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Liquid Measure Kindergarten Math Shapes Kindergarten Math Whole Numbers Kindergarten Math Numbers 1-10 Kindergarten Math Measurement First Grade Math Patterns & Sorting Kindergarten 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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