High School - Gateway 1

The materials reviewed for Math Nation AGA meet expectations for attending to the full intent of the mathematical content in the high school standards for all students. Examples of standards addressed by the courses of the series include:

• N-RN.2: In Algebra 2, Unit 3, Lesson 4, 3.4.3 Exploration Activity, Questions 2a and 3a, students rewrite exponential expressions containing positive rational exponents in radical notation. In Lesson 5, 3.5.2 Exploration Activity, Questions 2a and 3a, students rewrite exponential expressions containing negative rational exponents in radical notation. In 3.5.3 Exploration Activity, Questions 2 and 3, students use exponent rules to rewrite expressions containing rational exponents in radical notation and radical expressions in exponential form.

• A-APR.3: In Algebra 2, Unit 2, Lesson 5, 2.5.2 Exploration Activity, Questions 1-8, students use factored forms of polynomials to identify zeros of the polynomials. In Lesson 10, Practice Problems, Questions 1 and 2, students identify zeros of the polynomials and use the zeros to sketch rough graphs.

• A-CED.1: In Algebra 1, Unit 2, Lesson 2, 2.2.4 and 2.2.5 Exploration Activities, students create equations in one variable to represent blueberry purchases, summer earnings, and various quantities of car prices. In Lesson 9, 2.9.2 Exploration Activity, Questions 1-3, students write and solve equations to represent problems involving cargo shipping. In Lesson 20, 2.20.1 Warm-Up and 2.20.2 Exploration Activity, students write and solve inequalities to represent solutions to problems.

• F-IF.4: In Algebra 1, Unit 4, Lesson 3, 4.3.4 Exploration Activity, students interpret key features of a function and sketch a graph that models the temperature (W) of a pot of water (t) minutes after the stove is turned on. In Lesson 4, 4.4.4 Exploration Activity, Question 1, students complete a table, write a function, and sketch a graph that models the relationship between side length and area of a square.

• G-CO.5: In Geometry, Unit 1, Lesson 13, 1.13.3 Exploration Activity, students use a sequence of rigid transformations (translation, rotation, and reflection), to transform one triangle onto another. In Lesson 17, 1.17.6 Practice Problems, Question 1, students are given two congruent quadrilaterals and must determine a sequence of rigid transformations to transform quadrilateral ABCD onto quadrilateral A’B’C’D’. 

• G-C.2: In Geometry, Unit 6, Lesson 14, 6.14.4 Exploration Activity, students identify and describe relationships among chords that form an inscribed triangle and an inscribed angle within a circle to write a conjecture about the triangle. In Unit 7, Lesson 3, 7.3.3 Exploration Extension, students use a segment (AB) tangent to a circle, the measure of a central angle, and the length of a radius to calculate the length of segment AB (involves use of the definition of tangent and right triangle trigonometry). 

• S-CP.7: In Geometry, Unit 8, Lesson 6, 8.6.2, 8.6.3, and 8.6.4 Exploration Activities, students use the Probability Addition Rule: P(A or B) = P(A) + P(B) - P(A and B), to answer questions and interpret those answers about the following situations: state populations, multiples of numbers, and customers behavior at a coffee bar.

The materials reviewed for Math Nation AGA meet expectations for, when used as designed, allowing 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.

Examples of how the materials allow students to spend the majority of their time on widely applicable prerequisites (WAPs) include:

• N-RN.1: In Algebra 2, Unit 3, Lesson 3, 3.3.2 Exploration Activity, students use exponent properties and graphs of exponential functions (y=g^x) and (y=3^x) to extend the properties used with integer exponents to rational exponents. In 3.3.3 Exploration Activity, students use exponent rules and their understanding of roots to find exact values of exponential expressions. For example: 25^\frac{1}{2}, 8^\frac{1}{3} … etc.

