High School - Gateway 1
Back to High School Overview
Note on review tool versions
See the series overview page to confirm the review tool version used to create this report.
- Our current review tool version is 2.0. Learn more
- Reports conducted using earlier review tools (v1.0 and v1.5) contain valuable insights but may not fully align with our current instructional priorities. Read our guide to using earlier reports and review tools
Loading navigation...
Focus & Coherence
Gateway 1 - Partially Meets Expectations | 66% |
|---|---|
Criterion 1.1: Focus & Coherence | 12 / 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 the Glencoe Traditional series partially meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; spending the majority of time on content widely applicable as prerequisites; and allowing students to fully learn each standard. The materials partially meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school and making meaningful connections in a single course and throughout the series. The materials do not meet expectations for attending to the full intent of the modeling process and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards.
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 the Glencoe Traditional series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students.
The materials attend to the full intent of the following standards:
- N-RN.3: In Algebra 1, Extend 1-4, students complete a table by determining the sum and product of each set of rational numbers. Students use the table to prove that the set of rational numbers is closed under addition and multiplication. In Algebra 1, Extend 7-4 states that “a conjecture can be made that the sum or product of a nonzero rational number and irrational number is an irrational number.” Also in Extend 7-4, the materials provide proofs for a product of a nonzero rational number and an irrational number that is irrational and the sum of a rational number and an irrational number that is irrational.
- A-REI.4a: In Algebra 1, Lesson 9-5, students write and solve quadratic functions in vertex form by completing the square. In Algebra 1, Lesson 9-6, the derivation of the Quadratic Formula by completing the square is provided within the materials. In the Algebra 1, Interactive Student Guide (ISG), Solving by Using the Quadratic Formula, students follow steps to derive the Quadratic Formula by completing the square.
- F-IF.4: In Algebra 1, Lesson 1-8, students interpret intercepts of the graph, symmetry, relative extrema, and end behavior from graphs of functions. Students estimate where the function is increasing, decreasing, positive, and negative. In Algebra 1, Lesson 9-1, students determine maximum or minimum values of quadratic equations. In Algebra 2, Lesson 2-2, students examine a table of values depicting the change in height of a kicked football, describe symmetry in the graph of the table, and interpret what the symmetry implies about the ball. In Algebra 2, Lesson 2-3, students estimate the relative maxima and minima using a table of values. In Algebra 2, Lesson 9-5, students find the amplitude and period of trigonometric functions and graph the functions.
- F-IF.7b: In Algebra 1, Lesson 3-7, students graph step functions and piecewise-defined functions. In Algebra 1, Lesson 3-8, students graph absolute value functions. In Algebra 2, Lesson 2-5, students graph step functions, piecewise-defined functions, and absolute value functions. In Algebra 2, Lesson 5-4, students graph square root functions. In Algebra 2, Lesson 5-5, students graph cube root functions.
- G-CO.12: In Geometry, Lessons 1-2, 1-3, and 1-4, students work with the definition of constructions to copy a segment using a compass, construct a segment bisector, copy an angle, and construct an angle bisector using a straightedge and compass. In Geometry, Extend 1-5, students follow instructions to construct “a line perpendicular to a given line through a point on the line, or through a point not on the line.” Students use constructions to observe similarities between two constructions. Students also compare perpendicular bisector constructions to segment bisector constructions. In Geometry, Explore 2-7, students use dynamic geometric software to construct parallel lines and a transversal to explore angles. In Geometry, Lesson 2-9, the instructions for constructing parallel lines through a point not on the line is provided within the materials. In Geometry, Extend 3-5, students explore constructions of parallel lines and perpendicular bisectors using a reflective device.
- G-SRT.5: In Geometry, Lesson 4-2, students prove triangles are congruent using two-column proofs and students calculate missing values in congruent figures. In Geometry, Lessons 4-3 and 4-4, students prove triangles are congruent using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side congruence criteria, and students calculate values using congruent triangles. In Geometry, Lesson 4-5, students write two-column proofs to prove right triangles are congruent. In Geometry, Lesson 7-3, students prove triangles are similar using the Angle-Angle Similarity Criteria and students identify triangles as similar or not similar. If the triangles are similar, students calculate missing measures within each problem. In Geometry, Lesson 7-4, students prove triangles similar using Side-Side-Side or Side-Angle-Side similarity criteria and students use similar triangles to solve real-world scenarios.
