The instructional materials for Into Math Florida Grade 3 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Throughout the materials, there are sections that emphasize introducing concepts and developing understanding such as: “Build Understanding” and “Spark Your Learning”. Students have the opportunity to independently demonstrate their understanding with the “Check Understanding” and “On My Own” problems at the end of each lesson. For example: 

• Lesson 1.1, Build Understanding 1, students draw a picture to show equal groups and then tell how many groups, with how many in each group, for the problem: “Raj makes 5 robots like this on. How many arms do the 5 robots have?” (3.OA.1.1)
• Lesson 1.2, Spark Your Learning, “Ling is at a fair with her friends Jimmy and Pablo. At a game booth, they each get 4 balls. How many balls will Ling and her friends get? Show more than one way to find the number of balls." (3.OA.1.1)
• Lesson 6.2, Spark Your Learning, “Annie has 20 photographs to put onto pages in a book. She wants to make equal groups. Write questions that can be asked about the scenario. Show equal groups to answer one question." (3.OA.1.1)
• Lesson 13.1, Build Understanding, students compare pictures of flags to determine which are divided into equal parts and which are not. They use this knowledge to draw both types of flags. Then they name equal parts using words like fourths and eighths. (3.NF.1.1)
• Lesson 13.3, On My Own, Question 4, students shade four equal parts of a hexagon, then write the fraction in words and numbers. (3.NF.1.1)
• Lesson 13.6, Practice & HW Journal, Question 7, students are asked, “Each shape represents $$\frac{1}{2}$$ of a whole. Choose how many shapes to put together to make an amount that is great than 1. Draw your shapes.” (3.NF.1.1)
• Lesson 15.3, Practice & HW Journal, Question 8, Math on the Spot, students are asked, “Zach has a piece that is $$\frac{1}{4}$$ of a pie. Max has a piece of pie that is $$\frac{1}{2}$$ of a pie. Max’s piece is smaller than Zach’s piece. Explain how this could happen. Draw a picture to show your answer.” (3.NF.1.3d)

The instructional materials for Into Math Florida Grade 3 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The materials include problems and questions that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. Procedural skills and fluencies are primarily found in two areas of the materials. In "On Your Own,” students work through activities to practice procedural skill and fluency; additional fluency practice is found in “More Practice/Homework.”

• Lesson 4.6, Multiply by 9s, On My Own, Problem 5, 9 x 1 = __. Problem 6, 4 x 9 = __. Problem 7, ___ = 9 x 7. (3.OA.3.7)
• Lessons 7.3 and 7.4,  students practice multiplication and division with 2, 3, 4, 5, 6,  8, and 10. Different representations are presented for each operation. (3.OA.3.7)
• Lesson 7.7, students skip count by 2, 3, and 4, and look for patterns. They circle the numbers that are the same in each set. (3.OA.3.7)
• Lesson 9.2 students use mental math to find the sum or difference. For example in, Problem 5, 46 + 24 + ____ and Problem 6, 639 - 425 = ___.
• Lesson 10.2 students estimate and then find the sum of two multi-digit numbers. For example, in Problem 7, students solve 612 + 75; Problem 8, 546 + 56; and Problem 9, 324 + 119. (All problems are presented vertically) (3.OA.3.7)
• Lesson 10.4 students find the difference using place value and regrouping. (3.NBT.1.2)

The instructional materials for Into Math Florida Grade 3 meet expectations that the materials are designed so that teachers and students spend 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 knowledge of the grade-level. Students also have opportunities to independently demonstrate the use of mathematics flexibly in a variety of contexts. During Spark Your Learning, Independent Practice, and On My Own, students engage with problems that include real-world context and present opportunities for application. For example:

• Lesson 1.3, On My Own, students use multiplication and division within 100 to solve word problems. For example, “Solar cells on a solar panel collect sunlight which is converted into electricity. Solar cells are arranged on a frame to make a solar panel. Describe one way you could arrange 24 solar cells in an array to make a panel.” (3.OA.1.3)
• Lesson 1.4, Spark Your Learning, students use multiplication and division within 100 to solve word problems in situations. For example, “Andy designed the game board shown (picture provided of a flow chart). The game will have 21 squares. The squares need to be in equal rows. Show two different game board designs that can be made." (3.OA.1.3)
• Lesson 1.5, Exit Ticket, students use multiplication and division within 100 to solve word problems in situations. For example, “Diandre wants to measure the length of a kayak. He has a measuring stick that is 3 feet long.  How can Diandre use the measuring stick and a number line to help him find the total length of the kayak?” (3.OA.1.3)
• Lesson 3.3,On My Own, students solve, “Michael buys 2 packages of hamburger buns. Each package has 6 hamburger buns. How many hamburger buns are there? Show the equal groups. Write an equation for the problem.” (3.OA.1.3)
• Lesson 5.4, Homework, Problem 9, students solve two-step word problems using the four operations. For example, “Ava’s class bought 6 packages of balloons for a school celebration. Each package had 30 balloons. If 17 balloons were left over, how many balloons were used for the party?” (3.OA.4.8)
• Lesson 6.2, Spark Your Learning, students determine how 20 photos might be arranged into a photo album using equal groups. (3.OA.1.3)
• Lesson 8.4, On My Own, students write two equations with letters representing unknown to solve the problems.  An example is, “Jamie’s plant grows 3 inches each week for three weeks. During the fourth week, it growth 5 inches. How much does Jamie’s plant grow over the four weeks?” (MAFS.3.OA.4.8)
• Lesson 10.6, On My Own, students solve two-step word problems using the four operations. For example, “Write a two-step word problem with an unknown number. Write equations to model the problem. Then solve.” (3.OA.4.8)

