Math 8 Quarter 3 Project:
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The project handouts are displayed below. There is also a list of POSSIBLE controversial topics that students could use to create their five questions for their survey project. Please email your teacher if there are any questions, comments or concerns regarding the project.
NOTE: MRS.SHORE has extended the question due date for her class until THURSDAY February 26. MRS. Reyes has extended the questions due date for her class until Friday February 27. Math 1 students please email me to get your information and due dates. |
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Mrs. Shore & Mrs. Reyes
Math 8 classes
Math 8
Quarter 1 Unit 1:Exponents 8.EE.1 In 6th grade, students wrote and evaluated simple numerical expressions with whole number exponents (ie. 53 = 5 • 5 • 5 = 125). Integer (positive and negative) exponents are further developed to generate equivalent numerical expressions when multiplying, dividing or raising a power to a power. Using numerical bases and the laws of exponents, students generate equivalent expressions. 8.EE.2 Students recognize perfect squares and cubes, understanding that non-perfect squares and non-perfect cubes are irrational. Students recognize that squaring a number and taking the square root √ of a number are inverse operations; likewise, cubing a number and taking the cube root ³√ are inverse operations. 8.EE.3Students use scientific notation to express very large or very small numbers. Students compare and interpret scientific notation quantities in the context of the situation, recognizing that if the exponent increases by one, the value increases 10 times. Likewise, if the exponent decreases by one, the value decreases 10 times. Students solve problems using addition, subtraction or multiplication, expressing the answer in scientific notation. 8.EE.4Students understand scientific notation as generated on various calculators or other technology. Students enter scientific notation using E or EE (scientific notation), * (multiplication), and ^ (exponent) symbols. 8.EE.7Students solve one-variable equations including those with the variables being on both sides of the equals sign. Students recognize that the solution to the equation is the value(s) of the variable, which make a true equality when substituted back into the equation. Equations shall include rational numbers, distributive property and combining like terms. 8.NS.1 Students understand that Real numbers are either rational or irrational. They distinguish between rational and irrational numbers, recognizing that any number that can be expressed as a fraction is a rational number. The diagram below illustrates the relationship between the subgroups of the real number system. 8.NS.2 Students locate rational and irrational numbers on the number line. Students compare and order rational and irrational numbers. Students also recognize that square roots may be negative and written as - √28. Unit 2: Pythagorean Theorem and Volume 8.G.6 Using models, students explain the Pythagorean Theorem, understanding that the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle. Students also understand that given three side lengths with this relationship forms a right triangle. 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. 8.G.8 One application of the Pythagorean Theorem is finding the distance between two points on the coordinate plane. Students build on work from 6th grade (finding vertical and horizontal distances on the coordinate plane) to determine the lengths of the legs of the right triangle drawn connecting the points. Students understand that the line segment between the two points is the length of the hypotenuse. 8.G.9 Students build on understandings of circles and volume from 7th grade to find the volume of cylinders, finding the area of the base ∏r2 and multiplying by the number of layers (the height). Quarter 2 Unit 3: Transformations and Congruency 8.G.1 Students use compasses, protractors and rulers or technology to explore figures created from translations, reflections and rotations. Characteristics of figures, such as lengths of line segments, angle measures and parallel lines, are explored before the transformation (pre-image) and after the transformation (image).Students understand that these transformations produce images of exactly the same size and shape as the pre-image and are known as rigid transformations. 8.G.2 This standard is the students’ introduction to congruency. Congruent figures have the same shape and size. Translations, reflections and rotations are examples of rigid transformations. A rigid transformation is one in which the pre-image and the image both have exactly the same size and shape since the measures of the corresponding angles and corresponding line segments remain equal (are congruent).Students examine two figures to determine congruency by identifying the rigid transformation(s) that produced the figures. Students recognize the symbol for congruency (≅) and write statements of congruency. 8.G.3 Students identify resulting coordinates from translations, reflections, and rotations (90º, 180º and 270º both clockwise and counterclockwise), recognizing the relationship between the coordinates and the transformation. 