- S-ID.6a: In Algebra 1, Lesson 4-4, students create scatter plots to determine a relationship between the variables in a set of data and draw a line of best fit to create an equation in slope-intercept form best representing the data. In Algebra 1, Lesson 4-6, students write regression equations to represent data and use the equations to make estimations.
The materials do not attend to the full intent of the following standards:
- F-LE.3: In Algebra 1, Extend 9-8, students determine if a table of values represents a linear, quadratic, or exponential regression equation. Students are given instructions on how to use a graphing calculator to determine the regression equations. Students are not provided an opportunity to observe that a quantity increasing exponentially will eventually exceed a quantity increasing linearly or quadratically.
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 Glencoe Traditional series do not meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The instructional materials do not include some aspects of the modeling process across the series and students do not complete the entire modeling cycle independently due to excessive scaffolding. While aspects of the modeling process are present within the series, students do not make assumptions or develop their own solution strategies. Students analyze application problems and real-world scenarios, but the variables, parameters, units, and/or equations are frequently identified within the problems. Examples of students not completing the entire modeling cycle include:
- In Algebra 1, Chapter 1 Project, Want to be Your Own Boss, students develop a business plan as an entrepreneur. Students research challenges and factors involved in creating a business. Students write expressions representing rent, salary per employee, and other expenses. Students do not formulate their own variables as the materials state, “in terms of months m, employees x, or both months and employees.” Students also write expressions representing operating costs to evaluate costs for months with employees (A-CED.1). After the business plan is complete, students evaluate peer business reports to determine if the plans are valid based on the guidelines given within the rubric and description of the plan. Finally, students report, using presentation software, their business plans to their peers.
- In the Geometry Interactive Student Guide (ISG), Spherical Geometry, students use a diagram with approximate dimensions of a liquid propane tank containing five gallons of propane when full. Students identify a solid that models the tank in order to use the formula of the solid to calculate volume. The materials state, “Let h represent the height of propane left in the tank at any time and g represent the gallons of propane remaining. If the ratio of h to 14 is always equal to the ratio of g to 5, express h in terms of g” (A-CED.4). Students do not formulate variables independently or make assumptions about the problem. A second diagram of the fuel gauge showing the amount of propane in the tank is given. Students express the angle the pointer makes with the empty marker in terms of the volume of the fuel in the tank, g, and the height of the fuel in the tank, h (G-GMD.3, G-MG.1). Students validate the reasonableness of the answer and compute whether or not there is enough propane for a cookout.
- In the Algebra 2 ISG, Performance Task, A Complicated Greeting, students use technology to sketch a graph of the function $$p(t)=[\frac{-152}{65}\vert t-65 \vert+152]sin(\frac{9\pi}{130}t)+152$$. Students determine the maximum height of the Bungee Drop and write a function for the vertical height of a Ferris wheel with a radius of 150 feet and the lowest point at 4 feet. Students do not formulate variables as the materials state, “Write a function for the vertical height h of a point on the wheel at a certain time t such that it starts at a height of 4 feet.” Students calculate the number of times the two rides will reach the same height during three minutes of riding. Students do not make assumptions but are instructed to assume the rides are continuous. Students also do not validate or report their findings (F-TF.5).
- In Algebra 2, Lesson 8-6, the materials state, “Find a set of real-world data that appears to be normally distributed.” Students use the data to calculate the range of values associated with the distributions. Students do not make assumptions about the data but are told it must be normally distributed. Students also do not validate, report, or interpret the data (S-ID.4).
