## Alignment: Overall Summary

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series do not meet expectations for alignment to the MFAS. The instructional materials do not meet the expectations for focus and coherence in Gateway 1, and since the materials do not meet expectations in Gateway 1, they were not reviewed for rigor and the mathematical practices in Gateway 2 or usability in Gateway 3.

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## Gateway 1:

### Focus & Coherence

0
9
14
18
4
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
9
14
16
N/A
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

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## Gateway 3:

### Usability

0
21
30
36
N/A
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

### Criterion 1a - 1f

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).
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Criterion Rating Details

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series do not meet the expectations for focus and coherence in Gateway 1. The instructional materials partially include: the majority of time on the standards widely applicable as prerequisites (WAPs); engagement of students in mathematics at a level of sophistication appropriate to high school; connections in a single course and throughout the series; and explicit identification of, and building on, knowledge from Grades 6-8.

### 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.
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Indicator Rating Details

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series do not meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. The instructional materials omit standards across the courses of the series, and there are many instances where all aspects of standards are not addressed across the series.

Aspects of the following standards are not addressed across the courses of the series:

• N-RN.1.1: In Algebra 1, Semester A, 5.07, Learn A Closer Look: Rational Exponents, the definition of a rational exponent is given, but it is not derived from properties of integer exponents. In the first section, students review the properties of integer exponents, where all expressions contain either integers or variables. In the second section, students examine rational exponents, including examples of equivalent expressions written using a radical and a rational exponent, and there is one example which demonstrates how $$25^\frac{1}{2}$$ equals $$\sqrt{25}$$, after squaring both expressions. Students apply the properties to expressions containing rational exponents, but they do not explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents.
• A-REI.4.11: In Algebra 1, Semester B, 1.04, 3.02, and 4.08, students solve equations of the form f(x) = g(x) and solve systems of equations, including ones involving a linear and quadratic equation, with a table and by graphing. In Algebra 2, Semester B, 3.03, students solve additional systems of equations using a table and/or graphing, and the systems include rational, sine, constant, absolute value, logarithmic, and cubic functions. The materials do not explain, or have students explain, why the x-coordinate is the solution to f(x) = g(x).
• G-CO.1.2: In Geometry, Semester A ,1.06, Reflections, Rotations, and Translations, include transformations in the plane, but there is no evidence that tools such as transparencies or software are being used to represent the transformations. Definitions of isometric transformations as preserving distance and angle are given. Dilations are defined as not isometric, but the materials do not compare transformations that preserve distance and angle to those that do not. Lesson 1.10 includes rules that map points under transformations, but the materials do not describe the transformations as functions.
• G-CO.1.3: In Geometry, Semester A, 1.07 and 1.13, the rotational and reflectional symmetries of regular polygons are described, but rotations and reflections of rectangles, parallelograms, and trapezoids do not appear in the materials.
• G-CO.1.4: In Geometry, Semester A, 1.06, definitions of rotations, reflections, and translations are given in terms of angles and line segments, but no connections are made to circles, perpendicular lines, or parallel lines.
• G-CO.2.7: In Geometry, Semester A 3.05, the materials state that if triangles are congruent then their corresponding parts will be congruent, but the converse is not addressed. In lesson 3.04, students use side and angle congruence to determine if two figures are congruent, but the use of the definition of congruence in terms of rigid motions is not shown. Lessons 3.01 and 3.07 contain work related to congruent figures, but the materials do not provide the definition of congruence in terms of rigid motions.
• G-CO.4.13: In Geometry, Semester A, 3.10 and 3.11, students construct an equilateral triangle and a square, but the constructions do not result in the shapes being inscribed in a circle.
• G-SRT.1.1a: In Geometry, Semester A, 1.14, 6.01, and 6.02, students work with and construct dilations, however, the materials do not provide an explanation, or expect students to explore, that a dilation takes a line not passing through the dilation center to a parallel line and leaves a line passing through the center unchanged.
• G-SRT.1.3: In Geometry, Semester B, 1.02, the lesson provides an explanation of the AA criterion based on the interior angles of a triangle summing to 180 degrees. The lesson does not include the properties of similarity transformations as part of establishing the AA criterion.
• G-SRT.3.6: In Geometry, Semester B, 4.02-4.04 and 4.09, students use trigonometric ratios to find missing angles and side lengths in real-world and mathematical contexts. However, the materials do not connect similarity of right triangles to trigonometric ratios as properties of the acute angles.
• G-C.2.5: In Geometry, Semester B, 3.13, students use an arc length being proportional to the radius to find missing arc lengths and angle measurements, and they convert between degree and radian measures. In Lesson 3.14, students use the formula for the area of a sector to solve problems. Both the arc length and area of a sector formulas are derived, but the materials do not use similarity in the derivation of either formula.
• G-GPE.1.1: In Geometry, Semester B, 5.03, students examine the equation of a circle as it is derived using the distance formula. The materials do not explain why the distance formula is used to derive the equation of a circle, and there is no connection made to the Pythagorean Theorem. In Lesson 5.05, students complete the square to find the center and radius of a circle given by an equation.
• S-ID.1.3: In Algebra 1, Semester B, 5.07, the materials provide four examples where the medians of two box plots are compared, but none of the examples include interpretation of the effects of extreme data points. In 5.09, students identify outliers in a data set, but neither the materials nor students explain the effects of extreme data points when comparing two data sets.
• S-IC.2.6: In Algebra 2, Semester B, 7.01, students determine the information they want to gather and develop a plan for sampling a population. In Lesson 7.08, Learn A Closer Look: Evaluate Reports, students look at evaluation criteria such as Bias in Questioning and Correlation vs. Causation, and in Learn Mathcast; Evaluate Reports and Sampling Techniques, reports are evaluated by looking at claims and bias. The materials do not evaluate reports based on the examination of data.
• S-CP.1.2: In Algebra 2, Semester B, 5.03, the materials state that if two events are independent, the probability of the events occurring together can be calculated by multiplying the probabilities of each event occurring by itself. However, the materials do not state that if the probability of two events occurring together is equal to the product of the probabilities of each event occurring by itself then the two events are independent.
• S-CP.2.8:  In Algebra 2, Semester B, 5.03 and 5.04, the multiplication rule is used to determine probabilities of dependent events and if two events are independent, but the materials do not apply the general Multiplication Rule in a uniform probability model or interpret answers in terms of the model.
• S-MD.1.3: In Algebra 2, Semester B, 6.02, students examine examples of probability distributions and determine that the sum of the probabilities for each distribution is 1, and students represent the discrete probability distributions with frequency tables, probability tables, and bar graphs. In Algebra 2, Semester B, 6.04, binomial distributions are addressed, but no evidence of finding the expected value of a probability distribution was found in either lesson.