8.G.4 Similar figures and similarity are first introduced in the 8th grade. Students understand similar figures have congruent angles and sides that are proportional. Similar figures are produced from dilations. Students describe the sequence that would produce similar figures, including the scale factors. Students understand that a scale factor greater than one will produce an enlargement in the figure, while a scale factor less than one will produce a reduction in size. 8.G.5 Students use exploration and deductive reasoning to determine relationships that exist between the following: a) angle sums and exterior angle sums of triangles, b)angles created when parallel lines are cut by a transversal, and c) the angle-angle criterion for similarity of triangle. Students construct various triangles and find the measures of the interior and exterior angles. Students make conjectures about the relationship between the measure of an exterior angle and the other two angles of a triangle.(the measure of an exterior angle of a triangle is equal to the sum of the measures of the other two interior angles) and the sum of the exterior angles (360º).Using these relationships, students use deductive reasoning to find the measure of missing angles. Students construct parallel lines and a transversal to examine the relationships between the created angles. Students recognize vertical angles, adjacent angles and supplementary angles from 7th grade and build on these relationships to identify other pairs of congruent angles. Using these relationships, students use deductive reasoning to find the measure of missing angles. Unit 4: Functions 8.F.1 Students understand rules that take x as input and gives y as output is a function. Functions occur when there is exactly one y-value is associated with any x-value. Using y to represent the output we can represent this function with the equations y = x2 + 5x + 4. Students are not expected to use the function notation f(x) at this level. Students identify functions from equations, graphs, and tables/ordered pairs. 8.F.2 Students compare two functions from different representations. Quarter 3 and 4 Unit 5: Linear Functions 8.EE.5 Students build on their work with unit rates from 6th grade and proportional relationships in 7th grade to compare graphs, tables and equations of proportional relationships. Students identify the unit rate (or slope) in graphs, tables and equations to compare two proportional relationships represented in different ways. 8.EE.6 Triangles are similar when there is a constant rate of proportionality between them. Using a graph, students construct triangles between two points on a line and compare the sides to understand that the slope (ratio of rise to run) is the same between any two points on a line. 8.F.3 Students understand that linear functions have a constant rate of change between any two points. Students use equations, graphs and tables to categorize functions as linear or non-linear. Unit6: Linear Models and Patterns of Association 8.F.4 Students identify the rate of change (slope) and initial value (y-intercept) from tables, graphs, equations or verbal descriptions to write a function (linear equation).Students understand that the equation represents the relationship between the x-value and the y-value; what math operations are performed with the x-value to give the y-value. Slopes could be undefined slopes or zero slopes. 8.F.5 Given a verbal description of a situation, students sketch a graph to model that situation. Given a graph of a situation, students provide a verbal description of the situation. 8.SP.1 Bivariate data refers to two-variable data, one to be graphed on the x-axis and the other on the y-axis. Students represent numerical data on a scatter plot, to examine relationships between variables. They analyze scatter plots to determine if the relationship is linear (positive, negative association or no association) or non-linear. Students can use tools such as those at the National Center for Educational Statistics to create a graph or generate data sets. 8.SP.2 Students understand that a straight line can represent a scatter plot with linear association. The most appropriate linear model is the line that comes closest to most data points. The use of linear regression is not expected. If there is a linear relationship, students draw a linear model. Given a linear model, students write an equation. 8.SP.3 Linear models can be represented with a linear equation. Students interpret the slope and y-intercept of the line in the context of the problem. 8.SP.4 Students understand that a two-way table provides a way to organize data between two categorical variables. Data for both categories needs to be collected from each subject. Students calculate the relative frequencies to describe associations. |
Mrs. Reyes
Math 1 Classes (1st & 4th Period)
Math 1