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 Glencoe Traditional series meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs, and careers. The Interactive Student Guide (ISG) offers additional time on the WAPs, but there is no pacing guide to instruct teachers on its use. Examples of how the materials enable students to spend the majority of their time on the WAPs include:
- N-Q.1: In Algebra 1, Lesson 2-6, students determine the distance in centimeters when given the scale that 2 centimeters = 120 miles. Students calculate the actual height of a space shuttle from a model that is 110.3 inches tall when 1 inch equals 1.67 feet.
- A-SSE: In the Algebra 1 ISG, Variables and Expressions, students interpret the expression 8x+12.5y+6 by explaining what the coefficients and terms represent (A-SSE.1a). In Algebra 1, Lessons 7-1, 7-2, and 7-3, students apply the properties of exponents to rewrite expressions. In Algebra 2, Lesson 3-4, students rewrite expressions by factoring and, in Lesson 3-5, students rewrite functions in vertex form to identify the vertex (A-SSE.2). In the Algebra 1 ISG, Solving by Factoring, students calculate the zeros of quadratic functions by factoring (A-SSE.3a).
- F-IF.6: In Algebra 1, Lesson 3-3, students calculate the rate of change given ordered pairs or a graph. In Extend 7-9, students calculate the average rate of change of exponential functions. In Algebra 2, Lesson 1-3, students use a table showing Lisa’s temperature during a 3-day illness to calculate the average rate of change, determine if the answer is reasonable, and explain what the rate means.
- G-CO.9: In Geometry, Lesson 2-6, students prove the Supplement Theorem, the Complement Theorem, the Reflexive Property of Angle Congruence, the Transitive Property of Angle Congruence, and Right Angle Theorems. In the Geometry ISG, Proving Theorems About Angles, students write a paragraph proof for the Vertical Angle Theorem, the Supplement Theorem, and the Complement Theorem. In Geometry, Lesson 2-7, students write a two-column proof for the Alternate Exterior Angles Theorem and the Consecutive Interior Angles Theorem. In the Geometry ISG, Angles and Parallel Lines, students prove the Alternate Interior Angle Theorem by completing a chart and students complete a paragraph proof of the Perpendicular Transversal Theorem.
- S-IC.1: In Algebra 2, Lesson 8-1, students determine reasonable inferences and bias that might affect the validity of inferences based on random samples of data.
Indicator 1b.ii
The materials, when used as designed, allow students to fully learn each standard.
The instructional materials reviewed for the Glencoe Traditional series meet expectations for, when used as designed, letting students fully learn each non-plus standard. Although students fully learn many non-plus standards within the lessons, there are some non-plus standards which are minimally addressed within the lessons or are only available within the Interactive Student Guide (ISG).Examples of students fully learning the non-plus standards include:
- N-CN.2: In Algebra 2, Lesson 3-3, students use the relation $$i^2=-1$$ and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. In the Algebra 2 ISG, Real and Complex Numbers, students use the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
- A-CED.1: In Algebra 1, Lessons 2-1, 2-2, 2-3, and 2-4, students create linear equations in one variable and use them to solve problems. In Algebra 1, Lessons 5-1, 5-2, 5-3, 5-4, and 5-5, students create linear inequalities in one variable and use them to solve problems. In Algebra 1, Lesson 9-3, students write a quadratic equation representing the height of an object in terms of time and use the equation to calculate how long the object stays in the air. In Algebra 1, Lesson 9-6, students create an equation representing the area of text covering three-fourths of a poster and solve the equation using the quadratic formula to determine the margins of the poster. In Algebra 2, Lesson 1-1, students create linear equations in one variable and use the equation to solve problems. In the Algebra 2 ISG, Solving by Factoring, students create quadratic equations in one variable and factor the equations to solve problems. In Algebra 2, Lesson 6-2, students write an exponential function to represent a 2015 investment of $10,000 that grows to $16,960 by 2027 and use the function to determine the amount of money after a set number of years. In Algebra 2, Lesson 7-6, students create rational equations and inequalities in one variable to solve problems.
