High School - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 88% |
|---|---|
Criterion 1.1: Focus & Coherence | 16 / 18 |
Criterion 1.1: Focus & Coherence
Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
The instructional materials reviewed for Reveal Math Traditional meet expectations for focus and coherence. The materials attend to the full intent of the mathematical content contained in the high school standards, spend the majority of time on the CCSSM widely applicable as prerequisites, let students fully learn each non-plus standard, engage students in mathematics at a level of sophistication appropriate to high school, and explicitly identify and build on knowledge from Grades 6-8. The materials partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards and making meaningful connections in a single course and throughout the series.
Indicator 1a
The materials focus on the high school standards.*
Indicator 1a.i
The materials attend to the full intent of the mathematical content contained in the high school standards for all students.
The instructional materials reviewed for Reveal Math Traditional meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students.
Examples of where materials attend to the full intent of the standards include:
- N-RN.1: In Algebra 1, Module 8, Lesson 4, students explore nth roots through a number line activity to show the values of raising a number to the $$\frac{1}{2}$$ power, and students explain their reasoning for why different expressions with rational exponents and roots are equivalent.
- A-APR.3: In Algebra 2, Module 5, Lesson 5, students find the zeros of a polynomial using synthetic division and then sketch the graph. In Example 5, students analyze a real life example to find zeros and then also graph the function.
- F-BF.2: In Algebra 1, Module 4, Lesson 5, and Module 9, Lessons 5 and 6, students write both arithmetic and geometric sequences recursively and with an explicit formula.
- G-CO.1: In Geometry, Module 1, Lesson 2, the materials provide precise definitions in “Today’s Vocabulary” for concepts and provide questions that link the vocabulary with the mathematics students complete that day.
- G-GPE.5: In Geometry, Module 3, Lesson 8, the materials establish the relationship between slopes of parallel and perpendicular lines. In the activity “Watch Out”, students have to extend this relationship to the slopes of vertical and horizontal lines. Students then use these relationships to compare different forms of linear equations.
- S-IC.1: In Algebra 2, Module 10, Lesson 1, the materials provide a video lesson that highlights the different types of sampling. This provides students with clear examples to understand how to make inferences based on different types of samples.
The following standards are partially addressed in this series:
- A-SSE.1a: Students nor teachers are expected to interpret parts of expressions. Students often create expressions, but not interpret what parts of a given expression mean.
- G-CO.2: Students nor teachers compare transformations that preserve distance and angle to those that do not.
- G-GPE.1: Students nor teachers complete the square in the context of the equation of a circle.
The following standards are not addressed in this series:
- F-LE.3
- G-SRT.1a
Indicator 1a.ii
The materials attend to the full intent of the modeling process when applied to the modeling standards.
The instructional materials reviewed for the Reveal Math Traditional partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. Throughout the series, all aspects of the modeling process are present in isolation or in combination with other aspects, but there are no instances where students engage in the full modeling process without prompts or scaffolding from the materials.
Examples where students engage in aspects of the modeling process with prompts or scaffolding from the materials include, but are not limited to:
- In Algebra 1, Module 3, Lesson 6, students collect data about wrist and neck circumferences of their classmates and examine the data on a graph. From this data, students interpret if the function is either a linear or non-linear relationship and if the function is applicable to the real world (F-IF.5). Students do not define their variables in this scenario.
- In Algebra 1, Module 7, Performance Task, students determine how many hours Rue will work at two different jobs while trying to save money for a trip. The performance task has nine prompts that move students through different aspects of the modeling process, but students do not complete the modeling process on their own.
- In Algebra 1, Module 11, Ignite! Mathematical Modeling, students use a set of data to predict the price of a movie ticket in 2027. Students answer seven prompts that proceed through the aspects of the modeling process, and the prompts are scaffolded by the aspects of the modeling process. After the seven prompts are answered, students report their findings and more prompts are divided to help students provide a complete report.
- In Geometry, Module 8, Performance Task, students determine the results on the design and materials needed for a t-shirt based on different dilations being performed on the original figure in the design. The performance task has four prompts that move students through different aspects of the modeling process, but students do not complete the modeling process on their own.
- In Geometry, Module 11, Ignite! Mathematical Modeling, students design an aquarium that will support a certain number of two types of fish based on given parameters for the dimensions of the aquarium and information about what each type of fish needs to survive. Students answer seven prompts that proceed through the aspects of the modeling process, and the prompts are scaffolded by the aspects of the modeling process. After the seven prompts are answered, students report their findings and more prompts are divided to help students provide a complete report.
