The instructional materials for Into Math Florida Grade 7 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 Lessons 3.1 and 3.2, students develop conceptual understanding of integer addition and subtraction by representing the operations on number lines. For example, in Build Understanding, part A states, “Latrell spins a wheel to find out how many points he adds to his score. The wheel stops on “-5 points.” Use the number line to add -5 points to Latrell’s score. Then complete the equation.” (7.NS.1.1)
• In Module 5, students build understanding of multiplying and dividing rational numbers. For example, students represent multiplication of positive and negative numbers with repeated addition on a number line. In Lesson 5.2, students investigate signs of products as the number of negative factors change. (7.NS.1.2)
• In Lesson 7.1, Build Understanding, Question 2, students rewrite the discount expression p+p+0.60p as 2.60p and explain why the expressions are equivalent. In Lesson 7.2, On My Own, Question 6, students solve, “A pentagon has side lengths: (12 + 4x), (10 + 8x), (15 + 3x), (9 + 2x), and (14 + 3x). Write a simplified expression that represents the perimeter of the pentagon. Explain.” (7.EE.1.2)

The instructional materials for Into Math Florida Grade 7 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.

• Throughout Modules 3 and 4, students evaluate addition and subtraction problems with various rational numbers. For example, in Lesson 3.3, On My Own, “Questions 10-13, 102.8 − 98.6; 99.4 − 101.7; -98.6 + (-1.4); -19 + 11; Question 16, $$\frac{1}{2}$$ − (-$$\frac{1}{2}$$).” In Lesson 4.1 More Practice/Homework: “Question 10, 21 − 57; Question 12, -23 − (-5); Question 15, 24 − (-37).” (7.NS.1.1)
• Throughout Modules 5 and 6, students evaluate multiplication and division problems with various rational numbers. For example, in Lesson 5.2, On My Own, Question 7, “Find the product: (0.5)(-0.5)(-4)(-4)(-1)”; More Practice/Homework, Question 7, “Find each quotient: -27/5”. In Lesson 6.1, More Practice/Homework, Question 3, 5 - 44 $$\times$$ (0.75) - 18/ $$\frac{2}{3}$$ $$\times$$ 0.8+ (-$$\frac{4}{5}$$). (7.NS.1.2)
• In Lesson 7.2, students write linear expressions and apply properties of operations to generate equivalent expressions. For example, “students factor expressions using the GCF: 3x-24; students simplify expressions using properties of operations: (-r-5)-(-2r-4); students also expand expressions using the Distributive Property and then simplify the expressions: (4x-7.2)+(-5.3x-8).” (7.EE.1.1)
• In Lesson 7.4, students solve two-step equations involving rational numbers and equations written in the forms px + q = r and p(x+q) = r. For example, On My Own, Questions 8-15 and 19-27, students solve equations in this form, “-9d-1=17; 2+1/6a=-4; 2x-5=15”, etc.). (7.EE.2.4a)

The instructional materials for Into Math Florida Grade 7 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 Module 2, students solve multi-step ratio and percent problems. For example, in Lesson 2.1, Check Understanding, Question 1 states, “Peggy earned $20 for each lawn she mowed last summer. This summer, she raised her price to $23 per lawn. What is the percent of Peggy’s change?” In Lesson 2.2, On My Own, Question 8 states, “Shelly’s boutique had a labor day sale featuring 25% off any item. Tammy wanted to buy a blouse that originally sold for $21.99. To the nearest cent, how much will it cost her before tax to buy the blouse during the sale?” (7.RP.1.3)
• In Modules 4 and 5, students solve real-world problems involving the four operations with rational numbers. For example, in Lesson 4.4, Check Understanding, Question 1 states, “Soojin is adding some lengths of wood she used for a project. The lengths of wood are 1 $$\frac{2}{3}$$, 3 $$\frac{3}{4}$$, and 2 $$\frac{1}{4}$$ feet. How much wood did she use in all?” In Lesson 5.4, On My Own, Question 4 states, “A butterfly is flying 8 $$\frac{3}{4}$$ feet above the ground. It descends at a steady rate to a spot 6 $$\frac{1}{4}$$ feet above the ground in 1 $$\frac{2}{3}$$ minutes. What is the butterfly’s change in elevation per minute?” (7.NS.1.3)
• In Lesson 6.3, Check Understanding, Question 1 states, “A block of clay contains 20 4-ounce portions of clay. A ceramics teacher wants to use the block to make as many spheres of clay as possible, each weighing $$\frac{2}{5}$$ pound. How many spheres can she make?” In Lesson 6.2, students use estimation to check reasonableness, “The dimensions of a room are shown. Ivan wants to have the four walls painted. The painter says the area is 542.2 square feet. Estimate the total area that needs to be painted. Was the painter’s answer reasonable. Explain.” (7.EE.2.3)
• In Lesson 8.3, students write and solve two-step inequalities given a real-world scenario, “Ariana started a saving account with $240. She deposits $30 into her account each month. she wants to know how many months it will take for her account to have a balance greater than $500. Write and solve an inequality that represents this situation. How many months will it take for her account to have a balance greater than $500? Explain.” (7.EE.2.4b)

