6th Grade - Gateway 1

The materials reviewed for Open Up Resources Grade 6 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Program assessments include Pre-Unit Diagnostic Assessments, Cool Downs, Mid-Unit Assessments, Performance Tasks, and End-of-Unit Assessments which are summative. According to the Course Guide, “At the end of each unit is the end-of-unit assessment. These assessments have a specific length and breadth, with problem types that are intended to gauge students’ understanding of the key concepts of the unit while also preparing students for new-generation standardized exams. Problem types include multiple-choice, multiple-response, short answer, restricted constructed response, and extended response. Problems vary in difficulty and depth of knowledge.” Examples of summative End-of-Unit Assessment problems that assess grade-level standards include:

• Unit 1: Area and Surface Area, End-of-Unit Assessment: Version B, Problem 3, “A cube has side lengths of 8 inches. Select all the values that represent the cube’s volume in cubic inches. A. 8^2 B. 8^3 C. 6 $$\cdot$$ 8^2 D. 6 $$\cdot$$ 8 E. 8 $$\cdot$$ 8 $$\cdot$$ 8.” (6.EE.1)

• Unit 3: Unit Rates and Percentages, End-of-Unit Assessment: Version B, Problem 4, “It takes Andre 4 minutes to swim 5 laps. a. How many laps per minute is that? b. How many minutes per lap is that? c. If Andre swims 22 laps at the same rate, how long does it take him?” (6.RP.2, 6.RP.3b)

• Unit 4: Dividing Fractions, End-of-Unit Assessment: Version B, Problem 6, “How many \frac{1}{4} inch cubes does it take to fill a box with width 2\frac{1}{4} inches, length 2\frac{1}{2} inches and height 1\frac{3}{4} inches?” (6.G.2)

• Unit 7: Rational Numbers, End-of-Unit Assessment: Version A, Problem 4, “Select all the numbers that are common multiples of 4 and 6. A. 1 B. 2 C. 10 D. 12 E. 24 F. 40 G. 60” (6.NS.4)

• Unit 8: Data Sets and Distributions, End-of-Unit Assessment: Version A, Problem 2, “Here’s a dot plot of a data set (dot plot shown). Which statement is true about the mean of the data set? A. The mean is less than 5. B. The mean is equal to 5. C. The mean is greater than 5. D. There is not enough information to determine the mean.” (6.SP.5c)

The materials reviewed for Open Up Resources Grade 6 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each lesson is structured into four distinct phases: Warm Up, Instructional Activities, Lesson Synthesis, and Cool Down. This format ensures thorough engagement with grade-level problems and fully meets the educational standards.

The Warm Up initiates each lesson, either preparing students for the day’s topic or enhancing their number sense and procedural fluency. Following this, students participate in one to three activities that delve into the learning standard. These activities, detailed in the Activity Narrative, form the core of the lesson. After completing these activities, students reflect on and synthesize their new knowledge. The lesson concludes with a Cool Down phase, a formative assessment to gauge understanding. Additionally, each lesson includes Independent Practice Problems to reinforce the concepts.

The Warm Up initiates each lesson, either preparing students for the day’s topic or enhancing their number sense and procedural fluency. Following this, students participate in one to three activities that delve into the learning standard. These activities, detailed in the Activity Narrative, form the core of the lesson. After completing these activities, students reflect on and synthesize their new knowledge. The lesson concludes with a Cool Down phase, a formative assessment to gauge understanding. Additionally, each lesson includes Independent Practice Problems to reinforce the concepts.

Instructional materials engage all students in extensive work with grade-level problems. Examples include:

• Unit 1: Area and Surface Area, Section C: Triangles, Lessons 8: Area of Triangles, students use strategies to determine base and height of an associated parallelogram to determine the area of a triangle. Warm-Up: Composing Triangles, “Here is Triangle M. Han made a copy of Triangle M and composed three different parallelograms using the original M and the copy, as shown here. a. For each parallelogram Han composed, identify a base and a corresponding height, and write the measurements on the drawing. b. Find the area of each parallelogram Han composed. Show your reasoning.” Three decomposed parallelograms are shown. Activity 1: More Triangles, “Find the areas of at least two of the triangles below. Show your reasoning.” Students are shown 4 triangles drawn on centimeter grid paper. Practice Problems, Problem 5, “a. A parallelogram has a base of 3.5 units and a corresponding height of 2 units. What is its area? b. A parallelogram has a base of 3 units and an area of 1.8 square units. What is the corresponding height for that base? c. A parallelogram has an area of 20.4 square units. If the height that corresponds to a base is 4 units, what is the base?” Materials present all students with extensive work with grade-level problems of 6.G.1 (Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes: apply these techniques in the context of solving real-world and mathematical problems.) 

