8th Grade - Gateway 1

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for assessing grade-level content.

Each unit includes Form A and Form B Assessments as well as Tiered Assessments Form AT and Form BT, all of which include selected response and constructed response sections. Performance Tasks are also included with each unit. In addition, Gem Challenges are online, standards-based items for use after a standard has been addressed and are located after certain lessons. 

Examples of grade-level assessments include:  

• Unit 1, Equations, Online Gem Challenge 1, Problem 1: “Choose the equation that has no solution. 5x - 4 - x = 3x - 4; 5x - (4x+7) = 14x; 12 + 7x = 16 + 11x - 4x; 15 + 5x -4 = 8x + 6 -x”
• Unit 2, The Pythagorean Theorem, Form B, Part II, Problem 5: “Kelvin leaves home and walks 5 blocks east and 10 blocks north to the ball park. How far is the ball park from Kelvin’s home if he were to take a direct path? If necessary, round to the nearest tenth.” (8.G.8)
• Unit 5, Systems of Equations, Performance Task: “Jaylee wants to have a mural painted in her bedroom. Two separate artists have given her bids. Artist #1 charges an initial fee of $79.50 plus $1 per square foot. Artist #2 does not have an initial fee and charges $2.50 per square foot. Jaylee wants the mural to cover a wall that is 7 feet by 10 feet. Which artist will be the least expensive for this mural space? Show all work necessary to justify your answer. Which size of mural (in square feet) will be the same cost when painted by either artist? Show all work necessary to justify your answer. Jaylee decides she only wants to spend $120 on the mural from Artist #2. Give one set of dimensions that represent the largest rectangular mural she could get for this price. Use words and/or numbers to show how you determined your answer.” (8.EE.8a, 8.EE.8b, 8.EE.8c) 
• Unit 8, Exponent Properties, Form BT, Part II, Problem 4: “Simplify $$(4x^6)^0$$" (8.EE.1)
• Unit 9, Volume, Form A, Part II, Problem 7: “A cylindrical can of soda pop is 12 cm tall and has a diameter of 6 cm. The box for a 12-pack of soda pop has a length of 25 cm, a width of 19 cm and is 12.2 cm tall. The cans are placed in the box in three rows of 4. What is the volume of space that is not used when a 12-pack box of soda pop is full?” (8.G.9)

There are above grade-level assessment items that could be modified or omitted without impact on the underlying structure of the instructional materials. These items include:

• Unit 10, Form A, Part I, Problem 6c and 6d: “For numbers 6a – 6d, use the information in the table below to circle TRUE or FALSE for each statement.” Problems 6c and 6d address conditional frequency. (S-ID.5) “6c. The conditional frequency for carpoolers who own a car is 0.8.” “6d. The conditional frequency for carpoolers who do not own a car is 0.25.”

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for spending a majority of instructional time on major work of the grade. 

• The number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 8 out of 10, which is 80%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 38 out of 46, which is approximately 83%.
• The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 101 out of 118, which is approximately 86%. 

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

The instructional materials reviewed for EdGems Math Grade 8 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards and clusters are connected to major standards and clusters of the grade, and lessons address supporting standards while maintaining focus on the major work of the grade. Examples of supporting work being used to support the focus and coherence of the major work of the grade include:

• Lesson 1.4 connects 8.NS.1 and 8.EE.2 as students learn about square root and cube root and apply this knowledge to solve equations with rational exponents. An example is, “The volume of a cube is 512 cubic inches. What is the side length of the cube?”
• Lesson 5.6 connects 8.NS.1 and 8.EE.7 as students convert repeating decimals to rational numbers by solving equations.  Example 3 states, “What is $$0.\overline{83}$$ as a fraction?” The worked out example describes how to set up an equation and solve to convert the repeating decimal into a fraction.” 
• Lesson 9.3 connects 8.G.9 and 8.EE.4 as students find the volume of a sphere and must express the volume in scientific notation. An example is, “The equator is an imaginary line on the Earth's surface which divides the Earth into two equal hemispheres. It is approximately 24,901.55 miles long. Assuming the earth is perfectly round, what is the volume of the earth in cubic miles? Write your answer in scientific notation.” 
• Lesson 10.3 connects 8.SP.A and 8.EE.B as students create a scatter plot for a given set of data and “a. Find an equation for a line of best fit for the data set. b. Use the equation to predict how many pounds someone will lose if they work out for 40 hours.”

The instructional materials for EdGems Math Grade 8 meet expectations for being consistent with the progressions in the Standards. In general, the instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. In addition, the instructional materials give all students extensive work with grade-level problems.

Each Unit Overview describes how the work of the unit is connected to previous grade level work, for example:

• In the Unit 3 Overview, Proportional Relationships, work from prior grades is explicitly stated. “In this unit, students will be introduced to the concept of a function. They will learn how to determine if a relationship is a function by examining a graph or table. Then students will examine a specific type of function formed by a proportional relationship. In CCSS Grade 7, students worked with proportional relationships using graphs, tables, and equations. In Grade 8 CCSS, the students interpret the constant of proportionality (unit rate) as the slope of the graph. In this unit, students will progress from understanding the slope as the unit rate to calculating slope from a graph, a table or two ordered pairs.”