- A-REI.6: In Algebra 1, Lesson 6-1, students solve systems of linear equations by graphing. In Extend 6-1, students use graphing calculators to solve systems of linear equations. In Algebra 1, Lesson 6-2, students solve systems of linear equations by substitution. In Lessons 6-3 and 6-4, students solve systems of linear equations by elimination. In Algebra 1, Lesson 6-5, students determine the best method to solve systems of linear equations and solve them. In Extend 6-5, students solve systems of equations using augmented matrices.
- F-IF.7a: In Algebra 1, Lesson 3-1, students calculate x- and y-intercepts to graph linear equations. In the Algebra 1 ISG, Graphing Linear Functions, students graph linear functions and identify the intercepts. In Algebra 1, Lesson 9-1, students identify intercepts, maximum or minimum values, domain, and range, and students graph quadratic functions. In the Algebra 1 ISG, Graphing Quadratic Functions, students graph quadratic functions and identify the intercepts and the maximum or minimum value of the functions.
- F-TF.5: In Algebra 2, Lesson 9-5, students write trigonometric functions for real-world scenarios. In the Algebra 2 ISG, Graphing Trigonometric Functions, students determine the amplitude and period of the possible sine or cosine function representing the height above or below the axle of a ferris wheel at a state fair. Within the scenario, students find the value of f(0) to determine if the function has the form of $$f(\theta)=asinb\theta$$ or $$f(\theta)=acosb\theta$$. Students also write the trigonometric function and graph the function on the coordinate grid.
- G-CO.3: In the Geometry ISG, Symmetry, students identify rotational symmetry of a rectangle, parallelogram, isosceles trapezoid, and regular pentagon. Students determine the order and magnitude of symmetry for each figure. Students describe rotations of an equilateral triangle, a scalene triangle, and a regular hexagon that will map the figure onto itself. Students identify lines of reflectional symmetry in a rectangle, parallelogram, isosceles trapezoid, and a regular pentagon. Students also sketch graphs from a given description of the symmetry.
- G-GPE.2: In Geometry, Lesson 9-8, students derive the equation of a parabola given the focus and directrix. In the Geometry ISG, Equations of Parabolas, students follow steps to derive the equation of a parabola with directrix y=-p and focus F(0,p). Students also derive equations of parabolas given a focus and directrix to graph the parabola.
- S-ID.1: In Algebra 1, Lesson 10-2, students represent data through dot plots, bar graphs, and histograms, and from given sets of data, students create an appropriate graph of the data. In the Algebra 1 ISG, Performance Task, students make a box plot to represent the scores of two divers from 20 diving meets.
Examples of students fully learning standards through the ISGs include:
- A-APR.1: In Algebra 1, Lesson 8-1, students add and subtract polynomials and in Lesson 8-2, students multiply polynomials. In the Algebra 1 ISG, Adding and Subtracting Polynomials, students determine if the set of polynomials is closed under addition, subtraction, and multiplication.
- A-REI.1: In the Algebra 1 ISG, Equations, students explain each step in solving equations by using one or more mathematical properties.
- F-TF.8: In the Algebra 2 ISG, Verifying the Pythagorean Identity, students verify the Pythagorean identity using a circle on a coordinate grid with a radius equal to 1.
- G-SRT.1a: In the Geometry ISG, Dilations, students investigate properties of dilations using Geometer’s Sketchpad. In Geometry, Explore 7-1, students analyze the effect of dilations on figures.
- G-GMD.1: In the Geometry ISG, Circles and Circumference, students give an informal argument for the formula of the circumference of a circle. In the Geometry ISG, Volumes of Prisms and Cylinders, students write a general formula used to find the volume of cylinders and students also give an informal argument for the formula of the volume of pyramids using Cavalieri’s Principle.
- S-IC.5: In the Algebra 2 ISG, Designing a Study, students compare a control group and an experimental group of a memory test treatment. Students calculate mean scores of each group for comparison and use a calculator’s random number generator to decide if the differences between parameters are significant.
Students do not fully learn the following standard:
- A-REI.10: In Algebra 1, Lesson 1-7, students do not demonstrate understanding that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. Instead, the materials state, “Every solution of the equation is represented by a point on a graph. The graph of an equation is the set of all its solutions, which often forms a curve or a line.”
