5th Grade - Gateway 2

The instructional materials for My Math Florida Grade 5 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Examples where materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings include but are not limited to:

• The content in Chapters 1-6, and 8, 10, and 12 specifically and fully address standards which are explicitly outlined as conceptual standards. (5.NBT.1, 5.NBT.1, 5.G.2.3, and 5.NF.2.3 through 5.NF.2.6)
• The majority of the lessons in the series have a section "Investigate the Math" which targets conceptual understanding. This is contained in the online lesson presentation. For example, page 43B, Teacher Edition.
• All lessons in the series have a section called "Talk Math" which targets conceptual understanding. This is contained in the online lesson presentation. For example, page 771-772, Teacher Edition.
• The majority of the homework contains problems that provide students the opportunity to view and to demonstrate their conceptual understanding. For example, pages 193, 395-396, and 675-676, Teacher Edition and Student Edition.
• Procedures for division are presented in Grade 5. More attention is needed for the conceptual understanding of division to meet the standard.

Examples where Brain Builders enhance conceptual understanding include but are not limited to:

• Chapter 2, Lesson 5, Brain Builders, Item 4, students are given a table with powers of 10 and asked to find the prime factorizations using the patterns in the table. By using the patterns, students are developing conceptual understanding of powers of ten.
• Chapter 5, Lesson 6, Brain Builders, Item 18 states, “Write a real-world problem that can be solved by adding 1.99 and 2.49. Then draw a model to represent the solution.” Students contextualize the problem helping them build their conceptual understanding of adding decimals.
• Chapter 7, Lesson 1, Brain Builders, Item 15 states, “Show two different ways you can use parentheses to rewrite the expression 4 + 2 x 3 -1 so that the value is different. Explain why each expression has a different value.” Manipulating expressions and parenthesis helps students build a conceptual understanding of the properties of operations.

The instructional materials for My Math Florida Grade 5 meet expectations that the materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Lessons contain multiple examples of fluency practice pages.

• In the Student Edition, fluency practice pages are found in Chapters 2 and 4. For example, see Chapter 2, pages 143-144; and Chapter 4, pages 289-290.
• Homework contains multiple opportunities for students to practice fluency.
• Each chapter in the online Teacher Edition has additional fluency pages available for printing.
• "Sail through the Math," an app game for fluency, is available for purchase ($1.99).
• 5.NBT.2.5 has seven lessons out of 129 which address the standard and are in Chapters 2, 6, and 8.
• Procedural skills are present in the majority of the lessons. For example, page 404, Teacher Edition and Student Edition, contains procedural skill.

The instructional materials for My Math Florida Grade 5 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

• The Teacher Edition states "Math in My World," "HOT (Higher Order Thinking) Problems," and "Real-World Problem-Solving Readers" address application.
• While "Real-World Problem Solving Readers" are available to provide additional problems, they were not reviewed by EdReports.org. They are not included in the basic package with the Student and Teacher Editions, and were therefore considered supplementary.
• Most lessons begin with "Math in My World" which uses real-world problems to introduce concepts. For example, see Chapter 3, Lesson 10, page 215.
• The majority of "HOT Problems" address application. For example, see pages 122, 338, and 382, Teacher Edition and Student Edition.
• Real-world problems are found in the majority of lessons and homework assignments.
• Countdown to FSA provides performance tasks requiring application of the standards.

Examples where Brain Builders and Performance Events provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts include but are not limited to:

• Chapter 3, Lesson 1, Brain Builders, Item 12, “There are 15 cats ready for new homes at the pet store. There are 5 cages with cats in the store. If each cage has the same number of cats, how many cats are in each cage? Write two equations to model your work.” This item provides the opportunity for students to engage in application of mathematics.
• Chapter 5, Performance Event, each of the four parts relate to the planning of a mountain bike trip. Part D: “Sarah and her friends saved $840 altogether for the trip. Given the donation each person will give to the park and the expenses for meals and lodging, how much can they expect to have left at the end of the mountain bike trip? Explain.”
• Chapter 8, Lesson 6, Brain Builders, Item 5, “The fifth graders were given sandwiches for lunch during their field trip. Nathan ate 5/6 of his sandwich, Leroy ate 7/8 of his sandwich, and Sofia ate 3/4 of her sandwich. Who ate the greatest amount of their sandwich? Explain.”
• Chapter 10, Performance Event, each of the three parts relate to a university adding on to its sports center. Part C: “The cost of building the gym for fitness classes is $98 per square foot. Find the cost of constructing this gym. Explain.” This activity engages students in the application of mathematics.

The instructional materials for My Math Florida Grade 5 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the materials.

At the beginning of each lesson a "Rigor" section exists identifying levels of complexity by problem or exercise number. For example, Chapter 9, Lesson 3 has three problems for conceptual learning (understand concepts), 12 problems for fluency/procedural skill (apply concepts), and five problems for application (extend concepts).

The instructional materials for My Math Florida Grade 5 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout Grade 5. Overall, the instructional materials do not over-identify or under-identify the MPs, and the MPs are used within and throughout the grade.

• The Teacher Edition, pages T22-T24 state the MPs and the corresponding pages.
• The practices are identified throughout all 129 lessons. Each lesson focuses on three to four MPs.
• The Student Edition does indicate which mathematical practice with which the student is working in the lesson and in the homework.

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

Opportunities for students to share their thinking and analyze the thinking of others can be found in "Problem of the Day," "Talk Math," and "Brain Builders" portions of the lesson. The materials offer opportunities for students to construct viable arguments, but they infrequently prompt students to analyze the arguments of others. There are instances where the materials label portions of the lesson MP3, but students are not sharing their thinking or analyzing the thinking of others.

Examples where the instructional materials prompt students to construct viable arguments and/or analyze the arguments of others include but are not limited to:

• Chapter 1, Lesson 6, Brain Builders, Which One Doesn’t Belong?, Problem 24 states, “Circle the decimal that does not belong with the other three.” There are multiple correct answers, each requiring students to defend their choice.
• Chapter 2, Lesson 1, Brain Builders, Problem 7 states, “Laney wrote the prime factorization of 60 as 2 x 5 x 6 = 60. Is she correct? If not, what is the prime factorization of 60? Explain.” Students need to analyze Laney’s solution, and use mathematics to construct an argument to support their analysis.
• Chapter 8, Lesson 2, Talk Math states, “Explain which method you prefer to find the GCF of two numbers.” Students construct an argument explaining which method is prefered.

The instructional materials reviewed for My Math Florida Grade 5 meet expectations that the materials explicitly attend to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics that are consistently present throughout the materials.

• The special language of mathematics is a strength of the series.
• Individual vocabulary cards are found at the beginning of each chapter in the Student Edition.
• Vocabulary checks are included in some homework assignments. For example, Chapter 1, Lesson 1, page 16.
• Vocabulary assessments can be created online.
• Virtual word walls are available online.
• "Match the Pairs" is an interactive vocabulary component.
• "Check my Progress" assesses vocabulary.
• Each chapter begins with a foldable supporting vocabulary development.
• "My Math Words" is at the beginning some chapters. For example, Chapter 7, page 474.
• The Teacher, Student, and online editions contain extensive glossaries in English and Spanish.
• Lessons contain mathematical terminology.