8th Grade - Gateway 1

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8, Grade 8 meet expectations for assessing grade-level content.

The materials are organized by the Domains and Clusters delineated by CCSS. Each Cluster has a Milestone Assessment, and all assessments include multiple choice and/or multiple select. The assessments are aligned to grade-level standards, and examples include:

• In Milestone Assessment 8.EE.B, Question 10, “What is the slope of the line represented by the equation $$8x + 2y = 16$$? a) -4; 
b) 8
; c) 4
; d) -8.”

• In Milestone Assessment 8.F.A, Question 1, “The equation of a function is $$y = 8x - 2$$. What is the input when the output is 14? a) 110
; b) 14
; c) 1.5
; d) 2.”

• In Milestone Assessment 8.G.B, Question 9, “The diagonal distance between (0, 0) and another point is 15 units. What are the coordinates of the second point? a) (7, 8)
; b) (9, 12); c) (10, 5)
; d) (6, 13).”

• In Milestone Assessment 8.G.C, Question 2, “A cone has a radius of 8 feet and an approximate volume of 1,546 cubic feet. What is the height of the cone? Use 3.14 for pi. a) 23.08 feet; b) 23 feet; c) 23.05 feet; d) 23.5 feet.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 8 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials present opportunities for all students to meet the full intent of grade-level standards through extensive work with grade-level problems. Each lesson addresses one grade-level standard with all standards addressed over the course of the year. Lessons are three to four days long. There are opportunities within each lesson to practice the content of the standards including: Math Simulator, one to four questions; Practice Printable typically has six to ten questions;  Additional Practice has four to ten questions; Clicker Quizzes include six questions; and the teacher can assign a specific domain in Test Trainer Pro. Examples where the full intent is attended to include:

• In 8.EE.C.7a The Business Guru in YOU!, students give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. For example, Practice Printable Question 1, “Observe each equation and determine the number of solutions. In the blank, write one solution, infinite solutions, or no solution.” In Question 2, students determine values so that an equation has infinite solutions, and in Question 3, students determine values that result in no solution. 

• In 8.EE.C.8b Mars Rocks!, students solve systems of two linear equations in two variables algebraically. For Example, Additional Practice Question 2, “What is the solution to the system below? Solve using substitution x + 2y = 200; x + y = 50.”

• In 8.NS.A.2 Treasure Hunt, students approximate irrational numbers on a number line and in expressions. For example, Practice Printable Question 10, “Place each value on the numberline, and label it with the appropriate letter,”; Question 8, “Order each list of values from least to greatest (the list contains rational and irrational numbers).”

The Test Trainer Pro and Simulation Trainer are also designed to provide additional, grade-level work.

• In Test Trainer Pro, primarily used as a daily warm-up, teachers can assign a specific domain, but not standards. Teachers have access to the question bank in order to see what the questions are, but cannot edit them.

• In Simulation Trainer, the content matches the lesson, but students can provide any number as an answer, then watch the steps worked out (no words) in a solution video. They’re presented with the same question again and can put in the correct answer, then watch the same solution again. If they get it correct the first time, they also watch the solution video. The next questions are not novel, but the same situation with new numbers. If students miss one, it resets them to the beginning, no matter where they were in the assignment. It is possible that some students would never complete a Simulation Trainer.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 8 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 122 out of 159, which is approximately 77%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 25 out of 31 lessons, which is approximately 81%.

• The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is 30 out of 36, which is approximately 83%. 

A day-level analysis is most representative of the materials because this represents the class time that is devoted to major work of the grade including reviews, domain intensives, and assessments. As a result, approximately 77% of the materials focus on major work of the grade.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 8 meet expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of connections between supporting content and major work of the grade include:

• 8.G.B.8 Seeking Safe Harbor connects to 8.NS.A as students approximate irrational square roots when using the Pythagorean theorem to calculate the length of missing sides of triangles. In the Practice Printable, Question 1, “Point C is located at (4, -3) and Point D is located at (2, 5) Determine the distance between them to the nearest tenth of a unit.”