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 Glencoe Traditional series partially meet 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 do not vary the types of real numbers being used.
Examples where materials regularly use age appropriate contexts include:
- In Algebra 1, Lesson 2-2, students write one-step equations representing job occupations. Students are given approximations from the Bureau of Labor and Statistics and write one-step equations representing the number of people employed in production and repair occupations.
- In Geometry, Lesson 8-5, students complete a scenario involving two water slides 50 meters apart. The shorter slide has an angle of depression of 15 degrees and is approximately 15 meters tall. Students calculate the distance from the top of the tall water slide to the ground using characteristics of right triangles and angles of depression.
- In Algebra 2, Lesson 6-10, students encounter a scenario involving population growth in the state of Oregon. Students write an exponential growth equation representing the scenario. Students use the equation to predict the population of Oregon in 2025 and the year Oregon will have a population of six million people.
Examples where materials apply key takeaways from Grades 6-8 include:
- In the Algebra 1 Interactive Student Guide (ISG), Modeling: Exponential Functions, students apply key takeaways from ratios and proportional relationships (7.RP.A) by interpreting key features of both linear and exponential functions (F-LE.5, F-IF.4).
- In the Geometry ISG, Parts of Similar Triangles, students apply knowledge of proportional quantities (7.RP.2a) to explain how to calculate side lengths of similar triangles and prove triangle similarity (G-SRT.5).
- In Geometry, Lessons 2-5, 2-6, 2-7, and 2-9, students apply key takeaways of angles and line relationships (8.G.5) to prove segment and angle relationships (G-CO.9).
- In Algebra 2, Lesson 3-3, students perform operations on complex numbers (N-CN.1,2) using mathematical properties such as the commutative property of addition (6.EE.3).
Examples where materials do not vary the types of real numbers being used include:
- In Algebra 1, Lesson 8-1, students add and subtract polynomials. Within the problem sets, students write a polynomial in standard form with a rational coefficient.
- In the Algebra 1 ISG, Graphing Linear Functions, students interpret tables of linear models. All tables consist of integer x and y values, so students model real-world situations without interpreting or graphing non-integer values.
- In Geometry, Lesson 9-5, students calculate angle measures and arc lengths using characteristics of secants and tangents. All given angle measures and arc lengths are whole numbers. Students do not calculate using fractions or decimal values.
- In the Geometry ISG, Translations, students describe translations using mapping functions and translate figures given translation vectors. The translation vectors consist of integers, except for one translation vector with a decimal value of -2.5.
- In Algebra 2, Lesson 2-5, students graph piecewise, absolute value, and step functions. Students also write functions based on graphs. The majority of the functions utilize integer coefficients and constants, except for the decimal values of 0.5 and -0.5.
- In the Algebra 2ISG, Analyzing Graphs of Polynomial Functions, students complete a chart with integer x-values using the function $$f(x)=2x^3-7x^2+4x+4$$ and students graph polynomial functions given characteristics of polynomials. The majority of the polynomial characteristics involve integer values. Students graph one polynomial function with a relative maximum at x = -2.5.
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 Glencoe Traditional series partially meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. The materials include meaningful connections in a single course and throughout the series, but the materials also omit some connections in a single course or throughout the series. The materials identify connections within the series by listing prior standards addressed at the beginning of each chapter and lesson and each chapter begins with Then-Now statements connecting prior learning to expected learning for each lesson.
Examples where the materials foster coherence through meaningful mathematical connections in a single course or throughout the series include:
- In Geometry, Teacher Edition, Lesson 4-7, Track Your Progress, a chart is given with Then-Now statements. Teachers are provided the standards used within the lesson (G-CO.10, G-GPE.4) and the standards connected to the lesson (G-CO.7,8).
