6th Grade - Gateway 1

The instructional materials reviewed for HMH Into Math Grade 6 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 Interim Growth assessments.

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

• Unit 2 Performance Task states: "In Mexico, pesos are used as money. One U.S. dollar is worth about 19.8 pesos. How much is 1 peso worth in dollars? Show your work and round to the nearest cent."  (6.RP.3d)
• Module 4, Form A, Question 13 states: "Jake has a wooden board that measures 8.25 feet long. He cuts the board into pieces that each measure 0.75 feet so he can make signs. If Jake earns $15.95 for each sign he sells, how much money can he earn from the signs he makes from this board?" (6.NS.3)
• Module 8, Form A, Question 14 states: “The cost of a large pizza is $10.99. Each additional topping costs $1.25. Part A) Write an expression that can be used to find the cost of a pizza when x toppings are included. Part B) What is the cost of a large pizza with 3 toppings?” (6.EE.6)
• Module 15, Form A, Question 4 states: “Pedro counts the number of trucks that pass by his house each day for a week. He records his results in the table. Number of Trucks that Pass By: 2, 3, 4, 3, 6, 6, 12.  Which measure of center best represents the data shown?” (6.SP.5d)

The instructional materials reviewed for HMH Into Math Grade 6 meet 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 12 out of 16, which is approximately 75%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 47 out of 63, which is approximately 75%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 106 out of 137 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 75% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for HMH Into Math Grade 6 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 2.3 connects 6.NS.4 with 6.NS.6 as students find and use the GCF or LCM to compare rational numbers and solve various problems in multiple real-world situations. For example, "Cameron and Tatiana volunteer at the public library. Cameron shelves one book every 1/4 minute. Tatiana shelves one book every 3/10 minute. Who is quicker at shelving books? Explain how you found your answer."
• In Lesson 5.2, students “Find the unit rate of $5.15 per 5 pound bag,” which connects 6.NS.3 with 6.RP.2.
• In Lesson 6.3, students multiply decimals (6.NS.3) to convert between measurement units (6.RP.3d) and write equivalent ratios. For example, "Many water bottles contain 16 fluid ounces, or 1 pint of water. Drink labels often show the number of fluid ounces and the number of milliliters in a container. How many milliliters are in a 16-fluid-ounce drink?" 
• In Lesson 8.5, students find an equivalent expression (6.EE.3) using the distributive property (6.NS.4).
• In Lesson 11.2, students graph ordered pairs on the coordinate plane (6.NS.6) to create polygons and solve related problems (6.G.3).
• In Lesson 11.4, students graph polygons on the coordinate plane (6.G.3) and solve multiple related problems, including segment length, perimeter, and area (6.NS.8).
• In Lessons 12.1-12.4, students develop area formulas for various figures (6.G.1) and substitute numerical values into the formulas to evaluate the expressions (6.EE.2c).
• In Lesson 14.2, students summarize data in a dot plot (6.SP.1) and find the percentage of people that had more than 5 coins in their pocket or fewer than 7 coins in their pocket (6.RP.3c).

The instructional materials for HMH Into Math Grade 6 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 161 days: 105 days for lessons and 56 days for assessments.

• The Planning and Pacing Guide and the Planning pages at the beginning of each module in the Teacher Edition provide the same pacing information. 
• Grade 6 has five units with 16 modules which contain a total of 63 lessons. 
• The pacing guide designates 37 lessons as 2-day lessons and 26 as 1-day lessons, leading to a total of 100 lesson days; a “day” is defined as one period in a traditional structure. 
• Each unit includes a Unit Opener which would take less than one day. There are five Openers for Grade 6 (5 days).
• This is a total of 105 lesson days.

Assessments included:

• The Planning and Pacing Guide indicates a Beginning, Middle, and End of Year Interim Growth assessment that would require one day each (3 days). 
• Each module starts with a review assessment titled “Are You Ready?” There are 16 Modules (16 days).
• Each unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are 5 Performance Tasks for Grade 6 (5 days). 
• Each module has both a review and an assessment. There are 16 Modules (32 days). 
• Based on this, 56 assessment days can be added.

The instructional materials for Into Math Grade 6 meet expectations for being consistent with the progressions in the Standards. In general, the materials identify content from prior and future grade-levels and relate 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. 