• N-Q.1, F-IF.2, F-IF.5, F-IF.7, and F-LE.2: In Algebra 1, Unit 5, Lesson 8, 5.8.2 Exploration Activity, Question 2, students create a table, an equation, and a graph to represent mold growth on bread. In 5.8.4 Exploration Activity, students identify independent and dependent variables and create exponential equations to represent various problem situations. In 5.8.5 Exploration Activity, students decide on horizontal and vertical boundaries for the graph of the equation m=20(0.8)^t which represents the amount of medicine in a patient after an injection. In Lesson 15, 5.15.7 Practice Problems, Question 3, students complete a table and graph functions to compare loan balances at the end of each year. 

• A-SSE.3a: In Algebra 1, Unit 7, Lesson 9, 7.9.2 Exploration Activity, Question 2, students factor quadratic equations that have a lead coefficient of one and use the zero product property to solve them. In Lesson 10, 7.10.5 Exploration Activity, students solve quadratic equations, which have lead coefficients greater than one, by factoring with the use of the zero product, substitution, and distributive properties to reveal the zeros of the functions defined.

• A-SS3.3b: In Algebra 1, Unit 7, Lesson 22, 7.22.7 Practice Problems, Questions 3 and 4, students rewrite quadratic expressions in the vertex form by completing the square. In Lesson 23, 7.23.6 Practice Problems, Question 3, students use vertex forms of quadratic equations to identify minimum and maximum values of the functions. 

• A-CED.3 and A-REI.6: In Algebra 1, Unit 2, Lesson 12, 2.12.2 Exploration Activity, students complete tables, create systems of linear equations, and use graphing technology to create a graph that represents various problem situations involving a trail mix purchase. In 2.12.3 Exploration Activity, students create systems of linear equations to solve different word problems. 

• F-IF.1, F-IF.2, and F-IF.4: In Algebra 1, Unit 4, Lesson 2, 4.2.1 Warm-Up, students use graphs to determine the distance a dog is from a post as a function of the time after the owner left to go shopping. In 4.2.2 Exploration Activity, students use function notation to complete a table and interpret the meaning of function notation in the context of the Warm-Up problem. In 4.2.3 Exploration Activity, students complete tables involving inputs and outputs related to problem situations and identify which relationships are functions. In Lesson 3, 4.3.2 Exploration Activity, Questions 1-3, students interpret statements about smartphone use that use function notation. In Lesson 4, 4.4.6 Practice Problems, Question 2, students evaluate the function P(x) that represents the perimeter of a square as a function of its side length "x”, write an equation to represent the function P, and sketch a graph of P(x). In Lesson 5, 4.5.2 Exploration Activity, students compare the costs of two cell phone plans expressed as functions, evaluate functions for inputs in their domains, describe each data plan in words, and graph the functions on the same coordinate plane.

• G-SRT.4 and G-SRT.5: In Geometry, Unit 3, Lesson 14, 3.14.3 Exploration Activity, students use diagrams containing similar right triangles to prove the Pythagorean Theorem. In Lesson 15, 3.15.4 Exploration Extension, students fold the bottom left corner of a square piece of paper to the midpoint of the top edge. Students use similarity criteria of the right triangles formed and the Pythagorean Theorem to help prove the midpoint of the right edge of the paper is \frac{1}{3} of the way down the whole right side of the square piece of paper.

• S-IC.1 and S-IC.3: In Algebra 2, Unit 7, Lesson 3, 7.3.1 Warm-Up, students consider four options of selecting 100 people to find out how people feel about the state’s governor.  Students determine the benefits and drawbacks of each option and then decide which is the best option for including a representation of opinions from people across the entire state. In 7.3.2 Exploration Activity, a research group interested in comparing the effect of listening to different types of music on short-term memory gathers 200 volunteers. In Question 3, students decide the best option for randomly splitting the 200 volunteers into two groups to listen to the specified music genres. In 7.3.6 Practice Problems, Questions 2 and 3, students consider the best option for randomly selecting a population sample that most represents the entire population.