The following standards are not addressed in the series:

• N-CN.2.4-6
• N-VM.1.1-3
• N-VM.2.4-5
• N-VM.3.6-12
• A-APR.3.5
• A-REI.3.8-9
• F-TF.1.4
• F-TF.3.9
• G-C.1.4
• G-GPE.1.3
• S-CP.2.9
• S-MD.1.2,4
• S-MD.2.5-7

### Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
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Indicator Rating Details

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series do not meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. Overall, while there are opportunities for students to engage in some parts of the modeling process, students do not use the full modeling process when working with many of the modeling standards, and students have few, or no, opportunities to define problems, assign variables, modify their model (if needed), and report on results.

Examples of standards not addressed with the modeling process include:

• A-SSE.2.3: In Algebra 1, Semester B, 4.04, students convert between forms of a quadratic equation and interpret the parts of the new form, but students do not define the problem or validate. In Algebra 2, Semester A, 3.07, students are provided the dimensions of a football stadium and shown a solution pathway for the problem, which mitigates defining the problem and validating a solution.
• A-SSE.2.4: In Algebra 2, Semester B, 4.06, students write and solve equations for the sum of a finite geometric series, but they do not validate or report their results.
• A-CED.1.1: Students write and solve equations and inequalities, but they do not engage in the full modeling process. In Algebra 1, Semester A, 5.09, the real-world example includes writing and solving an equation, but students do not engage in any other aspects of the modeling process.
• A-CED.1.3: In Algebra 1, Semester A, 3.07, students write a system of equations from a context and find the solution to the system, but they do not interpret, validate, or report the results. In Algebra 2, Semester A, 1.10, the materials mention aspects of the modeling process: "Use the problem solving strategies you have learned to identify the known and unknown information, come up with a strategy, create a model (in this case, a linear programming model), solve the model, and then check your work." In Practice Apply It: Applications of Linear Programming, students are provided the constraints and do not interpret, validate, or report on their solution.
• F-IF.2.4: In Algebra 1, Semester A, 4.08, students interpret slope and intercepts. Throughout the examples, the materials display notes to help students with the interpretation of slope and intercepts. For problems in this lesson, the variables are defined for students, and students do not validate or report results.
• F-IF.2.5: In Algebra 1, Semester A, 4.09, equations and variables are provided for students. Students identify appropriate domains, but they do not engage in other aspects of the modeling process.
• F-IF.2.6: There are three lessons that address this standard (Algebra 1, Semester A, 6.06; Algebra 1, Semester B, 4.07; and Algebra 2, Semester B, 3.06). In these lessons, students use a procedure to calculate the average rate of change for the functions. In some problems, students interpret meaning in relation to the context, but other aspects of the modeling process are not present.
• F-BF.1.1a,b: In Algebra 1, Semester A, 7.04, students write explicit and recursive rules for geometric sequences, but they do not interpret, validate or report their results. In Algebra 1, Semester B, 4.04, students combine functions with arithmetic operations and interpret the meaning of the combined functions, but students do not validate or report their solutions. For example, functions 1 and 2 represent the heights to which different balls are thrown. The difference of the functions is the difference in heights at certain values of the domain. This is defined for students, and they do not validate or report results.
• F-BF.1.2: In Algebra 1, Semester A, 7.03, students complete a real-world problem about the number of seats per row in a movie theater growing as the row number is farther away from the screen. Students write an equation and solve for the number of seats in a given row. Students do not define the variables or validate and report the results. In practice problems, students choose the correct rule from a list.
• F-LE.1.1: No opportunities to engage in the modeling process were found for this standard. In general, students identify what function type is being represented based on a given equation, description, graph, or table.
• F-LE.1.2: In Algebra 2, Semester B, 4.02, Apply It, students write an explicit rule for a real-world arithmetic sequence and determine a number in the sequence for a given value. Students do not interpret or validate their solution as the length of time the patient will walk on the treadmill during the 15th week. In Algebra 1, Semester A, 7.07, Practice Apply It: Model Linear Relationships, students are guided through creating a linear function for the given data, and students do not interpret, validate and revise, or report their findings.
• F-LE.1.4: In Algebra 2, Semester A, 6.08, Apply It, students work within real-world contexts, but students solve for a specific value of the variable. Students interpret and identify the solution, but they do not define the problem or variables or validate their findings.
• F-LE.2.5: In Algebra 1, Semester A, 7.06, students interpret slope and y-intercept for linear relationships and initial values and r for exponential relationships, but the equations are provided for the students. Students do not validate their findings.
• G-GPE.2.7: In Geometry, Semester A, 6.01, students participate in a discussion forum where they are given a list of non-rectangular shaped states and decide on a method for finding the area in square miles. Students are directed to break the state into common shapes and to place them on a grid. Students post two replies to student solutions which include verifying the accuracy of the student solutions using the given measurements. Students do not define the problem or formulate a solution method.
• S-ID.2.6: In Algebra 1, Semester B, 6.08, students are shown examples with plotted data, and in Algebra 1, Semester B, 6.10, students are provided with the questions and create the regression lines. In Algebra 1, A Reference Guide, the materials compare quadratic and exponential models for a data set, but students do not formulate any comparisons. Also, in A Reference Guide, the materials demonstrate how residual plots can be used to determine if a line is a best fit for a set of data, but students do not revise models on their own based on residual plots.
• S-ID.3.9: In Algebra 1, Semester B, 6.07, the materials provide examples that highlight causation and lurking variables, but students do not formulate, interpret, or revise relationships between variables.
• S-IC.1.2: In Algebra 2, Semester B, 7.06, the materials provide a simulation which can be used to evaluate the fairness of a data-generating process, but students do not formulate a simulation. The materials also provide an analysis of a sample in order to evaluate an inference about a population, but students do not analyze a sample and make inferences as part of the modeling process.
• S-IC.2.4: In Algebra 2, Semester B, 7.07, students complete simulations which are provided within the materials, but they do not formulate simulations on their own.

