6th Grade - Gateway 1

The instructional materials for Spider Learning Mathematics, Grade 6, 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 2 Exam, a TEI item states, “Drag each ordered pair to the correct quadrant. [4.9, -3] [√9,√49].” Evaluating square roots of small perfect squares aligns to 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 √2 is irrational).
• In Unit 3 Exam, an O item states, “Which of the answers is equal to -1? A. - |7+2| - 5 B. |2| - 3 C. -5 + |2+8| D. |-10| - |-9|.” This question requires students to add and subtract negative and positive integers which aligns to 7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram). 
• In Unit 3 Exam, a FR item states, “Describe how to sort rational numbers if the numbers include whole numbers, decimals, fractions, etc. Sort the following numbers and explain the steps you took to make it easier to sort the numbers: 5/11, 26, -5.2, and √4.” Evaluating square roots of small perfect squares aligns to 8.EE.2. 
• In Unit 10 Exam, an O item states, “Based on this line of best fit, how tall could we predict that a 12-year-old would be? A. 75 inches, B. 45 inches, C. 55 inches, D. 65 inches.” Students are provided a scatterplot and a line of best fit. This item aligns to 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).

The instructional materials reviewed for Spider Learning Mathematics, Grade 6, 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 6 out of the 12 units, which is approximately 50%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 74 out of 180 lessons, which is approximately 41%.
• The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 15 out of 36 weeks, which is approximately 42%. 

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 41% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Spider Learning Mathematics, Grade 6, 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 6, Lesson 1 identifies 6.EE.1 with a lesson objective that addresses 1.OA.3, “Students will apply the Commutative Property of Addition to generate equivalent expressions.” The DOK 1 activity states, “Use the Commutative Property to match the number sentences that have the same sum.” The number sentences given are, “3 + 15 = ?; 3 + 5 = ?; 5 + 15 = ?” and the three responses are, “5 + 3 = ?; 15 + 5 = ?; 15 + 3 = ?”. This also aligns to 1.OA.6 as students use addition and subtraction within 20.
• In Unit 6, Lesson 14 identifies 6.EE.6. The DOK1 problem states, “Complete the steps for solving the following equation. 12t - 3 = 57.” This problem aligns to 7.EE.4a (Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently).
• In Unit 10, Lessons 1 through 5 are aligned to 8.SP.1. Lesson 2 states, “Match the colored point with its significance.” Students are provided a scatter plot and three statements, “When the temperature was 85 degrees, sales were $350; When the temperature was 94 degrees, sales were $340; When the temperature was 90 degress, sales were $400.” 

The instructional materials do not give all students extensive work with grade-level problems as there are 18 Grade 6 standards which are not addressed. These standards are:

• 6.RP.3a, 6.RP.3b, and 6.RP.3d;
• 6.NS.6a, 6.NS.7a, 6.NS.7b, 6.NS.7c, and 6.NS.7d;
• 6.EE.2a, 6.EE.2b, 6.EE.3, 6.EE.4, and 6.EE.6; and
• 6.SP.2, 6.SP.5a, 6.SP.5b, 6.SP.5c, and 6.SP.5d.

Spider Learning Mathematics, Grade 6, 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 1, Lesson 4 states, “As you can see, adding and subtracting decimals is very similar to adding and subtracting whole numbers;” in Unit 3, Lesson 1 states, “To compare rational numbers, we use many of the same strategies that we've used to compare numbers in the past;” and in Unit 4, Lesson 7 states, “In this lesson, you related equivalent ratios to your understanding of equivalent fractions.”

The instructional materials reviewed for Spider Learning Mathematics, Grade 6, 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 6 CCSSM cluster headings, for example:

• In Unit 1, the Lesson 2 objective is “Students will be able to compare decimal values.”
• In Unit 2, the Lesson 4 objective is “Students will convert mixed numbers into improper fractions.”
• In Unit 6, the Lesson 14 objective is “Students will solve two-step linear equations.” 
• In Unit 7, the Lesson 1 objective is “Students will solve two-step linear equations in real world applications.”
• In Unit 7, the Lesson 2 objective is “Students will identify a proportion.” 
• In Unit 10, the Lesson 2 objective is “Students will interpret bivariate data from a scatter plot.” 
• In Unit 11, the Lesson 2 objective is “Students will solve a linear inequality and sketch its solution interval on the number line.”

Spider Learning Mathematics, Grade 6, 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 5, Lesson 1 addresses 6.RP.3 with no connections to expressions and equations (6.EE). Daily Assignments include: “Grand City sells 4 DVDs for $36. Music City sells 3 DVDs for $27. Who has the better deal? A. Grand City; B. The unit price is the same for both stores; C. Music City” and “The unit price of grass seed is $4.50 per pound. How much would 7 pounds of grass seed cost? The total price would be _________.” The answer choices provided are: “ $30.50; $31.50; $29.50; $32.50.”
• In Unit 7, Lesson 2 addresses 6.RP.3c, and there is no content in the lesson that connects to other clusters or domains. The Daily Assignment states, “Which of the following is NOT an example of a ratio? A. 1:8; 9:19; 18:38; All of the above; None of the above.”
• In Unit 11, Lesson 11 addresses 6.NS.6c and does not connect to 6.RP.A as students plot points. The Daily Assignment states, “Which colored dot has the ordered pair of (30,5)? A. Blue; B. Red; C. Black; D. Green” and “Plot the point (0.3, -0.75)”.