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1 | Department/Grade- MATH. Middle/High School | |||||||||||||||||||||||||
2 | DESE Framework Standard | SECONDARY: Unit Essential Question. ELEMENTARY: Unit Essential Question OR I Can Statements | Estimated Dates of Unit | Supporting Activities within a Unit | Notes | |||||||||||||||||||||
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4 | MATH 6 | |||||||||||||||||||||||||
5 | 6.RP.3c 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. | Solve percent proportion problems. | May 4 - 15 | Screencastify Lessons with Google Slideshow, Zoom, Online Videos, Google Forms, Quizizz, Kahoots, EdPuzzle | ||||||||||||||||||||||
6 | 6.RP.3d Use ratio reasoning to convert measurement units within and between measurement systems; manipulate and transform units appropriately when multiplying or dividing quantities. | Use proportions to convert measurement units within the same, and within different, systems. | May 4 - 15 | |||||||||||||||||||||||
7 | 6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). | Solve for volume & SA of a cube | May 18 - 29 | Screencastify Lessons with Google Slideshow, Zoom, Online Videos, Google Forms, Quizizz, Kahoots, EdPuzzle | ||||||||||||||||||||||
8 | 6.G.A Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Wrap up solving for area of quads, triangles, and comoound by decomposing | May 18 - 29 | |||||||||||||||||||||||
9 | 6.Sp.B.5a, b, c, and d Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median, and/or mean) and variability (range and/or interquartile range), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. | Summarize and describe distribution of a data set with measures of center, variablility, and set characteristics | June 1 - 5 | Screencastify Lessons with Google Slideshow, Zoom, Online Videos, Google Forms, Quizizz, Kahoots, EdPuzzle | ||||||||||||||||||||||
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12 | MATH 7 | |||||||||||||||||||||||||
13 | 7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | How can we solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | 5/11/20 - 5/29/20 | Screencastify Lessons with Google Slideshow, Zoom, Online Videos, Flexbooks Interactives, Quizizz | ||||||||||||||||||||||
14 | 7.SP.c Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1⁄2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. | How to investigate chance processes and develop, use, and evaluate probability models. | Present - 5/08/20 | Wheel of Fortune Game, Make Your Own Carnival Game Project, Screencastify lessons, Zoom, Online Videos, Quizizz | ||||||||||||||||||||||
15 | 7.EE.B.4.b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. | Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Factor linear expressions. | 5/29/20-6/16/20 | Screencastify Lessons with Google Slideshow, Zoom, Online Videos, Flexbooks Interactives, Quizizz | ||||||||||||||||||||||
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18 | MATH 8 | |||||||||||||||||||||||||
19 | 8.EE.A-1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. | How to apply properties of exponents | April 27-May15 | Lessons/notes using videos and tutorials, practice sheets with answer keys, Wednesday Wonder including DESMOS and Socrative activities | All other Math 8 Standards were taught prior to school closure or in the last 3 week period. | |||||||||||||||||||||
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22 | ALGEBRA I | |||||||||||||||||||||||||
23 | N-RN-A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | How cane we use the definition of rational exponents to rewrite radicals using rational exponents? | Done | |||||||||||||||||||||||
24 | N-RN-A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. | How can we use the properties of exponents to rewrite expressions | Done | |||||||||||||||||||||||
25 | A-SSE-A-1 Interpret expressions that represent a quantity in terms of its context. | What does each quatity in given expressions represent in terms of its context? | Done | |||||||||||||||||||||||
26 | A-SSE-B-3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | How can we rewrite quadratic expressions to reveal various properties? | Done | |||||||||||||||||||||||
27 | A-APR-A-1 Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations. | How can we perform operations on polynomials in order to simplify as much as possible? | Done | |||||||||||||||||||||||
28 | A-APR.B-3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | How do we calculate zeros of polynomial functions in order to graph? | Done | |||||||||||||||||||||||
29 | A-CED-A-1-4 Create equations and inequalities in one variable and use them to solve problems. (Include equations arising from linear and quadratic functions, and simple root and rational functions and exponential functions.) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | How will we use variables to display relationships? | Done | |||||||||||||||||||||||
30 | A-REI-B-3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | What are the processes we will use to solve linear equations in one variable? | Done | |||||||||||||||||||||||
31 | A-REI-B-4 Solve quadratic equations in one variable. | What are the various methods we can use to solve quadratics? How can we identify which method is better to use? | Week of 04.20.20 | Guided Notes with answer keys; videos; Zoom Lessons; practice worksheets | ||||||||||||||||||||||
32 | A-REI-C-6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. | What are the methods and how can we solve systems of linear equations? | Done | |||||||||||||||||||||||
33 | A-REI-D-10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Show that any point on the graph of an equation in two variables is a solution to the equation. | What does a line or curve actually represent? | Done | |||||||||||||||||||||||
34 | A-REI-D-12 Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | How do we graph a linear inequality and what does the shaded region actually mean? | Done | |||||||||||||||||||||||
35 | F-IF-A-1-2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | What does function notation look like and mean? What do the domain and range represent of any function? | Done | |||||||||||||||||||||||
36 | F-IF-B-4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | How can we use graphs to model and interpret relationship? | Done | |||||||||||||||||||||||
37 | F-IF-C-7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | How do we graph various functions like quadratic and square root functions? | Week of 05.20.20 | Guided Notes with Answer keys provided; videos; Zoom lessons; Practice worksheets | ||||||||||||||||||||||
38 | F-IF-C-8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | How will the process of completing the square help us visualize characteristics of quadratics? | Done | |||||||||||||||||||||||
39 | F-LE-A-1-3 Distinguish between situations that can be modeled with linear functions and with exponential functions. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table). Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | How can we recognize linear, quadratic, and exponential functions when given various representations? | Week of 04.28.20 | Guided Notes with Answer keys provided; videos; Zoom lessons; Practice worksheets | ||||||||||||||||||||||