### 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.
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Indicator Rating Details

When used as designed, the instructional materials reviewed for the FuelEd Florida Summit Math Traditional series partially meet expectations for spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs and careers. The instructional materials for the series do not spend a majority of time on the WAPs, and some of the remaining materials address prerequisite or additional topics that are distracting.

The publisher-provided table of contents and alignment information indicate 525 lessons or sections across the series. These include Discussion, Your Choice, Review and Test. Most discussions are related to the standards, and Your Choice provides time for students to make up work, move ahead in the materials, or to review previous work. The materials indicate that less than half of the lessons or sections address the WAPS.

Similarly, in examining each course of the series independendent of the publisher-provided alignment information, evidence was found that the majority of the time is not spent on the WAP standards. Some of the materials address prerequisite topics that are not a part of the standards for high school mathematics, which are distracting in relation to the WAPs. Examples of this include the following:

• In Algebra 1, Semester A, 1.04, the lesson addresses understanding the process of solving an equation or inequality as answering a question (6.EE.2.5), which is noted in the lesson Introduction.
• In Algebra 1, Semester A, Unit 2, students spend most of the unit solving linear equations (8.EE.3.7) and inequalities (7.EE.2.4b) or applications of them.
• In Geometry, Semester B, 2.02 addresses finding the circumference and area of circles (7.G.2.4), and 2.06 addresses finding the volume of prisms and cylinders (8.G.3.9).

### Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.
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Indicator Rating Details

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series do not meet expectations for allowing students to fully learn each standard when used as designed. The materials do not enable students to fully learn the following standards.

