## 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 4 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 4 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 4 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 4 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 2 Performance Task, Question 2, “Hannah flies over the country and makes a round trip from California to New Hampshire. Raoul says the miles she traveled is equal to the quotient for 5286 ÷ 3. How many digits will the number of miles she traveled have? Explain your reasoning.” (4.NBT.2.6)
• Module 12, Form A, Question 6, students determine if two fractions with denominators of 10 and 100 are equivalent to a given decimal. The choices are $$\frac{9}{10}$$, $$\frac{9}{100}$$, .009; $$\frac{2}{10}$$, $$\frac{2}{100}$$, .20; and $$\frac{8}{10}$$, $$\frac{8}{100}$$, .80. (4.NF.3.6)
• Module 14, Form A, Question 5, students solve a story problem requiring addition and subtraction of fractions with like denominators. (4.NF.2.3d)
• Module 19, Form A, Question 9, “Marcus buys an 8-pound pumpkin. He takes it home and removes 12 ounces of seeds and pulp. How many ounces does his pumpkin weigh now?” (4.MD.1.2)
• End-of-Year-Test, Question 12, “The city council where Antonio lives is planning to make the downtown area a better place to visit. The city council plans to spend $59 each on 48 small lamp posts and$63 each on 55 park benches. How much more is Antonio’s city council planning to spend on park benches than on lamp posts?” (4.OA.1.3)

Above grade-level assessment items are present, but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. These items include:

• Modules 11 and 13, the following problems use denominators outside of the range of possible denominators for 4.NF: Module 11, Form A, Questions 2 and 13; Module 11, Form B Questions 2, 3, and 13; and Module 13, Forms A and B, Question 6.
• Module 20, Form A, Questions 10 and 13, students convert from millimeters to centimeters and from milliliters to liters. This is converting from smaller units to larger units and aligns to 5.MD.1.1.

#### 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 4 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 4 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 13 out of 21, which is approximately 62%.
• The number of Lessons devoted to major work of the grade (including supporting work connected to the major work) is 71 out of 108, which is approximately 66%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 108 out of 175 days, which is approximately 62%.

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 66% 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 4 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 4 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 10, Teacher Manual, Lessons 1-4, 4.OA.2.4 supports the major work of 4.NBT.2. For example, Lesson 2, Question 7, students decide if seven is a factor of 91 and justify their answer by using division. Lesson 3, Question 4, students solve a story problem by using four as a factor.
• Module 11, Teacher Manual, Lesson 4, connections are made between the major work of 4.NF.1 and the supporting work of 4.OA.2.4. In Question 2, students list the factors of eight and 12, referring to the fraction $$\frac{8}{12}$$. Students use common factors between eight and 12 to write equivalent fractions.
• Module 19, Teacher Manual, Lesson 5, 4.MD.2.4 supports the major work of 4.NF.1.2. For example, in Question 1, students plot fractions on a line plot requiring students to first create equivalent fractions, then compare and order them correctly along the line plot.
• Module 19, Lesson 5, On My Own, Question 7, 4.MD.2.4 supports the major work of 4.NF.2.3d when students solve fraction addition and subtraction problems with data given in line plots. For example, “A local pizzeria held a pizza eating contest. The fractions below (all with a denominator of 8) represent the amount of pizza each contestant ate in 5 minutes. Make a line plot to display the data. How much more pizza did the winner eat than the person who came in last place?”
##### 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 4 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 175 days, 123 days for lessons and 52 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 4 has 7 Units, with 21 Modules containing 108 lessons.
• The pacing guide designates 8 lessons as two-day lessons and 100 as one-day lessons, leading to a total of 116 days. The materials do not define the number of minutes in a lesson or instructional day.
• Each Unit includes a Unit Opener, there are seven Openers for Grade 4 (seven 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 123 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 seven Performance Tasks for Grade 4 (seven days).
• Each Module has both a review and an assessment. There are 21 Modules (42 days). Based on this, 52 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 4 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, Module 18, Lesson 2, builds upon work done on 2.MD.1.1 during Grade 2. The work will continue in 5th grade, Module 12, Lesson 1, with a focus on standards 5.MD.1.1. In Activate Prior Knowledge 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:

• In the beginning of each module includes a diagnostic assessment called “Are You Ready?” identifying prior knowledge needed for the current module. Module 5 shows the link to prior learning for Multiplication Facts as Grade 3, Modules 4 and 5 (3.OA.3.7) in the Data-Driven Intervention Chart. A narrative is provided for each skill on the page. “Multiplication Facts:  These items assess whether students are able to find the product of two 1-digit numbers using a variety of strategies. In upcoming lessons, students may use these strategies to multiply larger numbers.”
• Each lesson the standard of focus is explicitly connected to work in future and prior grades.  For instance, Module 20 Lesson 2 identifies the lesson focus as standard 4.MD.1.1.

