The instructional materials for Spider Learning Mathematics, Grade 8, do not meet expectations for assessing grade-level content. Above grade-level assessment items are present and cannot be modified or omitted without a significant impact on the underlying structure of the instructional materials. 

Unit Exam items are randomly assigned to students from a bank of items aligned to each standard, so item numbers are not referenced in this report. The Unit Exams include 30 objective items (O), 6 technology-enhanced items (TEI), and 4 free-response items (FR). 

Above grade-level content is found in most unit exams. These items cannot be modified or omitted without significantly modifying the materials, and examples of above grade-level assessment items include:

• In Unit 4 Exam, a TEI item states, “Determine the simplest form for each radical expression $$\sqrt{12}, \sqrt{48}, \sqrt{32}, \sqrt{18}$$” This item aligns to N-RN.2 (Rewrite expressions involving radicals and rational exponents using the properties of exponents).
• In Unit 4 Exam, a TEI item states, “What is the first step in solving the following equation for x, $$2\sqrt{x+5}=14$$? A. Subtract 5 from both sides. B. Multiply both sides by 2. C. Square both sides. D. Divide both sides by 2.” This item aligns to A-REI.2 (Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise).
• In Unit 8 Exam, a TEI item states, “The table below shows the values necessary to find the correlation coefficient.” The table shows that a x b has a value of 25, $$a^2$$ has a value of 34, and $$b^2$$ has a value of 24. The item states, “What is the correlation coefficient? Fill in the missing words of the explanation and answer below. Round all values to the nearest hundredth, if necessary. We need to use the formula. The numerator of the formula is ___________. The denominator is _________. If you substitute in the three values above, the numerator will be ________. After multiplying and taking the square root, the value of the denominator will be ________. Finally, we divide the numerator by the denominator to get a final value of ________.” There are the following choices to use to fill in the blanks: “a x b, 25, 28.57, $$\sqrt{a^2+b^2}$$, $$\sqrt{a×b}$$, 34, $$\sqrt{a^2×b^2}$$, 0.82, 24, 27.56, 0.88, 0.93” This item aligns to S-ID.8 (Compute [using technology] and interpret the correlation coefficient of a linear fit).
• In Unit 11 Exam, a FR item states, “Lindsay is an eighth grade entrepreneur who operates a candy store in the garage of her home on weekends. She uses the money to buy the latest fashion trends. The number (N) of outfits she can buy is determined by the amount (A) she charges for each piece of candy, the amount of candy that she sells, the total price (P) that she pays to purchase the candy, and the average cost of each outfit (O) she wants to buy. Therefore, her shopping liberties can be described by this literal equation: $$N=(AC-P)\div O$$. Solve the literal equation for: amount she charges, amount of candy she sells, total price she pays to purchase the candy, and average cost of each outfit.” This item aligns to A-CED.4 (Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations).

The instructional materials reviewed for Spider Learning Mathematics, Grade 8, do not meet expectations for spending a majority of instructional time on major work of the grade. 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7 out of the 12 units, which is approximately 58%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 100 out of 180, which is approximately 56%.
• The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 20 out of 36, which is approximately 56%.

A lesson-level analysis is most representative of the instructional materials because of the consistent structure of the units, where each unit has 15 lessons (3 devoted to assessment). As a result, approximately 56% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Spider Learning Mathematics, Grade 8, do not meet expectations for being consistent with the progressions in the Standards.

The instructional materials do not clearly identify content from prior and future grade-levels and do not use it to support the progressions of the grade-level standards. There is no information regarding the progression of the lesson standards from Grade 6 to Grade 8.