• N-RN.2.3: In Algebra 1, Semester A, 5.05, the sum and product of two rational numbers is described along with examples of each. Student explanations involve choosing from a drop down menu, which contain two choices, as part of the worked examples. In Algebra 2, Semester A, 2.02 and 2.03, the materials describe and give examples of combining irrational numbers. While students complete the described computations, students do not explain why the sums and products of rational and irrational numbers produce the type of number as described in the standard.
• N-Q.1.1: In Algebra 1, Semester A, 1.09 addresses unit conversions, and while some tasks involve multiple unit conversions, students do not use units to guide the solution of multi-step problems. In Lesson 4.08, students interpret slope and x- and y-intercepts of linear graphs and formulas based on the units given in the problems. However, students do not choose and interpret units consistently in formulas or the scale in graphs and data displays.
• N-CN.1.3: In Algebra 2, Semester A, 2.07, the materials address complex conjugates and provide three worked examples of the division of complex numbers using conjugates, but the students do not complete practice problems for this standard.
• A-SSE.1.1a In Algebra 1, Semester A, 1.10, students interpret parts of an expression by choosing an interpretation from a list or filling in a missing term based on a provided interpretation. In other lessons, students interpret expressions, but not parts of an expression.
• A-SSE.2.3b: In Algebra 2, Semester A, 3.08, students complete the square to solve quadratic equations but not to identify maximum or minimum values. In Algebra 2, Semester B, 2.06, students complete the square to identify a vertex in one question, but in three other questions, students either do not identify a maximum or minimum value or complete the square on their own.
• A-SSE.2.4: In Algebra 2, Semester B, 4.06, students use the formula for the sum of a finite geometric series to solve problems, but students do not derive the formula for the sum of a finite geometric series.
• A-APR.2.3: In Algebra 2, Semester A, 4.08, students graph the x- and y-intercepts of polynomial functions and answer questions about the end behavior of the functions. Students graph the intercepts of the functions but do not construct rough graphs of the polynomial function.
• A-APR.3.4: In Algebra 2, Semester A 3.06, students prove a polynomial identity that is presented in a drag-and-drop format, but students do not use the identity to describe a numerical relationship. Additionally, there are no proofs in the assessment for the lesson.
• A-REI.1.2: In Algebra 2, Semester A, 5.02, students solve radical equations, identifying any extraneous solutions, but do not show how they arise. In Algebra 2, Semester A, 5.03 and 5.09, students solve rational equations and identify extraneous solutions but do not give examples of how they may arise.
• A-REI.3.5: In Algebra 1, Semester B, 1.07, there are examples which use properties to explain why and how equations can be added or subtracted to solve a system, and students solve systems by elimination using only addition or subtraction. In 1.08, students see explanations of using the multiplication property of equality for creating equivalent equations and solving systems of equations by elimination. Students provide properties to justify the steps in solving a system of equations and solve systems using elimination with multiplication. Students, however, do not prove, or examine a proof, that replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
• A-REI.4.12: In Algebra 1, Semester A, Lesson 3.07, there is one problem where students practice graphing the solution for a system of inequalities. In all other problems in Algebra 1, Semester A, 3.06 and 3.07, and Algebra 2, Semester A, 1.01 and 1.07-1.09, students match a graph to an inequality or system of inequalities and do not graph the solutions themselves.
• F-IF.3.7: This standard is addressed in several lessons across Algebra 1 and Algebra 2, but students do not graph and show key features of the graphs by hand for the different types of functions. Students select graphs, fill in tables, and describe transformations. The graphing technology embedded in the materials allows for plotting points of the functions, but students do not sketch complete graphs.
• F-IF.3.8b: In Algebra 2, Semester A, 6.02, students rewrite expressions using the properties of exponents without a context and identify the appropriate equation for a context, but students do not interpret expressions for an exponential function.
• F-LE.1.1a: In Algebra 1, Semester A, 6.07, students complete examples comparing linear and exponential functions and the patterns of differences that are found in tables of values for linear and exponential functions. Based on this information, students decide whether a function is linear, exponential, or neither in Learn A Closer Look: Identify a Type from a Table. Students do not prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
