## Holidays

## Math

World HolidaysChristmas Day Numerical Proportions Seventh Grade Math Introduction to Probability Seventh Grade Math Introduction to Percent Seventh Grade Math The Pythagorean Theorem Seventh Grade Math Applications of percent Eighth Grade Math Perimeter and area Eighth Grade Math ### CO.8.1. Number Sense, Properties, and Operations

#### 8.1.1. In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line. Students can:

##### 8.1.1.a. Define irrational numbers.

##### 8.1.1.b. Demonstrate informally that every number has a decimal expansion. (CCSS: 8.NS.1)

###### 8.1.1.b.ii. Convert a decimal expansion which repeats eventually into a rational number. (CCSS: 8.NS.1)

##### 8.1.1.d. Apply the properties of integer exponents to generate equivalent numerical expressions. (CCSS: 8.EE.1)

##### 8.1.1.e. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. (CCSS: 8.EE.2)

##### 8.1.1.f. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. (CCSS: 8.EE.2)

##### 8.1.1.g. Use numbers expressed in the form of a single digit times a whole number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. (CCSS: 8.EE.3)

##### 8.1.1.h. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. (CCSS: 8.EE.4)

###### 8.1.1.h.i. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. (CCSS: 8.EE.4)

###### 8.1.1.h.ii. Interpret scientific notation that has been generated by technology. (CCSS: 8.EE.4)

### CO.8.2. Patterns, Functions, and Algebraic Structures

#### 8.2.1. Linear functions model situations with a constant rate of change and can be represented numerically, algebraically, and graphically. Students can:

##### 8.2.1.a. Describe the connections between proportional relationships, lines, and linear equations. (CCSS: 8.EE)

##### 8.2.1.b. Graph proportional relationships, interpreting the unit rate as the slope of the graph. (CCSS: 8.EE.5)

##### 8.2.1.d. 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. (CCSS: 8.EE.6)

##### 8.2.1.e. Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. (CCSS: 8.EE.6)

#### 8.2.2. Properties of algebra and equality are used to solve linear equations and systems of equations. Students can:

##### 8.2.2.a. Solve linear equations in one variable. (CCSS: 8.EE.7)

###### 8.2.2.a.i. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. (CCSS: 8.EE.7a)

###### 8.2.2.a.ii. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (CCSS: 8.EE.7b)

#### 8.2.3. Graphs, tables and equations can be used to distinguish between linear and nonlinear functions. Students can:

##### 8.2.3.a. Define, evaluate, and compare functions. (CCSS: 8.F)

###### 8.2.3.a.i. Define a function as a rule that assigns to each input exactly one output. (CCSS: 8.F.1)

###### 8.2.3.a.ii. Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (CCSS: 8.F.1)

###### 8.2.3.a.iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (CCSS: 8.F.3)

##### 8.2.3.b. Use functions to model relationships between quantities. (CCSS: 8.F)

###### 8.2.3.b.ii. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (CCSS: 8.F.4)

###### 8.2.3.b.iii. 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. (CCSS: 8.F.4)

###### 8.2.3.b.iv. Describe qualitatively the functional relationship between two quantities by analyzing a graph. (CCSS: 8.F.5)

###### 8.2.3.b.v. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. (CCSS: 8.F.5)

### CO.8.3. Data Analysis, Statistics, and Probability

#### 8.3.1. Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge. Students can:

##### 8.3.1.a. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. (CCSS: 8.SP.1)

##### 8.3.1.b. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (CCSS: 8.SP.1)

##### 8.3.1.c. 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. (CCSS: 8.SP.2)

### CO.8.4. Shape, Dimension, and Geometric Relationships

#### 8.4.1. Transformations of objects can be used to define the concepts of congruence and similarity. Students can:

##### 8.4.1.a. Verify experimentally the properties of rotations, reflections, and translations. (CCSS: 8.G.1)

##### 8.4.1.c. Demonstrate 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. (CCSS: 8.G.2)

##### 8.4.1.e. Demonstrate 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. (CCSS: 8.G.4)

#### 8.4.2. Direct and indirect measurement can be used to describe and make comparisons. Students can:

##### 8.4.2.b. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (CCSS: 8.G.7)

##### 8.4.2.d. State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (CCSS: 8.G.9)

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