Organization: McGraw-Hill
Product Name: Reveal Math Course 3 2020
Product Version: 1.2




Source:     IMS Online Validator
Profile:    1.2.0
Identifier: cc_v1p2
Timestamp:  Monday, September 14, 2020 09:37 AM EDT
Status:     VALID!
Conformant: true


-----    VALID!    -----
Resource Validation Results
The document is valid.


-----    VALID!    -----
Schema Location Results
Schema locations are valid.


-----    VALID!    -----
Schema Validation Results
The document is valid.


-----    VALID!    -----
Schematron Validation Results
The document is valid.


Curriculum Standards:


MAFS.6.NS.3.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. - 4f90be5f-2d92-4c88-bc18-34d3874d4075
MAFS.K12.MP.6 Attend to precision. - 340833b6-d1c4-44eb-9647-f79f7daf0030
NS.8.3.b determine both the positive and negative square roots of a given perfect square. - 24016C26-C725-11E6-8FA1-C9E9CCC8CA83
CCSS.Math.Content.6.EE.B Reason about and solve one-variable equations and inequalities. - 1E746F4A-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.G.2 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. - 61262f84-974b-4139-bf59-3b054be2f569
CCSS.Math.Content.8.EE.C.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 𝘹 = 𝘹𝘢, 𝘹𝘢𝘢 = 𝘹𝘢𝘢𝘢, or 𝘹𝘢𝘢𝘢𝘢 = 𝘹𝘢𝘢𝘢𝘢𝘣 results (where 𝘹𝘢𝘢𝘢𝘢𝘣𝘢 and 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣 are different numbers). - 1F399D6A-7053-11DF-8EBF-BE719DFF4B22
8.GM.1.a Verify that lines are mapped to lines, including parallel lines. - ad793138-3dea-4d22-9dcd-9744bcc2fbfd
MAFS.7.NS.1.2.c Apply properties of operations as strategies to multiply and divide rational numbers. - bf13f75d-893d-4a97-85ac-2145bc938b46
CCSS.Math.Content.8.F.A Define, evaluate, and compare functions. - 1F461EC8-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers. - 341d69d6-f079-4bc6-9e74-a0f087baeb49
CCSS.Math.Content.7.NS.A.2.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. - 1ED0C7D6-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. - 9aadcaf3-9c87-43e4-85ac-94bba7329393
CCSS.Math.Content.6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions. - 1E5EFE76-7053-11DF-8EBF-BE719DFF4B22
8.GM.1 Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology). - 4d0d8488-62d7-4923-8265-6b1951c33b6b
8.EE.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. - C59D9D4A-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. - 1EDE4C8A-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.F.2.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. - 6089c4da-f2df-48d7-a3a6-ba512874ad94
MAFS.8.SP.1 Investigate patterns of association in bivariate data. - 6fc197ec-34df-46f6-8b8b-08338bfeb315
8.F.1.d Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions. - 03ae2ab3-451c-4360-beb8-ff880668fa2d
3.C use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation. - 9F1ECB26-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.8.G.A.1.c Parallel lines are taken to parallel lines. - 1F57380C-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. - 1ECF626A-7053-11DF-8EBF-BE719DFF4B22
8.NS.2 Estimate and compare the value of irrational numbers by plotting them on a number line. - 8abc2cfe-51dd-4b38-89eb-3bb7f1b7f8a4
8.F.1 Explore the concept of functions. - ceef1a90-26a0-4069-a868-9d3463bd80b3
MAFS.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. - af3ceb2b-9f8c-40fc-a591-465675ef4e60
CCSS.Math.Content.7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations. - 1EDCE3A4-7053-11DF-8EBF-BE719DFF4B22
8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - C5A21C8A-96FF-11E0-9509-C03D9DFF4B22
MAFS.7.EE.1 Use properties of operations to generate equivalent expressions. - 0527d2ad-3dc8-46e5-b100-9b8e3c8f745f
8.EEI.2 Investigate concepts of square and cube roots. - 62896112-5b47-47dc-9bbd-fdcbee2238ca
MAFS.8.EE.3 Analyze and solve linear equations and pairs of simultaneous linear equations. - dac85def-825c-4085-84c9-6ca0e02ace8e
CCSS.Math.Content.8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - 1F59A7EA-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.G.1.1.b Angles are taken to angles of the same measure. - 903ce2cd-7e8c-4356-bf7b-367e86bacae1
2.D order a set of real numbers arising from mathematical and real-world contexts. - 9F1CD7E4-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations: - 1F530372-7053-11DF-8EBF-BE719DFF4B22
MAFS.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. - 50458c9e-ed0f-4cba-a28a-f4957022f614
5.G identify functions using sets of ordered pairs, tables, mappings, and graphs; - 9F245C30-0D0A-11E2-9583-8B2E9DFF4B22
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. - C5AB3AC2-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. - 1E1E82CE-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.F.2.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹, 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. - 7ecdef3a-4724-47df-9619-c69740336ee3
CCSS.Math.Content.7.EE.A Use properties of operations to generate equivalent expressions. - 1ED7DB02-7053-11DF-8EBF-BE719DFF4B22
8.GM.5.c Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal. - 813a8327-0289-44a4-a90c-24878d9922da
MAFS.K12.MP.2 Reason abstractly and quantitatively. - 3885dc10-69f7-4a9d-b273-ed83a569094a
CCSS.Math.Content.6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. - 1E5FE70A-7053-11DF-8EBF-BE719DFF4B22
MAFS.6.NS.2 Compute fluently with multi-digit numbers and find common factors and multiples. - c1801500-4a96-4f5a-88fc-259110d5d691
8.F.3.b Recognize that the graph of a linear function has a constant rate of change. - 1d0d10d4-cc24-4a7c-a960-be3e4b5f7bdb