There is one instance of off-grade level work that is not clearly marked:

• Module 20, Lesson 2, On My Own, Problems 3, 4, and 6, students convert from a larger unit to a smaller unit.  For example, 9 kilometers = ____ meters. Question 5 asks students to convert from a smaller unit to a larger one, 70mm = ___ cm.  Additionally, homework practice, Question 5, students convert from 6,000 m = ______ km (5.MD.1.1)

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 8, Lesson 3, Build Understanding, students relate area models to partial products to multiply two-digit by two-digit numbers. For example, Question 1B,  “How can you use an area model to show the product?” Question 1C, “How can you write multiplication sentences to find the partial products?” During On My Own, students solve Question 2: “Write and solve an equation for the area model.” Additional practice is provided in More Practice/Homework (4.NBT.2.5).
• Module 12, Lesson 4, Step It Out, students compare decimals to hundredths using hundredths grids, number lines, and place value charts. During On My Own, students solve Question 3, “Chris has two kittens, Oscar and Tiger. Which kitten is heavier? Shade the hundredths model for each weight, and locate the weights on the number line.” (4.NF.3.7)
• Module 19, Lesson 5, Step it Out, students represent and interpret measurement data in line plots. Question 1, “The weights of some cell phones and tablets are shown. How can you display these data using a line plot?” On My Own has six questions where students create line plots and interpret the data.  Question 7, “A local pizzeria held a pizza-eating contest. The fractions below represent the amount of pizza each contestant ate in 5 minutes. Make a line plot to display the data. How much more pizza did the winner eat than the person who came in last place?” (4.MD.2.4)

The materials relate grade-level concepts to prior knowledge from earlier grades. Example includes:

• Module 6, Lesson 2, Investigate Remainders, students build upon their prior knowledge of understanding division as separating objects into equal groups (3.OA.1.2) and representing division using arrays and bar models (3.OA.1.3). Students apply this knowledge to investigate remainders (4.NBT.2.6). For example, Module 6, Lesson 2, Question 2, students solve a word problem where 35 pencils are needed to make 8 party favor bags. Students create a drawing to show how all the pencils can be divided. Then, describe how many total pencils were drawn, how many pencils went into each bag, and how many pencils were left over (remainder) and to tell why.
##### 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 4 meet the 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:

• In Lesson 1.2, the learning objective, place value relationships to read and write multi-digit whole numbers to 1,000,000 in different forms is shaped by 4.NBT.1: Generalize place value understanding for multi-digit whole numbers.
• Lesson 11.7, the learning objective, comparisons to order fractions is shaped by 4.NF.1: Extend understanding of fraction equivalence and ordering.
• In Lesson 12.4 the learning objective, compare decimals using visual models, number lines, or place value is shaped by 4.NF.3: Understand decimal notation for fractions, and compare decimal 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:

• Module 11, Lesson 3, connects 4.NF.2 to 4.OA.1. For example, Question 2, students create a fraction equivalent to $$\frac{1}{2}$$, with 6 as the denominator. Then, students describe the relationship between the numerator and denominator of each fraction.
• Lesson 14.6, connects 4.NF.3 with 4.NF.1 when students use equivalent fractions to write fractions with denominators of 10 as denominators of 100, and then add like denominators. For example, On My Own, Question 9, “$$\frac{22}{100}$$ + $$\frac{7}{10}$$”.

