## Into Math Florida

##### v1
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
2020 Florida Next Gen Math Student Edition (Consumable) Grade 8 9781328497185 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Teacher Edition Volume 1 Grade 8 9781328497215 Houghton Mifflin Harcourt 2020
FL Next Gen Math Assessment Guide Grade 8 9781328526526 Houghton Mifflin Harcourt 2020
FL Next Gen Math Differentiated Instruction Masters Grade 8 9781328526632 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Teacher Edition Volume 2 Grade 8 9781328557315 Houghton Mifflin Harcourt 2020
Florida Into Math Planning and Pacing Guide Grade 8 9781328569301 Houghton Mifflin Harcourt 2020
Grade 4 FL Student Edition Volume 1 Units 1-3 9781328492760 Houghton Mifflin Harcourt 2020
Grade 4 FL Student Edition Volume 2 Units 4-7 9781328492777 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 1 Unit 1 M1-2 9781328493620 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 2 Unit 2 M3-4 9781328493644 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 3 Unit 2 M5 9781328493668 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 4 Unit 2 M6-7 9781328493675 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 5 Unit 3 M8-9 9781328493699 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 6 Unit 4 M10 9781328493712 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 7 Unit 4 M11 9781328493729 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 8 Unit 4 M12 9781328493736 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 9 Unit 4 M13 9781328493743 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 10 Unit 5 M14 9781328493774 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 11 Unit 5 M15-16 9781328493798 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 12 Unit 6 M17-18 9781328493811 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 13 Unit 7 M19 9781328493859 Houghton Mifflin Harcourt 2020
Grade 4 FL Teacher Edition Book 14 Unit 7 M20-21 9781328493866 Houghton Mifflin Harcourt 2020
Grade 4 FL Assessment Guide 9781328526489 Houghton Mifflin Harcourt 2020
Grade 4 FL Differentiated Instruction Masters 9781328526595 Houghton Mifflin Harcourt 2020
Grade 4 FL Practice & Homework Journal 9781328526700 Houghton Mifflin Harcourt 2020
Grade 4 FL Planning and Pacing Guide 9781328567819 Houghton Mifflin Harcourt 2020
Grade 5 FL Student Edition Volume 1 Units 1-3 9781328492890 Houghton Mifflin Harcourt 2020
Grade 5 FL Student Edition Volume 2 Units 4-8 9781328492906 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 1 Unit 1 M1 9781328493750 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 2 Unit 1 M2-3 9781328493767 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 3 Unit 1 M4-5 9781328493781 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 4 Unit 2 M6-7 9781328493804 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 5 Unit 3 M8 9781328493828 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 6 Unit 3 M9 9781328493835 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 7 Unit 4 M10 9781328493842 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 8 Unit 4 M11-12 9781328493873 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 9 Unit 5 M13-14 9781328493880 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 10 Unit 6 M15-16 9781328493897 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 11 Unit 7 M17-18 9781328493903 Houghton Mifflin Harcourt 2020
Grade 5 FL Teacher Edition Book 12 Unit 8 M19-20 9781328493910 Houghton Mifflin Harcourt 2020
Grade 5 FL Assessment Guide 9781328526496 Houghton Mifflin Harcourt 2020
Grade 5 FL Differentiated Instruction Masters 9781328526601 Houghton Mifflin Harcourt 2020
Grade 5 FL Practice & Homework Journal 9781328526717 Houghton Mifflin Harcourt 2020
Grade 5 FL Planning and Pacing Guide 9781328569127 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Student Edition (Consumable) Grade 6 9781328495402 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Teacher Edition Volume 1 Grade 6 9781328497192 Houghton Mifflin Harcourt 2020
FL Next Gen Math Assessment Guide Grade 6 9781328526502 Houghton Mifflin Harcourt 2020
FL Next Gen Math Differentiated Instruction Masters Grade 6 9781328526618 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Teacher Edition Volume 2 Grade 6 9781328557292 Houghton Mifflin Harcourt 2020
Florida Into Math Planning and Pacing Guide Grade 6 9781328569288 Houghton Mifflin Harcourt 2020
Grade 3 FL Student Edition Volume 1 Units 1-3 9781328492647 Houghton Mifflin Harcourt 2020
Grade 3 FL Student Edition Volume 2 Units 4-7 9781328492654 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 1 Unit 1 M1 9781328493507 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 2 Unit 1 M2 9781328493514 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 3 Unit 2 M3-4 9781328493521 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 4 Unit 2 M5-6 9781328493545 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 5 Unit 2 M7 9781328493569 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 6 Unit 2 M8 9781328493576 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 7 Unit 3 M9 9781328493583 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 8 Unit 3 M10 9781328493590 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 9 Unit 3 M11-12 9781328493606 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 10 Unit 4 M13-14 9781328493613 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 11 Unit 4 M15-16 9781328493637 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 12 Unit 5 M17 9781328493651 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 13 Unit 5 M18 9781328493682 Houghton Mifflin Harcourt 2020
Grade 3 FL Teacher Edition Book 14 Unit 6 M19-20 9781328493705 Houghton Mifflin Harcourt 2020
Grade 3 FL Assessment Guide 9781328526472 Houghton Mifflin Harcourt 2020
Grade 3 FL Differentiated Instruction Masters 9781328526588 Houghton Mifflin Harcourt 2020
Grade 3 FL Practice & Homework Journal 9781328526694 Houghton Mifflin Harcourt 2020
Grade 3 FL Planning and Pacing Guide 9781328567802 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Student Edition (Consumable) Grade 7 9781328497178 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Teacher Edition Volume 1 Grade 7 9781328497208 Houghton Mifflin Harcourt 2020
FL Next Gen Math Assessment Guide Grade 7 9781328526519 Houghton Mifflin Harcourt 2020
FL Next Gen Math Differentiated Instruction Masters Grade 7 9781328526625 Houghton Mifflin Harcourt 2020
2020 Florida Next Gen Math Teacher Edition Volume 2 Grade 7 9781328557308 Houghton Mifflin Harcourt 2020
Florida Into Math Planning and Pacing Guide Grade 7 9781328569295 Houghton Mifflin Harcourt 2020
Showing:

### Overall Summary

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for alignment to the Mathematics Florida Standards (MAFS). ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor. The materials partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

​The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

##### Indicator {{'1a' | indicatorName}}
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials for Into Math Florida Grade 5 meet the expectations for assessing grade-level content. An Assessment Guide, included in the materials, contains two parallel versions of each Module assessment, and the assessments include a variety of question types. In addition, there is a Performance Task for each Unit, and there are Beginning, Middle, and End-of-Year Interim Growth assessments.