MAFS.8.EE.2 Understand the connections between proportional relationships, lines, and linear equations. - 8251cb35-e9fa-496d-9b5b-dfb43e74b135
8.EEI.1 Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents. - 285eb371-4b7c-4a40-8817-1bde6811a406
8.EEI.8.b Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines. - e742636f-0f6f-461e-bfe5-5d11bdd82045
CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. - A6497ED0-6F89-11DF-BAEE-EA329DFF4B22
11.A model and solve one-variable, two-step equations and inequalities; - 9F1051AE-0D0A-11E2-9583-8B2E9DFF4B22
8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. - C5A99596-96FF-11E0-9509-C03D9DFF4B22
11.C write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships. - 9F115D74-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.6.NS.3.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. - e3d729ff-7887-499d-bba7-0eb4a3bfd06a
CCSS.Math.Content.8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - 1F624D6E-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. - 1F6E148C-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. - 1EB29FEA-7053-11DF-8EBF-BE719DFF4B22
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥² + 9𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥 + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥 – 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥 and 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦. - 5C5688E4-7377-11DF-A1E8-223D9DFF4B22
MAFS.8.SP.1.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. - 4c4c1bea-b551-4e6e-938c-f450b83dde84
MAFS.6.EE.1.1 Write and evaluate numerical expressions involving whole-number exponents. - 43c4ba36-948f-4d06-8ff6-374622a2814d
MAFS.K12.MP.3.1 Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - 78332818-27d5-4b06-9369-fd35deb0af11
CCSS.Math.Content.7.NS.A.1.c Understand subtraction of rational numbers as adding the additive inverse, 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱 – 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱 + (–𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. - 1ECD20F4-7053-11DF-8EBF-BE719DFF4B22
8.EEI.8.c Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection. - 5f1738c4-ee00-42e1-acdc-a60fb977ecd2
MAFS.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. - 77ac194b-7098-4bc9-b094-873db3a95c08
MAFS.6.RP.1.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - b9e527ce-d1c9-4684-8ba7-00cedec7c152
CCSS.Math.Content.7.RP.A.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. - 1EBB74C6-7053-11DF-8EBF-BE719DFF4B22
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. - 5C561224-7377-11DF-A1E8-223D9DFF4B22
PFA.8.16.d graph a linear function given the equation in y = mx + b form; and - 996B04E4-C726-11E6-B787-E9EBCCC8CA83
8.GM.4.a Dilate geometric figures using scale factors that are positive rational numbers. - fabcb2d8-23f2-4a27-97b5-d5657e9dcfc6
CCSS.Math.Content.8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. - 1F1FA9D2-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. - 1EC7A304-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.EE.3.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. - 3adb7ec6-d69d-4963-8314-de82011b87c9
8.DSP.3 Apply concepts of an approximate line of best fit in real-world situations. - 1e75f9e1-c9e1-4e24-9342-214c09f1b4c7
CCSS.Math.Content.8.EE.C.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. - 1F3AE526-7053-11DF-8EBF-BE719DFF4B22
8.F.4.a Understand that the slope is the constant rate of change and the y- intercept is the point where x = 0. - e2ad07a9-fffc-4626-8c09-0bd802dc998a
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. - 5C551ED2-7377-11DF-A1E8-223D9DFF4B22
CCSS.Math.Content.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. - 1E3FE838-7053-11DF-8EBF-BE719DFF4B22
8.F.4.c Construct a function in slope-intercept form that models a linear relationship between two quantities. - 7c847f9d-a6a6-4339-b746-f5bd96ea9f8d
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹, 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. - C5A46EFE-96FF-11E0-9509-C03D9DFF4B22
8.D use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. - 9F2BD8A2-0D0A-11E2-9583-8B2E9DFF4B22
7.D determine the distance between two points on a coordinate plane using the Pythagorean Theorem. - 9F296AF4-0D0A-11E2-9583-8B2E9DFF4B22
8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations). - 1df41c05-c6ce-4e8e-9689-521829cff80c
CCSS.Math.Content.7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. - 1ED58500-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.EE.1 Work with radicals and integer exponents. - 56c44c41-66d7-4862-aa7a-4f89eb3d2fe2
8.EEI.6.a Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles. - 6183ba31-6e03-4d3f-b4e9-65fadb233f2c
MAFS.8.G.2.6 Explain a proof of the Pythagorean Theorem and its converse. - 4eb06f5a-f0dd-4acd-97b4-cfd5c4f536e3
MAFS.8.G.3 Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. - 941cba33-148d-46ed-9d6d-5293f5522941
8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. - C592039A-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹, 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. - 1F4E8D1A-7053-11DF-8EBF-BE719DFF4B22
8.EEI.2.d Recognize that square roots of non-perfect squares are irrational. - e067078a-c053-4c84-9878-ddf4a4ee5378
MAFS.8.SP.1.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. - 2ed72bc0-754f-4f10-be2e-0113c528a261
MAFS.K12.MP.7.1 Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥² + 9𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥 + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥 – 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥 and 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦. - 753f388e-e7b0-4192-b79d-4dac6f0ca194
