5th Grade - Gateway 1

The instructional materials for HMH Into Math Grade 5 meet 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 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.5a)
• Module 2, Form A, Question 10, “A school earned $2,604 selling tickets to a fundraising event. If each ticket cost $14, how many tickets were sold?” (5.NBT.6)
• Module 6, Form A, Question 8, students solve a story problem by adding fractions with unlike denominators. (5.NF.2)
• Module 7, Form A, Questions 6-8, students add or subtract fractions and mixed numbers. (5.NF.1)
• Module 10, Form A, Question 4, students shade a model to represent the quotient of $$\frac{1}{6}\div2$$. (5.NF.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)
• End-of-Year-Test, Question 15, students find the difference in length between the longest and the shortest lions using a number line with fractional units. (5.MD.2)

The instructional materials reviewed for HMH Into Math Grade 5 meet expectations for spending a majority of instructional time on major work of the 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 176 days, which is approximately 77%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work and is not 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 HMH Into Math Grade 5 meet 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:

• Lesson 12.4, 5.MD.1 supports the major work of 5.NF.4, multiplication of fractions. Students multiply fractions and mixed numbers by whole numbers to convert among units of measure. 
• Lesson 12.3, 5.MD.2 supports the major work of 5.NF.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 number of cups of water?”
• Lesson 18.1, Question 9, 5.MD.1 supports the major work of 5.NBT.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. “Convert 58 g to kg, and question 10 Convert 6257 cL to L.”

The instructional materials for HMH Into Math Grade 5 meet 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 Edition provide the same pacing information. 
• Grade 5 has 8 units with 20 modules that contain 96 lessons. 
• The Planning and Pacing Guide designates 11 lessons as 2-day lessons and 85 as 1-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 8 unit openers for Grade 5 (8 days).
• Each lesson includes a variety of supplemental instruction such as reteaching lessons, flipbook lessons, etc. However, 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 included: 

• The Planning and Pacing Guide indicates a Beginning, Middle, and End-of-Year Interim Growth assessment that would require 1 day each (3 days). 
• Each unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are 8 Performance Tasks for Grade 5 (8 days). 
• Each module has both a review and an assessment. There are 20 modules (40 days). 
• Based on this, 51 assessment days can be added.

The instructional materials for HMH Into Math Grade 5 meet 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 which lists standards under the areas of Prior Learning, 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, “solve word problems involving multiplicative comparisons.” (4.OA.1 and 4.OA.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, 6.EE.2b, 6.EE.2c) 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? that explicitly identifies prior knowledge needed for the current module. 
• Within 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.7 as the focus for the lesson. The mathematical progressions, indicated in the Teacher Edition, show this builds upon work done with 4.NBT.4 during Grade 4 in Module 2, Lessons 1-3. This work will continue in Grade 6 with a focus on standard 6.NS.3. during Module 4, Lesson 1.

The materials give all students extensive work with grade-level problems. Students spend 4-8 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 Your Own Sections.  Additionally, Reteach and Challenge pages are available for each lesson which provide more practice with grade level work. 

For example: 

• Lesson 15.1, Build Understanding, students find place value patterns when multiplying by powers of 10. Question 1C “In which direction do the digits shift as you multiply by increasing powers of 10?” The On Your Own section has 23 questions that have students practice multiplication of whole numbers and decimals with powers of 10.  For example: Question 12: 843 = 100 x ___. (5.NBT.2)  
• Lesson 2.1, Build Understanding, Question 1, students use rectangular arrays, multiplication equations and related division equations to solve “A local theater group is performing a musical. The members arrange 105 chairs in 5 equal rows for the audience. How many chairs are in each row?” (5.NBT.6)
• Lesson 7.2, On Your Own, includes 17 grade level problems for students to practice addition and subtraction of fractions with unlike denominators. For example, Question 10 states “Mr. Braxton’s laptop memory is $$\frac{9}{10}$$ full. After deleting unneeded files, the memory is $$\frac{2}{3}$$ full. Mr. Singh’s laptop memory is $$\frac{9}{10}$$ full. After he deletes some files, the memory is $$\frac{3}{5}$$ full.  What fraction represents the part of the laptop memory that he deleted? Is your answer reasonable? How do you know?” (5.NF.1) 
• Lesson 13.4, students expand upon their learning of place value and comparing and ordering numbers  to decimals. (4.NBT.1 and 4.NBT.2) Question 4, students evaluate four percentages written as decimals and order them from least to greatest. (5.NBT.3b) 

The materials relate grade-level concepts to prior knowledge from earlier grades. The Teacher Edition clearly identifies the previous grade level work and explains how students will use these skills in upcoming lessons. For example:

• 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.
• Module 7, Are You Ready shows the link to prior learning for Explore Mixed Numbers as Grade 4, Lesson 15.2 (4.NF.3b) in the Data-Driven Intervention Chart. A narrative is provided for each skill on the page. In Explore Mixed Numbers, the 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.”
• Module 14, Lesson 14.3, Assess Reasonableness of Sums and Differences, asks students to build upon their prior learning of understanding “fluently added multi-digit numbers (Grade 4, Lessons 2.1 and 2.3)” and “fluently subtracted multi-digit whole numbers (Grade 4, Lessons 2.2 and 2.3.).” The lesson additionally includes a Make Connections section where it suggests Project the Interactive Reteach, Grade 4, Lesson 2.1. and Complete the Prerequisite Skills Activity where a problem is presented to the students. They are asked to identify the operation used to solve the problem and explain how they decided which operation to use.

The instructional materials reviewed for HMH Into Math 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. Examples 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.” 
• In Lesson 8.4 the learning objective is “Use a visual model to represent multiplication of fractions” which is shaped by 5.NF.2: “Apply and extend previous understandings of multiplication and division to multiply and divide fractions.”
• In Lesson  3.1 the learning objective is “Divide whole number dividends by 2-digit-divisors to find quotients with remainders” which is shaped by 5.NBT.2: “Perform operations with multi-digit whole numbers and with decimals to hundredths.”
• In Lesson 7.5 the learning objective is “Add fractions and mixed numbers with unlike denominators using properties” which is shaped by 5.NF.1: “Use equivalent fractions as a strategy to add and subtract fractions.” 

The materials include problems and activities that 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, 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 $$12 \times 50 \times 30$$ and $$10 \times 5 \times 15$$.
• Lesson 9.4 connects 5.NF.4b with 5.NBT.6 when students use fractional side lengths to solve real world problems with fraction multiplication. On My Own, Question 9 states “A square window has side lengths that are . . .  What is the area of the window?”
• 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)