- In Algebra 2, Module 2, Performance Task, students determine how to optimize Steven’s income from his business that specializes in computer application training and data entry support services using linear programming techniques. The performance task has six prompts that move students through different aspects of the modeling process, but students do not complete the modeling process on their own.
- In Algebra 2, Module 8, Ignite! Mathematical Modeling, students use a set of data to predict when the winning time for solving a Rubik’s cube will be less than 3 seconds. Students answer seven prompts that proceed through the aspects of the modeling process, and the prompts are scaffolded by the aspects of the modeling process. After the seven prompts are answered, students report their findings and more prompts are divided to help students provide a complete report.
- In Algebra 2, Module 10, Introduction, students interpret and report their findings. The materials provide some questions for students to ask themselves when doing a modeling problem, such as “What do you notice? What questions can you ask? What assumptions are you making?”, but these questions are not utilized with other modeling problems. Students pose questions about two different spinners and begin to formulate strategies for solving the questions they come up with about the spinners. Students do not define variables or compute the numerical answers to the questions they formulate (S-IC.1).
Indicator 1b
The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
Indicator 1b.i
The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.
The instructional materials reviewed for the Reveal Math Traditional meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers. The instructional materials spend a majority of the time on the WAPs, and the amount of time spent on the WAPs decreases across the courses of the series.
Examples of how the materials spend the majority of time on the WAPs include:
- In Algebra 1, Module 3, students represent functions in multiple ways, analyze graphs, and give the domain and range of graphs (F-IF). Throughout the first six lessons, students determine if given relations are functions, identify key features of functions, and determine the relationships between the different representations of the functions.
- In Algebra 1, Module 8, Lessons 4-6, students simplify expressions using the properties of exponents (N-RN.1) and apply those to operations with radical expressions. These lessons provide multiple opportunities for students to practice.
- In Geometry, the materials develop the relationships within and between similar triangles throughout Module 8 (G-SRT.B).
- In Algebra II, Module 2, Lesson 1, students write equations and inequalities that represent real world situations and solve them algebraically and by graphing (A-CED.1, 2).
Indicator 1b.ii
The materials, when used as designed, allow students to fully learn each standard.
The instructional materials reviewed for Reveal Math Traditional, when used as designed, meet expectations for letting students fully learn each non-plus standard. Overall, students would fully learn most of the non-plus standards when using the materials as designed.
The non-plus standards that would not be fully learned by students across the series include:
- A-SSE.4: Students do not derive the formula for the sum of a finite geometric series.
- F-TF.5: Students do not choose what trigonometric function to use as the trigonometric function is provided within the context of the problem.
- G-CO.8: Students examine triangle congruence, but they do not explain the criteria for triangle congruence on their own.
- G-SRT.1b: In Geometry, Module 8, Lesson 1, students complete one problem to verify the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
- S-CP.7: Students use the addition rule and find probabilities of events in Geometry, Module 12, Lesson 6. However, students do not interpret their answers in terms of the model.
Indicator 1c
The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
The instructional materials reviewed for the Reveal Math Traditional meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The instructional materials regularly use age-appropriate contexts, apply key takeaways from Grades 6-8, and vary the types of real numbers being used.
Examples of the materials using age-appropriate contexts include:
- In Algebra 1, Module 7 Assessment, students solve systems of equations in contexts that include: selling plastic and wood frames, building a pen for animals, different ages of people, and a kayak travelling on a stream.
- In Algebra 1, Module 11, Lesson 1, students interpret the graph of a jumping skateboarder.
- In Geometry, Module 1 Assessment, students create their own game on a basketball court and analyze different things about an animal shelter and a grooming service.
- In Geometry, Module 10, Lesson 1, students find the circumference of a traffic circle and a car rim.
- In Algebra 2, Module 2, Lesson 5, students write a system of equations that relates the difference between one-on-one and team games played in basketball.
- In Algebra 2, Module 4 Assessment, students create a polynomial function to model profit for a business.
- In Algebra 2, Module 9, Lesson 6, students solve rational equations to discuss Serena Williams’ winning percentages.
Examples of applying the key takeaways from Grades 6-8 include:
- In Algebra 1, Module 4, Lesson 2, students apply their understanding of slope and rate of change (8.EE.5b) to solve real-world problems. Students apply this understanding in Algebra 1, Module 4, Lesson 4 to transformations of linear functions (F-BF.3) and in Algebra 1, Module 5, Lesson 3 to lines of best fit (S-ID.6a).
