8th Grade - Gateway 1

The materials reviewed for Desmos Math 8 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 3, End Assessment: Form A, Screen 9, Problem 5, assesses 8.EE.5 as students compare different proportional relationships represented in different ways. “One day, three runners ran about 10 miles, each at their own constant speed. Which runner ran the fastest? Runner 1, Runner 2, Runner 3” The problem contains different visual representations for each runner. The representation for Runner 1 shows the graph of a line with distance (miles) on the vertical access and time (minutes) on the horizontal axis. The representation for Runner 2 shows a table with a column for time (minutes) and one for distance (miles) with five entries. The representation for Runner 3 shows an equation d=\frac{1}{8}t where t = time (minutes) and d = distance (miles).

• Unit 4, Quiz, Screen 9, Problem 5, assesses 8.EE.7b as students solve linear equations with rational coefficients, whose solutions require expanding expressions using the distributive property and collecting like terms. “Solve these equations on the paper supplement provided by your teacher. 1d+12=14-2s, 4(2r+5)=10r, -2(5+x)-1=3(x+3).”

• Unit 5, Quiz 2, Screen 3, Problem 2, assesses 8.F.5 as students sketch a graph that exhibits the qualitative features of a function described verbally. ”Consider the following situation: 55 people got on an empty bus. After 30 minutes, 40 of them got off the bus. After 15 more minutes, the rest of the passengers got off the bus. Sketch a graph that represents this situation. Then enter a label for each axis in the table below.” An interactive graph where students can sketch a graph is included.

• Unit 7, End Assessment: Form A, Screen 8,  Problem 7.1, assesses 8.EE.4 as students perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. “Calculate the combined mass of Earth and Pluto.” The mass of Pluto is given as 13,000,000,000,000,000,000,000 kg. The mass of Earth is given as 5.97\sdot10^{24}kg.

• Unit 8, End Assessment: Form A, Screen 10, Problem 7.1, assesses 8.G.7 as students apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world problems. “Wey Wey drops a pencil in her cup and notices it only fits diagonally. The pencil is 17 centimeters long and the cup is 15 centimeters tall. What is the diameter of the cup?” Students are given a drawing of a pencil in a cup with the above measurements.

The materials reviewed for Desmos Math 8 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 8 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:

• In Unit 1 and Unit 2, students engage with the full intent of 8.G.3 (Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates). In Unit 1, Lesson 5, Screens 6, 7, and 8, students apply the effect of reflection, translation and rotation respectively to a two-dimensional figure. Students are tasked with moving points of the pre-image on the coordinate plane to make the image based on the rigid motion asked. Once students are done they press the “Check My Work” button and the pre-image moves onto their image and they see if image they created is correct based on the coordinates. In Unit 2, Lesson 4, Screen 4, Dilate It #2, students are given a coordinate grid with a scalene triangle and asked to “Dilate this triangle with vertices at (-3,-3), (12,3), and (9,12) using center (0,0) and a scale factor of \frac{1}{3}.” 

• Unit 4, Lesson 3, Screen 7, Solving Equations, engages students with the full intent of 8.EE.7 (Solve linear equations in one variable). “Jaylin solved this equation from the card sort:

  15-7x=3+5x; 12-7x=5x; 12=12x; 1=x Is this correct?”

• Unit 5, Lesson 3, Screen 8, Card Sort, engages students with the full intent of 8.F.1 (Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output). Students complete a card sort. For example: “Sort the graphs according to whether or not y is a function of x.”

• Unit 8, Lesson 10, Screen 1, Warm-Up, engages students with the full intent of 8.G.7 (Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world context and mathematical problems in two and three dimensions). Students use the Pythagorean Theorem to solve real-life problems. “Alma is going to walk through the park from point A to point B. What distance will she walk?” There is a diagram of a map with the park shown. It is in a square block. Points A and B are on the ends of the diagonal of the square block.  The length of the blocks are 200 feet each.

While students engage with 8.EE.4 (Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities, e.g., use millimeters per year for seafloor spreading. Interpret scientific notation that has been generated by technology),  students have limited opportunities to work with operations with numbers written in different forms (scientific notation and decimals) to meet the full intent of the grade-level standards.

The materials reviewed for Desmos Math 8 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 7 out of 8, which is approximately 88%.

• The approximate number of lessons devoted to major work (including assessments and supporting work connected to the major work) is 110 out of 133, which is approximately 83%. 

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 110 out of 133, which is approximately 83%.

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 83% of the instructional materials focus on major work of the grade.

The materials reviewed for Desmos Math 8 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 5, Lesson 12, Screen 4, Using the Graph, connects the supporting work of 8.G.C (Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres) to the major work of 8.F.3 (Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear). “This function represents the relationship between the height and volume for cylinders with a radius of 5 centimeters. Use the movable point and the table to help you find the volume of each of the four cylinders. Express each volume in terms of \pi.” A table is given with four possible cylinders and their heights listed in cm. Students fill in the column for volume (cubic cm) using an interactive graph with a sliding tool. 

• Unit 6, Lesson 6, Screen 5, Measuring Turtles, connects the supporting work of 8.SP.2 (Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line) to the major work of 8.EE.6 (Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y=mx+b for a line intercepting the vertical axis at b). “Here is another scatter plot from the card sort. Enter a slope to fit a line to the data. (Your line will go through the red open point.)” Students are provided a graph with a scatter plot already plotted on it. 