### Rigor & Mathematical Practices

The instructional materials reviewed for Into Math Florida Grade 4 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 4 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 4 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, there are sections that emphasize introducing concepts and developing understanding such as: "Build Understanding" and "Spark Your Learning". Students have the opportunity to independently demonstrate their understanding with the "Check Understanding" and "On My Own" problems at the end of each lesson. For example:

• Lesson 1.22, Spark Your Learning, “Texas has a land area of two hundred sixty-eight thousand, five hundred ninety-seven square miles. It is the largest state in the southern U.S. How can you write the area of Texas in two different ways using numbers?” (4.NBT.1.2 )
• Lesson 6.4, students use area models and the distributive property to represent division. (4.NBT.2.5)
• Lessons 7.2, Build Understanding, students use base ten blocks to represent division with one-digit divisors. Problem 1, “Fran has 423 scrapbook stickers. She wants to put an equal number of stickers in 3 different scrapbooks. How many stickers can she put in each scrapbook? Find 423 ÷ 3. Use base ten blocks to show the division.” (4.NBT.2.6)
• Lesson 5.4 asks students to use the distributive property and partial products to multiply one-digit by four-digit numbers. (4.NBT.2.5)
• Module 11, Opening Activity, students are provided four different squares partitioned and shaded differently. In a “Turn and Talk” they are asked, “Which square’s shading represents a different amount?” and “How could you change the shading to make it represent the same amount as the others?” (4.NF.1.2)
• Lesson 11.1, Spark Your Learning, students are asked, “Liz and Alvin have the same go-karts in different colors. The fuel tank in Liz’s go-kart is $$\frac{2}{5}$$ full. The fuel tank in Alvin’s go-kart is $$\frac{1}{3}$$ full. Whose go-kart has more fuel? How do you know?” (4.NF.1.2)
• Lesson 11.2, Spark Your Learning, students are asked, “Compare Abbot’s and Rowan’s rope climbs. Who climbed higher? How do you know?" (table provided of $$\frac{5}{8}$$ vs $$\frac{4}{10}$$) - Visual of the same size rope and two students. (4.NF.1.2)
• Lesson 11.3, Check Understanding, students are asked, “Jason makes a $$\frac{5}{6}$$ turn on his skateboard. Kym makes a $$\frac{3}{4}$$ turn, and Sam makes a $$\frac{10}{12}$$ turn. Which two skaters make the same-size turn? Explain.” (4.NF.1.2)
• Lesson 11.5, Question 4, students are asked, “Jerry has two same size circles divided into the same number of equal parts. One circle has $$\frac{3}{4}$$ of the parts shaded, and the other has $$\frac{2}{3}$$ of the parts shaded. His sister says that the least number of pieces each circle could be divided into is 7. Is his sister correct? Explain." (4.NF.1.2)
• Lesson 11.6, Question 5, asks student to reason about “Isaiah hikes $$\frac{11}{12}$$ mile along the Lake View Trail. Cheryl hikes $$\frac{10}{8}$$ mile along the same trail. Who hikes farther? Use a fraction comparison strategy to support your reasoning.” (4.NF.1.2)
##### 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 4 meet the 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.”

• Module 2 focuses on Addition and Subtraction of Whole Numbers. In Lesson 2.1, On My Own, students “Estimate. Then find the sum,” for problems such as Problem 8, 609,987 + 123,654. In Lesson 2.2, More Practice, students “Estimate. Then find the difference” for problems 3-5. Problem 4 includes, 38,207 - 28,278. (4.NBT.2.4)
• Lesson 5.5, On My Own, Problems 6 - 8, “Estimate. Then write the problem vertically to find the product.” Problem 6, 6 x 523; Problem 7, 9 x 5,181; Problem 8, 8 x 6,719. (4.NBT.2.5)
• Module 7 Review, Divide and Check, Problem 7, 231 ÷ 5; Problem 8, 458 ÷3; Problem 12, 2,551 ÷7. (4.NBT.2.5)
• Lesson 8.1, On My Own, students multiply with tens. “Choose a method. Then find the product.” Problem 5, 29 x 80 = ___; Problem 6, 25 x 30 = ___; Problem 7, 90 x 16 = ___. (4.NBT.2.4)
• Lesson 15.3, On My Own, “Find the Sum.” Problem 7, 3$$\frac{1}{4}$$ + 1$$\frac{2}{4}$$ = ___; Problem 8, $$\frac{5}{6}$$ + $$\frac{5}{6}$$ + $$\frac{5}{6}$$ = ___.” (4.NF.2.3c)
• Additional fluency practice can be found in the More Practice/Homework activities.
##### 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 4 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 Spark Your Learning, Independent Practice, and On My Own, students engage with problems that include real-world context and present opportunities for application. For example:

• Lesson 3.4, On My Own, Problem 5, students solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. For example: “Aditi wants to make posters to show animals in the Everglades. She has 4 posters, and each poster can fit 8 pictures.  She wants to show 2 pictures of each type of animal. How many different types of animals can Aditi show on her posters? Write equations to model the problem.” (4.OA.1.3)
• Lesson 3.5, Problem 5, students make a model to solve a problem where a students wants to make a poster to show animals in the Everglades. “She has 4 posters each of which can fit 8 pictures. She wants to show 2 pictures of each animal. How many different animals can be shown on her posters?” (4.OA.1.3)
• Lesson 5.7, Homework, Problem 6, students solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. For example, “The Brown family is driving to Junction City, which is 426 miles away. The family drives 60 miles for each of the first 3 hours. Then they drive 55 miles for each of the next 4 hours. How far are they from Junction City?"  (4.OA.1.3)
• Lesson 14.3. On My Own, Model with Mathematics, students solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. For example, “Weston walks $$\frac{1}{4}$$ mile to school and $$\frac{1}{4}$$ mile home. How many miles does Weston walk? Use a visual fraction model, write an equation and find the distance, d.” (4.NF.2.3d)
• Lesson 5.6, Check Understanding, students multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. For example, “The Cat in the Hat is a short book with only 236 words. The library has 5 copies of this book. How many words appear in the books?” (4.NBT.2.5,6)
• Lesson 7.2, On My Own, students multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. For example, “Jackie places 552 photos of cats on 4 bulletin boards at the animal shelter. Each board has the same number of photos. How many photos are on each board?” (4.NBT.2.5,6)
• Lesson 7.4, Check for Understanding, students solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. For example, “There are 48 people going on a hike. Each pack has 8 bottles of water. How many packs are needed for each hiker to have 2 bottles? How can you check that your answer is reasonable?” (4.OA.1.3)
• Lesson 8.7, More Practice/Homework, students solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. For example, “A crane operator moves 6 shipping containers that weigh 215 tons each onto a barge. The same crane operator loads 4 more shipping containers that weigh 194 tons each onto the barge. How many tons of shipping containers did the crane operator load onto the barge? Write an equation to model the situation. How can you check if your answer is reasonable?” (4.OA.1.3)
• Lesson 14.5, On My Own, Problem 6, students solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. For example, “Oliver has a board that is $$\frac{10}{12}$$ foot long. After he cuts some off, he has $$\frac{7}{12}$$ foot left. How much did Oliver cut off? Model the problem with an equation and then answer the Problem." (4.NF.2.3d)
• Lesson 15.1, Homework 1, students solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. For example, “Olivia rode her bike for $$\frac{9}{10}$$ hour. She rode her electric scooter for $$\frac{3}{10}$$ hour. How much longer did Olivia ride her bike than her scooter?” (4.NF.2.3d)
• Lesson 16.2, Homework, Problem 1, students solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, “Adam is restoring old wagon wheels and needs to cut 3 wooden spokes that are each $$\frac{5}{8}$$ yard long. What is the total length of wood that he needs to cut? Write two equations modeling the problem and the solution.” (4.NF.2.4c)
• Lesson 16.3, On My Own Model with Mathematics,  students solve word problems involving multiplication of a fraction by a whole number. For example, “Lana bakes banana bread for a fundraiser. She uses $$\frac{3}{4}$$ cup of bananas in each loaf. She bakes 5 loaves. How many cups of bananas does she use? Describe a fraction model you could draw to represent the problem. Then model it with an equation and solve the problem.” (4.NF.2.4c)

Each Unit has a Performance Task involving real-world applications of the mathematics from the unit. For example, the Unit 3 Performance Task is about “Visiting New York City”. It has students calculate how much it will cost 20 people to go on a tour of Chinatown (4.OA.1.1), for 23 people to go to a show (4.OA.1.1), calculate how much a group comprised of adults and children would save by visiting one attraction vs. another (4.OA.1.2 and 4.OA.1.3), and calculate the number of postcards purchased by 52 tourists (4.NBT.1.2).

