6th Grade - Gateway 1

The materials reviewed for Desmos Math 6 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The assessments are aligned to grade-level standards and do not assess content from future grade levels. Each unit has at least one quiz and one End Assessment, which comes in Forms A and B. Quizzes and End Assessments are available in print and digital versions. Examples of assessment items aligned to grade-level standards include:

• Unit 2, End Assessment: Form A, Screen 2, Problem 1, assesses 6.RP.3 as students use ratio and rate reasoning to solve a real-world problem. “Makayla’s recipe for Orange Surprise uses 2 cans of orange juice for every 3 liters of soda water. How much soda water would Makayla need if she used 12 cans of orange juice? 13 liters of soda water, 18 liters of soda water, 15 liters of soda water, 8 liters of soda water.” 

• Unit 4, End Assessment: Form A, Screen 12, Problem 7.2, assesses 6.NS.1 as students interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. “Amir and his grandma are making roti, a Malaysian bread. Amir’s grandma uses a \frac{3}{4} - cup scoop. They need 5\frac{1}{2} cups of flour. How many of Amir’s grandma’s scoops do they need?”

• Unit 7, Quiz, Screen 8, Problem 5.1, assesses 6.NS.7 as students demonstrate understanding of the absolute value of a rational number as its distance from 0. “Is this statement always, sometimes, or never true? The absolute value of a number is negative.”

• Unit 8, Quiz, Screen 7, Problem 5, assesses 6.SP.2 and 6.SP.4 as students understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Students also display numerical data in plots on a number line. “Create two dot plots so that: They have at least 5 points each; Their centers are around 7; Dot Plot A has a larger spread than Dot Plot B.” An interactive number line where students can add points to create the dot plot is included.

• Unit 8, End Assessment: Form B, Screen 15, Problem 7, assesses 6.SP.4 and 6.SP.5c as students display numerical data in plots on a dot plot and find quantitative measures of center. “Create a dot plot with: At least five points; A median of 7; A mean that is greater than the median.” An interactive number line where students can add points to create the dot plot is included.

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

The materials provide opportunities for students to engage in extensive work and the full intent of all Grade 6 standards. Each lesson contains a Warm-up, one or more activities, an optional “Are You Ready for More?”, a Lesson Synthesis, and a Cool-Down. Each unit provides a Readiness Check and Practice Days. Readiness Checks provide insight into what knowledge and skills students already have. Practice Days provide opportunities for students to apply knowledge and skills from the unit. Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• Unit 1, Lesson 11, Student Worksheet, Activity 2, engages students with 6.G.4 (Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures). The students are given nets with polyhedra drawn on them, and the directions are: “Calculate the surface area and show your thinking.”

• Unit 4, Lesson 4, Practice Problems, Screen 3, Problem 1.4, engages students with 6.NS.1 (Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem). Students interpret quotients of fractions and create word problems involving division of fractions. “Abena wrote the expression 6\div\frac{3}{4} to represent how many potatoes fill 1 planter. Describe a situation that represents 8\div\frac{4}{5}.” 

• Unit 6, Lesson 4, Screen 9, Lesson Synthesis, engages students with the full intent of 6.EE.5 (Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true). There are four cards with equations on them and answers. “How can you tell if a value is a solution to an equation?”

• Unit 8, Lesson 3, Practice Problems, Screen 3, Problem 1.2, students engage in 6.SP.4 (Display numerical data in plots on a number line, including dot plots, histograms, and box plots). Students are given a dot plot ranging from 15 to 22 with dots located on several of the numbers. “A teacher brought a bowl of 20 jellybeans to class and asked each student in class to estimate the number of jellybeans in the bowl. The teacher used a dot plot to record each estimate. Were the students’ estimates accurate?” 

While students engage with 6.NS.4 (Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100...), there are limited opportunities for students to use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

The materials reviewed for Desmos Math 6 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Practice and assessment days are included. Any lesson marked optional was excluded.

• The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 6 out of 8, which is approximately 75%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 96 out of 136, which is approximately 71%. 

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 97 out of 137, which is approximately 71%.

A day-level analysis is most representative of the instructional materials because this contains all lessons including those that are more than one day. As a result, approximately 71% of the instructional materials focus on major work of the grade.

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

In most cases, materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. Examples of connections include:

• Unit 4, Lesson 12, Practice Problems, Screen 8, Explore, connects the supporting work 6.G.A (Solve real-world and mathematical problems involving area, surface area, and volume) to the major work of 6.NS.A (Apply and extend previous understandings of multiplication and division to divide fractions by fractions). “Determine the lengths of a, b, and c.” Students are given a diagram of a shape broken into four rectangles. One rectangle has an area of 4 sq. m. with a length of 6 m and width of a. Another rectangle has an area of 3 sq. m with length c and width b. The two remaining rectangles have an area of \frac{3}{4} sq. m with a side length of b and combined the widths add to a. 

• Unit 5, Lesson 12, Student Worksheet, Activity 2, Problem 1.1-1.2, connects the supporting work of 6.NS.B (Compute fluently with multi-digit numbers and find common factors and multiples) to the major work of 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). “Kweku is deciding between the DesWagon and the Desla Electric. He figures out that: The Desla Electric costs $11,900 more than the DesWagon. The cost of electricity for the Desla Electric is $0.03 per mile. The cost of gas for the DesWagon is $0.12 per mile. Kweku drives about 18,000 miles a year. How much money would he save in a year buying electricity for the Desla Electric compared to buying gas for the DesWagon? About how long would it take to make up for the higher sale price of the Desla Electric?”

