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

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.

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 x and cos x 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.