##### 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 4 meet the 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 5.2 builds conceptual understanding of multiplication through the use of area models and the distributive property. “How can you use the Distributive Property to break apart the base-ten blocks and find the product?” (4.NBT.2.5)
• Lesson 8.6 builds procedural fluency in multi-digit multiplication, “Estimate. Then choose a method to find the product.” This section includes six problems where students estimate two digit number multiplication like 43 x 35. (4.NBT.2.5)
• Lesson 12.6 emphasizes application of multi-step problem solving with money. For example, “Four friends earn a total of $5.00 by turning in cans for recycling. If the friends share the amount equally, how much does each get? Give your answer as a decimal amount.” (4.MD.1.2) Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example: • Unit 5, Performance Task, Problem 1, students use application to solve problems involving multiplication of fractions by whole numbers. “Enrique lives with his grandmother in an apartment building for senior citizens. He earns extra money by running errands for some of his grandmother’s neighbors. Enrique charges$4 for every $$\frac{1}{4}$$ hour he spends working. He spent $$\frac{2}{4}$$ hour going to the deli for Mr. McGuire, 1$$\frac{1}{2}$$ hours delivering papers for the apartment manager and $$\frac{3}{4}$$ hour picking up Mrs. Shultz’s groceries. Did Enrique ear enough money to buy a $49 video game? Explain your reasoning.” • Lesson 14.5 engages students in the application of addition and subtraction of fractions. “Ross is helping to make popcorn at the carnival. At the start of his shift, the container of kernels is $$\frac{11}{12}$$ full. During his two-hour shift, they use $$\frac{3}{12}$$ of the container. How full is the container after lunch? You can write an equation without first making a model. Draw a fraction model to solve the problem. How full is the container after lunch?” (4.NF.2.3d) • Lesson 14.3, Spark Your Learning, students use conceptual understanding to solve application problems. “Caleb enters a frog in a frog-jumping contest. His frog jumps twice. Caleb wants to find the total distance his frog jumps. Explain how can you determine the lengths of each of the frog’s two jumps, then find the total distance the frog jumped. (There is a visual of a frog jumping, a number line split up into 4 equal parts, with 0 and 1 labeled).” • Lesson 16.3, On My Own, Problem 9, “Lana bakes banana bread for a fundraiser. She uses $$\frac{3}{4}$$ cup of bananas in each loaf. She bakes 5 loves. How many cups of bananas does she use? Describe a fraction model you could draw to represent the problem. Then, model it with an equation and solve the problem.” (4.NF.2.4c) #### 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 4 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 4 partially meet the 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 MPs. For example: • The Planning and Pacing Guide outlines for teachers where to look for each of the MPs. It states that: “MP.1.1, MP.2.1, 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 in Lesson 16.4; MP.2.1 in Lesson 16.4 and Lesson 14.5; MP.3.1 in Lesson 6.2 and Lesson 12.6; MP.4.1 in Lesson 3.3 and Lesson 7.4; MP.5.1 in Lesson 14.5 and Lesson 13.6; MP.6.1 in Lesson 9.2 and Lesson 7.3; MP.7.1 in Lesson 4.5 and Lesson 3.3; and MP.8.1 in Lesson 9.2 and Lesson 11.1. • The Planning and Pacing Guide for the teachers has a section identified as Correlations for Mathematical Practices. In this section, the eight 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 materials. Each math practice has about 15 locations listed of where the teachers can look for specific Mathematical Practices. Examples are given by reference numbers to specific modules and lessons. Each math practice is also categorized as, “in every Spark Your Learning Lesson and in most lessons.” • In the Teacher's Edition in the margin under Homework & Test Prep, a section describes Mathematical Practices that can be seen within the Homework worksheet for students. • At the beginning of every lesson in the teacher edition a “Lesson Focus And Coherence” table is included. Inside the table is a list of Math Standards and Mathematical Practices. The Mathematical Practices list does not include the description of the Mathematical Practice, it simply lists the summary sentence. For example, Lesson 4.7, MP.3.1 is listed as “Construct viable arguments and critique the reasoning of others,” and MP.7.1 is listed as “Look for and make use of structure.” • Lesson 18.7 lists MP.1.1, “Make sense of problems and persevere in solving them," lists MP.2.1 “Reason abstractly and quantitatively,” and MP.6.1 “Attend to precision,” in the Lesson Focus and Coherence Section. • Lesson 4.7, MP.7.1, “Look for and make use of structure,” is identified in the Build Understanding teacher notes. Lesson 18.7, in “Step It Out,” lists MP.6.1, “Attend to precision.” • Lesson 16.3, lists MP.2.1 and MP.7.1 in the Teacher Edition Lesson Focus and Coherence section. MP.7.1 is identified in Build Understanding. Teacher