• In the Teacher Edition, the introduction for each module includes Mathematical Progressions, which lists standards under the areas of Prior Learning, Current Development, and Future Connections and clarifies student learning statements in these categories. For example, Module 5, Ratios and Rates states, “Prior Learning: Students generate equivalent fractions.” (4.NF.1); “Current Development: Students understand the concept of ratio and use ratio language to describe a relationship between two quantities.” (6.RP.1); “Future Connections: Students will identify the unit rate given a table, verbal description, equation, or graph.” (7.RP.2).
• The beginning of each module has Teaching for Success, which sometimes includes Make Connections. Make Connections references prior learning. For example Module 9 states, “In the past, students have worked with numerical expressions and they should also have used words and phrases such as more than, divided by, and minus to translate numerical expressions into words. Here students use their prior knowledge of expressions to develop an understanding of basic equations and inequalities.”
• In Activate Prior Knowledge at the beginning of each lesson, content is explicitly related to prior knowledge to help students scaffold new concepts.
• Some lessons provide direct scaffolding for students reminding them of prior learning. For example, in Lesson 8.2, Step It Out states, "You learned about the order of operations in a previous grade. Now we need to add exponents into our order of operations. Exponents are calculated after performing operations in parentheses or brackets."
• In Unpacking Math Standards found in the Teacher Edition, there is a discussion of how students use the skills they are learning in the future. For example, Lesson 1.1 states, “In the future, students will use this concept to fluently complete operations involving integers, including in algebraic representations of situations.” 
• Each module includes a diagnostic assessment, Are You Ready?, which explicitly identifies prior knowledge needed for the current module. For example, Module 2, Are You Ready? addresses finding equivalent fractions (4.NF.1), comparing fractions (4.NF.2), and comparing decimals (5.NBT.3b). In this module, students extend these skills to compare and order all rational numbers, including integers (6.NS.7).
• In the Module Opener, "Assess Prerequisite Concepts" identifies content as prerequisite knowledge including the grade and module where the prerequisite concept is addressed.  

Examples of the materials providing all students extensive work with grade-level problems include:

• In the Planning and Pacing Guide, there is a Correlations chart that outlines the mathematics in the materials. According to this chart, all grade-level standards are represented across the 16 modules.

Within each lesson, Check Understanding, On Your Own, and More Practice/Homework sections include grade-level practice for all students. Margin notes in the Teacher Edition also relate each On Your Own practice problem to grade-level content. Examples include:

• Lesson 1.3, Build Understanding, Question 1D states, ”Negative numbers are less than positive numbers. Does this mean that the absolute value of a negative number must be less than the absolute value of a positive number? Explain.” (6.NS.7d)
• Lesson 11.3, Spiral Review, Question 10 states, “A truck driver drives 245 miles and needs to drive m miles in all. Write an equation for the number of miles the driver has left to drive.” (6.EE.9)
• Lesson 11.3, On Your Own, Question 6 states, “What is the distance between point S and T? Are they in the same quadrant?” (6.NS.8, 6.NS.6b)

When work is differentiated, the materials continue to develop grade-level concepts. An example of this is Lesson 4.1, which involves adding and subtracting multi-digit decimals. The corresponding Reteach page provides step-by-step notes and a process for students to follow in order to access the concept and the Challenge page provides students lists of times achieved by runners and swimmers in the Olympics and students must answer addition and subtraction questions involving each: “At the 2012 Olympics in London, the men’s 4 × 100 meter relay team from Jamaica set a world record. Individually, the times of the splits were 10.28 seconds, 9.07 seconds, 9.09 seconds, and 8.7 seconds. The official record was 36.84 seconds. A) What was the total of their individual times?; B) How much greater was the total of their individual times greater than the world record?”

The instructional materials reviewed for HMH Into Math Grade 6 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:

• In Lesson 2.3, the learning objective is “Compare rational numbers using the GCF and LCM,” shaped by 6.NS.B.
• In Lesson 3.4, the learning objective is “Divide fractions and mixed numbers,” shaped by 6.NS.A.
• In Lesson 13.2, the learning objective is “Find the volume of a rectangular prism,” shaped by 6.G.A.
• In Lesson 9.4, both Learning and Language objectives are “Write and use equations to represent situations and solve problems” and “Describe the unknown quantity in a real-world situation; Explain why addition, subtraction, multiplication, or division should be used to model a situation,” shaped by 6.EE.B.

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. 

Examples include:

• In Lesson 9.3, students solve equations using rational numbers (6.EE.B), requiring a fraction divided by a fraction (6.NS.A).
• In Lesson 10.1, students determine independent and dependent variables from a table of values (6.EE.C) and find the unit rate from the given data (6.RP.A). 
• In Lesson 13.3, students find volume of rectangular prisms (6.G.A) given dimensions with decimal values (6.NS.B).
• In Lesson 16.5, students use decimals (6.NS.B) to find measures of variability (6.SP.B) that summarize student GPAs.