• 8.SP.A.3 The Slope of Sprouts connects to 8.F.4 as students write an equation for the line of best fit in a scatterplot and interpret the equation in terms of the situation. In the Practice Printable, Question 3 shows a scatterplot of study time and GPA. Students “write a linear equation that models the data'' and answer the questions, “What does the slope mean in this context?” and “What does the y-intercept mean in this context?”

• 8.EE.A.2 Ship Shape states, “This activity connects 8.EE.A. to 8.G.C, as it directly relates three-dimentional figures, cubic units and volumes to perfect cubes and cube roots.” In the Practice Printable, “This sugar cube box is a perfect cube and its volume is 1,728 cubic centimeters. The sugar cubes inside are 1 cm $$×$$ 1 cm $$×$$ 1cm. a) How many sugar cubes fit along the length of the box? b) How many sugar cubes fit along the width of the box? c) How many sugar cubes fit along the height of the box? d) How much cardboard is used to make the box?”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 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. Examples include:

• 8.EE.B.6 Ghost Island connects the major work of 8.EE.B to 8.F.B as students use functions to model relationships and derive linear equations in the form y=mx+b. In the Practice Printable, Question 1 states, “Determine the slope, y-intercept and equation of line n and line p.” A graphic of a coordinate plane with 2 lines is included for reference. Throughout the lesson, especially in the Teacher Instruction portion, there are also connections made to the major work of 8.G.A related to congruence and similarity, specifically similar triangles. For example, “We’ll learn more about similarity later in our geometry unit. But for now, let’s see how that helps us with slope between points on a line. In similar triangles, the ratios between corresponding sides are equal.”

• 8.F.B.5 Twin Tactics states, “This activity connects 8.F.B to 8.EE.B in that students will realize that graphs can look many different ways besides linear and can tell the story between two variables.” The Practice Printable provides students with opportunities to interpret graphs related to linear and nonlinear functions as well as one situation to sketch on a graph.

• In 8.F.A.3 Le Monsieur Chef, 8.F.A and 8.EE.B are connected as students identify linear and nonlinear equations and use the slope and y-intercept to prove linearity by completing tables, graphs, rules and interpreting the data. For example, in Practice Printable Question 3 states, “Determine if each situation can be modeled by a linear equation. If so, write the linear equation that models it. If not, write non-linear. a) On Day 0, there are 500 bacteria in a dish. The number of bacteria doubles every day after that. How many bacteria (y) are there after x days?; b) An online movie club charges a monthly fee of $8.00 and $2.00 per movie downloaded. What is the monthly cost (y) for x movies?”

• 8.G.A.5 Puppy Parallels connects the major work of 8.G.A to the major work of 8.EE.C as students write and solve equations to determine unknown angles. On the Clicker Quiz, Step 2 is as follows: “Subtract each angle from $$180\degree$$ to determine measures of exterior angles.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 8 meet expectations for clearly identifying content from future grades and relating it to grade-level work and explicitly relating grade-level concepts to prior knowledge from earlier grades.

Examples of clearly identifying content from future grades and relating it to grade-level work include:

• 8.EE.C.8a Show Me the Money identifies “Prerequisite Standards 6.EE.B.5, 7.EE.B.4, 8.EE.B.6” and Cluster Connections including “Direct Connection: In Show Me the Money, students will use their knowledge of linear equations to recognize that the solution to a system of two linear equations in two variables corresponds to the point of intersection (if any) of their graphs. Cross-Cluster Connection: This activity connects 8.EE.C to HSA.REI.C as students will solve systems of equations involving both linear and nonlinear equations.”

• 8.NS.A.1 Warp Speed states, “This activity connects 8.NS to HSN.RN.B as students in high school will further explore properties of rational and irrational numbers.”

Examples of explicitly relating grade-level concepts to prior knowledge from earlier grades include:

• 8.EE.A.3 Malaria Medicine states, “This activity connects 8.EE to 5.NBT and 6.RP in that students combine their knowledge of powers of 10 with their knowledge of ratios to express one variable as a numerical factor of another variable.”

• 8.EE.A.4 The Great Discovery states, “This activity connects 8.EE.A to 6.NS.B in that students will utilize their skills with decimal operations to add, subtract, multiply, and divide numbers in scientific notation.”