guidance suggests students make connections to previous work with fraction circles when multiplying fractions and how this problem can be shown with the circles. • Lesson 6.3, identifies MAFS.K12.MP.1.1 and MAFS.K12.MP.2.1, in the Teacher Edition Lesson Focus and Coherence section. • Lesson 12.5, identifies MP.6.1 and MP.8.1 in the Teacher Edition Lesson Focus and Coherence. MP.8.1 is identified in Step It Out. • Module 15, teacher edition indicates Lessons 15.1 through 15.4 promote MP.1.1, “Students read a problem three times with a specific focus each time. What is the situation about? What are the quantities in the situation? What are the possible mathematical questions that we could ask for the situation?" However, the materials over-identify the Math Practices, with some identified for every lesson. In addition, some Mat are incorrectly identified. For example: • MP.1.1 is labeled as in every lesson, but there is no explicit connections in Lessons 1.5, 4.1, and 5.2. • In the Planning & Pacing Guide, it states MP.2.1 is in every Spark Your Learning section of the series. However, in the Teacher Edition this is not identified on the Spark Your Learning Page. There is a missed opportunity to make a connection between the Spark Your Learning and MP.2.1 as identified in the Planning and Pacing Guide. • Multiple problems within a lesson include Mathematical Practice language with no direct connection to Mathematical Practices. For example, Lesson 18.7, Problem 3 states, “Attend to Precision,” prior to listing the question. Lesson 4.7, Problem 11, On My Own states, “Use structure,” language directly from MP.7.1. These Mathematical Practice phrases are in all modules and are in bold prior to the question or problem being posed. Lesson 12.1, Problem 2, On My Own, states, “Critique Reasoning” prior to the problem posed. For the most part, when identified, Mathematical Practices are used to enrich the mathematical content of the lessons. For example: • Lesson 12.5, Step It Out, MP.8.1 is identified and connected to students describing connections between coin values and ones, tenths, and hundredths. • Lesson 16.3, Build Understanding, identifies MP.7.1 as students multiply fractions. ##### Indicator {{'2f' | indicatorName}} Materials carefully attend to the full meaning of each practice standard The instructional materials reviewed for Into Math Florida Grade 4 partially meet the 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 13.6, Step it Out, “How could you model the situation with an addition equation?” • Lesson 6.1, On My Own, Problem 4, “Write a division equation to model the problem.” • Lesson 8.3, On My Own, Problem 2, “Write and solve an equation for the area model.” Examples of MP.5.1 being identified, where students do not choose tools strategically, as the tools are given to students include: • Lesson 12.1, On My Own, Problem 4, students place a mixed number on a number line. The number line is provided. • Lesson 15.5, On My Own, Problem 8, students explain how the Commutative and Associative Properties are used to add fractions and mixed numbers mentally in the problem; “Dylan wants to solve $$\frac{3}{8}$$ + 1$$\frac{7}{8}$$ + 2$$\frac{5}{8}$$...“ • Lesson 14.4, Step it Out, Problem 2, “Ruby has $$\frac{2}{3}$$ yard of string. She only needs $$\frac{1}{3}$$ yard to tie a knot. How much string will Ruby have after she cuts off $$\frac{1}{3}$$ yard?” The margin provides tool suggestions: pencil, fraction bar and number line. Examples of the instructional materials attending to the full meaning of the MPs include: • MP.1.1: In Lesson 1.1, Spark Your Learning, “Some museums keep collections of insect specimens as a historic record. Experts often inspect specimen cases for damage and check that labels are set correctly. Counting inventory is also important. How can you show the number of beetles in the Museum Insect Inventory?” Persevere, the Teacher Edition states, “If student needs support, guide them by asking, “What is the number you want to show? How can you use what you already know to show the number to the left of the hundreds place?” • MP.2.1: In Lesson 3.1, On My Own, Problem 4, students reason abstractly and quantitatively to answer, “Elbert won 6 prizes. Owen won 5 times as many prizes as Elbert. Owen writes the equation 5 x 6 = 30 to model the number of prizes he won. What is another way to write an equation to model the number of prizes Owen won?” • MP.7.1: In Lesson 5.4, Spark Your Learning, students look for and make use of structure to solve, “Ramy is in a Swim Club that helps children learn about competitive swimming. In one race, he swims 4 laps of the pool. Each lap is 24 feet long. How far does Ramy swim during the race?” Turn and Talk asks, “How could thinking about place value help you solve this problem?” • MP.8.1: In Lesson 8.5, Step It Out, students look for repeated reasoning to solve, “A celebration concert of piano ensemble class included students playing in unison on 12 standard pianos. A standard piano has 88 keys. How many keys needed to remain in sync throughout the performance? Write the problem vertically. Then use place value and regrouping to find the answer.” ##### 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 4 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 12.6, On My Own, students critique other’s reasoning, “Blake has$5.00. He sees some pencil packets that are \$1.05. Blake says that he can buy 5 packets. Is he correct? Why or why not?”