The materials reviewed for Math Nation AGA meet expectations for, when used as designed, allowing students to fully learn each standard. Examples of how the materials allow students to fully learn all of the non-plus standards include:

• N-Q.2: In Algebra 2, Unit 2, Lesson 1, 2.1.2 Exploration Activity, students construct an open-top box from a sheet of paper by cutting out a square from each corner and then folding up the sides. The side lengths of the squares students cut from the sheets of paper may vary in size. Students organize the data in a table and use it to calculate the volume of the constructed box. In the 2.1.3 Exploration Activity, each student creates a plan to determine how to construct a box with the largest volume, write an expression for the volume, and create a graph representing the volume.

• A-SSE.1: In Algebra 1, Unit 5, Lesson 7, 5.7.4 Exploration Activity, Questions 1 and 2, students interpret the meanings of a and b in the expression m=a \cdot b^t   which models the amount of medication in the body over time measured in hours, and determine what t = 0 and t = -3 means in the context. In Algebra 2, Unit 4, Lesson 6, 4.6.4 Exploration Activity, Questions 1 and 2, students explain why two expressions represent the same scenario. “A bacteria population starts at 1000 and doubles every 10 hours. 1. Explain why the expressions 1000 \cdot (2^\frac{1}{10})^h and 1000 \cdot 2^\frac{h}{10} both represent the bacteria population after h hours. 2. By what factor does the bacteria population grow each hour? Explain how you know.”

• A-REI.4b: In Algebra 1, Unit 7, Lesson 9, 7.9.2 Exploration Activity and 7.9.6 Practice Problems, Question 2, students solve quadratic equations with a lead coefficient of one by factoring and using the zero product property. In Lesson 10, 7.10.7 Practice Problems, Question 3, students solve quadratic equations with a lead coefficient greater than one by factoring and using the zero product property. In Lesson 12, 7.12.3 Exploration Activity, Questions 1-5, students solve quadratic equations that have integer solutions by completing the square. In Lesson 14, 7.14.4 Exploration Activity, Questions 1-6, students are given examples of three methods for solving quadratic equations (factoring, substitution, and completing the square) and must use each method at least once to solve the equation. In Lesson 15, 7.15.6 Practice Problems, Question 1, students solve quadratic equations by finding the square roots of both sides of the equation. In Lesson 18, 7.18.6 Practice Problems, Question 6, students solve quadratic equations by factoring or completing the square and then verify the solutions by using the quadratic formula. In Lesson 19, 7.19.6 Practice Problems, Question 5, students solve quadratic equations by using the quadratic formula and then verify the solutions by factoring. In Algebra 2, Unit 3, Lesson 18, 3.18.6 Practice Problems, Question 2, students write possible complex solutions to quadratic equations in the form of abiwhere a and b are real numbers.

• F-BF.3: In Algebra 1, Unit 4, Lesson 14, 4.14.3 Exploration Activity, students experiment with different values for a and b to determine changes to the graphs of f(x)=x+a and g(x) =x+b. In the 4.14.5 Exploration Activity, students match each function to the graph that represents it and use graphing technology to verify the accuracy of their matches. In Algebra 2, Unit 5, Lesson 1, 5.1.4 Exploration Activity, students work in pairs to identify the effects of given graph transformations and sketch the transformed graphs. In Lesson 2, 5.2.1 Warm-Up, students use graphing technology to graph f(x) = x^2(x - 2) and the following transformations: h(x) = x^2(x - 2) - 5  and  g(x) = (x - 4)^2(x - 6).  Students describe the changes to the original function. In Lesson 5, 5.5.6 Practice Problems, Question 1, students use graphs to classify functions as odd, even, or neither. In Lesson 6, 5.6.3 Exploration Activity, Questions 1-10, students work in pairs to use algebraic expressions to classify functions as odd, even, or neither.

