throws. How many three-point baskets did the Spartans make?” (8.EE.3.8c)
• In Lesson 11.3, students use the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. For example, in Check Understanding, Question 1 states, “Computer monitors are measured diagonally, from corner to corner. If the screen of a 40-inch monitor is 35 inches wide, what is its height?”; Question 3, “A child has an empty box that measures 4 inches by 6 inches by 3 inches. What is the length of the longest pencil that will fit into the box, given that the length of the pencil must be a whole number of inches? Do not round until your final answer.” (8.G.2.7)
• In Lesson 3.3, students create and apply open-ended linear equations to real-world scenarios such as, “A business breaks even when their production costs are equal to their revenue. The expression 120 + 4x represents the cost of producing x items. Decide on a selling price for each item and write an expression for the revenue generated by selling all x items. How many items would you need to sell at your chosen price to break even? Write an equation and solve it.” Answers can vary. (8.EE.3.7)
• In Lesson 9.1, students conduct a survey of students in their class and interpret the results of the data by way of a two-way bivariate table. For example, “Conduct a survey of students in your class. Each student that you survey would be asked whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Record your survey data in the table. Is there evidence that those students who have a curfew also tend to have chores? Explain.” (8.SP.2.4)

The instructional materials for Into Math Florida Grade 8 meet expectations for the three aspects of rigor not always being treated together and not always being treated separately. In general, two, or all three, of the aspects are interwoven throughout each module. The Module planning pages include a diagram showing the first few lessons addressing understanding and connecting concepts and skills and the last lessons addressing applications and practice.

All three aspects of rigor are present independently throughout the program materials, and examples include:

• In Lesson 2.1, students develop conceptual understanding of dilations. During Build Understanding, students measure the angles and side lengths of a triangle, then draw another triangle with side lengths half of the original. In the remainder of the lesson, students analyze the characteristics of pairs of figures, identify if the pairs are proportional, and identify if the pair represents a reduction or enlargement.
• In Lesson 11.3, On My Own Question 4, students apply the Pythagorean Theorem to find the length of the longest diagonal in a wardrobe closet measuring 36 inches by 24 inches by 96 inches.
• In Lesson 12.1, students develop procedural skill in using properties of exponents. During Build Understanding, students write expanded form of exponents and use prior knowledge to simplify expressions. Within On Your Own and More Practice/Homework problems, students apply these properties to simplify expressions such as $$\frac{9^{-2}\times9^7}{9^3}$$.

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials, examples include: 

• In Lessons 8.1-8.3, students develop procedural skill in creating scatter plots by graphing relationships between two variables, using the plot to draw, and analyzing trend lines. Students apply trend lines to interpreting data in real-world contexts. For example, “The average length of an animal’s life is related to the average length of pregnancy for that type of animal. The scatter plot shows data for several different types of animals.  A) Sketch a trend line to model the data. Circle the outliers and explain how they influence your choice for the trend line.  B) How would the trend line change if the outliers were removed?  C) The average length of pregnancy for a polar bear is 240 days. Use the trend line to estimate the average length of a polar bear’s life.”
• In Lesson 13.1, students build conceptual understanding in Spark Your Learning by comparing the volume of a rectangular prism to the volume of a cylinder in order to derive the formula for a cylinder. Students develop procedural skill by applying the formula to solve multiple problems involving volume of a cylinder. For example, “The height of the cylindrical container shown is 7 inches. Find the volume of the cylinder.” Additional questions provide diagrams of cylinders for students to find the volume.

The instructional materials for Into Math Florida Grade 8 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.

At the end of the lesson, Apply and Practice provides a variety of exercises which allow students to independently show their understanding of the material. Exercises are designed for students to demonstrate understandings and skills in application and non-application settings. Test Prep and Spiral Review also include exercises.

The instructional materials for Into Math Florida Grade 8 meet the expectations that the design of assignments is intentional and not haphazard.