Unit 1 Patterns of Chage http://mathwithclayton.wikispaces.com/file/view/unit01.pdf Description: Understanding relationships between variables is key to the study of algebra and is the focus of this unit of study. Exploring a wide variety of relationships between variables from real-world situations introduces students to the broad idea of rate of change. Connecting rates of change to patterns found in graphs, tables, and algebraic rules gives students an opportunity to think about representing the relationship between two variables in a variety of ways. Students are introduced to iterative or recursive change, using the words NOWand NEXT to get a sense of recursive change. Students also focus on how to write symbolic rules for relations among variables. This unit also explores the use of the table-building and graphing capabilities of their calculators to study linear and nonlinear relationships. Unit 2 Pattern in Data http://math.buffalostate.edu/~wilsondc/MED588/CPunit02Patterns_in_Data.pdf Description: Students will develop tools and strategies that will help them make sense of data and communicate their conclusions. The focus will be on displaying data (to observe shape, location, outliers, clusters, and gaps) and then computing and interpreting summary statistics, such as measures of center (mean, median, and mode) and measures of variability (range, inter quartile range, and standard deviation). Unit 3: Linear Models and Patterns of Association http://math.buffalostate.edu/~wilsondc/MED%20600/unit03.pdf Description: In studying relationships between variables, one of the simplest but most important patterns is linear. Students identify connections between multiple representations of linear relationships. Students explore techniques for distributions of bivariate data. Students will describe the shape of a scatter plot and are introduced to the vocabulary of correlation.Students understand strong versus weak correlation and positive versus negative correlation data. Another numerical measurement of the strength of a linear relationship, Pearson’s correlation coefficient r, is developed and used in practical applications. Students also learn whether a strong correlation between two variables necessarily implies a cause-and-effect relationship. Characteristics of the least squares regression line and residuals are explored. Unit 4: Exponential Functions (Unit 5 in the book) https://mathwithclayton.wikispaces.com/file/view/unit05.pdf Description: Many relationships between variables are non-linear. Exponential functions are commonly used in a variety of real-world situations. For example, exponential functions are used to solve problems related to population change, interest on investments, half-lives of drugs, spread of and cleanup of pollution, and radioactive decay. The two main topics in studying exponential functions are the areas of exponential growth and exponential decay. Students learn that exponential functions can be written using a function rule f(x)= abx.In this rule, a represents the starting value when x=0, and brepresents the rate of change. Students identify that in a recursive relationship for exponential functions, to move from one value to the next, a common multiplier is used. For example tn+1= tnx b or NEXT = NOW x b, including initial value for t0 or NOW. Moving between the multiple representations of tables, graphs, real-world contexts and function rules (both explicit and recursive) and observing the connections deepens students' understanding of the rate of change modeled in each case. Unit 5: Patterns in Shape Description: This unit integrates two-dimensional and three-dimensional shapes. It focuses on developing and using formulas to compute volume of cylinders, cones, pyramids, and spheres.These skills can be applied to many real-world applications such as packaging and optimizing use of materials needed to make a particular shape.Calculations of appropriate units and conversions between them are also included. Unit 6: Quadratic Functions Description: An important nonlinear function category is quadratics. Understanding characteristics of quadratic functions and connections between various representations are developed in this unit. In the table form of a quadratic function, the change in the rate of change distinguishes it from a linear relationship. In particular, looking at the second rates of change or differences is where a constant value occurs. The symmetry of the function values can be found in the table. The graphical form shows common characteristics of quadratic functions including maximum or minimum values, symmetric shapes (parabolas), location of the y-intercept, and the ability to determine roots of the function. This unit explores the polynomial form [f (x) = ax2 + bx + c] and factored form [f(x) = a (x -p ) (x - q)] of quadratic functions and the impact of changing the parameters a, b, and c.Connections should be made between each explicit form and its graph and table. Real-world situations that can be modeled by quadratic functions include projectile motion, television dish antennas, revenue and profit models in business, and the shape of suspension bridge cables. Students learn to distinguish relationships between variables that are functions from those that are not They use f(x)notation to represent functions and identify domain and range of functions. Test Practice http://www.classzone.com/books/algebra_1/oltp_welcome.cfm | ||||||||||||||||||||||||||||||||