• Unit 6, Lesson 4, Practice Problems, Screen 3, Problem 1.2, connects the supporting work of 6.NS.B (Compute fluently with multi-digit numbers and find common factors and multiples) to the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities). “Vihaan says the solution to x+1.8=5 is x=6.8. Explain how you know that this is incorrect.” Students are given a diagram of a balanced hanger with a block with the number five attached to one end and two blocks, one that says x and 1.8 respectively, attached to the other end. 

• Unit 7, Lesson 11, Screen 10, Cool-Down, connects the supporting work of 6.G.3 (Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems) to the major work of 6.NS.8c (Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate). Students are asked to, “Enter coordinates for point D to complete the rectangle,” and “Enter the length of the segment that connects points A and B.”Students are given a graph with three points of a rectangle shown, a table is provided with Points A, B, C, D and respective coordinates (-4,5), (-4,-3) and (-2,-3).

The materials reviewed for Desmos Math 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.

There are multiple connections between major clusters and/or domains and supporting clusters and/or domains. Any connections not made between clusters and/or domains are mathematically reasonable. Connections between major clusters or domains include:

• Unit 6, Lesson 6, Screen 6, Limes, connects the major work of 6.RP.A (Understand ratio concepts and use ratio reasoning to solve problems)to the major work of 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions). “Limes cost $2.40 per pound. How much should you charge for p pounds of limes?”

• Unit 7, Lesson 6, Practice Problems, Screen 8, Problem 3.1, connects the major work of 6.NS.C (Apply and extend previous understandings of numbers to the system of rational numbers) to the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities). “One day in Boston, the temperature was above 52\degree and below 60\degree. Make one graph to represent temperatures above 52\degree and another graph to represent temperatures below 60\degree.” Students are given two separate number lines both ranging from 30 to 80.

Connections between supporting clusters or domains include:

• Unit 5, Lesson 6, Screen 6, Multiplying Decimals, connects supporting work 6.G.A (Solve real-world and mathematical problems involving area, surface area, and volume) to the supporting work of 6.NS.B (Compute fluently with multi-digit numbers and find common factors and multiples). “1. Drag the point to help you multiply 4.5\cdot2.9. 2. Calculate the area of each part. The total area will be calculated for you.” Students are given a diagram of a rectangle with a length of 4.5 units, and width of 2.9 units. Students can drag a point on the rectangle to split it into four smaller rectangles of various lengths and widths.

• Unit 8, Lesson 2, Screen 8, Book Plots, connects the supporting work of 6.SP.A (Develop understanding of statistical variability) to the supporting work of 6.SP.B (Summarize and describe distributions). “This dot plot shows the number of books Antwon's classmates read in a month. Write a question that this dot plot could help you answer.” The plot is titled Number of Books Read this Month and has 20 dots spread from 0 to 12.

The materials reviewed for Desmos Math 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.

Content from future grades is identified and related to grade-level work. These references can be found within many of the Unit Summaries, Unit Facilitation Guides, and/or Lesson Summaries. Examples of connections to future grades include:

• Unit 3, Lesson 5, Screen 7, Jamal’s Strategy, connects 6.RP.2 (Understand the concept of a unit rate a\b associated with a ratio a:b with b\ne0, and use rate language in the context of a ratio relationship) to work in 7th grade.  In Grade 7 students compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units (7.RP.1). During the lesson students develop conceptual understanding of unit rates and use them to solve problems. Students are given a picture, “Make Your Own; $0.40 per oz.; 2.5 oz. per dollar.” A strategy is shown that circles the 2.5 oz. and draws an arrow to 7\cdot2.5=17.5 ounces. “Here is how Jamal figured out how much soft serve you can get for $7. How do you think Jamal knew which unit rate to use?”

• Unit 8, Lesson 15, Screen 5, David’s Claim, connects the work of 6.SP.B (Summarize and describe distributions) to the work in 7th grade. In Grade 7 students use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations (7.SP.4). During this lesson students use their knowledge of data displays to summarize and describe data. Students are given two box plots showing Movie Budgets in millions of dollars. One plot is labeled Originals and the other plot is labeled Sequels. “David said: Original films have higher budgets than sequels because the highest-budget film is an original. What do you think about David's claim?”  

Materials relate grade-level concepts from Grade 6 explicitly to prior knowledge from earlier grades. These references can be found within many of the Unit Summaries, Unit Facilitation Guides, and/or Lesson Summaries. Examples of connections to prior knowledge include:

• Unit 4, Unit Facilitation Guide, Connections to Prior Learning, connects 6.NS.1 (Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fraction) to work in Grade 3 and Grade 4. “The following concepts from previous grades and units may support students in meeting grade-level standards in this unit: Understanding division as an unknown factor problem. (3.OA.B.6), Explaining why two fractions are equivalent and generating equivalent fractions. (4.NF.A.1)”

• Unit 5, Unit Facilitation Guide, Lesson 2, Purpose, connects 6.NS.3 (Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation) to work in Grade 5. In Grade 5 students add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used (5.NBT.7).  During the lesson, “Students revisit what they have learned about place value in previous grades and make connections between place value and the decimal representation of numbers. Students then use these relationships to add and subtract decimals.”