• Lesson 7.2, On My Own, students critique others' reasoning, “Mara completes this division. Is her answer correct? Why or why not?”
• In Lesson 11.1, Turn and Talk, “Why is it important that the size of the fuel tanks in the go-karts is the same?” and “How do you know your answer is correct?”
• In Lesson 15.1, Turn and Talk, “One classmate represented this problem with an equation and another used subtraction. Who is correct and how do you know?”
• In Lesson 15.4, Turn and Talk, “A classmate says that you just need to subtract the whole number from the whole number and the fraction from the fraction to solve this problem. How would you respond?”
##### 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 4 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 Lesson 21.1, “Why do we need to change hours to minutes?,” “How could you use reasoning to solve this problem without using the table?,” and in Lesson 12.3, “What do you need to know in order to find the time that Inez finishes? How can you find that out?”
• Critique, Correct, and Clarify is a strategy used to assist students in constructing viable arguments. For example, in Lesson 18.2, On My Own, Problem 5, “Point out to students that Problem 5 has an error. 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 19.2, On My Own, Problem 19, asks students to analyze the reasoning of a fictitious student. Teacher guidance says, “Point out that in Problem 19 Jimmy’s reasoning is not complete. Encourage students to describe why his reasoning is incomplete and review explanations with a partner. Students should refine their responses after their discussions with a partner.”
• In Lesson 4.1, Connect Math Ideas, Reasoning, and Language states, “Select students who used various strategies and have them share how they solved the problem with the class. As they explain their thinking, encourage other students to raise their hands and critique the reasoning.”
• In Lesson 1.5, Optimize Output, “Point out to students that the Turn and Talk asks how it is possible for two different estimates to both be correct. Encourage students to describe the thought processes of Anja and Liam and review explanations with a partner. Students should refine their responses after their discussions with a partner.“
• The Teacher Edition includes Turn and Talk in the margin notes to prompt student engagement. For example, in Lesson 15.2, “Select students who used various strategies and have them share how they solved the problem with the class. Encourage students to ask questions of their classmates. Using rectangular arrays is based on prior knowledge and should be shared first. Then have another student share a solution using base ten blocks.”
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Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Into Math Florida Grade 4 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 11.2, “A known size or amount that helps you understand a different size of an amount is a benchmark. Common benchmarks are 0, $$\frac{1}{2}$$, and 1.” In Lesson 4.1, “The Identity Property of Multiplication states that the product of any number and 1 is that number.”
• 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 Module 8 it states, “By giving all students regular exposure to language routines in context, you will provide opportunities for students to listen, speak, read, and write about mathematical situations and develop both mathematical language and conceptual understanding at the same time.”
• In Sharpen Skills in the lesson planning pages, some lessons include Vocabulary Review activities. For example, in Lesson 20.1, “Objective: Students review vocabulary used to classify triangles by angles and by sides.” “Materials: markers, poster paper” “Have students work in small groups to create a poster. Have students divide their posters into two sections: Classify Triangles by Sides and Classify Triangles by Angles. In the first section, have them write the terms scalene, isosceles, and equilateral. In the second section, have them write the terms acute, right, and obtuse. Have students draw an example of each type of triangle and write a definition for each term. Have each group share their poster with another group.”
• Guide Student Discussion provides prompts related to understanding vocabulary such as in Module 1, “Listen for student who correctly use review vocabulary as part of their discourse. Students should be familiar with the terms place value, greater than, less than, equal to, and compare. Ask students what they mean if they use those terms.” “Rounding to the nearest 10, what numbers round to 860?” “Rounding to the nearest 100, what numbers round to 900?” “Given the size of the ranges, what is a good strategy for determining how to place numbers in the table?”
• 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 4 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.