• Unit 3: Unit Rates and Percentages, Section A: The Burj Khalifa, Lesson 1: The Burj Khalifa, students solve unit rate problems. Activity 1: Window Washing, “A window-washing crew can finish 15 windows in 18 minutes. If this crew were assigned to wash all the windows on the outside of the Burj Khalifa, how long would the crew be washing at this rate?” Activity 2: Climbing the Burj Khalifa, “In 2011, a professional climber scaled the outside of the Burj Khalifa, making it all the way to 828 meters (the highest point on which a person can stand) in 6 hours. Assuming they climbed at the same rate the whole way: a. How far did they climb in the first 2 hours? b. How far did they climb in 5 hours? c. How far did they climb in the final 15 minutes?” Cool Down: Going Up? “The fastest elevators in the Burj Khalifa can travel 330 feet in just 10 seconds. How far does the elevator travel in 11 seconds? Explain your reasoning.” Practice Problems, Problem 3, “The cost of 5 cans of dog food is $4.35. At this price, how much do 11 cans of dog food cost? Explain your reasoning.” Materials present all students with extensive work with grade-level problems of 6.RP.2 (Understand the concept of unit rate a/b associated with a ratio a:b with b \not= 0, and use rate language in the context of a ratio relationship.)

• Unit 6: Expressions and Equations, Section B: Equal and Equivalent, Lesson 11: The Distributive Property (Part 3), students write equivalent expressions using the distributive property. Activity 2: Writing Equivalent Expressions Using the Distributive Property, “The distributive property can be used to write equivalent expressions. In each row, use the distributive property to write an equivalent expression. If you get stuck, consider drawing a diagram.” One row shows, “(9-5)x.” Cool Down: Writing Equivalent Expressions, “a. Use the distributive property to write an expression that is equivalent to 12 + 4x. b. Draw a diagram that shows the two expressions are equivalent.” Practice Problems, Problem 3, “Select all the expressions that are equivalent to 16x +36. A. 16(x+20) B. x(16+36) C. 4(4x+9) D. 2(8x+18) E. 2(8x+36)" Materials present students with extensive work with grade-level problems of 6.EE.3 (Apply the properties of operations to generate equivalent expressions).

Instructional materials provide opportunities for all students to engage with the full intent of grade-level standards. Examples include: 

• Unit 2: Introducing Ratios, Section A: What are Ratios?, Lesson 1: Introducing Ratios and Ratio Language, students describe two quantities at the same time. Warm Up: What Kind and How Many?, students see a variety of color cubes connected together and brainstorm various ways to sort them. Activity 1: The Teacher’s Collection, students use ratio language to describe dinosaurs that are shown in a picture, “The ratio of purple to orange dinosaurs is 4 to 2.” Activity 2: The Student’s Collection, students write ratios to describe items from their own collection that were brought from home, “Write at least two sentences that describe ratios in the collection. Remember, there are many ways to write a ratio.” Cool Down: A Collection of Animals, students see a picture of dogs, mice and cats, “Write two sentences that describe a ratio of types of animals in this collection.” The materials meet the full intent of 6.RP.1 (Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.)

• Unit 4: Dividing Fractions, Section B: Meaning of Fraction Division, Lesson 7: What Fraction of a Group, students divide quantities into groups, even when they can’t make a whole group. Warm Up: Estimating a Fraction of a Number, Problem 1, “Estimate the quantities: a. What is \frac{1}{3} of 7? b. What is \frac{4}{5} of 9\frac{2}{3}? c. What is 2\frac{4}{7} of 10\frac{1}{9}?” Activity 2: Fractional Batches of Ice Cream, Problem 2, students write and solve division equations, “One batch of an ice cream recipe uses 9 cups of milk. A chef makes different amounts of ice cream on different days. Here are the amounts of milk she used: Monday: 12 cups, Tuesday: 22\frac{1}{2} cups, Thursday: 6 cups, and Friday: 7\frac{1}{2} cups. What fraction of a batch of ice cream did she make on these days? For each day, write a division equation, draw a tape diagram, and find the answer. a. Thursday. b. Friday.” Cool Down: A Partially Filled Container, “There is \frac{1}{3} gallon of water in a 3-gallon container. What fraction of the container is filled? a. Write a multiplication equation and a division equation to represent the situation. b. Draw a tape diagram to represent the situation. Then, answer the question.” Practice Problems, Problem 2, “Whiskers the cat weighs 2\frac{2}{3} kg. Piplio weighs 4 kg. For each question, write a multiplication equation and division equation, decide whether the answer is greater than 1 or less than 1, and then find the answer. a. How many times as heavy as Piglio is Whiskers? b. How many times as heavy as Whiskers is Piglio?” The materials meet the full intent of 6.NS.1 (Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.) 