Examples of assessment items aligned to grade-level standards include:

• Unit 1, Performance Task, Questions 2 and 3, students find volumes of rectangular prisms. “The factory makes boxes that each hold one candle. The boxes measure 1 inch x 1 inch x 9 inches. The factory owner makes a stack of 40 candle boxes. What is the volume of the stack? Show your work.” (5.MD.3.5a)
• Module 2, Form A, Question 10, “A school earned $2,604 selling tickets to a fundraising event. If each ticket costs$14, how many tickets were sold?” (5.NBT.2.6)
• Module 6, Form A, Question 8, students solve a story problem by adding fractions with unlike denominators. (5.NF.1.2)
• Module 7, Form A, Questions 6-8, students add or subtract fractions and mixed numbers. (5.NF.1.1)
• Module 10, Form A, question 6, students shade a model to represent the quotient of $$\frac{1}{6}$$ ÷ 2. (5.NF.2.7a)
• Module 12, Form A, Question 3, “Ms. Yang left work at 5:15 p.m. She went to the gym for 90 minutes, and then it took her 40 minutes to drive home. What time did Ms. Yang get home?” (5.MD.1.1)
• End-of-Year-Test, Question 18, students find the difference in weight between the heaviest and the lightest bags of apples using a number line with fractional units. (5.MD.2.2)

#### Criterion 1.2: Coherence

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

##### Indicator {{'1b' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Into Math Florida Grade 5 meet the expectations for spending a majority of instructional time on major work of grade.

• The number of Modules devoted to major work of the grade is 15 out of 20, which is approximately 75%.
• The number of Lessons devoted to major work of the grade (including supporting work connected to the major work) is 83 out of 96, which is approximately 86%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 135 out of 166 days, which is approximately 81%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work and isn’t dependent on pacing suggestions. As a result, approximately 86% of the instructional materials focus on major work of the grade.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

##### Indicator {{'1c' | indicatorName}}
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Into Math Florida Grade 5 meet the expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of how the materials connect supporting standards to the major work of the grade include:

• Module 12, Lesson 3, 5.MD.2.2 supports the major work of 5.NF.1.1, add and subtract fractions with unlike denominators. Students make line plots with fractional units, then use the line plot to answer questions such as, “What is the total liquid volume of the water in the jars?”
• Module 12, Lesson 4, 5.MD.1.1 supports the major work of 5.NF.2.4, multiplication of fractions.  Students multiply fractions and mixed numbers by whole numbers to convert among units of measure.
• Module 18, Lesson 1, Question 9, 5.MD.1.1 supports the major work of 5.NBT.1.2, multiplying and dividing with powers of 10. Students shift the decimal point to either multiply or divide by a power of 10 to solve conversion problems. For example, “Convert 58 g to kg, and question 10 Convert 6257 cL to L.”
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials for Into Math Florida Grade 5 meet the expectations that the amount of content designated for one grade-level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 166 days, 115 days for lessons and 51 days for assessments.

• The Planning and Pacing Guide and Planning pages at the beginning of each module in the Teacher's Edition provide the same pacing information.
• Grade 5 has 8 Units, with 20 Modules containing 96 lessons.
• The pacing guide designates 11 lessons as two-day lessons and 85 as one-day lessons, leading to a total of 107 days. The materials do not define the number of minutes in a lesson or instructional day.
• Each Unit includes a Unit Opener, and there are eight Openers for Grade 5 (eight days).
• Each lesson includes a variety of supplemental instruction such as reteaching lessons, Flipbook lessons, etc. There is no guidance around building in days for differentiation, therefore no additional days were added.
• This is a total of 115 lesson days.

Assessments include:

• The Planning and Pacing Guide indicates a Beginning, Middle, and End of Year Interim Growth assessment that would require one day each (three days).
• Each Unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are eight Performance Tasks for Grade 5 (eight days).
• Each Module has both a review and an assessment. There are 20 Modules equating 40 days. Based on this, 51 assessment days can be added.
##### Indicator {{'1e' | indicatorName}}
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials for Into Math Florida Grade 5 meet the expectations for the materials being consistent with the progressions in the Standards. In general, the materials identify content from prior and future grade-levels, as well as relating grade-level concepts explicitly to prior knowledge from earlier grades. In addition, the instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.

The introduction for every Module in the Teacher Edition includes “Mathematical Progressions Across the Grades” identifying standards under the areas of Prior Learning, for Current Development, and Future Connections, as well as clarifying student learning statements in these categories. For example, at the start of Module 4, Prior Learning is listed as, “Interpreted a multiplication equation as a comparison”, “represented verbal statements of multiplicative comparison as a multiplication equations”, and “solved word problems involving multiplicative comparisons.” (4.OA.1.1,2) Future Connections are listed as, “will write numerical expressions involving whole-number exponents”, “will identify parts of an expression using mathematical terms”, and “will evaluate algebraic expressions for specific values of their variables using the order of operations.” (6.EE.1.1, 6.EE.1.2b, 6.EE.1.2c) In the Activate Prior Knowledge section at the beginning of each lesson, content is explicitly related to prior knowledge to help students scaffold new concepts. Additional features of the materials further support the progressions of the standards. These include:

• The beginning of each module includes a diagnostic assessment called “Are You Ready?” explicitly identifying prior knowledge needed for the current module.
• In each lesson, the standard of focus is explicitly connected to work in future and prior grades.  For example, Module 14, Lesson 3 identifies 5.NBT.2.7 as the focus for the lesson. The mathematical progressions, indicated in the teacher edition, show this builds upon work done with 4.NBT.1.4 during Grade 4 in Module 2, Lessons 1-3.  This work will continue in 6th grade with a focus on standards 6.NS.2.3 during Module 4, Lesson 1.

The materials give all students extensive work with grade-level problems. Students spend four to eight days within each module and one day per lesson. Each lesson includes a Problem of the Day to activate prior knowledge, a Spark your Learning portion as an introduction to the day’s learning goals that usually embeds partner or group work to solve a problem. Each lesson includes grade level work in the Build Your Understanding, Step It Out, and On My Own. Additionally, Reteach and Challenge pages are available for each lesson which provide more practice with grade level work. For example:

• Module 2, Lesson 1, Build Understanding, Question 1, students use rectangular arrays, multiplication equations and related division equations to solve, “Anthony has 128 songs on his digital music player.  He divides the songs equally into 8 playlists. How many songs are in each playlist?" (5.NBT.2.6)
• Module 7, Lesson 2, On My Own, includes 17 grade level problems for  students to practice addition and subtraction of fractions with unlike denominators. For example, Question 10, “ Mr. Braxton’s laptop memory is $$\frac{9}{10}$$ full. After deleting unneeded files, the memory is $$\frac{2}{3}$$ full. What fraction represents the part of the laptop memory that he deleted? Is your answer reasonable? How do you know?” (5.NF.1.1)
• Module 13, Lesson 4, students expand upon their learning of place value and comparing and ordering numbers, 4.NBT.1.1,2, to decimals. Question 4, students evaluate four percentages written as decimals and order them from least to greatest (5.NBT.1.3b).
• Module 15, Lesson 1, Build Understanding, students find place value patterns when multiplying by powers of 10. Question 1C, “How do the digits shift as you multiply by increasing powers of 10?” The On My Own section has 30 questions that have students practice multiplication of whole number and decimals with powers of 10. For example, Question 12, 100 x 553.2 (5.NBT.1.2).