MAFS.8.F.1.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. - 65166b59-93df-42bd-a976-660745aa08ae
PS.8.13.b make observations about data represented in scatterplots; and - 1DF78332-C726-11E6-AF99-A671BF03DF2F
8.EEI.3.c Estimate and compare the relative size of two quantities in scientific notation. - 9c957ec3-77ae-4df0-b901-4c889cc67cc4
MAFS.8.F.1 Define, evaluate, and compare functions. - e9818474-08d8-4863-b430-d242d74bd34b
CCSS.Math.Content.8.EE.C Analyze and solve linear equations and pairs of simultaneous linear equations. - 1F368576-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.NS.1.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱 and 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲 are integers, then –(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱/𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲) = (–𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱)/𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱/(–𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲). Interpret quotients of rational numbers by describing real-world contexts. - 5526b516-9ec3-4ede-8383-1bb5811b7875
CCSS.Math.Content.8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. - 1F3C4218-7053-11DF-8EBF-BE719DFF4B22
MAFS.K12.MP.8.1 Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦 – 2)/(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥 – 1) = 3. Noticing the regularity in the way terms cancel when expanding (𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥 – 1)(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥 + 1), (𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥 – 1)(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥² + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥 + 1), and (𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥 – 1)(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥³ + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥² + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. - 464690b2-2313-4a93-a9da-ea512f6b7ed6
CCSS.Math.Content.7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. - 1EC61534-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.NS.1.2.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. - e7623cd2-ab35-4226-aa58-f271d92baa57
5.I write an equation in the form 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥 + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏 to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations. - 9F254A96-0D0A-11E2-9583-8B2E9DFF4B22
5.C contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation; - 9F228B3A-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.K12.MP.5 Use appropriate tools strategically. - 7fb94672-da71-44b5-950f-b57258b31b63
MAFS.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems. - 8bc4c4c6-0b0f-4c3c-a418-a34db69fa64c
8.GM.4.b Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image. - 46b7cf65-c0cc-4435-8913-2f97ed07a240
8.GM.3.a Use coordinate geometry to describe the effect of transformations on two-dimensional figures. - decf4bbd-132d-4a3d-a26d-bdc207ec8025
8.EEI.5.a Graph proportional relationships. - bd04e711-8891-4d76-96fa-260d7e8624a0
8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. - C5A85A32-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. - A6430F50-6F89-11DF-BAEE-EA329DFF4B22
CCSS.Math.Content.8.EE.C.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. - 1F41FC3A-7053-11DF-8EBF-BE719DFF4B22
8.GM.1.b Verify that corresponding angles are congruent. - 41eff222-88ad-4ab2-9086-52ef35b28f1e
7 The student applies mathematical process standards to represent linear relationships using multiple representations. The student is expected to represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥 + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏. - 9F090340-0D0A-11E2-9583-8B2E9DFF4B22
2.B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line; - 9F1BE3DE-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.7.NS.A.2.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. - 1ED49A78-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.8.F.B Use functions to model relationships between quantities. - 1F4D12C8-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.G.1.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. - 04b1cf07-e06f-4356-97f8-7938f054152c
MG.8.5 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. - 489FB182-C725-11E6-8A30-53E9CCC8CA83
8.F.4 Apply the concepts of linear functions to real-world and mathematical situations. - 043c3e69-630b-4ba0-81f9-67a7d77245ce
8.DSP.3.a Find an approximate equation for the line of best fit using two appropriate data points. - b1fdf334-03cb-4963-a845-444c0ad17ac5
CCSS.Math.Content.8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. - 1F665990-7053-11DF-8EBF-BE719DFF4B22
MG.8.6.a solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids; and - 5AB326BA-C725-11E6-A759-DEE9CCC8CA83
8.EE.8 Analyze and solve pairs of simultaneous linear equations. - C59CF138-96FF-11E0-9509-C03D9DFF4B22
5.B represent linear non-proportional situations with tables, graphs, and equations in the form of 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥+𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏, where 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏 ≠ 0; - 9F221290-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.K12.MP.6.1 Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. - cc88d0e7-1375-41f3-89ff-b0557b54b359
8.EEI.6 Apply concepts of slope and y - intercept to graphs, equations, and proportional relationships. - 136847e5-9f0b-455f-9e61-0a7d92d1e1df