Each Unit has a Performance Task involving real-world applications of the mathematics from the unit. For example, the Unit 3 Performance task has students follow one child, a baseball card collector, throughout his day. Students estimate the number of baseball cards he has at the end of the day (3.NBT.1.1), tell the time of his various stops throughout the day (3.MD.1.1), determine the perimeter of his baseball card display (3.MD.4.8), and how many coins he has but not counting money (3.OA.1.3).

The instructional materials for Into Math Florida Grade 3 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. In general, two, or all three, of the aspects are interwoven throughout each module. The module planning pages include a  progression diagram showing the first few lessons focused on understanding and connecting concepts and skills. The last lessons focus on applying and practicing.

All three aspects of rigor are present independently throughout the program materials. For example: 

• Modules 4, 7, 9 and 10, students develop procedural skill and fluency with finding products, working with related facts, and division. Students also implement estimation and mental math to support the addition and subtraction for the grade level. (3.OA.3.7, 3.NBT.1.2)
• Lesson 8.4, On My Own, students engage in application in Problem 7, “Write a two-step word problem that can be solved using two equations with different operations.” (MAFS.3.OA.4.8)
• Lesson 16.1 builds conceptual understanding of equivalent fractions. Students draw visual models and use number lines to show fraction equivalence. (3.NF.1.3b)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example: 

• Lesson 7.6 attends to procedural skill and application related to multiplication and division with seven and nine. For example, “The 28 students in Van’s class are on a field trip to a cave. They are divided into groups of 7 for a tour of the cave. How many groups are there?” (3.OA.2.5)
• Lesson 13.6, Spark Your Learning, attends to conceptual understanding and application. For example, “Emilio cuts his pizzas into fourths. If he has 9 slices, show the different amounts of pizza that Emilio could sell. Name each fraction and show.” (3.NF.1.1 and 3.NF.1.2)
• Unit 4, Performance Task, attends to conceptual understanding and application. Students create number lines to visually see equal parts and then use them to solve real-world problems. For example,“Yoshi makes a large sandwich, he cuts the sandwich into 8 equal parts. He wants to put $$\frac{5}{8}$$ of the sandwich on a plate. How many pieces of the sandwich does he need? Draw a number line to solve the problem. Then write your answer.”
  

The instructional materials for Into Math Florida Grade 3 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 materials distinguish between problems and exercises within each lesson. Lessons include: Spark Your Learning, Build Understanding, Check Understanding, and On My Own. Spark Your Learning Problems activate prior knowledge and introduce new mathematics to students. Build Understanding includes problems that help students build conceptual understanding of the mathematics topic being taught.

Check Understanding and On My Own sections include exercises that ask students to use the newly learned mathematics in each lesson. Additional practice and Homework is available in a seperate student edition, providing more exercises for students to solve.

The instructional materials for Into Math Florida Grade 3 meet the expectations that the design of assignments is intentional and not haphazard.

Overall, lessons are intentionally sequenced and scaffolded so students develop in their understanding of 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 that utilize concrete and abstract representations and increase in complexity.

Exercises are given in intentional sequences. In general, lessons are designed to begin with activating prior knowledge and build toward conceptual development and procedural skill. In Spark Your Learning, students use manipulatives and/or visual models to experiment with the mathematics. Thus developing a concrete or representational understanding. This is followed by a Turn and Talk with a partner allowing students to process the connections they have found. Throughout the lessons, students are provided scaffolding with new content in Build Understanding and Step It Out, where the abstract concept is broken down into smaller steps with additional turn and talk opportunities, and students are provided with independent exercises to build understanding and mastery. Check Understanding provides a mid-lesson check in and can be used to indicate the need to differentiate learning for students. Students practice the abstract concept in On My Own.

The instructional materials for Into Math Florida Grade 3 meet the expectations for having a variety in what students are asked to produce.

In Spark Your Learning, Build Understanding, and Step It Out, students use visuals to show their thinking. Turn and Talk questions frequently ask students to construct arguments and give explanations. There are opportunities for students to produce answers and solutions in On My Own, while also providing opportunities for students to provide written explanations. Throughout the materials, students represent mathematics using equations.

Homework assignments include a variety of responses from fluency to higher level thinking. For example, Lesson 7.1 the Homework assignment has seven problems. The first problems ask students to write an equation to model a real-world situation. The next two problems ask students to complete a visual model of an equation. In Problems 4-6, students find the unknown in an equation and use a table in the last question to solve a word problem.