Overall, lessons are intentionally sequenced and scaffolded so students develop understanding 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 utilizing concrete and abstract representations and increase in complexity.

• Spark Your Learning serves to motivate and set the stage for students to learn new material and persevere through a related mathematical task.
• Build Understanding and Step It Out provide opportunities for students to learn and practice new mathematics, as well as “connect important processes and procedures” according to the Planning and Pacing Guide.
• Check Understanding provides a formative assessment opportunity after instruction.
• On My Own, More Practice/Homework, Test Prep, and Spiral Review in each lesson support students in developing independent mastery of the current lessons, as well as reviewing material from previous lessons.
• Lessons are in a logical order and build coherence throughout the grade level.

The instructional materials for Into Math Florida Grade 8 meet the expectations for having a variety in what students are asked to produce, for example:

• Show written calculations and solutions
• Verbally defend or critique the work of others to show understanding
• Analyze double number lines and bar diagrams
• Build models for a problem by using diagrams and equations
• Use a diagram and a coordinate plane to represent a linear equation
• Compare multiple representations - table, graph, equation, situation - of data
• Use a digital platform to conduct and present their work
• Use manipulatives, especially in small groups, to represent mathematics
• Construct written responses to explain their thinking
• Performance Tasks: Grade 8, Unit 3, Back to the Future. “Although time travel often occurs in movies and books, it isn’t possible in real life. But if it were possible, companies would probably exist to see trips!” This is followed by 5 questions requiring students to use functions to represent data and find relationships.
• STEM activities - Examples include: Grade 8, Unit 6, "Light travels at a speed of about 186,000 miles per second. How many miles does light travel in one hour? Write your answer in standard form and as a number multiplied by a power of ten.”
  

The instructional materials reviewed for Into Math Florida Grade 8 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 involve extensive use of manipulatives however, when they are included, they are consistently aligned to the expectations and concepts in the standards.
• Most hands-on manipulatives are integrated in supplemental, small-group, differentiated instruction activities and warm-up options.
• Examples of manipulatives include: Two-color counters, calculator, coins, number cubes, playing cards, string, square tiles, unit cubes, colored chips, algebra tiles, grid paper, index cards, anchor charts, ruler, compass, protractor, geometry software, bar diagrams, fraction strips, number lines, decimal grids, x-y tables, and pie charts.

The instructional materials for Into Math Florida Grade 8 meet the expectations for providing quality questions to help guide students’ mathematical development.

There are Guided Student Discussion questions and sample student answers throughout the Teacher Edition including on the Module opener page, Warm Up Options, Spark Your Learning, Build Understanding, Common Errors, and Step It Out pages corresponding to tasks or exercises on the page. Each module review also contains suggested questions intended to have students summarize concepts and skills developed within the module.

Each lesson introduction poses an essential question intended to guide student learning. For example, in Lesson 13.4, the Essential Question is, “How can you use volume formulas to solve problems involving cylinders, cones, and spheres?”

The Spark Your Learning planning page in the Teacher Edition includes examples of student work which show On Track, Almost There, and Common Errors. Each example has suggested questions for teachers to correct or advance student thinking. For example, in Lesson 11.1, Almost There about Pythagorean Theorem: “What is the area of each of the smaller squares? What is the area of the larger square? Do you see a relationship among these areas?”

The instructional materials for Into Math Florida Grade 8 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, a variety of information is provided to help teachers understand the materials in order to present the content. Each lesson identifies the relevant content standards and Mathematical Practices, an Essential Question, Learning Objective, Language Objective, materials needed, and Mathematical Progressions Across Grades that containing 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.

Two prompts in each module are related to Online Ed: “Assign the auto-scored Are You Ready for immediate access to data and grouping recommendations.” The other prompt being, “Assign the auto-scored Module Test for immediate access to data.” Within lessons, multiple prompts are presented: Warm-Up Options and Step It Out both have an icon, “Printable & projectible.”; “More print and digital resources for differentiation are available in the Math Activities Center.”; and “Assign the auto-scored Check Understanding for immediate access to the data and recommendations for differentiation.”