• Unit 8: Data Sets and Distributions, Section A: Data, Variability, and Statistical Questions, Lesson 2: Statistical Questions, students determine whether questions are statistical and describe data variability. Warm Up: Pencils on a Plot, students measure and collect pencil length data, “a. Measure your pencil to the nearest \frac{1}{4} inch. Then, plot your measurement on the class dot plot. b. What is the difference between the longest and shortest pencil lengths in the class? c. What is the most common pencil length? d. Find the difference in lengths between the most common length and the shortest pencil.” Activity 1: What’s in the Data? Problem 2, “How are survey questions 3 and 5 different from the other questions? Question 3: What grade are you in? Question 5: How many inches are in 1 foot?” Activity 2: What Makes a Statistical Question? Problem 5, “How many minutes of recess do sixth-grade students have each day? a. Is variability expected in the data? yes or no b. Is the question statistical? yes or no.” Cool Down: Questions About Temperature, “Here are two questions: Question A: Over the past 10 years, what is the warmest temperature recorded, in degrees Fahrenheit, for the month of December in Miami, Florida? Question B: At what temperature does water freeze in Miami, Florida? a. Decide if each question is statistical or non-statistical. Explain your reasoning. b. If you decide that a question is statistical, describe how you would find the answer. What data would you collect?” Practice Problems, Problem 3, “Here is a list of questions about the students and teachers at a school. Select all the questions that are statistical questions. A. What is the most popular lunch choice? B. What school do these students attend? C. How many math teachers are in the school? D. What is a common age for the teachers at the school? E. About how many hours of sleep do students generally get on a school night? F. How do students usually travel from home to school?” The materials meet the full intent of 6.SP.1 (Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.)

The materials reviewed for Open Up Resources Grade 6 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

When implemented as designed, the majority (at least 65%) of the materials, when implemented as designed, address the major clusters of the grade. Examples include:

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5 out of 8, approximately 63%.

• The number of lessons devoted to major work of the grade, including supporting work connected to major work is 86 out of 133, approximately 65%. 

• The number of instructional days devoted to major work of the grade and supporting work connected to major work (includes required lessons and assessments) is 91 out of 141, approximately 65%. 

An instructional day analysis is most representative of the materials, including the required lessons and End-of-Unit Assessments from the required Units. As a result, approximately 65% of materials focus on major work of the grade.

The materials reviewed for Open Up Resources Grade 6 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Each lesson contains Learning Targets that provide descriptions of what students should be able to do after completing the lesson. Standards being addressed are identified and defined. Materials connect learning of supporting and major work to enhance focus on major work. Examples include:

• Unit 1: Area and Surface Area, Section C: Triangles, Lesson 10: Bases and Heights of Triangles, Activity 2: Some Bases are Better than Others, connects the supporting work of 6.G.1 (Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes) to the major work of 6.EE.2c (Evaluate expressions at specific values of their variables). Students identify the base and height of a triangle and use them to find the area of a triangle, “For each triangle, identify and label a base and height. If needed, draw a line segment to show the height. Then, find the area of the triangle. Show your reasoning. (The side length of each square on the grid is 1 unit.)” Students are given four triangles on grids to calculate area.

• Unit 4: Dividing Fractions, Section D: Fractions in Lengths, Areas, and Volumes, Lesson 14: Fractional Lengths in Triangles and Prisms, Cool Down: Triangles and Cubes, Problems 1 and 2, connects the supporting work  6.G.1 (Find the area of right triangles, other triangles, and special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes) and 6.G.2 (Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism) to the major work of 6.NS.1 (Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions). Students use what they know about fractions and operations to find the area of triangles and the volume of prisms, “A triangle has a base of 3$$\frac{2}{5}$$ inches and an area of 5$$\frac{1}{10}$$ square inches. Find the height of the triangle. Show your reasoning. Answer each of the following questions and show your reasoning. a. How many cubes with an edge length of $$\frac{1}{3}$$ inch are needed to build a cube with an edge length of 1 inch? b. What is the volume, in cubic inches, of one cube with an edge length of $$\frac{1}{3}$$ inch?” 

