7th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Does Not Meet Expectations | 21% |
|---|---|
Criterion 1.1: Focus | 0 / 2 |
Criterion 1.2: Coherence | 0 / 4 |
Criterion 1.3: Coherence | 3 / 8 |
The instructional materials for Spider Learning Mathematics Grade 7 do not meet expectations for focus and coherence in Gateway 1. The materials do not meet the expectation for focus as they assess above grade-level content and do not spend at least 65% of class time on major work of the grade. The materials do not meet expectations for coherence as they do not follow the progressions of the standards, provide students with extensive work with grade-level problems, and do not foster connections at a single grade where appropriate and called for by the Standards.
Criterion 1.1: Focus
The instructional materials for Spider Learning Mathematics Grade 7 do not meet expectations for assessing topics before the grade-level in which the topic is introduced. There are above-grade level assessment items present on unit exams.
Indicator 1a
The instructional materials for Spider Learning Mathematics, Grade 7, 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 3 Exam, an O item states, “What is the GCF of the following group of monomials: $$34x^2y, 51xy^2z, 85y^2z^3$$. A. $$4y^2z$$ B. $$17y^2$$ C. 17y D. 3y ” This item aligns to A-SSE.2 (Use the structure of an expression to identify ways to rewrite it).
- In Unit 8 Exam, an O item states, “The volume of a cylinder is found by multiplying pi times the radius squared times the ⬜” A drop down menu of choices are given, “area, circumference, height, diameter.” This item aligns to 8.G.9 (Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems).
- In Unit 12 Exam, a TEI item states, “Use the diagram of the parking lines below to answer the questions that follow. Assume lines are parallel if they appear to be.” The diagram shows three parallel lines cut by a transversal with two angles labeled “4x + 40” and “6x + 10.” Students answer the following questions: “What is the value of “x” in the diagram above? The angle with the measure 4x+40 is equal to ⬜ degrees. The angle with the measure 6x + 10 is equal to ⬜ degrees. Which angle is larger, angle A or angle B? Angle ⬜ is larger. The measure of angle C is ⬜ degrees.” This item aligns to 8.G.5 (Use informal argument to establish facts about the angle sum and exterior angle of triangles about the angles created when parallel lines are cut by and transversal, and the angle-angle criterion for similarity of triangles).
Criterion 1.2: Coherence
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
The instructional materials for Spider Learning Mathematics Grade 7 do not meet expectations for students and teachers using the materials as designed devoting the majority of class time to the major work of the grade. Overall, the instructional materials spend 21% of class time on the major work of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Spider Learning Mathematics, Grade 7, 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 3 out of the 12 units, which is approximately 25%.
- The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 38 out of 180 lessons, which is approximately 21%.
- The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 8 out of 36 weeks, which is approximately 22%.
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 21% of the instructional materials focus on major work of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials for Spider Learning Mathematics Grade 7 do not meet expectations for coherence. The materials include an amount of content viable for one school year, and make some connections between supporting work and the major work of the grade. However, the materials do not attend to the progressions of the standards, students do not have opportunities to engage in extensive work with grade level content as many grade-level standards are not addressed in the materials. In addition, the materials do not include lesson objectives shaped by the clusters or domains of the standards, and do not include connections between major clusters and domains, or supporting clusters and domains.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Spider Learning Mathematics, Grade 7, partially meet expectations for supporting work enhancing focus and coherence simultaneously by engaging students in the major work of the grade
Each lesson addresses one standard, so supporting work standards are taught in isolation and rarely connect to the major work of the grade. The materials contain missed opportunities to enhance the focus and coherence simultaneously by engaging students in the major work of the grade, for example:
- In Unit 6, Lesson 1, Daily Assignments, students answer, “Angles that have a sum of 90o are called A. complementary angles; B. adjoining angles; C. supplementary angles; D. adjacent angles” (7.G.5), but this is not connected to the major work of the grade.
- In Unit 6, Lesson 3, Daily Assignments, students “Identify which pair of angles is complementary from the diagram below. [Diagram Provided] A. ABC and CBD; B. ABC and DBE; C. CBD and DBE; D. There are no complementary angles in this picture” (7.G.5), but this is not connected to the major work of the grade.
Some examples of supporting work connected to major work of the work of the grade include:
- In Unit 8, Lesson 2 connects the supporting standard, 7.G.6, with the major standard, 7.NS.3, in the following Daily Assignment Problem: “Jamal is painting a door that is 7 feet tall, 3.5 feet long, and 0.25 feet wide. What is the surface area of the door? A. 40.5 $$ft^2$$; B. 54.25 $$ft^2$$; C. 54 $$ft^2$$; D. 40.25 $$ft^2$$.”
- In Unit 8, Lesson 11 connects the supporting standard, 7.G.1, with the major standard, 7.RP.1, when students use proportional reasoning as they analyze scale drawings in the following Daily Assignment Problem: “A dog owner is creating a scale drawing of a doghouse she wants to build. The doghouse will be 5 feet long and 3 feet wide. She wants to use a scale of 1 inch: 2 feet. What will be the dimensions of the drawing? 3 inches x 5 inches; 3 inches x 1.5 inches; 3 inches x 3 inches; 6 inches x 3 inches.”