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42 | GEOMETRY | |||||||||||||||||||||||||
43 | G-CO-A-1-2-5 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. | Transformations in the Plane | Week of 06.08.20 | Kahn Academy videos, scaffolded google docs, select worksheets | ||||||||||||||||||||||
44 | G-SRT-A-1-a-b Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. | Similarity Transformation | Week of 06.08.20 | Similarity compiled packet. | ||||||||||||||||||||||
45 | G-SRT-B-4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. | Prove Theorems on Similarity | Done | |||||||||||||||||||||||
46 | G-SRT-C-6-7-8 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Explain and use the relationship between the sine and cosine of complementary angles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. | Trig Ratios to Solve Right Triangles | Done | *College 2 will cover this in Algebra II next year. | ||||||||||||||||||||||
47 | G-C-B-5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. | Arc lengths, Areas of Sectors of Circles | Week of 04.27.20 | scaffolded google docs, select worksheets | ||||||||||||||||||||||
48 | G-GPE-B-4-5 Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). | Use Coordinates to Prove Geometric Theorems | Done | |||||||||||||||||||||||
49 | G-GMD-A-1 & 5 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | Explain Volume Formulas and Use them to Solve Problems | Week of 05.18.20 | Kahn Academy videos, scaffolded google docs, select worksheets | ||||||||||||||||||||||
50 | G-MG-A-1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). | Apply Geometric Concepts in Modeling Situations | Done | |||||||||||||||||||||||
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53 | ALGEBRA II | |||||||||||||||||||||||||
54 | A-SSE-A-1 Interpret expressions that represent a quantity in terms of its context. | How can we interpret the structure of linear, quadratic, exponential, polynomial, and rational expressions? | Done (H); Mid May to June (C1/C2) | Guided notes with answer keys provided, Sreencastify and related videos, Zoom meetings, worksheet or textbook problems, worked out solutions | ||||||||||||||||||||||
55 | A-SSE-B-3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | How can write expressions in equivalent forms to solve problems? | Done (H/C1)/(early May C2) | Guided notes with answer keys provided, related videos, Zoom meetings, worksheet or textbook problems, worked out solutions | ||||||||||||||||||||||
56 | A-APR-A-1 Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations. | How can we perform arithmetic operations on polynomials? | Done | |||||||||||||||||||||||
57 | A-APR.B-3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | How do we understand the relationship between zeros and factors of polynomials? | Done | |||||||||||||||||||||||
58 | A-REI-D-10-12 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Show that any point on the graph of an equation in two variables is a solution to the equation. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | How do we represent and solve equations and inequalities graphically? | Done | |||||||||||||||||||||||
59 | F-BF-B-3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x, f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. (Include linear, quadratic, exponential, absolute value, simple rational and radical, logarithmic and trigonometric functions.) Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph. (Include recognizing even and odd functions from their graphs and algebraic expressions for them.) | How do we build new functions from existing functions? | Done | |||||||||||||||||||||||
60 | F-IF-C-7-10 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Translate among different representations of functions (algebraically, graphically, numerically in tables, or by verbal descriptions). Compare properties of two functions each represented in a different way. Given algebraic, numeric and/or graphical representations of functions, recognize the function as polynomial, rational, logarithmic, exponential, or trigonometric. | How can you analyze different types of equations uing graphs, equations, and translations from parent functions? | Done | |||||||||||||||||||||||
61 | F-BF-A-1 Write a function (linear, quadratic, exponential, simple rational, radical, logarithmic, and trigonometric) that describes a relationship between two quantities. | How can you write a linear, exponential and quadratic function to represent a sequence both recursively and explicitly? | May 10-May 24 (H/C2), Done (C1) | Completed notes, online videos, textbook work, supporting answer keys | ||||||||||||||||||||||
62 | F-BF-A - 2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | How can you write arithmetic and geometric sequences both recursively and explicitly? | May 10-May 24 (H), Done (C1/C2) | Completed notes, online videos, textbook work, supporting answer keys | ||||||||||||||||||||||
63 | F-LE-A-1-3 Distinguish between situations that can be modeled with linear functions and with exponential functions. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table). Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | How do the graphs and functions of linear, quadratic and exponential equations compare? | Done | |||||||||||||||||||||||
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66 | PRECALCULUS | |||||||||||||||||||||||||
67 | F-IF-B-4&6 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. | How do we interpret functions that arise in applications in terms of the context (linear, quadratic, exponential, rational, polynomial, square root, cube root, trigonometric, logarithmic)? | Done | |||||||||||||||||||||||
68 | F-IF-C-7-10 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Translate among different representations of functions (algebraically, graphically, numerically in tables, or by verbal descriptions). Compare properties of two functions each represented in a different way. Given algebraic, numeric and/or graphical representations of functions, recognize the function as polynomial, rational, logarithmic, exponential, or trigonometric. | Analyze Functions using different representations | Done | |||||||||||||||||||||||
69 | F-BF-A-1-2 Write a function (linear, quadratic, exponential, simple rational, radical, logarithmic, and trigonometric) that describes a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. | Build a function that models a relationship between two quantities | Done | |||||||||||||||||||||||
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72 | AP STATISTICS | |||||||||||||||||||||||||
73 | SI-C-A-4 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | How can we understand statistics as a process for making inferences about population parameters based on a random sample from that population? | Present - 05.22.20 | Guided notes, videos, inference worksheets, mock AP tests | ||||||||||||||||||||||
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