• Unit 5: Arithmetic in Base Ten, Section D: Dividing Decimals, Lesson 13: Dividing Decimals by Decimals, Activity 1: Placing Decimal Points in the Quotient, Problem 1, connects the supporting work of 6.NS.3 (Fluently add, subtract, multiply, and divide multi digit decimals using the standard algorithm for each operation) to the major work of 6.EE.4 (Identify when two expressions are equivalent). Students use base-ten understanding of numbers to move the decimal point in the divisor and then use their understanding of equivalent expressions to move the decimal in the quotient, “Think of one or more ways to find 3 ÷ 0.12. Show your reasoning.”

The materials reviewed for Open Up Resources Grade 6 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

Each lesson contains Learning Targets that describe what the students should be able to do after completing the lesson. The standards being addressed are identified and defined.

Materials connect major work to major work throughout the grade level when appropriate. Examples include.

• Unit 6: Expressions and Equations, Section B: Equal and Equivalent, Lesson 7: Revisit Percentages, Activity 2: Puppies Grow Up, Revisited, Problems 1-3, connects the major work of 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions.) to the major work of 6.RP.A (Understand ratio concepts and use ratio reasoning to solve problems.) Students use repeated calculations and then write an algebraic expression with a variable to solve problems, “Puppy A weighs 8 pounds, which is about 25% of its adult weight. What will be the adult weight of Puppy A? Puppy B weighs 8 pounds, which is about 75% of its adult weight. What will be the adult weight of Puppy B? If you haven’t already, write an equation for each situation. Then, show how you could find the adult weight of each puppy by solving the equation.” 

• Unit 6: Expressions and Equations, Section D: Relationships Between Quantities, Lesson 16: Two Related Quantities (Part 1),  Activity 1: Painting the Set, connects the major work of 6.EE.C (Represent and analyze quantitative relationships between dependent and independent variables.) to the major work of 6.RP.A (Understand ratio concepts and use ratio reasoning to solve problems.) Students write two equations relating the two quantities in the ratio and represent them with graphs, “Lin needs to mix a specific color of paint for the set of the school play. The color is a shade of orange that uses 3 parts yellow for every 2 parts red. a. Complete the table to show different combinations of red and yellow paint that will make the shade of orange Lin needs. b. Lin notices that the number of cups of red paint is always \frac{2}{5} of the total number of cups. She writes the equation  r = \frac{2}{5}t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know. c. Write an equation that describes the relationship between r  and y where y is the independent variable. d. Write an equation that describes the relationship between r  and y where y is the independent variable. e. Use the points in the table to create two graphs that show the relationship between r and y. Match each relationship to one of the equations you wrote.” Students use the applet in presentation mode.

• Unit 7: Rational Numbers, Section B: Inequalities, Lesson 8: Writing and Graphing Inequalities, Activity 1: Stories About 9, Problem 1, connects the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities.) to the major work of 6.NS.C (Apply and extend previous understandings of numbers to the system of rational numbers.) Students represent real-world situations with inequality statements and identify possible values which make it true, “Drag the green and red open points over the blue points, matching each story, graph, and description. A fishing boat can hold fewer than 9 people. A food scale can measure up to 9 kilograms of weight. Lin needs more than 9 ounces of butter to make cookies for her party. A magician will perform her magic tricks only if there are at least 9 people in the audiences.” Students use an applet in presentation mode to match situations with solutions.

Materials provide connections from supporting work to supporting work throughout the grade level when appropriate. Examples include:

• Unit 8: Data Sets and Distributions, Section C: Mean and MAD, Lesson 12: Using Mean and MAD to Make Comparisons, Activity 1: Which Player Would You Choose? Problem 2, connects the supporting work of 6.NS.B (Computer fluently with multi-digit numbers and find common factors and multiples.) to the supporting work of 6.SP.B (Summarize and describe distributions.) Students calculate MAD and compare data sets, “An eighth-grade student decided to join Andre and Noah and kept track of his scores. His data set is shown here. The mean number of baskets he made is 6. a. Complete the table. b. Calculate the MAD. Show your reasoning. c. Draw a dot plot to represent his data and mark the location of the mean with a triangle. d. Compare the eighth-grade student’s mean and MAD to Noah’s mean and MAD. What do you notice? e. Compare their dot plots. What do you notice about the distributions? f. What can you say about the two players’ shooting accuracy and consistency?”