• G-CO.10: In Geometry, Unit 1, Lesson 21, 1.21.2 and 1.21.3 Exploration Activities, students can use different transformations to prove the sum of the angles in a triangle is 180 degrees.  In each of these activities, students use technology to create a triangle. For 1.21.2 Exploration Activity, the base of the triangle is extended to form a line. Using a rotation, students can construct a line parallel to the line extended by the base, that goes through the opposite vertex of the triangle. Using properties of angles associated with parallel lines, students can show the sum of the angles in a triangle is 180 degrees. For 1.21.3 Exploration Activity, students can translate the triangle created two ways along different directed line segments, such that the three triangles meet at the same point. Then students can use vertical angles to show that the sum of the angles in a triangle is 180 degrees. In Unit 2, Lesson 6, 2.6.4 Exploration Activity, students use an auxiliary line and side-angle-side congruence to prove base angles of an isosceles triangle are congruent. In Lesson 10, 2.10.6 Practice Problems, Question 6, students use a reflection to prove base angles of an isosceles triangle are congruent. In Unit 3, Lesson 4, 3.4.1 Warm-Up, students show corresponding angles of dilated figures are congruent. For 3.4.4 Exploration Activity, students prove corresponding segments of dilated figures are parallel. In Lesson 5, 3.5.2 Exploration Activity, students use the definition of dilation and scale factors to prove the segment connecting the midpoints of two sides of a triangle is half as long as the third side. In 3.5.5 Lesson Summary, the proofs from 3.4.4 and 3.5.2 are connected to show that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side of the triangle. In Unit 6, Lesson 16, 6.16.4 Exploration Activity, students prove that the medians of a triangle intersect at a point.

• S-ID.5: In Algebra 1, Unit 3, Lesson 1, 3.1.3 Exploration Extension, students create a two-question survey, collect data from 20 students, and organize the data in a two-way frequency table. In 3.1.6 Practice Problems, Question 1, students use a completed two-way frequency table to answer questions based on the data in the table. In Lesson 2, 3.2.2 Exploration Activity, students explore the relationship between a two-way frequency table and a two-way relative frequency table. Students use completed relative frequency tables to complete segment bar graphs and answer questions by interpreting relative frequencies in the context of the data. Questions involve joint, marginal, and conditional probabilities. In Lesson 3, 3.3.2 Exploration Activity, Question 1, students calculate relative frequencies based on data found in a two-way frequency table and interpret the relative frequencies in the context of the data. For Questions 2 and 3, students determine possible associations within the data and explain their reasoning. In Lesson 4, 3.4.3 Exploration Activity, Questions 1 and 2, students use a scatter plot to predict trends in the data. In Geometry, Unit 8, Lesson 4, 8.4.3 Exploration Activity, Questions 1 and 2, students calculate relative frequencies and interpret them in the context of the data. Questions involve joint, marginal, and conditional probabilities. For 8.4.4 Exploration Extension, Questions 1 and 2, students create a relative frequency table and answer questions related to the data.

The materials reviewed for Math Nation AGA meet expectations for requiring students to engage in mathematics at a level of sophistication appropriate to high school. The materials regularly use contexts appropriate for high school students, use various types of real numbers, and provide opportunities for students to apply key takeaways from Grades 6-8.

Examples of problems that allow students to engage in age-appropriate contexts include:

• Algebra 1, Unit 1, Lesson 13, 1.13.6 Practice Problems, Question 1, students compare three drivers’ mean and standard deviation times to predict who will win the next race. “Three drivers competed in the same fifteen drag races. The mean and standard deviation for the race times of each of the drivers are given. Driver A had a mean race time of 4.01 seconds and a standard deviation of 0.05 seconds. Driver B had a mean race time of 3.96 seconds and a standard deviation of 0.12 seconds. Driver C had a mean race time of 3.99 seconds and a standard deviation of 0.19 seconds. A. Which driver had the fastest typical race time? B. Which driver’s race times were the most variable? C. Which driver do you predict will win the next drag race? Support your prediction using the mean and standard deviation.” For all questions the students have the following choices: “A. Driver A B. Driver B C. Driver C.” (S-ID.2)

• Geometry, Unit 1, Lesson 16, 1.16.3 Exploration Extension, students use a picture of artwork containing a frieze pattern to identify lines of symmetry, angles of rotation, and translations found in the pattern. (G-CO.3)