- In Unit 9, Lesson 4 connects the supporting standard, 7.SP.2, with the major standard, 7.RP.3, when students solve the following Daily Assignment Problem: “At one university a survey was conducted to determine how many students are earning a Bachelor of Science versus a Bachelor of Arts. The survey was given to a small representative sample as the results are located below. [Bachelor of Science 24; Bachelor of Arts 15] If the university has approximately 5,080 students enrolled, how many total students are pursuing a Bachelor of Science? A. 24; B. 2,989; C. 3,126; D. 121,920.”
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials reviewed for Spider Learning Mathematics, Grade 7, meet expectations that the amount of content designated for one grade-level is viable for one year. As designed, the instructional materials can be completed in 180 days.
- Each of the 12 units in Spider Learning Mathematics, Grade 7, contain 15 lessons for a total of 180 lessons.
- Within each unit, 3 of the 15 days are assessment days. Quizzes take place at Lessons 5 and 10, and the Unit Exam takes place on Lesson 15.
Spider Learning Mathematics has a Scope and Sequence in a separate document containing the standards addressed for each lesson. Each lesson contains a Pre-Test (5-7 minutes); Interactive Video (5-10 minutes), Introduction to the Lesson Objective (2-3 minutes); DOK1, DOK2, and DOK3 Activities (5-8 minutes each); Summary (2-3 minutes); Post Test (5-7 minutes); and Daily Assignment (10 minutes), for a total class period of 44-64 minutes.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for Spider Learning Mathematics, Grade 7, 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 6 identifies 7.G.5, but the lesson addresses 8.G.5, “Use informal arguments to establish facts about the angle sum and exterior angle triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.”
- In Unit 7, Lesson 1 addresses 4.G.2, “Classify two-dimentional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absences of angles of a specified size. Recognize right triangles as a category, and identify right triangles.”
- In Unit 8, Lesson 12 identifies 7.G.2, but it is aligned to 7.G.5 “Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.”
The instructional materials do not give all students extensive work with grade-level problems as there are nine Grade 7 standards which are not addressed. These standards are:
- 7.NS.1a
- 7.NS.2a
- 7.NS.2b
- 7.NS.2c
- 7.EE.2
- 7.G.2
- 7.SP.7a
- 7.SP.7b
- 7.SP.8c
Spider Learning Mathematics, Grade 7, 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 to content from earlier grades.
- The materials provide students some general statements relating to prior grade-level concepts. For example, in Unit 3, Lesson 9, Objective and Introduction states, “The words ‘algebraic equation’ are enough to make some people nervous, but the truth is an equation is just a statement that tells us two things that are equal. ‘Algebraic’ just means that there is a variable in the equation to represent an unknown value. You can use algebraic equations to tell you anything from how much your hair has grown in a year to how many hours you worked this summer. As we explore solving equations, remember that this knowledge will help you use Algebra as a tool in your own life,” and in Unit 8, Lesson 3, Objective and Introduction states, “Do you remember the formula for surface area of a rectangular prism using a net, which is one possible method.”
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to 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.
The instructional materials reviewed for Spider Learning Mathematics, Grade 7, 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 7 CCSSM cluster headings, for example:
- In Unit 1, the Lesson 7 objective is “Students will convert mixed numbers into improper fractions.”
- In Unit 2, the Lesson 1 objective is “Students will solve applications by adding or subtracting decimal values.”
- In Unit 3, the Lesson 2 objective is “Students will evaluate algebraic expressions using order of operations with given values.”
- In Unit 5, the Lesson 8 objective is “Students will determine a whole quantity given a part of the whole and its percentage.”
- In Unit 6, the Lesson 2 objective is “Students will classify angles according to their measures.”
- In Unit 10, the Lesson 1 objective is “Students will calculate the mean and median of a set of numeric data.”
Spider Learning Mathematics, Grade 7, 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 12, Lesson 2 does not connect 7.NS.A to 7.EE.A, Use properties of operations to generate equivalent expressions, or 7.EE.B, Solve real-life and mathematical problems using numerical and algebraic expressions and equations. The Daily Assignment states, “Karli bought 4 notebooks that cost $2.05 each and a pencil for $0.89. What was the total cost for her school supplies? A. $8.89; B. $9.09; C. $10.56; D. $11.76.”
- In Unit 12, Lesson 6 addresses 7.RP.2 and does not connect to 7.EE.B, Solve real-life and mathematical problems using numerical and algebraic expressions and equations. The Daily Assignment states, “Use the information below to answer the question that follows. The distance from your house to the park and back is approximately 3.5 miles. You can walk at an average of 2.5 miles per hour. If you decided to walk to the park and back home, how long would the walk take?” The response choices provided are: “Approximately 1.4 hours; Approximately 30 minutes.”