• Unit 9: Putting it All Together, Section A: Making Connections, Lesson 1: Fermi Problems, Activity 2: Stacks and Stacks of Cereal Boxes, connects the supporting work of 6.NS.B (Compute fluently with multi-digit numbers and find common factors and multiples.) to the supporting work of 6.G.A (Solve real-world and mathematical problems involving area, surface area, and volume.) Students estimate the total volume occupied by all of the breakfast cereal purchased in a year in the United States, “Imagine a warehouse that has a rectangular floor and that contains all of the boxes of breakfast cereal bought in the United States in one year. If the warehouse is 10 feet tall, what could the side lengths of the floor be? Vital information to have on hand includes: Every year, people in the U.S. buy 2.7 billion boxes of breakfast cereal. A “typical” cereal box has dimensions of 2.5 inches by 7.75 inches by 11.75 inches.”

The materials reviewed for Open-Up Resources Grade 6 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The Course Guide contains a Scope and Sequence explaining content standard connections. Some Unit Overviews, Lesson Narratives, and Activity Syntheses describe the progression of standards for the concept being taught. Each Lesson contains a Preparation section identifying learning standards (Building on, Addressing, or Building toward). Content from future grades is identified and related to grade-level work. Examples include:

• Unit 1: Area and Surface Area, Unit 1 Overview, “In grade 8, students will understand “identical copy of” as “congruent to” and understand congruence in terms of rigid motions, that is, motions such as reflection, rotation, and translation. In grade 6, students do not have any way to check for congruence except by inspection, but it is not practical to cut out and stack every pair of figures one sees. Tracing paper is an excellent tool for verifying that figures “match up exactly,” and students should have access to this and other tools at all times in this unit. Thus, each lesson plan suggests that each student should have access to a geometry toolkit, which contains tracing paper, graph paper, colored pencils, scissors, and an index card to use as a straightedge or to mark right angles. Providing students with these toolkits gives opportunities for students to develop abilities to select appropriate tools and use them strategically to solve problems (MP5). Note that even students in a digitally enhanced classroom should have access to such tools; apps and simulations should be considered additions to their toolkits, not replacements for physical tools. In this grade, all figures are drawn and labeled so that figures that look congruent actually are congruent; in later grades when students have the tools to reason about geometric figures more precisely, they will need to learn that visual inspection is not sufficient for determining congruence. Also note that all arguments laid out in this unit can (and should) be made more precise in later grades, as students’ geometric understanding deepens.”

• Unit 2: Introducing Ratios, Unit 2 Overview, “...After some work with double number line diagrams, students use tables to represent equivalent ratios. Because equivalent pairs of ratios can be written in any order in a table and there is no need to attend to the distance between values, tables are the most flexible and concise of the three representations for equivalent ratios, but they are also the most abstract. Use of tables to represent equivalent ratios is an important stepping stone toward use of tables to represent linear and other functional relationships in grade 8 and beyond. Because of this, students should learn to use tables to solve all kinds of ratio problems, but they should always have the option of using discrete diagrams and double number line diagrams to support their thinking.”

• Unit 7: Rational Numbers, Section A: Negative Numbers and Absolute Value, Lesson 7: Comparing Numbers and Distance from Zero, Activity 2: Info Gap: Points on the Number Line, “In this info gap activity, students use comparisons of order and absolute value of rational numbers to determine the location of unknown points on the number line. In doing so students reinforce their understanding that a number and its absolute value are different properties. Students will also begin to understand that the distance between two numbers, while being positive, could be in either direction between the numbers. This concept is expanded on further when students study arithmetic with rational numbers in grade 7.”

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include:

• Unit 1: Area and Surface Area, Section A: Reasoning to Find Area, Lesson 2: Finding Area by Decomposing and Rearranging, Lesson Narrative, “This lesson begins by revisiting the definitions for area that students learned in earlier grades. The goal here is to refine their definitions (MP6) and come up with one that can be used by the class for the rest of the unit. They also learn to reason flexibly about two-dimensional figures to find their areas, and to communicate their reasoning clearly (MP3).”

• Course Guide, Scope and Sequence, Unit 2: Introducing Ratios, “Work with ratios in grade 6 draws on earlier work with numbers and operations. In elementary school, students worked to understand, represent, and solve arithmetic problems involving quantities with the same units. In grade 4, students began to use two-column tables, e.g., to record conversions between measurements in inches and yards. In grade 5, they began to plot points on the coordinate plane, building on their work with length and area. These early experiences were a brief introduction to two key representations used to study relationships between quantities, a major focus of work that begins in grade 6 with the study of ratios.”

• Unit 4: Dividing Fractions, Section A: Making Sense of Division, Lesson 1: Size of Divisor and Size of Quotient, Building on, students relate prior work in 5th grade “5.NBT.6 Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models,” to current work related to dividing fractions in 6th grade.