##### Indicator {{'3a' | indicatorName}}
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 4 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.

##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials for Into Math Florida Grade 4 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 4 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 9.1 Homework has six problems. The first problem asks students to construct an argument given constraints about the size of a piece of fabric if there is enough information to find the area. The next four problems are fluency problems with finding area and the last problem ask students to compare two sets of garden plans to determine which has the greater area.

##### Indicator {{'3d' | indicatorName}}
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 4 meet the 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 use two color counters to represent the following problem, “The fourth-graders make gift bags for the school bake sale. Each bag has 8 treats. How many treats do the students use to make 70 gift bags? Represent how many treats are in 7 bags.” The manipulatives provide opportunities for students to develop a conceptual model of problems that they will then represent in pictorial form in their student workbook.

Examples of manipulatives for Grade 4 include: Base Ten Blocks, connecting cubes, fraction circles, fraction strips, grid paper, number line, pattern blocks, protractor, ruler, scale, square dot paper, and two color counters.

Lesson 16.3, students create visual models with fraction strips or fraction circles to show multiplication of fractions by a whole number. They write equations to describe their visual models.

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

##### Indicator {{'3e' | indicatorName}}
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 3 are not distracting or chaotic and support students in engaging thoughtfully with the subject.

The entire series, both print and digital, follows a consistent format, which promotes familiarity with the materials and makes finding specific sections more efficient. The page layout in the materials is user-friendly. Tasks within a lesson are numbered to match the module and lesson numbers. Though there is a lot of information given, pages are not overcrowded or hard to read. Graphics promote understanding of the mathematics being learned. Student practice problem pages include enough space for students to write their answers and provide explanations. The digital format is easy to navigate, but students have to scroll without being able to view much of the information at one time.

#### 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 4 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.

##### Indicator {{'3f' | indicatorName}}
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 4 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 8.6, Activate Prior Knowledge, “What is one strategy you could use when you multiply by 7?” In the same lesson, the Step It Out Turn and Talk states, “How can you use the Distributive Property to solve the problem?”
• Lesson 20.2, Spark Your Learning, includes questions in the margin notes, “What objects in the classroom are about 1 cm long? What objects are about 1 m long?” “How could you use classroom objects to act out the problem?” “What visual models can you draw to represent lengths or comparison?” and “What comparison words could you use to describe the length?”
• Lesson 13.4, Build Understanding, provides two questions, “How could you figure out what angle measure is equivalent to one-fourth of a circle?” and “How could you figure out what angle measure is equivalent to two ninths of a circle?”
##### Indicator {{'3g' | indicatorName}}
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 4 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 4 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 11.3, this table lists the 3rd grade standard supporting the 4th grade on-level standard and what 5th grade standard this will lead into. The explanation is a brief set of bullets and does not include any tasks or examples for the teacher.
• Professional Learning notes are present in each lesson. In Lesson 11.3, Professional Learning, discusses “Using Mathematical Practices.”
##### 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 4 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 4 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 4 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 4 includes a Math on the Spot video for Lessons 4 and 5.
##### 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 4 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 4 partially meet the 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 4 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 4 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 4 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 4 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 4 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 4 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 4.1 the Learning Mindset asks, “What do I already know that can help me multiply by tens, hundreds, and thousands on my own?”

#### 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 4 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 4 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 4 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 4 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 5.4, Spark Your Learning has this prompt, “The Monstrosity Roller Coaster has seats for 136 riders.  The roller coaster completes 4 runs each half hour. If all the seats on the roller coaster are filled, how many people can ride in a half hour.” This problem provides multiple entry points and solution strategies for students. However, Spark Your Learning is not present in every lesson.

Support for Turn and Talk in the Teacher Edition provides suggestions to help students using a variety of strategies. Teachers are often prompted to “Select students who used various strategies and have them share how they solved the problem with the class.”

##### 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 4 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 4 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 3 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• Lessons contain a variety of tasks that interest students of various demographic and personal characteristics.
• Names and wording are chosen with diversity in mind. The materials include various names throughout the problems that are used in ways that do not stereotype characters by gender, race, or ethnicity.
• When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways that do not express gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies.
• When people are shown, there is a balance of demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials reviewed for Into Math Florida Grade 4 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 4 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 4: 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 4 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 4 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 4 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 4 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 4 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 4 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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