The materials relate grade-level concepts to prior knowledge from earlier grades. Examples include, but are not limited to:

• The Teacher Edition for each of these pages clearly identifies the previous grade level work and explains how students will use these skills in upcoming lessons. For example, Module 7, Are You Ready?, shows the link to prior learning for Explore Mixed Numbers as Grade 4, Lesson 15.2 (4.NF.2.3b) in the Data-Driven Intervention Chart. A narrative is provided for each skill on the page. “Explore Mixed Numbers: These items assess whether students are able to find the mixed number equivalent to a given fraction greater than 1. In the upcoming lessons, students  will use this skill when adding and subtracting mixed numbers.”
• At the beginning of each Module, prior learning from earlier grade is indicated along with future connections. For example, Module 19 student current development will be around 5.G.1.1,2 and 5.OA.2.3. Prior learning from standards 4.G.1.1 and 4.OA.2.4 are identified. Future connections are listed as 6.NS.3.6 and 6.NS.3.8.
##### Indicator {{'1f' | indicatorName}}
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings, and examples of this include:

• The Module 19 learning objective “Graphs and Patterns” is shaped by the cluster heading 5.OA.2: Analyze patterns and relationships, and 5.G.1: Graph points on the coordinate plane to solve real-world and mathematical problems.
• Lesson  3.1, learning objective, “Divide whole number dividends by 2-digit-divisors to find quotients with remainders” is shaped by 5.NBT.2: Perform operations with multi-digit whole numbers and with decimals to hundredths.
• Lesson 7.5, learning objective, “Add fractions and mixed numbers with unlike denominators using properties” is shaped by 5.NF.1: Use equivalent fractions as a strategy to add and subtract fractions.
• Lesson 8.4, learning objective, “Use a visual model to represent multiplication of fractions” is shaped by 5.NF.2: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important, and examples of this include:

• Lesson 5.6, connects 5.MD.3 with 5.NBT.2 when students use multi-digit multiplication to find the volume of composed figures. Question 11, students find the volume of two connected rectangular prisms with dimensions 12 x 50 x 30 and 10 x 5 x 15.
• Lesson 8.3, Represent Multiplication with Unit Fractions, connects 5.NF.2 with 5.NBT.2. For example, Question 2b, students use what they know about multiplication equations to model a problem.
• Module 19 connects graphing in the coordinate plane (5.G.1) with generating two numerical patterns (5.OA.2).

### Rigor & Mathematical Practices

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

##### Indicator {{'2a' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Into Math Florida Grade 5 meet the 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, sections 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, Spark Your Learning, asks students, “On a road trip, Anna and her family stop at a ranch where bales of hay are being weighed. Describe the relationship between the two weights. How can you use the relationship to compare the weight?” (5.NBT.1.1)
• Lesson 2.3, Spark Your Learning, asks students, “One of Florida’s tallest buildings is 900 Biscayne Bay. It stands 650 feet tall. The building has 63 floors. If each floor is approximately the same height, about how tall is one floor of the 900 Biscayne Bay building?” (5.NBT.2.6)
• Lesson 3.4, On My Own, students solve, “Tina’s Treat Truck sold three times as much ice cream in August than in September. She sold twice as much in September than in October. She sold 927 pounds of ice cream during the three months. Represent the amount of ice cream sold with a bar model. Write an equation to show the amount represented by each box of the bar model. How much ice cream did Tina sell in September? Explain how you know.” (5.NBT.2.6)
• Lesson 8.1, Check for Understanding, Question 1, students solve, “At nine o’clock $$\frac{5}{8}$$ of the 16 cats at the party go home. How many cats go home at nine o’clock? Draw a visual model to find the answer.” (5.NF.2.4)
• Lesson 8.5, Spark Your Learning, asks students, “A contractor buys rectangular floor tiles for a home that he is building. How could you find the area of the tile? Draw a visual model to show how you can find the area of the tile. Explain your reasoning.” (5.NF.2.4)
• Lessons 10.5, On My Own Problem 11, “Mae uses the expression 5 ÷ $$\frac{1}{6}$$ to solve a problem. Write a word problem that can be modeled by the expression. Draw a visual representation to show the quotient.” (5.NF.2.7)
• Lesson 13.2, On My Own, students reason on what decimal has “$$\frac{1}{10}$$ of the value of 0.08 and what decimal has 10 times as much as the value of .008? Explain.” (5.NBT.1.1)
• Lesson 14.4, More Practice and Homework, Question 6, Math on the Spot, asks students, “Tania measure the growth of her plant each week. The first week, the plant’s height measured 2.65 decimeters. During the second week, Tania’s plant grew .7 decimeter. How tall was Tania’s plant at the end of the second week? Describe the steps you took to solve the problem.” (5.NBT.2.7)
• Lesson 15.2, students use visual models and base ten representations to represent multiplication with decimals and whole numbers. (5.NBT.2.7)
• Lesson 15.5, students use an area model to multiply decimals by decimals. (5.NBT.2.7)
• Lesson 16.1, students utilize visual models such as fraction strips/bar model to add fractions with different denominators. (5.NBT.2.7)
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials for Into Math Florida Grade 5 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.”

• In Lesson 1.6, students develop multiplication fluency. In On My Own, Problems 9 and 10, students refer to a table with costs to find the money earned by selling multiples of items in the table. For example, Problem 9, “If the store sells 35 filing cabinets and 14 tables, how much does it earn?" (5.NBT.2.5)
• In Lesson 2.4, students use partial quotients to solve multi-digit division problems. On My Own, Problem 8, “2,352 ÷ 48.” More Practice/Homework, Problem 6, “8,632 ÷ 29.” (5.NBT.2.6)
• Lesson 8.3, On My Own, students write an equation before multiplying. Problem 3 asks students to use an area model to multiply “1$$\frac{1}{4}$$ by 1$$\frac{1}{3}$$.” (5.NF.2.6)
• Lesson 8.5 presents opportunities for students to practice fluency with multiplication of fractions in both the Check for Understanding and On My Own. For example, Problem 4, “Find the product. $$\frac{4}{9}$$ x $$\frac{3}{5}$$; and Problem 9, $$\frac{3}{8}$$ x $$\frac{3}{7}$$.” (5.NF.2.4)
• Lesson 14.4, On My Own, students practice subtracting decimals. “Problem  15, Find the Difference, 27.64 - 16.98;” “Problem 18, Find the unknown number: ___ - 4.63 = 1.7.” (5.NBT.2.7)
##### Indicator {{'2c' | indicatorName}}
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials for Into Math Florida Grade 5 meet the 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 Independent Practice and On My Own, students engage with problems that include real-world context and present opportunities for application. For example:

• Lesson 3.2, On My Own, Problem 13, “Anderson has 212 coins in his collection. He wants to keep all of his coins in a binder. He can store 24 coins on each binder page. He finds 212 ÷ 24 to be 8, r20, so he buys 8 pages. Does Anderson buy the correct number of pages. Explain.” (5.NBT.2.6).
• Lesson 8.4, On My Own, student solve real-world problems involving multiplication of fractions and mixed numbers. For example, “Write a story context that can be modeled with the equation $$\frac{1}{4}$$ x $$\frac{8}{12}$$ = $$\frac{2}{12}$$. Then draw a visual model to represent the problem.” (5.NF.2.6)
• Lesson 8.4. Homework, Problem 1, “Dominick’s doctor tells him to take a one-half dose of medicine. One dose equals $$\frac{2}{3}$$ tablespoon. Draw a visual model to find the amount of medicine Dominick needs. Write and solve an equation to go with your visual model. How many tablespoons is a one-half dose?” (5.NF.2.6)
• Lesson 8.7, On My Own, Problem 10, students solve real-world problems involving multiplication of fractions and mixed numbers. “Sam is using craft felt to carpet two rooms in her dollhouse. Both rooms are $$\frac{5}{6}$$ ft by $$\frac{7}{8}$$ ft. How many square feet of craft felt does she need to carpet both rooms? Explain your reasoning.” (5.NF.2.6)
• Lesson 9.2, More Practice/Homework, Problem 1, student solve real-world problems involving multiplication of fractions and mixed numbers. “Samantha runs on the Lakeside Trail. She runs 2 and one half times around the loop and then walks the remainder of the way. Write and solve an equation to model the distance Samantha runs.” (5.NF.2.6)
• Lesson 9.1, On My Own, Problem 5, students are given mixed number length and width of a step ands asked to find the largest square tile of any size she can use so that the tiles fit exactly, and then explain how the tiles show the area of the step. (5.NF.2.6 )
• Lesson 9.4, On My Own, Problem 4, students solve real-world problems involving multiplication of fractions and mixed numbers. “The area of Milo’s bathroom is 40 square feet. The area of his bedroom is 2$$\frac{3}{4}$$ times as great as the area of his bathroom. What is the area of his bedroom?” (5.NF.2.6)
• Lesson 9.9, Problem of the Day, students solve real-world problems involving multiplication of fractions and mixed numbers. For example, students determine how much water would go into four beakers if they each held $$\frac{2}{8}$$ liter of water. Students are prompted to draw a model. (5.NF.2.6)
• Lesson 10.3, On My Own, Problem 7, students solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions. “Consider the expression $$\frac{1}{5}$$ ÷ 3. Write two different word problems that can be represented by this expression. Draw a visual model to represent the problem  and then solve. What does the quotient represent in each problem?” (5.NF.2.7c)
• Lesson 11.2, On My Own, “Maggie has a goal of jogging 100 miles. The distance she runs each day is the same unit fraction. What are some possible fractions of a mile she can run each day and the number of days will it take her to reach her goal? Explain how you found your answers." (5.NF.2.7c)
• Lesson 11.4, On My Own, students solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions. “Kecia buys $$\frac{1}{4}$$ pounds of peppers. She cuts the peppers into 6 equal sized strips. How much of one whole pound is each strip? Represent the problem on a number line (number line with range 0 to 1 given, no intervals labeled)." (5.NF.7c)
• Lesson 11.5,  On My Own, Problem 9, students solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions. “For the equation $$\frac{1}{10}$$ ÷ 4 = b: Write a word problem.” Students draw a visual model for the problem as well. (5.NF.2.7c)
• Lesson 11.6, On My Own, students solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions. “To make a homemade ‘lava lamp’ you can mix vegetable oil, food coloring, and $$\frac{1}{4}$$ tablet of baking soda. How many lava lamps can you make if you have 5 tablets of baking soda?” (5.NF.2.7c)
• Lesson 15.6, On My Own, student find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. “The average heart rate of a giraffe is 65 beats each minute. The average heart rate of a horse is 44 beats each minute. How many more times does a giraffe’s heart beat in 2.75 minutes than a horse’s heart does?” (5.NBT.2.6,7)
• Lesson 17.6, On My Own, Problem 6, “Carlos sells coupon booklets for $5.50 apiece. He makes$60.50. Monica sells the same books for $4.75 each and makes$57. Who sells more booklets? How many more?” (5.NBT.2.7)

Each Unit has a Performance Task involving real-world applications of the mathematics from the unit. For example, the Unit 4 Performance Task is called Trail Teamwork and has students: determine what fraction of a 10-mile long hiking trail each of four people is in charge of cleaning, determining the distance between equidistant signs along a trail (3 signs within $$\frac{1}{2}$$ mile), determine how many trees are planted if every $$\frac{1}{4}$$ mile a tree is planted, (5.NF.2.7c), and create line plots to show the heights of those trees after a few weeks.

##### Indicator {{'2d' | indicatorName}}
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials for Into Math Florida Grade 5 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 page includes 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:

