5th Grade - Gateway 1

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

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

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

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

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

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

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

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

• Module 12, Lesson 3, 5.MD.2.2 supports the major work of 5.NF.1.1, add and subtract fractions with unlike denominators. Students make line plots with fractional units, then use the line plot to answer questions such as, “What is the total liquid volume of the water in the jars?”
• Module 12, Lesson 4, 5.MD.1.1 supports the major work of 5.NF.2.4, multiplication of fractions.  Students multiply fractions and mixed numbers by whole numbers to convert among units of measure.
  
• Module 18, Lesson 1, Question 9, 5.MD.1.1 supports the major work of 5.NBT.1.2, multiplying and dividing with powers of 10. Students shift the decimal point to either multiply or divide by a power of 10 to solve conversion problems. For example, “Convert 58 g to kg, and question 10 Convert 6257 cL to L.”

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

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

Assessments include:

• The Planning and Pacing Guide indicates a Beginning, Middle, and End of Year Interim Growth assessment that would require one day each (three days).
• Each Unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are eight Performance Tasks for Grade 5 (eight days).
• Each Module has both a review and an assessment. There are 20 Modules equating 40 days. Based on this, 51 assessment days can be added.

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

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

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

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

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

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

• The Teacher Edition for each of these pages clearly identifies the previous grade level work and explains how students will use these skills in upcoming lessons. For example, Module 7, Are You Ready?, shows the link to prior learning for Explore Mixed Numbers as Grade 4, Lesson 15.2 (4.NF.2.3b) in the Data-Driven Intervention Chart. A narrative is provided for each skill on the page. “Explore Mixed Numbers: These items assess whether students are able to find the mixed number equivalent to a given fraction greater than 1. In the upcoming lessons, students  will use this skill when adding and subtracting mixed numbers.”
• At the beginning of each Module, prior learning from earlier grade is indicated along with future connections. For example, Module 19 student current development will be around 5.G.1.1,2 and 5.OA.2.3. Prior learning from standards 4.G.1.1 and 4.OA.2.4 are identified. Future connections are listed as 6.NS.3.6 and 6.NS.3.8.

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

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

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

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

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