MAFS.8.NS.1.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. - 13d3d2c0-957d-4864-a633-dcbac4d39315
2.A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers; - 9F1B6F1C-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.8.G.2 Understand and apply the Pythagorean Theorem. - 5563d779-eefa-4070-add9-e14790b67f0f
8.9.A Understand that a three-dimensional object can be represented as a two-dimensional model that represents views of the object from different perspectives. - 17137B4C-5EAD-11DD-B27F-63029DFF4B22
MAFS.7.NS.1.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. - 12f9d784-82f8-48df-bf18-e91c217cb151
10.B differentiate between transformations that preserve congruence and those that do not; - 9F2DB14A-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.6.EE.A.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. - 1E676A20-7053-11DF-8EBF-BE719DFF4B22
8.F.3.a Define an equation in slope-intercept form (y = mx + b) as being a linear function. - 8f297cd2-3dec-4092-bec7-509de325f66b
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. - C5B095E4-96FF-11E0-9509-C03D9DFF4B22
MG.8.7.b identify practical applications of transformations. - 86CA84C8-C725-11E6-B442-5571BF03DF2F
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. - A630F7A2-6F89-11DF-BAEE-EA329DFF4B22
8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). - C58E9F84-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.7.NS.A.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱 and 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲 are integers, then –(𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱/𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲) = (–𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱)/𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱/(–𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲). Interpret quotients of rational numbers by describing real-world contexts. - 1ED1FDF4-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - 1ED93CAE-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Practice.MP7 Look for and make use of structure. - A648672A-6F89-11DF-BAEE-EA329DFF4B22
8.F.3 Interpret the equation 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹 + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. - C5A2FE5C-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. - 1F611A98-7053-11DF-8EBF-BE719DFF4B22
2.A classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers; - 9EDBF850-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.8.G.A.1.b Angles are taken to angles of the same measure. - 1F55D2E6-7053-11DF-8EBF-BE719DFF4B22
MAFS.6.NS.3.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - b30cc0e2-e28c-4024-aa51-4090f5b9beea
MAFS.8.G.1.1.a Lines are taken to lines, and line segments to line segments of the same length. - f57cdb34-591b-4951-bb62-41be911fd396
MAFS.K12.MP.2.1 Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. - 0331111e-4349-473a-ae23-5b4b6572bb0c
MAFS.8.F.1.3 Interpret the equation 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹 + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. - 35a1ce3b-f167-4ff5-9cdd-8cbbdbbe5e3c
8.GM.3 Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software). - 13a3bb3d-e7c8-4ef6-a513-fe2a770253be
CCSS.Math.Content.8.EE.B Understand the connections between proportional relationships, lines, and linear equations. - 1F3029E2-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.RP.1.2 Recognize and represent proportional relationships between quantities. - 7c33b320-8b15-4141-a09b-b2d10f2a3012
8.NS.3 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions. - ed3ee740-9953-48d5-8ad2-1b3a9b9e8ee6
8.EEI.7.a Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides. - 586d9bc4-115b-46a0-94d1-04e9745609de
8.GM.2.b Reflect geometric figures with respect to the x - axis and/or y - axis. - 4991592d-e8b5-4905-a420-2753978fb017
MAFS.8.EE.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. - 262305a0-d0c6-49b5-bbac-29190e21236e
6.A describe the volume formula 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵ℎ of a cylinder in terms of its base area and its height; - 9F2633F2-0D0A-11E2-9583-8B2E9DFF4B22
8.EEI.4.a Multiply and divide numbers expressed in both decimal and scientific notation. - d8fb1f5f-a8c3-4c54-a478-d510df573e1b
MAFS.7.EE.1.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - 717b1a64-7df5-4071-936a-4f5c4bab72a3
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. - 5C559BA0-7377-11DF-A1E8-223D9DFF4B22
CCSS.Math.Content.6.RP.A.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - 1E31940E-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.NS.1.3 Solve real-world and mathematical problems involving the four operations with rational numbers. - c540025f-5167-4f59-b73a-67d8eb49011a
CCSS.Math.Content.7.RP.A.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. - 1EB93512-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.G.1.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. - 2976f57c-63d7-4eb5-9048-26ff05c61bfe
8.F.4.d Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation. - 3e827428-b52a-45c5-86c1-01e83931d7eb
8.EEI.5 Apply concepts of proportional relationships to real-world and mathematical situations. - 5ae3f29b-8640-47f4-8fde-fe3dfcf904c7
8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹 for a line through the origin and the equation 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹 + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣 for a line intercepting the vertical axis at 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣. - C598E444-96FF-11E0-9509-C03D9DFF4B22