The instructional materials reviewed for Into Math Florida Grade 3 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

At the beginning of the lesson, the materials indicate what materials/manipulatives will be needed, and the student pages include a picture of the manipulative they will use. For example in Lesson 1.2, students use two color counters, connecting cubes, or a number line to represent the following problem, "Ling is at a fair with her friends Jimmy and Pablo. At a game booth, they each get 4 balls. How many balls with Ling and her friends get?” The manipulatives provide opportunities for students to develop a conceptual model of problems that they will represent in pictorial form in their student workbook.

Examples of manipulatives for Grade 3 include: Base Ten Blocks, connecting cubes, fraction circles, fraction strips, geo board, money, number line, pattern blocks, ruler, square dot paper, and two color counters.

Lesson 4.5, color tiles are referenced as needed in the Almost There small-group option for differentiated instruction. Students use the tiles to make arrays, write an equation to represent the array, then rearrange the tiles to show the changing order of the factors.

The materials rely on pictures of manipulatives. When physical manipulatives are used in the Lesson Materials in the Teacher Edition, it is not always clear how they are to be used. There is sometimes direction for how they can be used in Differentiation.

The instructional materials for Into Math Florida Grade 3 meet the expectations for providing quality questions to help guide students’ mathematical development.

Throughout the Teacher Edition questions are posted to help support teachers with questions to guide students’ mathematical development. Activate Prior Knowledge, Spark Your Learning, Build Understanding, Learn Together, and Turn & Talk, consistently provide questions to drive student discussion. For example:

• Lesson 7.2, Spark Your Learning, Persevere, provides the following questions for teachers, “What is the question asking you to do? How can you use the number of equal groups and the number in each group to write a multiplication question and a division question? How can you represent your question?” In the same lesson, the Step It Out Turn & Talk states, “What is the greatest number of multiplication and division facts that can be written for a set of numbers? What is the least? Provide examples.”
• Lesson 15.4, Spark Your Learning, includes two questions, “How do you know what the whole is in the problem?” and “How can you use visual models to find who picked the greater amount of cherries?”  
• Lesson 7.4, Step it Out, includes three questions, “How can you find the number of lanes at Gutter Alley?” “What are you counting in each problem as you count by tens?” and “Why can you choose to count up or count back to divide?”

The instructional materials for Into Math Florida Grade 3 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, there is a variety of information that can 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 contain 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.

There are two prompts in each module related to Online Ed: “Assign the auto-scored Are You Ready for immediate access to data and grouping recommendations.” and “Assign the auto-scored Module Test for immediate access to data.” Within lessons, there are multiple prompts: 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 3 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 notes, “Algebra as a course of study today is integrated around four progressions of elementary and 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 K-5, 6-7, and Grade 8/Algebra fit into these progressions.

The instructional materials for Into Math Florida Grade 3 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, there are notes, strategies, sample guided discussion questions, and possible misconceptions that provide 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 3 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• There are Reteach and Challenge activities for each lesson.
• Each Module includes Plan for Differentiated Instruction that provides 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.

There are 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 3 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The Planning and Pacing Guide, Teacher Support, Access and Equity, and Spark Your Learning Tasks are “designed as ‘low-floor/high ceiling’ tasks that all students can access but that can also be extended to provide challenge.” Teachers are provided guidance on how to assist various levels of learners, depending on how they respond to the problem. For example, Lesson 3.3, Spark Your Learning has this prompt, “Your community will use wind turbines to bring electricity to homes. Each wind turbine has 3 blades. Choose a number of wind turbines for your community from 1 to 9. How many blades are there in all? Show two different ways to find the total number of blades.” This problem provides multiple entry points and solution strategies for students. However, Spark Your Learning is not present in every lesson.

Support for Turn and Talk in the Teacher 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 3 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, there is further support in place for English Language Learners (ELLs) and other special populations:

There is Language Development to support English Learners in each module which includes linguistic notes that provide strategies intended to help students struggling with key academic vocabulary such as: “Speak with students about words that can have multiple meanings…," and “Visual cues help students…” Language Development also includes information about the Language Routines embedded in the instructional materials: Three Reads; Stronger and Clearer Each Time; Compare and Contrast; Critique, Correct, and Clarify. These are identified by a pink box throughout lessons with speech bubble that identifies the Language Routine to be used.  In addition, there are supports for special populations including:

• Language Objectives are included in every lesson.
• Reteach and RtI worksheets that can be assigned online or printed.
• Turn and Talk prompts designed to support students, for example, “go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”
• A multi-lingual glossary is available online.

The instructional materials for Into Math Florida Grade 3 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. Teachers may choose to utilize 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 3 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• Lessons contain a variety of tasks that interest students of various demographic and personal characteristics.
• Names and wording are chosen with diversity in mind. The materials include various names throughout the problems that 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 that do not express gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies.
• When people are shown, there is a balance of demographic and personal characteristics.