• Lesson 3.4, Problem 5, students solve an application problem, “Students at a local elementary school raised $3273 during a charity event. The money raised will be shared equally among 3 different charities. How much money will each charity receive? Write an equation to model the situation. Then solve.” (5.NBT.2.6) • Lesson 5.5 develops procedures for finding volume of rectangular prisms. Students learn the formula and then use it in 19 different problems. (5.MD.3.5b) • Lesson 16.1 develops conceptual understanding of multiplication with decimals using hundredths grids. In each of the problems, students color grids to represent the products of two decimals. (5.NBT.2.7) 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 10.4, Build Understanding, Problem 1, students use their understanding of fractions to solve a real-world problem. “The nature preserve has a 3-mile long trail for birdwatchers. The ranger divides the birdwatcher trail in $$\frac{1}{2}$$ mile sections and names each section after a different bird. How many of these sections does the trail have? A. Complete to describe the situation and model it with an expression.‘The trail is ___ miles long and is divided into ____ mile sections. This can be modeled by the expression ___.'” • Lesson 11.1, More Practice and Homework, students represent the situation for each problem with a visual model. They then write a division equation and a related multiplication equation. Problem 1, “Marcos has 4 gallons of gasoline for his lawn mower. How many lawns can he mow if each lawn uses $$\frac{1}{4}$$ gallon of gasoline?" Students engage in application and conceptual understanding as they complete the problem. • Lesson 11.3, On My Own, Problem 3, students use application and conceptual understanding, “Write and solve a word problem that can be represented with the visual model.” The visual model shows five hexagons partitioned into six pieces each. (5.NF.2.7c) #### Criterion 2.2: Math Practices Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice The instructional materials reviewed for Into Math Florida Grade 5 partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified but not clearly labeled throughout the materials, and the instructional materials support the standards’ emphasis on mathematical reasoning. ##### Indicator {{'2e' | indicatorName}} The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. The instructional materials reviewed for Into Math Florida Grade 5 partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level. The Math Practices are identified at the unit, module and lesson level. In addition, information in the Planning and Pacing Guide also include references to the Mathematical Practices. For example: • The Planning and Pacing Guide outlines for teachers where to look for each of the SMPs. It states, “MP.1.1, MP.3.1, and MP.5.1 are paired with Spark Your Learning tasks. When students connect understanding they have developed with more efficient procedures, MP.7.1 and MP.8.1 are being attended to. This helps student explain and justify their procedures with MP.4.1. MP.2.1 and MP.6.1 are attended to within lessons that ask students to apply procedures in practice.“ • All Mathematical Practices are clearly identified throughout the materials, for example, MP.1.1 is identified in the Spark Your Learning tasks; MP.2.1 is identified in Lesson 10.5, and Lesson 9.2; MP.3.1 in Lesson 11.1 and Lesson 16.2; MP.4.1 in Lesson 12.1 and Lesson 15.2; MP.5.1 in Lesson 11.1 and Lesson 6.1; MP.6.1 in Lesson 10.5 and Lesson 1.3; MP.7.1 in Lesson 9.2 and Lesson 1.1; and MP.8.1 in Lesson 1.3 and Lesson 15.1 • The Planning and Pacing Guide for the teachers has a section identified as Correlations for Mathematical Practices. In this section the 8 Mathematical Practices are listed in a table with a detailed description (from the common core documents) of the practice as well as “some examples,” of where the practice is included in the text series. Each math practice has 11-14 locations listed of where the teachers can look for specific Mathematical Practices. • In the Teacher Edition, in the margin under Homework & Test Prep, a section describes Mathematical Practices that can be seen within the Homework worksheet for the students. However, the materials over-identify the Math Practices, with some identified for every lesson. In addition, some MPs are incorrectly identified. For example: • MP.1.1 and MP.3.1 are identified as “in every lesson.” • MP.2.1 is identified as “in every Spark Your Learning Lesson and in most lessons.” • MP.4.1, MP.5.1, MP.6.1, MP.7.1, and MP.8.1 are identified as, “in most lessons.” according to the correlations chart. • Lesson 8.4 and Lesson 8.5 indicates that a focus on MP.6.1. However there is no reference to this standard in the lessons. • Lesson 8.6 indicates a focus on MP.3.1. However, in the planning it states that MP.5.1 and MP.6.1 are the focus. • Lesson 20.1 indicates that MP.3.1 will be addressed however in the lesson is is actually MP.4.1. • In Modules 6 through 11, MP.1.1 is not explicitly identified as a part of any lesson. • In the Planning and Pacing Guide, the materials indicate Lesson 6.2 addresses MP.1.1. However, in the Lesson Plan in the teachers edition it is not indicated. Also, MP.1.1 is labeled in the correlations chart as in every lesson, but there is no explicit connections in Lessons 1.3, 9.1, or 15.6. • Multiple problems within a lesson include Mathematical Practice language with no direct connection to the Mathematical Practices. For example, Lesson 5.2, Problem 4, states, “Attend to Precision,” prior to listing the question. Lesson 15.5, Problem 12, states, “Critique Reasoning.” These Mathematical Practice phrases are in all modules and are in bold prior to the question or problem being posed. For the most part, when identified, Mathematical Practices are used to enrich the mathematical content of the lessons. For example: • Lesson 4.2, Problem 1 identifies MP.3.1 students evaluate Rafiq’s reasoning in comparing two expressions and be able to explain whether or not Rafiq made an error. • Lesson 15.1, More Practice/Homework, identifies MP.7.1 in Problem 15, as students extend their reasoning of multiplication patterns with decimals to higher order powers of 10. ##### Indicator {{'2f' | indicatorName}} Materials carefully attend to the full meaning of each practice standard The instructional materials reviewed Into Math Florida Grade 5 partially meets expectations that the instructional materials carefully attend to the full meaning of each practice standard. The materials do not attend to the full meaning of MP.4.1 and MP.5.1. Students have limited opportunity to create models or choose tools. Models are often provided for the students, and they use tools as directed by the materials. Examples where MP.4.1 is identified, but students do not engage with the full intent of MP.4.1 as the directions tell students what models to use include: • Lesson 7.6, Step it Out, problems encourage students to draw bar models to represent the problem. • Lesson 9.4, Step It Out, students are prompted to write an equation for, “Toni has a plaque that is 5$$\frac{1}{2}$$ inches wide and 8$$\frac{1}{2}$$ inches long. Toni hangs her plaque on a wall. How much wall space does the plaque cover?” • Lesson 9.4, Step it Out, “Write and solve an equation to model the problem using fractions greater than 1.” • In Lesson 10.4, On My Own, students solve whole number by unit fraction division problems and they are prompted to draw visual models to complete and investigate the equations. Examples of MP.5.1 being identified, where students do not choose tools strategically, as the tools are given to students include: • In Lesson 14.1, Build Understanding: students are directed on which tool to use, “What base-ten blocks do you use to show 0.36 and 0.15?” • In Lesson 14.3, On My Own, Problem 5, students are directed on which tool to use, “Justify your answer using the number line.” • In Lesson 14.4, On My Own, Problem 6, students are directed on which tool to use, “Use the addition chart to find the price.” Examples of the instructional materials attending to the full meaning of the MPs include: • MP.1.1: In Lesson 7.1, Spark Your Learning, “Ms. Fong mixes amounts of water, glue, and laundry detergent together to make slime. Each amount is a fraction of a liter. Use a visual model to estimate the total number of liters of ingredients she mixes together.” Persevere, the Teacher Edition states, “If student needs support, guide them by asking, 'What do you need to find? What about these fractions makes them difficult to add? How could you use fraction strips to estimate the sum?'" • MP.2.1: In Lesson 14.5, Step It Out, Problem 1, students reason abstractly and quantitatively to answer, “Santiago is at the store with his brother. He reads the total for his purchase on the cash register and realizes that he has only$4.73. His brother pays the difference. How much does Santiago’s brother pay? Write an equation to estimate how much Santiago’s brother pays.”
• MP.6.1: In Lesson 20.2, On My Own, Problem 7, students learn to attend to precision, "Compare the triangles: Name one attribute that three of the triangles have. Name one attribute that one of the triangles has.
• MP.7.1: In Lesson 1.1, Build Understanding, students look for and make use of structure to solve, "Complete each column in the table. How does the number of zeros in each number change?," "In the '10 times as much' column? In the '1 times as much' column? In the '$$\frac{1}{10}$$ of' column?"
• MP.8.1: In Lesson 17.1, On My Own, Problem 2 students look for repeated reasoning to solve, “The container holds 100 servings of juice. Show a pattern to find the amount of juice in one serving. How many gallons are there in one serving?”
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Into Math Florida Grade 5 meet the expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Student materials consistently prompt students to construct viable arguments and analyze the arguments of others. A common strategy in these materials is Turn and Talk with a partner about the related task. Often these Turn and Talks require students to construct viable arguments and analyze the arguments of others. In addition, students are often asked to justify their reasoning in practice problems, especially in those problems labeled “Critique Reasoning.”

• Lesson 1.2, Practice & Homework Journal, Problem 7, Math on the Spot What’s the Error?, “Sophia said that the expanded form for 605,970 is 6000,000 + 50,000 + 900 + 70. Describe Sophia’s error and give the correct answer.”
• Lesson 4.2, Critique Reasoning, Problem 4, “James is making banners for his airplanes to pull. Each banner is 5 feet long and is attached by a 10-foot long rope. He models the total length of the banners and rope for six airplanes with the numerical expression 6 x (5 + 10). He says the total length for six planes is five times as much as the total length needed for one plane. Correct his error."
• Lesson 4.4, On My Own, Problem 11, “Deshawn says the he can evaluate the expression 7 + (3 x 8) - 5 without parentheses and get the same answer. Is Deshawn correct? Explain how you know.”
• Lesson 6.6 On My Own, Problem 12, “Carl and Maeve are asked to think of a fraction and multiply it by 5,267. Carl thinks of $$\frac{5}{6}$$. Maeve thinks of $$\frac{7}{7}$$. They both say their product is less than 5,267. Are they correct? Explain.”
• Lesson 8.6, Spark Your Learning, “The painting shown is resized to 3.4 of its original size. How does the height of the resized painting compare to the height of the original painting? Is the height of the resized more than or less than $$\frac{3}{4}$$ foot? Draw a visual model to represent your thinking. Justify your reasoning."
• Lesson 11.5, Turn and Talk, “Why should you divide each half of the rectangle into 4 equal groups?” and “Does it matter what visual model you use to help you find the quotient of a unit fraction divided by a whole number? Why might you choose one model over another? Explain.”
• Lesson 15.5, Turn and Talk, “Is your answer reasonable? Explain how you know.”
##### Indicator {{'2g.ii' | indicatorName}}
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Into Math Florida Grade 5 meet the expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Many of the lesson tasks are designed for students to collaborate, with teacher prompts to promote explaining their reasoning to each other. Independent problems provided throughout the lessons also have teacher guidance to assist teachers in engaging students.