• Algebra 2, Unit 5, Lesson 11, 5.11.2 Exploration Activity, students are given a graph showing data that represents the temperature of a bottle of water after it has been removed from the refrigerator. Students use graphing technology to apply sequences of function transformations to match data and determine how well their chosen models match the data. (F-BF.1b, F-BF.3, F-LE.B, and S-ID.6a)

Examples of problems that allow students to engage in the use of various types of real numbers include:

• Algebra 1, Unit 2, Lesson 20, 2.20.2 Exploration Activity, students write inequalities that contain decimal values to determine possible values of x, the number of hours a person can mow a lawn without refilling the lawn mower gas tank. The lawn mower has a 5-gallon gas tank and 0.4 gallons of gas are utilized per hour to mow a lawn. (A-CED.1)

• Geometry, Unit 5, Lesson 17, 5.17.6 Practice Problems, Question 1, students calculate the weight of five washers each having the following measures: inner diameter - \frac{1}{4} inch, outer diameter - \frac{3}{4} inch, and a thickness of \frac{1}{4} inch. The density of the metal the washers are made of is 0.285 pounds per cubic inch. (G-MG.2)

• Algebra 2, Unit 3, Lesson 17, 3.17.5 Exploration Activity, Question 1, students solve quadratic equations by completing the square to determine how many real or non-real solutions they have. Solutions can be rational, irrational, or complex. (N-CN.7, and A-REI.4b) 

Examples of problems that provide opportunities for students to apply key takeaways from Grades 6-8 include:

• Algebra 1, Unit 4, Lesson 18, 4.18.2 Exploration Activity, students use the information from a table to determine what time a cell phone battery will be 100% charged (F-IF.6, and F.BF.1).  This activity builds on 6.RP.1, understanding the concept of a ratio; 6.RP.3c, find a percent of a quantity as a rate per 100; and 7.RP.3, using proportional relationships to solve multistep ratio and percent problems.

• Geometry, Unit 8, Lesson 5, 8.5.2 Exploration Activity, students utilize a Venn diagram to describe subsets of a sample space and to calculate probabilities related to the sample space (S-CP.1). This activity builds on 7.SP.8a, the probability of a compound event is the fraction of outcomes in the sample space, and 7.SP.8b, for an event described in everyday language identify the outcomes in the sample space which compose the event.

• Algebra 2, Unit 7, Check Your Readiness, Question 2, students utilize a table that details the number of views of an advertisement on three different social media networks. Students use this data to: a. determine which social media network has the greatest mean number of views for the week and b. determine which social media network has the greatest standard deviation for the number of views for these seven days while explaining their reasoning for both (S-ID.2). This activity builds on 6.SP.3, recognizing that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

The materials reviewed for Math Nation AGA 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. 

Examples where the materials foster coherence and make meaningful connections within a single course include:

• Algebra 1, Unit 6, Lesson 8, students use area diagrams to reason about the product of two sums and to write equivalent expressions and use the distributive property to write equivalent quadratic expressions (A-SSE.2). In the Mid-Unit Assessment, Question 3, students select equivalent expressions to represent the product of two binomials (A-SSE.2). In Unit 7, Lesson 6, 7.6.2 Exploration Activity, students use a diagram to show different forms of quadratic expressions are equivalent (A-SSE.2). In Lesson 7, 7.7.2 Exploration Activity, students complete a table by writing equivalent quadratic expressions in factored and standard form (A-SSE.2). In Lesson 9, 7.9.2 Exploration Activity, students solve quadratic equations by factoring and using the zero product property (A-SSE.3a and A-REI.4b). In Lesson 22, 7.22.1 Warm-Up, students use equivalent forms of a quadratic expression to identify the vertex, and x and y intercepts of the graph that represents the expression (F-IF.8a). In 7.22.2 Exploration Activity, Questions 1 and 2, students convert quadratic expression from vertex form to standard form and vice versa (A-SSE.3a, and A.SSE.3b).  