The instructional materials for Into Math Florida Grade 7 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 12.1, the materials address conceptual understanding of statistics by having students determine where to locate a fast-food restaurant. Students discuss the terms population, sample, representative, and bias and identify them in different contexts. Students participate in class discussion and Turn and Talk, making generalizations and inferences, before working independently. In Build Understanding, students answer, “Which of the representative samples of the population is more representative of the population? Explain.”
• In Module 8, students develop procedural skill by writing, solving, and graphing the solutions to one- and two-step inequalities. The inequalities incorporate rational numbers in various forms, i.e. integers, fractions, and decimals. An example is, “...solve the inequality. Graph the solution. -$$\frac{3}{4}$$m + $$\frac{1}{4}$$ $$\ge$$ 4 $$\frac{3}{4}$$”.
• In Lesson 15.4, students conduct simulations and find experimental probabilities, “Allie is a softball player. She has a batting average of 0.600. This means Allie gets a hit 60% of the time. Design a simulation using slips of paper and a box to predict the probability of Allie getting a hit in at least 2 of her next 5 at bats. Perform the simulation and use your results to predict the probability of Allie getting a hit in at least 2 of her next 5 at bats.”

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 Lesson 5.3, students develop conceptual understanding of converting fractions to decimals using multiple representations including a double number line with one side as decimals and one side as fractions and long division. Students develop procedural skill by converting fractions to decimals in numerous problems such as, “Hayley is buying herbs. She wants to buy ⅚ ounce of basil. The scale she is using to weigh the basil displays the weight as a decimal. How will she know when the display on the scale is correct to the tenths’ place? Explain your reasoning.”
• In Lesson 10.1, students develop conceptual understanding of the formula for circumference by examining the relationship between circumference (C), diameter (d), and pi. Students complete a table finding the ratio, C/d, for various circular objects, and they rewrite pi = C/d to reveal the formula for the circumference of a circle. Throughout the remainder of the lesson, students use the formula to solve real-world problems, for example, “Toni rides the Ferris wheel shown for 15 revolutions. A. How far does Toni travel in one revolution? How far does Toni travel for the entire ride?”

The instructional materials for Into Math Florida Grade 7 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 7 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 7 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 7, Unit 3, Jessica’s Cell Phone Plan. “Jessica’s cell phone plan charges her a monthly fee plus a charge for each text message she sends. The cost of her cell phone is shown in the table.” This is followed by 6 questions relating to evaluating data and generating equations to compare options.
• STEM activities - Examples include: Grade 7, Unit 4, “A rectangular electronic game board is 16.5 inches by 12 inches. It includes a grid with 8 rows of 8 squares, each 0.5 inch on a side. When you aim at any of the red squares, data are collected on the accuracy of the laser hits. What are the ratios of (a) the area of one square to the area of the board, and (b) the combined area of the squares to the area of the board? Explain.”
  

The instructional materials reviewed for Into Math Florida 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 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 7 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 the Lesson 4.2, the Essential Question is, “How can you calculate the difference of two integers?”

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 7.1, On Track about Linear Expressions: “How can we verify a written rule?”

The instructional materials for Into Math Florida 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 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 7 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 Grade 7 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 7 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 7 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 7, Lesson 1.1, “Introduce the problem. Ask them if they have ever used a recipe. Tell students to discuss and share with their 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 7 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 7 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 7 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.