• The Teacher Edition provides Guided Student Discussion with guiding questions for teachers to create opportunities for students to engage in mathematical discourse. For example, in Module 14, “How can you tell that the 4-digit number at the top of the subtraction problem is less than 2,000?” In Module 19, “What would have happened if the instruction in step D had the pattern start at 95 instead of 83?”
• Critique, Correct, and Clarify is a strategy used to assist students in constructing viable arguments. For example, in Lesson 1.4, On My Own, “Have students work out the steps to multiply on their own. Encourage students to describe the error and review explanations with a partner. Students should refine their responses after their discussions with a partner.” In Lesson 5.4, On My Own, Problem 12, “Point out to students that Problem 12 can be solved more than one way. As shown, the volume of the new cube can be multiplied by the number of cubes: 8 x (2 x 3 x 4). Or the length of each side of the cube can be doubled: 4 x 6 x 8. Encourage students to describe different ways of solving the problem with their partners. Students should refine responses after their discussions.”
• Lesson 2.4 asks students to tell if an estimate is reasonable and explain why. Teacher guidance says, “Problem 3 Construct Arguments shows that students need to determine the reasonableness of a quotient.”
• The Teacher Edition includes Turn and Talk in the margin notes to prompt student engagement. For example, in Lesson 11.1, Build Understanding, “Have students share their reasoning. For students who are struggling, suggest that they compare the multiplication expression with their visual models”  The Turn and Talk builds off of earlier discussion questions such as, “What math problem do you need to solve? How can you show the number of pounds of potato salad? How can you show the divisor in your visual model?”.
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Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Into Math Florida Grade 5 meet the expectations for explicitly attending to the specialized language of mathematics. The materials provide explicit instruction on communicating mathematical thinking with words, diagrams, and symbols. The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them. Examples found throughout the materials include:

• At the beginning of each module, Key Academic Vocabulary is highlighted for the teacher.  The sections include both Prior Learning - Review Vocabulary, and Current Development - New Vocabulary. Definitions are given for each vocabulary word.
• Within the Student pages, new vocabulary is introduced in highlighted sections called Connect to Vocabulary. For example, in Lesson 4.1, “You can model a context mathematically using a numerical expression. A numerical expression is a mathematical phrase that uses only numbers and operation signs.” In Lesson 20.3, “There are two accepted definitions of a trapezoid. One definition defines a trapezoid as having exactly one pair of parallel sides. The other definition defines a trapezoid as having at least one pair of parallel sides.”
• In the Module planning pages, a Linguistic Note on the Language Development page provides teachers with possible misconceptions relating to academic language. For example, in Unit 1, “Many English words have multiple meanings that can interfere with comprehension. For example, flat and long are typically used as adjectives, however, they also name the base-ten blocks used for understanding multi-digit place values. Point out that the articles 'a' and 'the' in front of these words are a strong clue to their meaning.”
• In Sharpen Skills in the lesson planning pages, some lessons include Vocabulary Review activities. For example, in Lesson 20.1, “Objective: Students review ty.” “Materials: markers, poster paper” “Have students work in types of polygons. List the following review terms on the board- triangle, decagon, hexagon, octagon, quadrilateral- Ask students to discuss what attributes all of these figures have in common. Then have students identify the specific characteristics of each. Have students form and each student should draw an example of each figure listed. Students should compare their figures.”
• Guide Student Discussion provides prompts related to understanding vocabulary such as in Module 6, “Listen for students who correctly use review vocabulary as part of their discourse. Students should be familiar with the terms fraction, sum, like denominator, and mixed number. Ask students what they mean if they use those terms.” “Why can’t you count the number of shapes in the puzzle to determine the number of equal parts in the whole puzzle?” “How can you tell how many large triangles will fit in the puzzle?” "How can you use this fact to write a fraction for each large triangle?” “How can you use these facts to find the fractional area of each small triangle?”
• Vocabulary is highlighted and italicized within each lesson in the materials.
• There is a vocabulary review at the end of each Module. Students complete a fill-in-the-blank with definitions or examples, create graphic organizers to help make sense of terms, or the teacher is prompted to make an Anchor Chart where students define terms with words and pictures, trying to make connections among concepts.

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

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The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

The instructional materials for Into Math Florida Grade 5 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. Step It Out sections help students to develop procedural skill and fluency.

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.

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Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials for Into Math Florida Grade 5 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 the Spark Your Learning section of Lessons, 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 the Build Understanding and Step It Out sections, 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. The Check Understanding section 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 the On My Own.

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There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials for Into Math Florida Grade 5 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 ask for a variety of responses from fluency to higher level thinking. For example, the Lesson 4.4 Homework has seven problems. One problem is a multi-step word problem. One asks students to describe how they would solve {[24 / (6 - 2)] - 4} x 3. Four problems ask students to use parentheses to make an expression equal to a provided value and the last problem asks students to critique the reasoning of another students work that is provided.

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Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for Into Math Florida Grade 5 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 4.1, students are asked to model a situation with two color counters. “The Mifflin Elementary School drum line is made up of 14 fourth-grade drummers and 12 fifth-grade drummers. The fourth-grade drummers stand in a line, and the firth grade-drummers sand in a line behind them.” Students use two color counters or a visual model to create a representation. The manipulatives provide opportunities for students to develop a conceptual model of problems they will represent in pictorial form in their student workbook.

Lesson 6.3, Spark Your Learning, students are encouraged to use a visual representation to show $$\frac{7}{10}$$ and $$\frac{2}{5}$$. They use fraction tiles to make equivalent fractions in order to subtract the fractions. The work with fraction tiles is connected to the written method for making equivalent fractions and subtracting fractions.

Examples of manipulatives for Grade 5 include: Base Ten Blocks, connecting cubes, fraction strips, grid paper, ruler, number line, square tiles, and two color counters.

The materials rely heavily on pictures of the manipulatives. When physical manipulatives are called for 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.

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The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials for Into Math Florida Grade 5 are not distracting or chaotic and support students in engaging thoughtfully with the subject.