MAFS.7.RP.1.3 Use proportional relationships to solve multistep ratio and percent problems. - 0b75b187-9efa-41ab-88bd-610c6f4e76fc
8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. - C5A92C5A-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.8.EE.C.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. - 1F3DA5D6-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.6.NS.C Apply and extend previous understandings of numbers to the system of rational numbers. - 1E4523FC-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. - 98d51b29-de67-4abe-b7a6-32150edd2e62
MAFS.7.NS.1.1.c Understand subtraction of rational numbers as adding the additive inverse, 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱 – 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱 + (–𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. - 29db58cc-f23f-4cdb-bb9b-ad7acaf9f8f2
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - 5C54A65A-7377-11DF-A1E8-223D9DFF4B22
8.F.5.b Sketch the graph of a function from a verbal description. - 9c444856-63a2-44f0-9a09-a39aa32c200f
9.B represent discrete paired data on a scatterplot; and - 9ED34A84-0D0A-11E2-9583-8B2E9DFF4B22
PFA.8.16.e make connections between and among representations of a linear function using verbal descriptions, tables, equations, and graphs. - A2B6B5AC-C726-11E6-8995-A872BF03DF2F
MAFS.K12.MP.3 Construct viable arguments and critique the reasoning of others. - 0ab2c4e3-2b87-4dd9-a12b-353a486762fa
CCSS.Math.Content.8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. - 1F4742BC-7053-11DF-8EBF-BE719DFF4B22
8.F.1.c Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions. - 8b9ba5a7-99cc-4565-af30-44fde0355d3d
10.C explain the effect of translations, reflections over the 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲𝑥- or 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲𝑥𝑦-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; and - 9F2E295E-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. - 1EEF675E-7053-11DF-8EBF-BE719DFF4B22
8.EEI.7 Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations. - a4de0455-bd06-43c8-be0f-8cde744ac699
8.F.4.b Determine the slope and the 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲𝑥𝑦𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions. - 0f804b0c-bfe3-4dd7-aa3e-123704c3e066
CCSS.Math.Content.8.F.A.3 Interpret the equation 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲𝑥𝑦𝑦𝘺 = 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲𝑥𝑦𝑦𝘺𝘮𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲𝑥𝑦𝑦𝘺𝘮𝘹 + 𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘹𝘺𝘹𝘺𝑥𝑥𝑥𝑦𝑥𝑦𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑦𝑚𝑥𝑏𝑏𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲𝘺𝘮𝘹𝘣𝘺𝘮𝘹𝘣𝑉𝐵𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘱𝘲𝘱𝘲𝑥𝑦𝑦𝘺𝘮𝘹𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. - 1F4AA754-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. - 1F26B254-7053-11DF-8EBF-BE719DFF4B22
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. - 5C53AC00-7377-11DF-A1E8-223D9DFF4B22
2.C convert between standard decimal notation and scientific notation; and - 9F1C5BDE-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.8.EE.C.7 Solve linear equations in one variable. - 1F38705C-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. - 1E4879DA-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Practice.MP6 Attend to precision. - A647016E-6F89-11DF-BAEE-EA329DFF4B22
CCSS.Math.Content.6.NS.C.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - 1E4CFA28-7053-11DF-8EBF-BE719DFF4B22
3.A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation; - 9F1DBFEC-0D0A-11E2-9583-8B2E9DFF4B22
8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. - C5AC79D2-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.7.NS.A.2.c Apply properties of operations as strategies to multiply and divide rational numbers. - 1ED3352A-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.EE.3.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. - 207cb9e9-38dc-47ae-b3c9-cae133b56c2c
CCSS.Math.Content.7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. - 1EE9F0EE-7053-11DF-8EBF-BE719DFF4B22
4.B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and - 9F202BB0-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.6.NS.2.2 Fluently divide multi-digit numbers using the standard algorithm. - 5b40d095-6c96-48e6-9ff4-8e5db4197220
8.GM.5.b Discover and use the relationship between interior and exterior angles of a triangle. - 808e84a6-3850-49c9-a7ad-5af074fbd10a
8.F.5 Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations. - 8209046a-3266-44d9-ab1c-e992c822df68
MAFS.7.EE.2.4.a Solve word problems leading to equations of the form 34𝘱34𝘱𝘹 + 34𝘱𝘹𝘲 = 34𝘱𝘹𝘲𝘳 and 34𝘱𝘹𝘲𝘳𝘱(34𝘱𝘹𝘲𝘳𝘱𝘹 + 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲) = 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳, where 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱, 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲, and 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. - 535bbd08-5ee8-43b0-9eaa-036060b2a38d
8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. - C59588C6-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software. - 1F527D08-7053-11DF-8EBF-BE719DFF4B22
8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - C5ABA494-96FF-11E0-9509-C03D9DFF4B22
PFA.8.16.b identify the slope and y-intercept of a linear function, given a table of values, a graph, or an equation in y = mx + b form; - 86C14286-C726-11E6-AB0D-B4EBCCC8CA83