- In the Algebra 2 ISG, Solving Quadratic Equations by Graphing, students graph quadratic equations to find solutions and in the Algebra 2 ISG, Solving by Factoring, students solve quadratic equations by factoring. In the Algebra 2 ISG, Solving by Using the Quadratic Formula and the Discriminant, the materials state, “You have solved some quadratic equations by graphing, by factoring, and by completing the square” (F-IF.8a; A-SSE.2) and students solve quadratic equations by using the quadratic formula. (N-CN.7; A-SSE.1b)
- In Algebra 1, Lesson 2-1, students write and solve equations in one variable (A-CED.1). In Geometry, Lesson 2-7, students find the value of the variable in the figure given parallel lines and a transversal by writing and solving equations in one variable (G-CO.9, A-CED.1).
- In Algebra 1, Lessons 6-1, 6-2, 6-3, and 6-4, students use substitution, elimination, and graphing to solve systems of equations (A-REI.6). In Algebra 1, Lesson 9-7, the materials state, “Like solving systems of linear equations, you can solve systems of linear and quadratic equations by graphing the equation on the same coordinate plane.” Students make connections between methods of solving systems of linear equations with solving systems of linear and quadratic equations. Students also solve systems of linear and quadratic equations graphically or algebraically (A-REI.7).
Examples where the materials do not foster coherence by omitting some appropriate and required connections in a single course or throughout the series include:
- In Geometry, Lessons 3-1, 3-2, and 3-3, students transform figures by reflection, rotation, translation, and dilation (G-CO.A,B). In Algebra 2, Lesson 2-6, students perform and describe transformations of parent functions (F-BF.3). There is no connection made to the transformations in the previous course.
- In Algebra 2, Lesson 3-2, students solve quadratic equations by graphing (A-REI.4). There is no connection made to Algebra 1, Lesson 9-3, where students also solve quadratic equations by graphing. Many of the examples in both lessons are identical.
- In Algebra 1, Lesson 9-5, students solve quadratic equations by completing the square (A-REI.4b). In Geometry, Lesson 9-7, students create equations of circles by completing the square (G-GPE.1). In Algebra 2, Lesson 3-5, students solve quadratic equations by completing the square involving real and complex solutions (A-REI.4b). There is no connection made between the courses involving completing the square.
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 Glencoe Traditional series do not meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The instructional materials do not allow students to extend their previous knowledge by making connections between Grades 6-8 and high school concepts.
Throughout the series, the materials provide Track Your Progress sections in the Teacher Edition. These include the Mathematical Background needed for the lesson as well as a Then-Now-Next chart. The chart provides previous standards connected to the lesson, standards taught within the lesson, and standards being taught in the future. Some of the standards from Grades 6-8 are listed, but standards from Grades 6-8 are often presented as new standards for students to learn. The following examples are examples where the materials do not explicitly identify and/or build upon standards from Grades 6-8:
- In Algebra 1, Lesson 1-2, students use order of operations to evaluate equations and simplify expressions. There is no connection made to students applying properties of operations to expand expressions (7.EE.1). Order of operations is presented as a new standard and students are given the steps of the order of operations within a Key Concept chart.
- In Algebra 1, Lessons 2-2, 2-3, and 2-4, students solve one-step, two-step, and multi-step equations in one variable. There is no connection made to students solving equations in one variable (8.EE.7).
- In Algebra 1, Lesson 5-1, students write and solve inequalities with one variable. There is no connection made to constructing simple inequalities in one-variable (7.EE.4).
- In Algebra 1, Lessons 6-1 through 6-4, students solve systems of equations using graphing, substitution, or elimination. There is no connection made to 8.EE.8 in which students solve pairs of simultaneous linear equations.
- In Geometry, Lessons 3-1, 3-2, and 3-3, students perform transformations on geometric figures. There is no connection made to the effects of transformations on two-dimensional figures (8.G.A).
- In Geometry, Lesson 8-2, students use the Pythagorean Theorem and its converse to solve problems. There is no connection made to 8.G.7 in which students apply the Pythagorean Theorem and its converse to calculate unknown side lengths of right triangles. Within the same lesson, students prove the converse of the Pythagorean Theorem and students are provided with a proof of the Pythagorean Theorem using geometric mean. There is no connection made within the lesson to proving the Pythagorean Theorem (8.G.6).
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.