• Unit 6, Practice Day 2, Student Worksheet, Activity 2, Graph A, connects the supporting work of 8.SP.3 (Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept) to the major work of 8.F.4 (Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values). “1. Draw a line of fit to model the data. 2. Estimate the slope of the line of fit. 3. What is the meaning of the slope in this situation?” Students are provided a scatter plot with the (x-axis) labeled “Time (hours)” and the (y-axis) labeled “Money (dollars).” 

• Unit 8, Lesson 2, Screen 5, Square Roots, connects the supporting work of 8.NS.A (Know that there are numbers that are not rational, and approximate them by rational numbers) to the major work of 8.EE.2 (Use square root and cube root symbols to represent solutions to equations of the form x^2=p and x^3=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that \sqrt{2} is irrational). Students are tasked with filling a table with either, “Side Length of Square (units)” or “Area of Square (square units)”. “Enter the remaining side lengths and areas for the squares in the table.” 

The materials reviewed for Desmos Math 8 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 3, Lesson 5, Screen 9, Write an Equation, connects the major work of 8.EE.B (Understand the connections between proportional relationships, lines, and linear equations) to the major work of 8.F.B (Use functions to model relationships between quantities). “The graph shows the linear relationship between height and time for each flag. Write an equation for the height of Flag C. Then press ‘Check My Work.’ Use the sketch tool if it helps you with your thinking.” Students are given a graph with three different lines, and a table with two columns (one labeled Flag and one labeled Equation). The equations for Flag A and B are given. 

• Unit 5, Lesson 4, Screen 10, Lesson Synthesis, connects the major work of 8.F.A (Define, evaluate, and compare functions) to the major work of 8.F.B (Use functions to model relationships between quantities). “Sort the cards representing the same choice of independent and dependent variables into two groups (3 cards per group).” There are six cards in total with the following written on them: “Question: How many cups do you need to stack as tall as a basketball player?” and “Question: How tall is a stack of cups?”, “Independent Variable: Number of Cups  Dependent Variable: Height of stack” and “Independent Variable: Height of stack  Dependent Variable: Number of Cups” and, “Equation: c=\frac{h-10}{2}” and, ”Equation: h=2c+10.”

• Unit 8, Practice Day 2, Student Worksheet, Problem 5, connects the major work of 8.G.B (Understand and apply the Pythagorean Theorem) to the major work of 8.EE.A (Expressions and Equations Work with radicals and integer exponents). “Pablo wanted to see if a 12-inch straw would fit inside a small rectangular box. He noticed that it only fits diagonally. The box has a height of 2 inches and width of 3 inches. What is the length of the box?”  Students are provided a diagram with a rectangular box with a straw inside, the straw length, height and width of the box are given.

Connections between supporting clusters or domains include:

• Unit 5, Lesson 13, Practice Problems, Screen 3, Problem 2, connects the supporting work of 8.G.C (Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres) to the supporting work of 8.NS.A (Know that there are numbers that are not rational, and approximate them by rational numbers). “A cylinder and a cone have the same height and radius. The height of each is 5 centimeters, and the radius is 2 centimeters. Calculate the volume of the cylinder and the cone (rounded to the nearest tenth). Use 3.14 as an approximation for \pi .”

• Unit 6, Lesson 2, Practice Problems, Screen 5, Problem 4.2, connects supporting work of 8.NS.A (Know that there are numbers that are not rational, and approximate them by rational numbers) to the supporting work of 8.G.C (Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres). Students use an approximation of \pi to calculate the volume of a cylinder and graph the result. “There are many cylinders with a radius of 6 meters. Let h represent the height in meters and V represent the volume in cubic meters. Sketch the graph of the equation, using 3.14 as an approximation for \pi.”

The materials reviewed for Desmos Math 8 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 2, Unit Summary, connects the work of 8.G.A (Understand congruence and similarity using physical models, transparencies, or geometry software) to the work in high school. “Lesson 8 uses properties of similarity to determine unknown side lengths of triangles in the context of shadows. This work lays the foundation for trigonometry and other triangle relationships in high school.”

• Unit 7, Unit Facilitation Guide, Section 1: Exponent Properties (Lesson 1-6), connects 8.EE.1 (Know and apply the properties of integer exponents to generate equivalent numerical expressions) to the work in high school. “Students identify and create equivalent expressions involving positive, negative, and zero exponents. This builds on students' work with expressions involving positive whole number exponents in Grade 6. In high school, students will investigate properties of non-integer exponents.”

Materials relate grade-level concepts from Grade 8 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 3, Lesson 4, Summary, About This Lesson, connects 8.EE.B (Understand the connections between proportional relationships, lines, and linear equations) to the work in 7th grade. “After revisiting examples of proportional relationships in the previous lessons, this lesson is the first of several lessons that moves from proportional relationships to linear relationships with positive rates of change…They [Students] make connections between the rate of change of the relationship and the slope of a line representing the relationship. In this lesson, the focus is proportionality vs. linear relationships and rate of change…” 7.RP.2a (Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

• Unit 4, Unit Facilitation Guide, Connections to Prior Learning, connects 8.EE.C (Analyze and solve linear equations and pairs of simultaneous linear equations) to the work in 6th and 7th grades. “The following concepts from previous grades may support students in meeting grade-level standards in this unit: Applying the distributive property to generate equivalent expressions. (6.EE.A.3), Combining like terms to generate equivalent expressions. (6.EE.A.3, 7.EE.A.1), Solving problems by writing and solving equations with variables on one side of the equation. (6.EE.B.7, 7.EE.B.4.a), Understanding what it means for a value to be a solution to an equation. (6.EE.B.5).“