• F-LE.1.1b: In Algebra 1, Semester A, 6.07, students calculate the constant rate of change in linear situations and recognize the difference between linear and exponential relationships. The materials provide examples of situations where a quantity changes at a constant rate per unit relative to another, but students do not recognize situations where that will happen.
• F-TF.1.2: In Algebra 2, Semester A, 7.06, the materials state that angles can wrap around the unit circle multiple times in either direction. In a few problems, students determine the reference angle determined by the terminal side of an angle and subsequently find a specific trigonometric value associated with that reference angle. In Algebra 2, Semester B, 1.02, students read, "Since an angle may wrap around the unit circle more than once and may also rotate in a negative direction, the graph of a sinusoidal function continues without end. So y=sin and cos have a domain of all real numbers, or (−∞,∞) using interval notation." Students do not provide their own explanation using the unit circle as justification of the extension of trigonometric functions to all real numbers.
• F-TF.2.6: In Algebra 2, Semester A, 7.10, the materials include an explanation for restricting the domain of a trigonometric function so that it is one-to-one in order to have an inverse that is also a function, but students do not demonstrate an understanding of  restricting a trigonometric function to a domain on which it is strictly increasing or strictly decreasing allows its inverse to be constructed.
• G-CO.1.5: In Geometry, Semester A, 1.11, students work with geometry software to translate points, and there is one problem where students specify a sequence of transformations that carry a given figure onto another, On Your Own: Practice Question 5.
• G-CO.2.6: In Geometry, Semester A, 3.12, students do not transform figures or predict the effect of a given rigid motion. In Learn: Real World Math, students predict the rigid motions needed to move a puzzle piece into its proper position, but there is no other evidence found for this standard.
• G-CO.3.9: In Geometry, Semester A, 5.02, the materials state, "A postulate is a mathematical statement that is assumed to be true, so the corresponding angles postulate can be assumed to be true. It can be used to prove the other three theorems." In Geometry, Semester A, 3.03, students use the theorems, but students prove vertical angles are congruent by filling in the reasons in a proof. Students also fill in reasons for proofs related to transversals and perpendicular bisectors.
• G-SRT.2.4: In Geometry, Semester B, 1.04, the proof of the Triangle Proportionality Theorem is completed in Learn On Your Own. Students fill in statements and reasons in separate problems, but they do not prove theorems about triangles on their own.
• G-SRT.3.7: In Geometry, Semester B, 4.05, students use the relationship between the sine and cosine of complementary angles to determine missing ratios and solve equations involving angles in Learn and Practice, but students do not provide explanations of this relationship or how to use it to solve problems.
• G-GPE.2.4: In Geometry, Semester A, 4.05, students use the slope criteria and coordinates to determine if lines are parallel or perpendicular, and in 4.06, students use coordinates of vertices to determine what shape is formed. All questions are in multiple-choice or drag-and-drop format, and students do not complete an entire proof independently.
• G-GPE.2.5: In Geometry, Semester A, 4.05 and 4.06, students use the slope criteria for parallel and perpendicular lines to solve geometric problems, but students do not prove the slope criteria.
• S-ID.2: In Algebra 1, Semester B, 5.06, there are examples comparing data sets, and students complete two practice problems comparing range and IQR of two data sets. Students select missing word(s) or choose from a drop down box to complete the comparisons. In Algebra 1, Semester B, 5.07, students complete one example showing a comparison of the medians of two box plots, and in 5.08, students compare the measures of center between two data sets in one problem.
• S-ID.1.4 In Algebra 2, Semester B, 6.12, students use a Standard Normal Table to estimate population percentages, but students do not use technology, such as calculators or spreadsheets, to estimate areas under the normal curve.
• S-ID.2.6a: In Algebra 1, Semester B, 6.12, students decide on the best model (linear, quadratic, or exponential) for a scatterplot. Students find r values for tabular data and determine whether a linear, quadratic, or exponential function fits best by visual inspection. Students, however, do not consider the context when determining whether a certain function is a best fit for the data.
• S-CP.1.4: In Algebra 2, Semester B, 5.01 and 5.04, students interpret two-way frequency tables, but there are no instances where students constructed them.
• S-CP.1.5: In Algebra 2, Semester B, 5.01 and 5.04, students examine conditional probability and independence, but no instances are found where students explain the concepts of conditional probability and independence in everyday language and everyday situations.

### Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
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Indicator Rating Details

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series partially meet the expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The instructional materials regularly use age-appropriate contexts and apply key takeaways from Grades 6-8, yet the materials do not vary the types of real numbers being used.

Each A Closer Look: starts by asking “Remember This” and sharing content from prior grades. This content often comes from Grades 6-8 but is not identified as such. Examples of applying the key takeaways from Grades 6-8 include the following:

• In Algebra 1, Semester B, 4.02, the lesson addresses standard form of a quadratic function, and Remember This reminds students about two negatives in front of a number. “The expression -(-4) is read as the opposite of negative 4, and the opposite of negative 4 is positive 4…”
• In Geometry, Semester A, 3.04, the lesson addresses corresponding parts of congruent polygons, and Remember This includes, “A polygon is a closed figure made up of line segments. For two polygons to be congruent, they must have the same size and shape but not necessarily the same orientation. If the two polygons are congruent, it means that their corresponding side lengths and angle measures are equal.”
• In Geometry, Semester A, 6.05, the lesson addresses similar polygons. The first A Closer Look includes, “Some characteristics between congruent figures and similar figures are alike and some are different. Both kinds of figures contain equivalent corresponding angles. However, congruent figures contain equivalent corresponding sides, and similar figures contain proportional corresponding side lengths.”
• In Algebra 2, Semester A, 5.06, the lesson addresses adding and subtracting rational expressions. Remember This includes, “like terms are terms that have the same variable(s) with the same exponents.”