The printed and digital materials follow a consistent format. Teacher editions provide information for teachers to be able to access digital resources. There is room for students to record answers and show their thinking. Features of the materials are consistently presented, and the use of colored fonts supports identification of lesson components. For example, Turn and Talk opportunities are highlighted in yellow and Check for Understanding is always in red font. Visual images mirror the situation in the problem or can be used by students as they solve the problem. For example, Module 5, Lesson 5, Step it Out, includes a drawing of a fish tank on the side of the problem. Students use the dimensions draw on the fish tank to write a formula for the volume.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

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Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials for Into Math Florida Grade 5 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 4.2, Activate Prior Knowledge, provides teachers with the following questions, “Where did you put the parentheses? Why? Which operation will you do first to evaluate the expression? What should happen in your word problem when the expression shows addition? What should happen in your word problem when the expression shows division?”
• Lesson 19.4, Step it Out, includes questions for teachers to ask students, “What do you notice about the numbers in Antonia’s pattern?” “What do you notice about the numbers in Connor’s pattern?” and “How does writing the numbers as ordered pairs help you analyze their relationship?”
• Lesson 13.3, Spark Your Learning, includes four questions, “How do you round a whole number, like 853, to the nearest ten?” “How does the value of the number 15.04 compare to the value of the number 15.040?” ”Which digits in the numbers 15.042 and 15.046 have the place value of hundredths?” and “How is the process of estimating related to the process of rounding?”
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Materials contain a teacher's 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, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials for Into Math Florida Grade 5 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.”

##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains 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.

The instructional materials for Into Math Florida Grade 5 partially meet the expectations for containing adult-level explanations so that teachers can improve their own knowledge of the subject. The materials include adult-level explanations of the grade-level content, but the materials do not include adult-level explanations of advanced mathematics concepts so that teachers can improve their own knowledge of the subject.

This materials include explanations and examples of the course level mathematics specifically for teachers that can improve their own knowledge of the subject. In the Teacher Edition modules are examples and support for the adult in the math classroom as it relates to grade-level standards. For example:

• The Mathematical Progressions table in each module and lesson highlights Prior Learning, Current Development, and Future Connections. In Lesson 14.2, this table lists the 4th grade standard supporting the 5th grade on-level standard and what 6th grade standard this will lead into.
• Professional Learning notes are present in each lesson. In Lesson 14.2, Professional Learning, discusses “Using Mathematical Practices, "This lesson provides students with an opportunity to use base-ten blocks and draw quick pictures to subtract decimals. Like they did with the previous tools in adding decimals, students adapt the tools to subtract decimals like they did with whole numbers. Developing proficiency with these tools will enable students to understand the principles of using place-value strategies to regroup when subtracting.”
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The instructional materials for Into Math Florida Grade 5 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.

##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials for Into Math Florida Grade 5 provide a list of lessons in the Teacher's Edition, cross-­referencing the standards addressed, and a pacing guide.

Each course in this series includes a Planning and Pacing Guide encompassing the standards and pacing (number of days) for each lesson. There is another standards chart in the Planning and Pacing Guide listing each standard and correlation to Student Edition Lessons. In the Teacher Edition, pacing is provided in the module planning pages, and the standards contained in each lesson are identified with written descriptions, as well as listed under Current Development in the Mathematical Progressions chart.

##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials for Into Math Florida Grade 5 include strategies for parents to support their students progress. The Family Resources tab include several resources for parents, including:

• “Family letters inform families about the skills, strategies, and topics students are encountering at school.” Each module includes a letter, found online in four languages, providing vocabulary, a home activity, and discussion prompts. This letter is available in English, Spanish, Haitian-Creole, and Portuguese.
• Math on the Spot videos are available for specific lessons within a module. For example, Module 10 includes a Math on the Spot video for Lessons 1 and 3.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials for Into Math Florida Grade 5 explain instructional approaches used and how they are research-based.

The Planning and Pacing Guide contains Teacher Support Pages including a section on Supporting Best Practices. “Into Math was designed around research-based, effective teaching practices such as those described in Principles to Actions (NCTM 2014).” These include:

• Establish mathematics goals to focus learning.
• Implement tasks that promote reasoning and problem solving.
• Use and connect mathematical representations.
• Facilitate meaningful mathematical discourse.
• Pose purposeful questions.
• Build procedural fluency from conceptual understanding.
• Support productive struggle in learning mathematics.
• Elicit and use evidence of student thinking.

The Planning and Pacing Guide describes four design principles from the Stanford Center for Assessment, Learning, and Equity (SCALE) that “promote the use and development of language as an integral part of instruction”. These principles are: Support sense-making; Optimize output; Cultivate conversation; and Maximize linguistic and cognitive meta-awareness. To address this, the instructional materials include language routines that “help teachers embrace these principles during instruction.” Each module contains a Language Development page in the Teacher Edition stating where the language routines should be used. On the lesson pages of the Teacher Edition, there are Support-Sense Making boxes that describe how the language routine can be used. Also, there are notes in the margin of the teacher’s edition providing connections from the strategy to the principle.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

The instructional materials reviewed for Into Math Florida Grade 5 partially meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, and assessments that clearly denote which standards are being emphasized.

##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials for Into Math Florida Grade 5 meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

• At the beginning of the year, students’ prior knowledge is gathered through a Prerequisite Skills Inventory. “This short-answer test assesses core precursor skills that are most associated with on-grade success.” (Assessment Guide)
• Each Module begins with Are You Ready, a diagnostic assessment of prior learning related to the current grade-level standards. Intervention materials are provided to assist students not able to demonstrate the necessary skills. Commentary for each standard explains how the prior learning is relevant to the current Module’s content.
• Prior learning is identified in the Mathematical Progressions section at the beginning of each Module and lesson of the Teacher Edition.
##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials for Into Math Florida Grade 5 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• The module overview in the Teacher Edition contains “Common Errors” as students engage in an introductory task and provides questioning strategies intended to build student understanding.
• The Spark Your Learning planning page for each lesson in the Teacher Edition includes a Common Error section related to the content of the lesson identifying where students may make a mistake or exhibit misunderstanding. There is a rationale that explains the likely misunderstanding and suggests instructional adjustments or steps to help address the misconceptions.
• There are also “Watch For” boxes and question prompts highlighting areas of potential student misconceptions.
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials for Into Math Florida Grade 5 partially meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• Each lesson ends with a few Spiral Review questions for ongoing practice in the More Practice/Homework section.
• Online interactive lessons and homework practice provide students with immediate notification that answers are correct or incorrect, but do not provide feedback for changing incorrect answers..
• The online lessons are the same as in the print textbook and provide immediate notification of correct or incorrect answers, but do not provide feedback for changing incorrect answers.
• Each Module Review has a scoring guide/checklist, so students know which questions they answer correctly. The scoring guide/checklist does not provide feedback for changing incorrect answers.
• Digital assessments are auto-scored and generate recommendations that can provide feedback to teachers, but not directly to students.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials for Into Math Florida Grade 5 meet the expectations that assessments clearly denote which standards are being emphasized.

The Lesson Focus and Coherence page indicates the CCSSM that will be addressed within the lesson. Throughout the lesson are formative assessments in the Check for Understanding, On My Own, and More Practice/Homework. Each Module has an End of Module Test, the standards associated with each problem on this test can be found on the Individual Record Form within the Assessment Guide Book.

Each Unit has a summative Performance Task including the standards in the teacher pages of the Assessment Guide, although the individual questions do not indicate which standards are being assessed.