- In Geometry, Module 3, students use relationships between lines and angles (8.G.5) to prove segment and angle relationships in Lessons 5 and 6 (G-CO.9).
- In Algebra 2, Module 3, students add and subtract complex numbers by combining like terms (8.EE.7b) and using the commutative property of addition (6.EE.3).
The materials vary the types of real numbers being used. Within the Learn sections, the majority of numbers used are integers. Within the practice sections and assessments, there are more non-integer problems and solutions. Examples of this include:
- In Algebra 1, Module 2, Lesson 6, the materials provide a variety of solution types for the proportional solutions. Most of the solutions are whole numbers, but there are a variety of decimal and integer solutions throughout the lesson.
- In Algebra 1, Module 11, Lesson 6, students solve many types of quadratic equations that have whole number, rational, and irrational solutions.
- The Geometry Module 2 assessment has decimal solutions to problems for surface area and volume problems in various contexts.
- In Geometry, Module 9, Lesson 4, students use both rational and irrational numbers to find the missing side lengths of right triangles.
- In Algebra 2, Module 5, Lesson 5, students find integer, irrational, and imaginary roots of polynomial functions.
Indicator 1d
The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.
The instructional materials reviewed for the Reveal Math Traditional partially meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. Lessons within units and individual courses build upon and connect to each other. However, the materials do not make several connections across the courses.
Within each course, “Coherence” indicates what students have learned previously, what they are currently learning, and what they will learn next. Examples of these connections within courses include:
- In Geometry, Module 5, Lesson 1, students solve problems using the triangle sum and exterior angle theorems (G-CO.10), which is connected to the previous learning of transformations and symmetries in Geometry, Module 4, Lesson 6 (G-CO.3). The materials extend this to the future learning of proving triangles congruent in Geometry, Module 5, Lesson 2 (G-SRT.5).
- In Algebra 2, Module 3, Lesson 1, students graph quadratic functions and identify key features of those graphs (A-CED.1). The materials connect this to previous learning in Algebra 2, Module 1, Lesson 7, of identifying and manipulating graphs of other types of functions (A-CED.1). This is also connected to the future learning of solving quadratic equations using graphs in Algebra 2, Module 3, Lesson 2 (A-CED.2, F-IF.4).
Examples of connections that are not made across courses include, but are not limited to:
- In Algebra 1, Module 2, students use proportional relationships to solve real-world problems. In Geometry, Module 8, Lessons 5 and 6, students use proportions in triangle relationships, and in Algebra 2, Module 8, Lesson 6, students use proportions in solving rational equations. There are no connections made for either the teacher or students as to how these lessons are connected.
- In Geometry, Module 9, students examine trigonometric ratios in right triangles. In Algebra 2, Module 11, students encounter trigonometric functions and the unit circle. There is no connection made between trigonometric ratios from Geometry and how they can be used with the unit circle and trigonometric functions.
- In Algebra 2, Module 3, Lesson 3, students have imaginary numbers as solutions to quadratic equations. The lesson states, “In your math studies so far, you have worked with real numbers. However, some equations, such as $$x^2 + x + 1 = 0$$ do not have real solutions.” There is not a connection for teachers or students to content from previous courses.
Indicator 1e
The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
The instructional materials reviewed for the Reveal Math Traditional meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards.
The instructional materials build on knowledge from Grades 6-8, and they explicitly identify standards from Grades 6-8 in the teacher materials throughout the series. Standards from Grades 6-8 are explicitly identified for many lessons in Vertical Alignment, and each module indicates prerequisite skills with “Are you Ready?”, which includes a bulleted list of skills not explicitly related to standards from Grades 6-8.
The following are examples of where the materials build on and explicitly identify standards from Grades 6-8:
- In Algebra 1, Module 4, Lesson 2, students “expand their understanding of and fluency with linear functions (first studied in Grade 8) to graphing linear functions by using a table and by using intercepts. They apply their understanding of slope and rate of change by solving real-world problems.” (8.EE.5,6)
- In Algebra 1, Module 8, Lesson 4, students extend their understanding of the properties of integer exponents (8.EE.1) as they encounter rational exponents.
- In Geometry, Module 9, Lesson 5, students solve problems using trigonometric ratios (G-SRT.6), which builds on their understanding of ratios (6.RP, 7.RP), similarity (8.G.4), and right triangles (8.G.B).
- In Algebra 2, Module 6, Lesson 4, students use their understanding of square roots and cube roots from Grade 8 (8.EE.2) to graph and solve radical equations (F-IF.7b).
Indicator 1f
The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.