MAFS.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. - d20d06e9-6442-49a0-8f16-bd94d3cc66b0
8.GM.8 Find the distance between any two points in the coordinate plane using the Pythagorean Theorem. - 3aa9a86b-e0f7-4b44-95f3-e7e90d1ca83e
MAFS.6.NS.3 Apply and extend previous understandings of numbers to the system of rational numbers. - ce84cbd5-eac0-4b0b-bf6c-4311036c7d9f
MAFS.7.RP.1.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. - a63f040b-c2a1-4f32-9dc1-7bea05ec3e35
CCSS.Math.Content.7.EE.B.4.a Solve word problems leading to equations of the form 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹 + 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲 = 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳 and 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳𝘱(34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘹 + 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘹𝘲) = 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳, where 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱, 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲, and 34𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. - 1EE190CA-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. - 1F5F88B8-7053-11DF-8EBF-BE719DFF4B22
MAFS.K12.MP.1.1 Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. - db656dba-3ee7-423e-9020-626812d8c8d3
8.G.6 Explain a proof of the Pythagorean Theorem and its converse. - C5AAD082-96FF-11E0-9509-C03D9DFF4B22
12.D summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution. - 9EF3B81E-0D0A-11E2-9583-8B2E9DFF4B22
8.GM.5 Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal. - 32144841-ec70-487b-84c0-dc8bbdd7121e
CCSS.Math.Content.8.EE.A Work with radicals and integer exponents. - 1F2530C8-7053-11DF-8EBF-BE719DFF4B22
8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. - C58E06DC-96FF-11E0-9509-C03D9DFF4B22
8.GM.2.c Translate geometric figures vertically and/or horizontally. - ce5b88f4-bd59-4ab5-a67d-427198d4d321
8.EEI.2.a Find the exact and approximate solutions to equations of the form x² = p and x³ = p where p is a positive rational number. - e29c841c-a886-48cd-8dc9-d9c916695bea
8.EEI.8.a Graph systems of linear equations and estimate their point of intersection. - 9a571d75-1259-4fe8-9899-8b364319e4bf
CCSS.Math.Content.8.G.A.1.a Lines are taken to lines, and line segments to line segments of the same length. - 1F5487CE-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. - 1F319AA2-7053-11DF-8EBF-BE719DFF4B22
PFA.8.17 The student will solve multistep linear equations in one variable with the variable on one or both sides of the equation, including practical problems that require the solution of a multistep linear equation in one variable. - 76671E14-C727-11E6-AD10-4273BF03DF2F
CCSS.Math.Content.8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. - 1F5A8638-7053-11DF-8EBF-BE719DFF4B22
8.EEI.5.b Interpret unit rate as the slope of the graph. - 548a011b-6b96-4996-901c-a9f69fe04415
MAFS.8.G.1.1.c Parallel lines are taken to parallel lines. - 5b59eea4-2f9e-4e0c-be6f-6387157c2fc6
CCSS.Math.Content.8.G.C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. - 1F642008-7053-11DF-8EBF-BE719DFF4B22
11.A construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data; - 9F2F9014-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. - 1EE09E22-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.G.2.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - 4e00cff0-0a3f-4199-8b2a-11056c4c5b6a
MAFS.6.EE.1.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. - 18ef41e0-8040-463b-badf-b9c76760ebec
MAFS.7.NS.1.2.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. - 02e76175-0331-4e07-aa87-eda20ed69cde
MG.8.9.a verify the Pythagorean Theorem; and - A9BB3C20-C725-11E6-A8C2-9EEACCC8CA83
MAFS.8.G.3.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. - 6b3e99c5-9d62-4b00-a8a2-909ca3c21f17
PFA.8.16.a recognize and describe the graph of a linear function with a slope that is positive, negative, or zero; - 7F38AB12-C726-11E6-9E4F-E4EBCCC8CA83
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. - 5C5422D4-7377-11DF-A1E8-223D9DFF4B22
CCSS.Math.Content.8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 34𝘺 = 34𝘺𝘮34𝘺𝘮𝘹 for a line through the origin and the equation 34𝘺𝘮𝘹𝘺 = 34𝘺𝘮𝘹𝘺𝘮34𝘺𝘮𝘹𝘺𝘮𝘹 + 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣 for a line intercepting the vertical axis at 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣. - 1F34E2FC-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.8.G.B Understand and apply the Pythagorean Theorem. - 1F5E1C9E-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.EE.3.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹 = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢, 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢 = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢, or 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢 = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣 results (where 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢 and 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣 are different numbers). - 0e595aa8-da99-42e2-8e1c-d4052b3c7547
CCSS.Math.Content.8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. - 1F4FD706-7053-11DF-8EBF-BE719DFF4B22
8.C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; and - 9F2B5F62-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.8.SP.1.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. - fad7fe16-7ca8-41fb-a982-948f76b39915
8.EEI.8 Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions. - d6606528-ac71-4476-9c22-49150a1f22a1
CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm. - 1E3EC138-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.EE.2.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. - 9363a0ab-0c0e-42c8-8087-c1d47e142616
MAFS.K12.MP.7 Look for and make use of structure. - 4b6d6fc7-f9ff-4e3c-89c9-3642b61650a0
MAFS.8.SP.1.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. - 5c7985c2-455b-4609-a53f-3c6a4ce8ca7a
CCSS.Math.Content.6.NS.C.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. - 1E4EBC5A-7053-11DF-8EBF-BE719DFF4B22
MAFS.8.G.1.1 Verify experimentally the properties of rotations, reflections, and translations: - beb495c9-71fc-4e42-bb92-718ed1466832
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦 – 2)/(34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥 – 1) = 3. Noticing the regularity in the way terms cancel when expanding (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥 – 1)(34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥 + 1), (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥 – 1)(34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥² + 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥 + 1), and (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥 – 1)(34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥³ + 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥² + 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. - 5C56FF86-7377-11DF-A1E8-223D9DFF4B22
CCSS.Math.Content.8.SP.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. - 1F715E62-7053-11DF-8EBF-BE719DFF4B22
8.EEI.3 Explore the relationship between quantities in decimal and scientific notation. - a0d359c1-b9fc-4efc-afee-99c3dc05a1b1
MAFS.8.EE.3.7 Solve linear equations in one variable. - d370e9c3-659d-4110-a4d4-e54312d04498
MAFS.K12.MP.1 Make sense of problems and persevere in solving them. - efdcc5ef-fe77-460b-b67c-303a7528d39d
2.E extend representations for division to include fraction notation such as 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎/34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏 represents the same number as 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎 ÷ 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏 where 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏 ≠ 0. - 9EDDDB84-0D0A-11E2-9583-8B2E9DFF4B22
8.EEI.4 Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems. - 185e8526-ab2b-40de-b958-f9cbf805bf0d
CCSS.Math.Content.8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. - 1F6CB2F4-7053-11DF-8EBF-BE719DFF4B22
8.EE.8.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. - C59E48EE-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. - 1F2B2D84-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. - 1E629B3A-7053-11DF-8EBF-BE719DFF4B22
7.A solve problems involving the volume of cylinders, cones, and spheres; - 9F280D62-0D0A-11E2-9583-8B2E9DFF4B22
4.A use similar right triangles to develop an understanding that slope, 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚, given as the rate comparing the change in 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦-values to the change in 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥-values, (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦₂ - 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦₁)/ (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥₂ - x₁), is the same for any two points (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥₁, 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦₁) and (34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥₂, 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦₂) on the same line; - 9F1FB266-0D0A-11E2-9583-8B2E9DFF4B22
9 The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to identify and verify the values of 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥 and 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦 that simultaneously satisfy two linear equations in the form 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦 = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥 + 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏 from the intersections of the graphed equations. - 9F2C4FA8-0D0A-11E2-9583-8B2E9DFF4B22
8.F.5.a Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous). - b8ac4025-e32a-406a-99e9-3d8940de19db
5.H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and - 9F24D278-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.8.EE.3.8 Analyze and solve pairs of simultaneous linear equations. - 40f59586-e0b6-471a-8f8a-602a2a24be37
CCSS.Math.Content.8.SP.A Investigate patterns of association in bivariate data. - 1F69AE60-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.EE.2.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. - d4254c8a-34a7-43af-90c9-cf2612cd0b0f
MAFS.7.EE.2 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. - 84704cc3-a1f2-40ad-8699-ea628597af61
NS.8.2 The student will describe the relationships between the subsets of the real number system. - 0671F4DC-C725-11E6-9476-B270BF03DF2F
MAFS.6.EE.1.2 Write, read, and evaluate expressions in which letters stand for numbers. - d9778b4b-9a14-4e70-ad22-d0e40da9bc0c
MAFS.8.EE.1.2 Use square root and cube root symbols to represent solutions to equations of the form 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹² = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱 and 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹³ = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹𝘱, where 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹𝘱𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. - 31922f5c-2d13-4455-9775-6785a6e9340a