##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials for Into Math Florida Grade 5 partially meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

• Each lesson has a diagnostic assessment, Are You Ready, correlated to standards and a suggested intervention for struggling students. The materials state that when using Online Ed, teachers can assign the Are You Ready digitally “for immediate access to data and grouping recommendations.”
• “Check Understanding is a quick formative assessment in every lesson used to determine which students need additional support and which students can continue on to independent practice or challenges.” (Planning and Pacing Guide) Check Understanding presents a limited number of questions, usually 1-3, which includes a digital option that can be “auto-scored online for immediate access to data and recommendations for differentiation.”
• The Individual Record Forms in the Assessment Guide suggest Reteach Lessons that teachers can use for follow-up based on the Module assessments, but there are no other suggestions for follow-up with students or guidance to teachers.
• The Individual Record Forms for the Prerequisite Skills Inventory, Beginning-of-Year Test, Middle-of-Year Test, and End-of-Year Tests do not suggest Reteach Lessons or provide other guidance teachers can use for follow-up with students.
• The Performance Task Rubrics for the Unit Performance Tasks do not suggest Reteach Lessons or provide other guidance teachers can use for follow-up with students.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials for Into Math Florida Grade 5 include Scales to Track Learning Goals at the end of each lesson. The Teacher Edition introduction states, “The scales below can help you and your students understand their progress on a learning goal. Scales are also available in Module Resources.”

Each lesson contains “I can” scales with four levels of  “I Can” statements written in increased difficulty. While a note saying, “The scales below can help you and your students understand their progress on a learning goal” is present, there is no explicit indication of how to use these scales.

At the end of On My Own section, is a Learning Mindset prompt where students write a response to reflect on the lesson. For example, from Lesson 5.1 the Learning Mindset asks, “What is still unclear about unit cubes?”

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials reviewed for Into Math Florida Grade 5 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials for Into Math Florida Grade 5 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.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials for Into Math Florida Grade 5 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.”

##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials for Into Math Florida Grade 5 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 15.2, Spark Your Learning has this prompt, “Mary is shopping at the grocery store. She weighs a banana as shown. What is the weight of 3 bananas the each weighs the same amount shown on the scale? Show your thinking.” A picture of a scale shows the banana weighs 0.28 pound. This problem has multiple entry points and solution methods. 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.”

##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials for Into Math Florida Grade 5 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.
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials for Into Math Florida Grade 5 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.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials for Into Math Florida Grade 5 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.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials reviewed for Into Math Florida Grade 5 provide opportunities for teachers to use a variety of grouping strategies.

In the Planning and Pacing Guide a section titled, “Grouping and Recommendations" is provided. This section states, “One of the most valuable and time-saving tools for teachers is the Recommend Groups tool online. It synthesizes data from assessments and places students into leveled groups, which teacher can modify as needed. Recommended lesson-level resources for each group surfaced in the tool and can quickly be assigned to each group.”

• Each lesson provides teachers with a differentiated plan including small-group options.
• The materials provide students with self-directed activities at math centers.
• Throughout the materials, ample opportunities for students to Turn and Talk with a partner are provided.
• Using the Check for Understanding, the teacher is directed to pull students into small groups and use the Teacher Tabletop Flipchart.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials reviewed for Into Math Florida Grade 5 encourage teachers to draw upon home language and culture to facilitate learning.

• The student glossary is in both English and Spanish.
• Each Module includes School-Home Letters in multiple languages: Spanish, English, Portuguese, and Haitian Creole.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

The instructional materials reviewed for Into Math Florida Grade 5: integrate some technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

The instructional materials reviewed for Into Math Florida Grade 5 are web-based and compatible with multiple Internet browsers.

• The materials are platform-neutral and compatible with Chrome, ChromeOS, Safari, and Mozilla Firefox.
• Materials are compatible with iPads, laptops, Chromebooks, and other devices connected to the internet with an applicable browser. Online use was difficult on a Chromebook, scrolling and loading issues as well as difficulty seeing all pieces of the interactive editions was evident.
• The materials are not compatible with an Android device (using Chrome browser). Although the website can be reached, it is not possible to zoom in or out, nor can one move the screen, so a student cannot access the entire screen.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials reviewed for Into Math Florida Grade 5 include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology through a website called Online ED, which parallels the print textbook. Only one module per grade is currently available in the digital format, so some of the evidence is stated in the materials but has not actually been observed.

• Lesson problems from the Student Edition, assessments, and unit performance tasks are provided to be completed and scored using technology, providing students with feedback on whether the answers are correct or incorrect.
• Online Ed is designed to make recommendations for differentiation after auto-scoring of Check Understanding problems within each lesson.
• Growth monitoring assessments are “designed to be administered in 40 minutes, 3 times per year. The system utilizes a secure bank of assessments to adapt to each student’s ability and maps progress on the Quantile Framework.” (Pacing Guide)
• Assessments can be created using a question bank that repeats the questions presented throughout the interactive lessons. However, teachers cannot modify questions nor add new questions.
• The online system has dynamic reporting by assignment or standards. If teachers are using the online system, they can view student progress for interim growth, module readiness, and lesson practice and homework.
##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

The instructional materials reviewed for Into Math Florida Grade 5 are intended to include opportunities for teachers to personalize learning for all students. Full functionality of online materials is not accessible at the time of this review.

• Teachers can assign lesson problems and assessments, as well as view assessment analytics.
• Teachers can group students according to individual needs. The online component has Recommended Groups that “synthesizes data from assessments and places students into leveled groups.” (Pacing Guide) Recommended lesson resources can be assigned to each group.
• Teachers can create assessments using a bank of items.

The instructional materials reviewed for Into Math Florida Grade 5 provide minimal opportunity to be adapted for local use. Full functionality of online materials is not accessible at the time of this review.

• Pieces of a lesson can be assigned directly to students or groups of students.
• There is a question bank for teachers to create assessments. The bank repeats the questions that are already included in each lesson, and these questions cannot be modified.
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

The instructional materials reviewed for Into Math Florida Grade 5 do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.

##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

The instructional materials reviewed for Into Math Florida Grade 5 integrate some technology including digital lessons and virtual tools. Students can complete tasks and activities from the Student Edition through an interactive format.

• Students can draw pictures, create shapes, and type to show their thinking on the interactive lessons using a virtual sketchpad. Students complete tasks such as shading in bar diagrams, drag and drop the correct values into a table, or graph an equation. (Note: The backspace button, generally used to make a correction, is interpreted as the “back” button, returning to the previous screen and losing all work.)
• Only one Module per grade is currently available in the interactive lessons, so there is no way to know if the sketchpad is the only manipulative offered. No other virtual manipulatives were found.
• On the Spot videos of specific lesson problems are in the online student resources and provide the opportunity for students to review their work with their families by watching the video. These focus on content rather than MPs.

## Report Overview

### Summary of Alignment & Usability for Into Math Florida | Math

#### Math K-2

The instructional materials reviewed for Into Math Florida Grades K-2 meet expectations for alignment to the Mathematics Florida Standards (MAFS) and usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The instructional materials reviewed for Into Math Florida Grades 3-5 meet expectations for alignment to the Standards and usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 6-8

The instructional materials reviewed for Into Math Florida Grades 6-8 meet expectations for alignment to the Standards and usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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