Age-appropriate contexts are found throughout the series, and most lessons have Apply It, which includes a real-world problem with age-appropriate context. Examples of this include:

• In Algebra 1, Semester A, 2.05, students complete a problem about distance, time, and speed of trains with people (“you and a friend”) traveling on vacation.
• In Algebra 1, Semester B, 4.02, a quadratic function represents the profit for sales of a particular stuffed animal which students use to answer questions.
• In Geometry, Semester B, 2.02, students find the circumference of a ferris wheel at a fair.
• In Algebra 2, Semester A, 6.02, a scientist working at a soybean farm analyzing exponential growth of aphids provides the context for a problem.
• In Algebra 2, Semester B, 5.03, students determine the probability of certain characteristics based on genetic make-up of parents.

Lessons across the series were reviewed for the types of numbers used within problems and as final solutions. While there were lessons which contained various rational numbers, common fractions were often used, and decimals were typically tenths or hundredths. Examples of this include:

• In Algebra 1, Semester A, 2.04, the lesson addresses solving equations with variables on both sides of the equation. There are two problems that have an answer that is not an integer.
• In Algebra 1, Semester A, 6.06, this lesson addresses average rate of change, and most of the numbers are positive, whole numbers. One example answer is $$63.\overline{3}$$, and it is rounded to 63. The real-world math problem includes 1.875, and there are a few decimals, in tenths, in the worked examples and practice problems.
• In Algebra 1, Semester B, 1.09, there are problems that involve decimals, which are related to money and percents.
• In Geometry, Semester A, 4.02, there are a few decimals in the perimeter and area problems. There were two problems that had a decimal to the hundredths place, but all other decimals were in tenths. There were no fractions in the problems or the examples.
• In Geometry, Semester A, 6.03, there are a few common fractions and decimals, in tenths, within the scale factor problems.
• In Geometry, Semester B, 2.02, the only decimal not written in tenths is $$\pi$$. No fractions were evident, and most of the numbers are integers.
• In Algebra 2, Semester A, 2.04, there is one section and a few problems that involve fractional exponents, but the majority of the numbers used are integers and natural numbers.
• In Algebra 2, Semester B, 2.03, some of the solutions (when making tables or finding points on a graph) are fractions, and there are few decimals throughout the lesson.

### 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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series partially meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series, where appropriate and where required by the standards.

Lessons within units build upon the work of previous lessons within the Algebra 1, Geometry, and Algebra 2 courses respectively. Some connections are made within Quick Check and Remember This. However, the materials miss several connections within and across the courses of the series.

The following are examples of connections not made within and across courses:

• In Geometry, Semester A, 3.07 and 3.08, the criteria for triangle congruence (ASA, SAS, and SSS) are explained and used to determine if two triangles are congruent, but the materials do not provide, or expect from students, an explanation of how the triangle congruence criteria are connected to the definition of congruence in terms of rigid motions.
• In Geometry, Semester A, 6.05 and 6.06 include reminders about identifying corresponding parts, Learn: Remember This, and a description of the similarity of two images based on dilation, "Because images created by dilations are proportional to their pre-images, two polygons are similar if and only if one is congruent to the image of the other by a dilation" (Reference Guide). Students, however, use the proportionality of the sides to determine a possible scale factor and check the scale factor for all sides to verify similarity. Lesson 6.06 mentions dilation and scale factors, but students use proportional ratios rather than referencing scale factor and dilation or similarity transformation. In Geometry, Semester B, 4.09 does not connect to similarity transformations from Semester A.
• In Geometry, Semester A, 1.10 and 1.11 use similar vocabulary to what is used in Algebra 1, specifically in regard to functions. However, the materials do not connect translations of geometric figures to translations of algebraic functions, such as quadratic functions, through the same notation, (x+h, y+k). Additionally, in Algebra 2, the materials do not connect geometric transformations with the transformation of logarithmic and trigonometric functions.
• In Algebra 2, Semester B, 2.03, the materials state that rational functions include polynomial expressions in the numerator and denominator. However, the materials do not connect roots for the numerator and denominator to important features, such as zeros and asymptotes, of the rational function.