Each Unit Overview includes Learning Progression, and each Learning Progression includes statements identifying what students have learned in earlier grades and what students will learn in future grades, for example:

 Unit 7, Unit Overview, In earlier grades, students have…

• Recognized that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (6.NS.6) 
• Used facts about angles and side lengths to determine information about polygons. (7.G.2 and 7.G.5)

In future grades, students will… 

• Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. (G-CO.6) 
• Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (G-CO.8)

There are multiple opportunities for students to work with grade-level problems. There are exercises contained within each Student Lesson, Explore activity, Student Gem (online activities to provide practice with the content), Online Practice & Gem Challenge (only in some lessons), Exit Card, and Performance Task. For example:

• In Lesson 4.6, students describe the functional relationship between two points (8.F.5). In Exercise 4, students “Choose the best story for each graph. Explain your reasoning.” Students examine a graph that shows a nonlinear relationship between speed and time and choose from: “A. A bus pulls over at a bus stop.” “B. A runner sprints to finish a race.” or “C. A person walks at a constant rate.” In Exercise 9, students “Sketch a graph for each story. Label the x- and y-axes for each situation.” “A person riding a bike is riding at a constant speed and then slows down to stop at a stop sign. Graph time on the x-axis and speed on the y-axis.”

The materials include one example of off grade-level content that is not identified that distracts students from engaging with the grade-level standards:

• Lesson 10.4, Bivariate Data and Frequency Tables, includes conditional frequency (S-ID.5).  For example, Example 2 states, “Use Marsha’s data about flu shots and sickness to answer the questions. a. Find the relative frequencies for the two-way table in Example 1 showing the possible relationship between those who had a flu shot and those who were sick with the flu. b. Explain one observation from the relative frequencies. c. What is the conditional frequency that someone with a flu shot will not get sick?”

Each unit includes a Parent Guide with Connecting Math Concepts, which includes, “Past math topics your child has learned that will be activated in this unit and Future math this unit prepares your child for.” For example, in Unit 2, Pythagorean Theorem, “Past math topics your child has learned that will be activated in this unit; determining if three side lengths can form a triangle; graphing points on a coordinate plane and determined distance between two horizontal or vertical points.” “Future math this unit prepares your child for; understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles; using trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems; using coordinates to compute perimeters of polygons and areas of triangles and rectangles.” 

Each Lesson Guide includes Teaching Tips, which often include connections from prior or future grades, for example:

• Lesson 4.4, Linear Equations in Other Forms, connections to future grades, “In Algebra I, students will learn strategies to graph linear equations that are in standard form and point-slope form without converting to slope-intercept form. At Grade 8, students should focus on converting any linear equation into slope-intercept form in order to graph.”
• Lesson 6.1, Alternate Exterior and Interior Angles, connections to prior grades, “The beginning of the lesson reviews angle pairs students have learned in Grade 7 standards. You may have students look at these pairs and share with a partner what they understand about each pair or you may choose to put the terms on the board at the start of the lesson and have students recall the pairs in a group to see how many they remember.”

In each Lesson Guide, Warm Up includes problems noted with prior grade-level standards. For example:

• Lesson 1.3, Concepts and Procedure (7.NS.3), Question 30, Skill: Operations with rational numbers. Find the value of each rational expression:
• a. 3/4 + (− 1/2)
• b. 1-2/5 − (− 1/10)
• c. – 5/6 (− 3/10)
• d. 3-1/3 ÷ 1/5
• e. – 5/8 + (− 1/4)
• f. (3-1/6 )(2-2/5)
• Lesson 5.6, Converting Repeating Decimals to Fractions, Concepts and Procedure (7.NS.2d), Question 12, Skill: Converting decimals to fractions. Write each decimal as a fraction or mixed number in simplest form:
• a. 0.3
• b. 0.6
• c. 0.5
• d. 0.25
• e. 0.15
• f. 1.25

The instructional materials for EdGems Grade 8 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

Examples of learning objectives that are visibly shaped by CCSSM cluster headings include:

• The objective of Lesson 1.3, “I can determine if a linear equation in one variable has no solution, one solution or infinitely many solutions” is shaped by 8.EE.C, Analyze and solve linear equations and pairs of simultaneous linear equations.
• The objective of Lesson 2.1, “I can apply the Pythagorean Theorem to solve problems in two and three dimensions,” is shaped by 8.G.B, Understand and apply the Pythagorean Theorem.
• The objective of Lesson 4.3, “I can write a linear equation in slope-intercept form when given information about the line” is shaped by 8.F.A, Define, evaluate, and compare functions.
• The objective of Lesson 7.2, “I can translate an image on a coordinate plane,” is shaped by 8.G.A, Understand congruence and similarity using physical models, transparencies, or geometry software.
• The objective for Lesson 10.1, “I can read, create and describe the associations in scatter plots,” is shaped by 8.SP.A, Investigate patterns of association in bivariate data.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important, and examples include:

• Lessons 2.1 and 2.2 connect 8.EE.A and 8.G.A as students write and solve equations with integer exponents to find missing side lengths of right triangles using the Pythagorean Theorem. 
• Lesson 4.4 connects 8.F.A and 8.EE.B as students use linear equations and rewrite them in slope intercept form. 
• Lesson 6.5 connects 8.EE.C and 8.G.A as students write and solve equations to determine unknown angles. 
• Lesson 4.3 connects 8.F.B and 8.F.A as students model real-world problems with functions by interpreting the start value and the slope which connects understanding linear equations by describing linear functions and involves comparing different representations of a function.