4th Grade - Gateway 2

The instructional materials for My Math Florida Grade 4 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 specifically and fully address standards which are explicitly outlined as conceptual standards (4.NBT.1, 4.NBT.2 and 4.NF.1).
• Of the 119 lessons, 51 are focused specifically on the conceptual understanding standards.
• Most 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 491B, Teacher Edition.
• All lessons in the series have a section "Talk Math" which targets conceptual understanding. This is contained in the online lesson presentation. For example, page 491-492, Teacher Edition.
• The majority of the homework contains problems which provide students the opportunity to view and to demonstrate their conceptual understanding. For example, pages 83, 661, and 673-674, Teacher Edition and Student Edition.
• Procedures for division is emphasized in Grade 4. More attention is needed for the conceptual understanding of division.
• Procedures for multiplication is emphasized in Grade 4. More attention is needed for the conceptual understanding of multiplication.

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

• Chapter 6, Lesson 1, Brain Builders, Item 25 provides three division expressions for students to order from least to greatest by the quotients. Students develop a conceptual understanding of place value and division.
• Chapter 7, Lesson 3, Brain Builders, Item 14 states, “Write a sequence with at least 5 terms that forms a pattern. Identify the rule. Apply your rule to a new starting value to produce a new sequence.” Students develop a conceptual understanding of how patterns affect sequences depending on the starting number.
• Chapter 8, Lesson 6, Brain Builders, Item 20’s picture shows two area models of the fractions 3/4 and 1/2. The wholes are different sizes and students are asked to find another student’s mistake in reasoning about which is greater. Students develop the conceptual understanding that wholes need to be the same when comparing two fractions.

The instructional materials for My Math Florida Grade 4 meet expectations that the materials give attention throughout the year to individual standards, which sets an expectation of procedural skill and fluency. Lessons contain multiple examples of fluency practice pages.

• Lessons contain multiple examples of fluency practice pages.
• In the Student Edition, fluency practice pages can be found in Chapters 2 and 6. For example, Chapter 2, pages 119-120, and Chapter 6, pages 399-400.
• Homework contains multiple opportunities for students to practice fluency.
• A "Fact Dash" game is available online with the student login to practice fluency. Students can select the operation and number facts.
• Each chapter in the online Teacher Edition has additional fluency pages available for printing.
• "Sail through the Math" is an app game for fluency and is available for purchase ($1.99).
• Seven lessons out of 119 address 4.NBT.2.4 and are in Chapter 2.
• Procedural skills are present in the majority of the lessons. For example, page 169, Teacher Edition and Student Edition, contains procedural skill.

The instructional materials for My Math Florida Grade 4 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.
• The majority of lessons begin with "Math in My World" which uses real-world problems to introduce concepts. For example, Chapter 7, Lesson 2, page 419.
• The majority of "HOT Problems" address application (for example, pages 488, 508, and 514, 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 2, Performance Event, each of the five parts relates to a ski club trip and the fundraising to pay for events. Part A: “Eight students and one adult plan to go to Snowflake Ski Resort for a day of skiing. Students lift tickets cost $8 each and adult lift tickets cost $12 each. Lunch at the lodge cost $7 per person. Each person gets lunch at the lodge. The resort also offers a group package for 12 people of any age that includes lift tickets and lunch for a total of $125. The club wants to spend the least amount of money possible. Should it purchase individual lunches and lift tickets or the group package? Explain your reasoning.”
• Chapter 6, Lesson 10, Brain Builders, Item 14, “There are 408 students at a school. The cafeteria holds up to 90 students at a time. Are four lunch periods enough to allow every student to have lunch in the cafeteria? Explain.”
• Chapter 9, Performance Event, each of the 4 parts relate to cleaning products Clara makes. Part B: “Clara found a box of Secret Ingredient #2 that was 5/6 full, and another box that was 4/6 full. She wants to put 2/6 box in each of 4 buckets of glass cleaner. Does she have enough of Secret Ingredient #2 to fill all the buckets? Explain.” This activity engages students in the application of mathematics.
• Chapter 13, Lesson 4, Brain Builders, Item 6, “Eric created a rectangular patio using 1-foot square paving stones, which are sold in batches by the dozen. The patio measures 7 feet by 8 feet. How many batches of paving stones did Eric need? Explain (Hint: 1 dozen = 12)." This item provides the opportunity for students to engage in application of mathematics.

The instructional materials for My Math Florida Grade 4 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 to identify levels of complexity by problem or exercise number. For example, Chapter 10, Lesson 6 has four problems for conceptual learning (understand concepts), eight problems for fluency/procedural skill (apply concepts), and five problems for application (extend concepts).

The instructional materials for My Math Florida Grade 4 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout Grade 4. 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 119 lessons. Each lesson focuses on three to four practices.
• The Student Edition does indicate which MP with which the student is working in the lesson and in the homework.

The instructional materials reviewed for My Math Florida Grade 4 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 there are few opportunities for students to analyze the arguments 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 2, Lesson 1, Problem of the Day, students construct an argument for “What do these numbers have in common? 135, 468, 24, 2, 468, 79.” Students are prompted to share what observations they made in identifying what the numbers have in common.
• Chapter 6, Lesson 2, Problem of the Day, students are prompted to describe how they solved the problem.
• Chapter 4, Lesson 8, Brain Builders, Which One Doesn’t Belong?, Problem 19 states, “Circle the multiplication problem that does not belong. Explain.” Students must select which does not belong in a set of four items and justify why it does not belong.
• Chapter 4, Lesson, 1, Talk Math states, “Can you write 2 + 3 + 4 = 9 as a multiplication sentence? Explain.” Students need to analyze the addition equation, and construct an argument as to why this addition equation cannot be written as multiplication.

The instructional materials reviewed for My Math Florida Grade 4 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 10, Lesson 1, page 636.
• 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 5, page 274.
• The Teacher, Student, and online editions contain extensive glossaries in English and Spanish.
• Lessons contain mathematical terminology.