• Geometry, Unit 2, Lesson 1, 2.1.2 Exploration Activity, Questions 1-4, students are given triangle ABC congruent to triangle DEF and must: 1) determine the sequence of rigid motions that takes one triangle onto the other, 2) find the image of a segment after a transformation, 3) explain how they know those segments are congruent, and 4) justify that an angle is congruent to another angle (G-CO.5, and G-CO.6). In Lesson 7, 2.7.2 Exploration Activity, students prove the Angle-Side-Angle Triangle Congruence Theorem by using a sequence of rigid motions (G-CO.6, G-CO.7, G-CO.8, and G-CO.10). In Unit 3, Lesson 9, 3.9.1 Warm-Up, students use the Angle-Side-Angle Triangle Congruence Theorem and dilation to show similarity between two triangles (G-SRT.2, and G-SRT.3). In Lesson 15, 3.15.6 Practice Problems, Question 2, students can find the length of a segment in a right triangle with the use of the Pythagorean Theorem (G-SRT.8). In Unit 4, Lesson 6, 4.6.3 Exploration Activity, Questions 1 and 2, students use trigonometric ratios to find side lengths in right triangles (G-SRT.8). In Unit 6, Lesson 1, 6.1.3 Exploration Activity, Questions 1 and 2, students calculate side lengths of right triangles placed in the coordinate plane by using the Pythagorean Theorem, and the angle measures by using trigonometric ratios (G-SRT.8). In Question 3, students can explain how they know the right triangles are congruent with the use of the definition of congruence (G-CO.5 and G-CO.B). In Question 4, students determine a sequence of rigid motions that take one triangle onto the other (G-CO.7).

• Algebra 2, Unit 2, Lesson 5, 2.5.1 Warm-Up, students make observations about functions in the factored form and their graphs (A-APR.B, and F-IF.4). In 2.5.2 Exploration Activity, students use equations in the factored form to determine the values of x that make the equation equal to zero (A-APR.3). In 2.5.3 Exploration Extension, students write polynomial equations using specific values for x. In 2.5.4 Exploration Activity, students work in groups to match equations to graphs or verbal descriptions (F-IF.9). In 2.5.6 Practice Problems, Question 2, students identify the polynomial that has zeros when x = -2, \frac{3}{4}, 5.  For Question 3, students identify the x-intercepts for the graph of f(x) = (2x - 3)(x - 4)(x + 3) (F-IF.4). In Lesson 7, 2.7.4 Exploration Activity, students use horizontal intercepts to write equations and graph polynomials (A-APR.B, and F-IF.7c).

Examples where the materials foster coherence and make meaningful connections across courses include:

• Algebra 1, Unit 3, Lesson 3, students analyze data with the use of two-way frequency tables to determine possible associations between variables (S-ID.5). In 3.3.2 Exploration Activity, Question 2, students determine if a possible association between age and shoe preference exists with the use of a two-way frequency table that contains various age groups and their sneaker preferences (S-ID.5). In Geometry, Unit 8, Lesson 4, students use two-way frequency tables to analyze data by finding relative frequencies and estimating probabilities (S-ID.5). In 8.4.6 Practice Problems, Question 3, students create a two-way relative frequency table based on a given table containing information about heart rates of people who live at different altitudes. Students then use the relative frequency table to calculate probabilities (S-CP.4). In Algebra 2, Unit 7, Lesson 2, students analyze data given different study types: survey, observational study, or experimental study (S-IC.3). In 7.2.6 Practice Problems, Question 1, students determine what type of study is needed to find out how many hours a per week, on average, a student spends on homework. Question 2, students select designs that describe observational studies that are not surveys. Question 3, students determine how researchers could design an experiment to determine the effects of flavanols on blood flow from the different types of chocolate (S-IC.3).