7.NS.2.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. - C5700A2E-96FF-11E0-9509-C03D9DFF4B22
8.EE.7 Solve linear equations in one variable. - C59A7AE8-96FF-11E0-9509-C03D9DFF4B22
NS.8.1 The student will compare and order real numbers. - F0375298-C724-11E6-9A18-F2E8CCC8CA83
MG.5.13.b investigate the sum of the interior angles in a triangle and determine an unknown angle measure. - 09952E32-C666-11E6-8E1D-C56ABF03DF2F
CCSS.Math.Content.8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. - 1F6B252E-7053-11DF-8EBF-BE719DFF4B22
MAFS.6.EE.2 Reason about and solve one-variable equations and inequalities. - a971566c-0f10-4450-8b7c-8c0e1e160ab5
8.GM.9 Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders. - 2c3e01bf-d67c-4f9f-b39f-7055885e2dcc
MAFS.7.RP.1.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. - f1ba40b5-3f95-4218-88d0-a8f81e6dbfb2
8.GM.2 Apply the properties of rigid transformations (rotations, reflections, translations). - 1e0d5096-efdb-4e0e-a566-f78922228d2f
8.NS.1.a Recognize the differences between rational and irrational numbers. - 3ff580f6-6369-4a33-a465-496c4277ed20
CCSS.Math.Content.8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers. - 1F1E4754-7053-11DF-8EBF-BE719DFF4B22
8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. - C5AEABBC-96FF-11E0-9509-C03D9DFF4B22
8.EEI.3.a Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ≤ a < 10 and b is an integer. - 7e00f440-0649-46fe-93fa-e49a3d6eb103
MAFS.K12.MP.8 Look for and express regularity in repeated reasoning. - 6ff0dba2-4ea2-454f-8c62-e326c5d5841a
CCSS.Math.Content.8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. - 1F5BA5FE-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.8.EE.C.8.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. - 1F3F09DA-7053-11DF-8EBF-BE719DFF4B22
MAFS.7.G.1.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. - 476cba8c-c379-45c1-a664-39e697a361ff
MAFS.K12.MP.4 Model with mathematics. - f68eaa41-9ef2-4f61-941b-e67b099f9c02
8.F.3 Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions). - ac285cdc-a3b9-4324-93eb-7affaea40dd1
MAFS.8.F.1.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - d9cf8c40-bfc5-423c-8281-4f2082b2ade8
MG.8.7.a given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane; and - 7CC43E60-C725-11E6-A1F2-76EACCC8CA83
CCSS.Math.Content.7.RP.A.2 Recognize and represent proportional relationships between quantities. - 1EB72628-7053-11DF-8EBF-BE719DFF4B22
PS.8.13.a represent data in scatterplots; - 16395A3A-C726-11E6-8878-23EBCCC8CA83
8.F.3.c Provide examples of nonlinear functions. - 390de1ba-d518-45fc-a476-f689124edbfd
CCSS.Math.Content.7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. - 1EC1E018-7053-11DF-8EBF-BE719DFF4B22
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹𝘱𝘱𝘹² = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹𝘱𝘱𝘹𝘱 and 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹𝘱𝘱𝘹𝘱𝘹³ = 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹𝘱𝘱𝘹𝘱𝘹𝘱, where 34𝘺𝘮𝘹𝘺𝘮𝘹𝘣𝘣𝘹𝘢𝘢𝘢𝘢𝘣𝘢𝘣𝑦𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑎𝑏𝑎𝑏𝑏𝑚𝑦𝑥𝑦𝑦𝑥𝑥𝑦𝑥𝑦𝑥𝑦𝑦𝑚𝑥𝑏𝘹𝘱𝘹𝘱𝘱𝘹𝘱𝘹𝘱𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. - C5935A42-96FF-11E0-9509-C03D9DFF4B22
10.D model the effect on linear and area measurements of dilated two-dimensional shapes. - 9F2EA8A2-0D0A-11E2-9583-8B2E9DFF4B22
MAFS.K12.MP.4.1 Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. - e779da50-d12e-4314-966c-08e1656d94a3
CCSS.Math.Practice.MP4 Model with mathematics. - A6446404-6F89-11DF-BAEE-EA329DFF4B22
PFA.8.15.a determine whether a given relation is a function; and - 5FC8D8F6-C726-11E6-89CF-6F72BF03DF2F
8.EEI.3.b Translate between decimal notation and scientific notation. - 04e97317-3dc3-45a7-b32b-e93abe1a3d71
8.GM.7 Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles. - 3c6fe97c-eca6-437d-9f80-864c59256f97
CCSS.Math.Content.8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. - 1F2E953C-7053-11DF-8EBF-BE719DFF4B22
8.EE.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. - C59FABA8-96FF-11E0-9509-C03D9DFF4B22
MG.8.9.b apply the Pythagorean Theorem. - B1231C9E-C725-11E6-A4B9-9AEACCC8CA83
MAFS.8.G.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - fbfc9efe-da5a-4183-befd-a59c09d46a2a
CCSS.Math.Content.7.G.B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. - 1EEE21BE-7053-11DF-8EBF-BE719DFF4B22
8.F.1.a Understand that a function assigns to each input exactly one output. - 679479c4-cd4d-4f49-8a2f-fcc5e30dea3a
8.F.1.e Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function. - e32a82e5-6306-4ba1-aec4-877dd43d714f
8.NS.1 Explore the real number system and its appropriate usage in real-world situations. - bdccfdcf-f41b-4040-8cbf-d956a6f38c3f
8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. - C5A4E03C-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.7.G.A Draw, construct, and describe geometrical figures and describe the relationships between them. - 1EE8951E-7053-11DF-8EBF-BE719DFF4B22
8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. - C5A18C02-96FF-11E0-9509-C03D9DFF4B22
CCSS.Math.Content.8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - 1F48652A-7053-11DF-8EBF-BE719DFF4B22
6.C use models and diagrams to explain the Pythagorean theorem. - 9F2727B2-0D0A-11E2-9583-8B2E9DFF4B22
7.C use the Pythagorean Theorem and its converse to solve problems; and - 9F28F664-0D0A-11E2-9583-8B2E9DFF4B22
CCSS.Math.Content.8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. - 1F585250-7053-11DF-8EBF-BE719DFF4B22
CCSS.Math.Content.6.NS.B Compute fluently with multi-digit numbers and find common factors and multiples. - 1E3D3EC6-7053-11DF-8EBF-BE719DFF4B22
7.NS.2 Apply and extend previous underst