The instructional materials for Into Math Florida Grade 8 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 Across the Grades which lists prior learning, current development, and future connections. Similarly, the beginning of each lesson in the Teacher Edition includes Mathematical Progressions showing 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 discusses the “four progressions of middle school content leading to the Algebra course: Number and Operations, Operations and Algebraic Thinking, Statistics and Probability, and Functions” and includes a table showing how the domains in Grades 3-5, 6-7, and Grade 8/Algebra fit into these progressions.

The instructional materials for Into Math Florida Grade8 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 Across the Grades 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, notes, strategies, sample guided discussion questions, and possible misconceptions are provided 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 My Own or More Practice/Homework.

The instructional materials for Into Math Florida Grade 8 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• Reteach and Challenge activities are located in each lesson.
• Each module includes Plan for Differentiated Instruction providing teachers with teacher-guided, Small-Group Options and self-directed Math Center Options based on student need: “On Track/Mixed Ability, 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.

Three “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.” and 3) “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy.”

The instructional materials for Into Math Florida Grade 8 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

• Each Unit includes a STEM Task and a Unit Project which include multiple entry-points and a variety of solution strategies. Teachers are provided with possible answers, as well as What to Watch For tips, including: “Watch for students who become discouraged by a task and quickly give up. Strategies that may help these students include: working with a supportive partner, dividing the task into smaller steps, and reminding themselves that working at a difficult task is valuable, even if the task is not completed. Taking on new challenges is how we learn.” and “Watch for students who are reluctant to stretch themselves on a challenging task. Encourage these students to: identify similarities between the current task and tasks they have completed successfully in the past, identify one or more promising strategies or approaches, and try one of the strategies.”
• Each lesson begins with Spark Your Learning, an open-ended problem allowing students to choose their entry-point for applying mathematics and can be solved in a variety of ways. Suggestions in the Teacher’s Edition help students access the context of the problem. For example, in the side margin of the Teacher’s Edition, Motivate provides prompts such as in Grade 8, Lesson 5.2, “Introduce the problem. Ask students if they have ever set daily goals in reading or running or some other activity. Invite students to discuss and share with their partner or team members in a small group.”
• Support for Turn and Talk in the Teacher’s Edition provides suggestions to help students using a variety of strategies. Teachers are often prompted to, “Select students who used various strategies and have them share how they solved the problem with the class.”

The instructional materials for Into Math Florida Grade 8 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, further support in place for English Language Learners (ELLs) and other special populations:

• For ELLs, Language Development in each module includes linguistic notes providing strategies intended to help students struggling with key academic vocabulary such as: “Speak with students about words that can have multiple meanings….”, “Listen for students who do not distinguish between minus...and the negative sign.”, and “Visual cues help students…”
• Language Objectives are included in every lesson.
• Teacher Tabletop Flipchart Activities are referenced in the Teacher’s Edition for RtI support.
• Reteach, RtI Tier 2, and RtI Tier 3 worksheets can be assigned online or printed.
• Turn and Talk prompts are designed to support students in other special populations such as, “go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”

The instructional materials for Into Math Florida Grade 8 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:

• Optional lessons are provided online and teachers may choose to utilize them 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’s Edition provides ideas for extending the task.

The instructional materials for Into Math Florida Grade 8 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• Lessons contain a variety of tasks that are of interest to students of various demographic and personal characteristics.
• Names and wording are chosen with diversity in mind. The materials include various names throughout the problems (e.g. Jayson, Suyin, Malik, Tressa, Anton, Jasmine, Yu, Felice, Sonia, Roselyn, Tracy, Tran, Arie, Miguel, Maria) and are used in ways that do not stereotype characters by gender, race, or 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.
• When people are shown, a balance of demographic and personal characteristics.