• Geometry, Unit 4, Lesson 7, 4.7.3 Exploration Activity, students apply trigonometric ratios in context problems to calculate heights of buildings (N-Q.2 and G-SRT.8). In Algebra 2, Unit 6, Lesson 2, 6.2.2 Exploration Activity, students apply right triangle trigonometry to calculate values for sines, cosines, and tangents of angles, using given information about side lengths and/or angles in right triangles (G-SRT.C).

• Algebra 1, Unit 7, Lesson 12, 7.12.3 Exploration Activity, students practice solving quadratic equations by completing the square (A-REI.4b). In Lesson 13, 7.13.2 Exploration Activity, students solve quadratic equations containing common fractions and decimals by completing the square (A-REI.4b). In Lesson 14, 7.14.3 Exploration Activity, Question 1, students use the pattern for squaring a binomial and completing the square to rewrite each expression in standard form as perfect square trinomial and as binomial squared. For Question 2, students solve quadratic equations by completing the square (A-SSE.2, and A-REI.4b). In Geometry, Unit 6, Lesson 6, 6.6.3 Exploration Activity, Question 1, students rewrite the equation of a circle by completing the square to find the center and radius of the circle (A-SSE.2, and G-GPE.1).

The materials reviewed for Math Nation AGA meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The materials explicitly identify content from Grades 6-8 and support the progressions of the high school standards. Connections between Grades 6-8 and high school concepts are present and allow students to extend their previous knowledge. Grades 6-8 standards are explicitly identified and connected to the high school standards in the Teacher Support materials in every unit and the following sections: Teacher Guide, Unit At A Glance, Lesson Plans, and Teacher Presentation Materials. Grade 6-8 standards are not explicitly identified in the student materials.

Examples of where the materials make connections between Grades 6-8 and high school concepts, and allow students to extend their previous knowledge include:

• Algebra 1, Unit 3, Lesson 5, 3.5.1 Warm-Up, students extend their knowledge of straight lines being used to model relationships between two quantitative variables and assess the fit of a scatter plot by looking at the closeness of the data points to the line (8.SP.2) by informally assessing the fit of a function. (S-ID.6b)

• Algebra 1, Unit 5, Lesson 15, 5.15.2 Exploration Activity, Questions 1-4, students solve a multi-step, real-life mathematical problem involving a loan of $450 with an annual interest rate of 18%. Students apply properties of the operations to calculate the amounts owed on the loan at the end of specific time periods (7.EE.3) by using a recursive process. Lastly, students write an explicit expression for the amount owed on the loan at the end of x years (F-BF.1a).

• Geometry, Unit 5, Lesson 7, 5.7.1 Warm-Up, Questions 1 and 2, students can use equations of the form x^3 = p, where x represents a scale factor and p represents a specified volume, to calculate scale factors of dilated cubes needed to produce certain volumes that have perfect cube measures (8.EE.2). In Questions 3 and 4, students can use the same type of equation to estimate scale factors of dilated cubes that have volumes that are not perfect cubes (8.NS.2). In 5.72 Exploration Activity, Questions 1 and 2, students apply the process used in the previous Warm-Up Activity to solve a context problem involving calculating scale factors needed for dilating cube-shaped boxes to specified volumes (8.EE.2 and 8.NS.2). In Question 3, students complete a table that shows the relationship between volumes (x) and scale factors (y). In Question 4, students use the points in the table to create a graph that represents this relationship (F-IF.7b). In Question 5, students write an equation that represents the relationship between the volume of the dilated box and the scale factor (A-CED.2).

• Geometry, Unit 8, Lesson 3, 8.3.2 Exploration Activity, Questions 1-3, students use sample spaces, created using different methods: an organized list, a table, and a tree diagram, that represent outcomes of the same compound event (7.SP.8b) to calculate the number of possible outcomes for the event and answer questions about subsets of the sample space (S-CP.1).

• Algebra 2, Unit 3, Lesson 5, 3.5.1 Warm-Up, students apply properties of exponents while they mentally evaluate numerical expressions (8-EE.1), which in some cases requires them to change the expression into a different format (N-RN.2).