8th Grade - Gateway 1

The instructional materials reviewed for HMH Into Math Grade 8 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:

• Module 1, Form A, Question 7 states: “Graph the image of the triangle after it is translated 4 units down and reflected across the y-axis.” (8.G.3)
• Unit 6 Performance Task states: “Kevin makes a cylinder-shaped candle. He uses a metal can as a mold. The can has a radius of 6 centimeters and a height of 18 centimeters. How much wax is needed to fill the metal can? Show your work.” (8.G.9)
• Module 7, Form B, Question 8 states: "Brianna is comparing the price for two different bicycle rental companies. Option A charges a fixed fee and an hourly rate. Option B charges per hour with no fixed fee. The system of equations shows the total cost, y, for x hours. [system given: y = 6x + 16; y = 14x] Part A: Graph the system of equations. Part B: What is the cost in dollars  when the two plans cost the same amount?" (8.EE.8c)
• Module 11, Form A, Question 8 states: “Two boards are resting against each other to form an isosceles triangle as shown in the diagram. What is the height, h, rounded to the nearest hundredth in.?” (8.G.7)
  

The instructional materials reviewed for HMH Into Math Grade 8 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 9 out of 13, which is approximately 69%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 39 out of 50, which is approximately 78%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 101 out of 132 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 78% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for HMH Into Math Grade 8 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:

• In Lesson 8.3, students use scatter plots and equations of trend lines to analyze data. For example, On Your Own Question 8 states: "According to the equation of the trend line, each additional hour spent studying raises test scores by how much? How do you know?" (8.SP.3 and 8.EE.5)
• In Lesson 11.3, students use the Pythagorean Theorem (8.G.7) to find side lengths and rational approximations of irrational numbers (8.NS.2) to determine appropriate solutions. For example, given a 2m x 2m x 2m cube, “What is the longest rod that can fit in this cube? Round to the nearest tenth and show your work.”
• In Lesson 11.3, students apply the Pythagorean Theorem (8.G.2) to calculate the height of a cone (8.G.9). For example, given the radius of Cone A is 10 cm and the slanted side is 17 cm and the radius of Cone B is 12 cm and the slanted side is 18 cm, “Which is taller, Cone A or Cone B” By how much? Round to the nearest hundredth.”
• In Module 13, students solve problems about the volumes of cones, cylinders, and spheres (8.G.9) using square and cube roots (8.EE.2).
• In Lesson 13.1, students find the volume of a cylinder (8.G.9) with dimensions expressed in scientific notation (8.EE.4) and express the volume in scientific notation.
• In Lesson 13.2, students use the formula for the volume of cylinders (8.G.9) to model relationships between quantities (8.EE.5 and 8.F.4): “Consider a set of cones that all have a radius of 1 centimeter. The heights of the cones are 1 centimeter, 2 centimeters, 3 centimeters, 4 centimeters, 5 centimeters. A) Complete the table. Leave the volumes in terms of pi. B) Is the relationship in the table a proportional relationship? C) Write an equation that gives the volume y of a cone with radius 1 centimeter if you know the height x of the cone. Describe the graph of the equation.”

The instructional materials for HMH Into Math Grade 8 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 with assessments can be completed in 154 days: 106 days for lessons and 48 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 8 has six units with 13 modules which contain a total of 50 lessons. 
• The pacing guide designates all 50 lessons as 2-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 six Openers for Grade 8 (6 days).
• This is a total of 106 lesson days.

Assessments included:

• The Planning and Pacing Guide (page 20) indicates a Beginning, Middle, and End of Year Interim Growth test that would require 1 day each (3 days). 
• Each module starts with a review assessment titled “Are You Ready?” There are 13 modules (13 days).
• Each unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are six Performance Tasks for Grade 8 (6 days). 
• Each module has both a review and an assessment. There are 13 modules (26 days). 
• Based on this, 48 assessment days can be added.

The instructional materials for Into Math Grade 8 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 7 System of Linear Equations states, “Prior Learning: Students wrote and solved one-variable equations.” (7.EE.4); “Current Development: Students use graphing to determine the approximate solution to a system.” (8.EE.8); “Future Connections: Students will represent constraints by systems of equations.” (A-CED.3)
• In Activate Prior Knowledge at the beginning of each lesson, content is explicitly related to prior knowledge to help students scaffold new concepts.
• In Lesson 9.2, Spark Your Learning states, “Using what you know about proportion and percent, what information can you determine from the table?”
• Each module includes a diagnostic assessment, Are You Ready?, that explicitly identifies prior knowledge needed for the current module. For example, in Module 3, Are You Ready? addresses solving one-step equations (6.EE.7) and writing and solving two-step equations (7.EE.4a).
• 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 13 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:

• In Lesson 5.4, Question 9 states, “Given a graph and a graphic with sizes labeled, students solve “A rain barrel and a cistern are filling at constant rates. The amount of water in the rain barrel over time is shown in the graph. The amount of water in the cistern is given by y = 200x, where x is the time in hours and y is gallons of water. A) How fast is the rain barrel filling? How fast is the cistern filling? B) If both the barrel and the cistern were empty at t = 0, which would completely fill first? Explain.” (8.EE.5)
• In Lesson 11.1, More Practice Question 5 states, ‘As the students explain a proof of the Pythagorean Theorem, they solve “A) Find the missing side of a triangle with leg length 5 yards and hypotenuse 13 yards. B) Find the missing side of a triangle with leg length 30 yards and hypotenuse 78 yards. C) How are the lengths of the leg and hypotenuse in Part A related to the lengths of the leg and hypotenuse in Part B? D) How is the length of the missing side in Part A related to the length of the missing side in Part B?” (8.G.6)

When work is differentiated, the materials continue to develop grade-level concepts. An example of this is Lesson 4.3, which involves work with transversals and identification of angles. The corresponding Reteach page provides guided notes for students to follow in order to access the concept and the Challenge page has two parallel lines cut by two transversals where students must solve for x using algebraic expressions given in three angles.

The instructional materials reviewed for HMH Into Math Grade 8 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 7.2, the learning objective is “Solve a system of two linear equations by graphing,” shaped by 8.EE.C.
• In Lesson 8.2, the learning objective is “Use trend lines to describe a linear relationship between two variables,” shaped by 8.SP.A.
• In Lesson 12.1, the learning objective is “Develop and use the properties of integer exponents,” shaped by 8.EE.A.
• In Lesson 5.3, both Learning and Language objectives are “Graph proportional relationships; Interpret unit rate as the slope of the graph of a proportional relationship” and “Explain how to find the unit rate of a proportional relationship from graphs and tables and how to determine whether a graph should be continuous or discrete based on the situation it represents,” shaped by 8.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 4.1, students write and solve an equation (8.EE.C) to determine the measures of the angles of a triangle (8.G.A).
• In Lesson 5.1, students determine that triangles are similar (8.G.A) by finding two pairs of congruent angles and comparing the slopes of the triangles (8.EE.B).
• In Lesson 6.2, students identify linear and nonlinear equations (8.F.A) by examining the slopes and y-intercepts of the equations (8.EE.B).
• In Lessons 11.1 and 11.2, students solve equations for missing side lengths resulting from the Pythagorean Theorem (8.EE.A and 8.G.A).