In the Teacher view of materials, The Hub (customized for each use situation) includes a Scope and Sequence which identifies the standards and objective for each lesson, however, there are cases where the standards are incorrectly identified in the lesson or the lesson is focused on above or below grade-level standards. Examples include:

• In Unit 4, Lesson 11 identifies A-REI.4b, but the lesson aligns with 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.”
• In Unit 5, Lesson 1 identifies 8.EE.5, but the lesson aligns to 6.RP.3. For example, DOK2 activity states, “Reduce the ratio 25 to 10 to lowest terms. A. 5 to 2; B. 5 to 1; C. 25 to 2; D. 2 to 5.”
• In Unit 9, Lesson 11 identifies 8.G.1 instead of 8.G.9, but the lesson aligns to 7.G.4, “Know the formulas for the area and circumference of a circle and use them to solve problems.”
• In Unit 11, Lesson 1 identifies 8.EE.5 in the Scope and Sequence, but the objective states, “Students will solve literal equations for a specified variable,” which aligns to A-CED.4, “Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.” The Daily Assignment TEI question states, “Solve the following literal equation for the variable $$X_f:dX=X_f-X_i$$" Students can choose from "$$::X_f=dX+X_i;$$ $$::X_f=dX-X_i;$$ $$::X_f=X_i-dX$$.” 

The instructional materials do not give all students extensive work with grade-level problems as there are 11 Grade 8 standards which are not addressed. These standards are:

• 8.EE.8c;
• 8.F.4 and 8.F.5;
• 8.G.2, 8.G.3, 8.G.4, 8.G.5, 8.G.7, and 8.G.8; and
• 8.SP.2 and 8.SP.3.

Spider Learning Mathematics, Grade 8, does not explicitly relate grade-level concepts to prior knowledge from earlier grades.

• The Scope and Sequence document contains the standard assigned for each lesson, but does not relate it to content from earlier grades.
• The materials provide students some general statements relating to prior grade-level concepts. For example, in Unit 6, Lesson 3, the Objective and Introduction states, “Previously, you looked at graphs of functions. One way to tell if a graph represented a function was to use the vertical line test.” It does not explicitly identify the 7th grade standards on which the lesson builds, nor the high school standard that will come next in the progression. In Unit 3, Lesson 8, the Objective and Introduction states, “As you have previously learned, we can express a rational number as a fraction or a decimal using a series of steps. Now we are going to expand a little further by finding the percentage equivalence for a rational number. A percentage is another way of expressing what portion something is of a whole, and it can also be used to express the difference between two scenarios.”

The instructional materials reviewed for Spider Learning Mathematics, Grade 8, do not 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 not visibly shaped by Grade 8 CCSSM cluster headings, for example:

• In Unit 1, the Lesson 8 objective is “Students will multiply mixed numbers.”
• In Unit 1, the Lesson 14 objective is “Students will solve application problems using percents.”
• In Unit 2, the Lesson 1 objective is “Students will understand positive exponents and express them in expanded form.”
• In Unit 3, the Lesson 7 objective is “Students will write mixed numbers as decimal values and vice versa.”
• In Unit 5, the Lesson 2 objective is “Students will reduce a rate to a unit rate.”
• In Unit 11, the Lesson 11 objective is “Students will identify the domain and range of a relation.”

Spider Learning Mathematics, Grade 8, does not identify more than one standard in any lesson, which presents few opportunities to 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 Unit 2, Lesson 6 does not connect 8.F.A, Define, evaluate and compare functions, to 8.EE.B, Understand the connections between proportional relationships, lines, and linear equations. All Daily Assignment problems provide opportunities to identify whether a graphed relationship is a function, but none include the opportunity to graph a relationship and make the connection to a function. For example, “Simplify $$2^3×2^5$$ using the Product Property. A. $$2^{12}$$;; B. $$4^{15}$$; C. $$4^{8}$$; D. $$2^{8}$$” and “Read the following statement and choose the correct word to fill in the blank from the list at the bottom. The Zero Exponent Property states that any base raised to an exponent of 0 is equal to _________.” The answer choices provided are: “Itself; 0; 1” 
• In Unit 12, Lesson 14 does not connect 8.F.A, Define, evaluate, and compare functions, to 8.F.B, Use functions to model relationships between quantities as students do not have opportunities to construct graphs. The Daily Assignment states, “Which solution goes with this graph?” (Graphs are included.) “Jaden walks two miles on a hike before eating lunch. After lunch, he walks at a pace of three miles per hour; Taylor buys pens that cost two dollars each. If she buys the pens online, she will also have to pay four dollars for shipping; Aaron is buying boxes of rice at three-quarters of the regular price. He also buys a bottle of olive oil for five dollars; Jordan has three individual granola bars in his backpack, and then buys 4 boxes of granola bars.”