The following are examples of connections made within and across courses:

• In Algebra 1, Semester B, 1.02, Quick Check, includes graphing linear equations with technology, and Remember This reviews standard form of a linear equation and x- and y-intercepts. Another Remember This addresses slope-intercept form of a linear equation, and students make connections as they graph systems of linear equations.
• In Algebra 2, Semester A, 5.09, Quick Check, includes solving linear equations with variables on both sides, and this is connected to several Remember This sections that include solving rational equations with possible extraneous solutions, using the least common denominator to solve rational equations, and solving formulas in the the form of a rational equation for specific variables.
• In Algebra 2, Semester B, 4.02, the materials connect sequences to functions (over the set of positive integers) from Algebra 1 by stating “Arithmetic sequences are actually discrete linear functions that consist of only the points.” Also, in 4.03, the materials state, “Geometric sequences are discrete exponential functions that include only points.”

### Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the FuelEd Florida Summit Math Traditional series partially meet the expectations for explicitly identifying and building on knowledge from Grades 6-8 to the high school standards.

The materials do not identify standards from Grades 6-8 in the Teacher Editions or Reference Guides. For all courses, each semester begins with a Readiness Checkpoint Assessment, which does identify standards aligned to the assessment, but the alignment of standards is not to individual items. Each of the readiness assessments indicate standards from Grades 6-8, except for the Algebra 2, Semester B assessment which identifies high school standards. For each assessment, there is Standards and Objectives Proficiency, which describes how well students perform for each of the standards identified on the readiness assessment. No guidance is provided relating assessed standards from Grades 6-8 to the lessons within the instructional materials.

At the beginning of most sections in Learn: A Closer Look (Remember This), a prerequisite skill or concept is revisited, and this information reminds students of prior knowledge. However, standards from Grades K-8 are not explicitly identified, and there is no specific description of how these concepts connect to the high school standards, if there is a connection. Examples of this include:

• In Algebra 1, Semester A, 1.02, the students are reminded that the fraction ⅗ means 3 divided by 5 (5.NF.2.3), which equals 0.6, and this is used to simplify numerical expressions, including order of operations (6.EE.1.1). There is no connection to high school standards.
• In Algebra 1, Semester A, 3.02, students are reminded how to plot an ordered pair on a coordinate plane (5.G.1.1 and 6.NS.3.6c) in preparation for plotting the solutions for the graph of an equation in two variables (A.REI.4.10).
• In Geometry, Semester A, 5.02, students review the definition of an angle (4.G.1.1) in preparation for exploring angle properties of parallel lines (8.G.1.5). There is no connection to high school standards.
• In Geometry, Semester B, 2.09, students review terminology related to circles and the area formula for a circle (7.G.2.4), but there is no explicit connection to creating an informal argument for finding the area or volume of objects (G-GMD.1.1).

### 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.
Narrative Evidence Only
+
-
Indicator Rating Details

During the review of the FuelEd Florida Summit Math Traditional series, the mathematics standards for Florida did not identify plus (+) standards. All mathematics standards for Florida are considered in indicators 1ai through 1e for this series.

## Rigor & Mathematical Practices

#### Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

### Criterion 2a - 2d

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.

### Indicator 2a

Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
N/A

### Indicator 2b

Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
N/A

### Indicator 2c

Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.
N/A

### Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.
N/A

### Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

### Indicator 2e

The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

### Indicator 2f

The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

### Indicator 2g

The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

### Indicator 2h

The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

## Usability

#### Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

### Indicator 3c

There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
N/A

### Indicator 3d

Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

### Indicator 3e

The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

### Indicator 3h

Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.
N/A

### Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
N/A

### Indicator 3j

Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

### Indicator 3k

Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
N/A

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
N/A

### Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
N/A

### Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

### Indicator 3p

Materials offer ongoing assessments:
N/A

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

### Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

### Indicator 3q

Materials encourage students to monitor their own progress.
N/A

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

### Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
N/A

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

### Indicator 3u

Materials provide support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

### Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
N/A

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
N/A

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

### Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

### Indicator 3ac

Materials can be easily customized for individual learners.
N/A

### Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
N/A

### Indicator 3ac.ii

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A
abc123

Report Published Date: 2019/07/15

Report Edition: 2018

## Math High School Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.