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American Symbols & HolidaysThanksgiving Day Division Third Grade Math Measurement Fourth Grade Math Addition Facts First Grade Math Subtraction Facts First Grade Math Compare and Order Fractions Fifth Grade Math Patterns First Grade Math ### CO.7.1. Number Sense, Properties, and Operations

#### 7.1.1. Proportional reasoning involves comparisons and multiplicative relationships among ratios. Students can:

##### 7.1.1.a. Analyze proportional relationships and use them to solve real-world and mathematical problems. (CCSS: 7.RP)

##### 7.1.1.b. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (CCSS: 7.RP.1)

##### 7.1.1.c. Identify and represent proportional relationships between quantities. (CCSS: 7.RP.2)

###### 7.1.1.c.i. Determine whether two quantities are in a proportional relationship. (CCSS: 7.RP.2a)

###### 7.1.1.c.ii. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (CCSS: 7.RP.2b)

##### 7.1.1.d. Use proportional relationships to solve multistep ratio and percent problems. (CCSS: 7.RP.3)

###### 7.1.1.d.i. Estimate and compute unit cost of consumables (to include unit conversions if necessary) sold in quantity to make purchase decisions based on cost and practicality (PFL).

###### 7.1.1.d.ii. Solve problems involving percent of a number, discounts, taxes, simple interest, percent increase, and percent decrease (PFL).

#### 7.1.2. Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently. Students can:

##### 7.1.2.a. Apply understandings of addition and subtraction to add and subtract rational numbers including integers. (CCSS: 7.NS.1)

###### 7.1.2.a.iii. Demonstrate p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. (CCSS: 7.NS.1b)

###### 7.1.2.a.vi. Demonstrate subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). (CCSS: 7.NS.1c)

###### 7.1.2.a.vii. 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. (CCSS: 7.NS.1c)

###### 7.1.2.a.viii. Apply properties of operations as strategies to add and subtract rational numbers. (CCSS: 7.NS.1d)

##### 7.1.2.b. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers including integers. (CCSS: 7.NS.2)

###### 7.1.2.b.i. Apply properties of operations to multiplication of rational numbers. (CCSS: 7.NS.2a)

###### 7.1.2.b.ii. Interpret products of rational numbers by describing real-world contexts. (CCSS: 7.NS.2a)

###### 7.1.2.b.iii. Apply properties of operations to divide integers. (CCSS: 7.NS.2b)

###### 7.1.2.b.iv. Apply properties of operations as strategies to multiply and divide rational numbers. (CCSS: 7.NS.2c)

###### 7.1.2.b.v. Convert a rational number to a decimal using long division. (CCSS: 7.NS.2d)

##### 7.1.2.c. Solve real-world and mathematical problems involving the four operations with rational numbers. (CCSS: 7.NS.3)

### CO.7.2. Patterns, Functions, and Algebraic Structures

#### 7.2.1. Properties of arithmetic can be used to generate equivalent expressions. Students can:

##### 7.2.1.a. Use properties of operations to generate equivalent expressions. (CCSS: 7.EE)

###### 7.2.1.a.i. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. (CCSS: 7.EE.1)

###### 7.2.1.a.ii. Demonstrate that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. (CCSS: 7.EE.2)

#### 7.2.2. Equations and expressions model quantitative relationships and phenomena. Students can:

##### 7.2.2.b. 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. (CCSS: 7.EE.3)

##### 7.2.2.c. 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. (CCSS: 7.EE.4)

###### 7.2.2.c.i. Fluently solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. (CCSS: 7.EE.4a)

###### 7.2.2.c.iii. 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. (CCSS: 7.EE.4b)

###### 7.2.2.c.iv. Graph the solution set of the inequality and interpret it in the context of the problem. (CCSS: 7.EE.4b)

### CO.7.3. Data Analysis, Statistics, and Probability

#### 7.3.1. Statistics can be used to gain information about populations by examining samples. Students can:

##### 7.3.1.a. Use random sampling to draw inferences about a population. (CCSS: 7.SP)

###### 7.3.1.a.ii. Explain that random sampling tends to produce representative samples and support valid inferences. (CCSS: 7.SP.1)

#### 7.3.2. Mathematical models are used to determine probability. Students can:

##### 7.3.2.a. Explain that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. (CCSS: 7.SP.5)

##### 7.3.2.b. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. (CCSS: 7.SP.6)

##### 7.3.2.c. Develop a probability model and use it to find probabilities of events. (CCSS: 7.SP.7)

###### 7.3.2.c.i. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (CCSS: 7.SP.7)

###### 7.3.2.c.ii. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (CCSS: 7.SP.7a)

##### 7.3.2.d. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (CCSS: 7.SP.8)

###### 7.3.2.d.i. Explain that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. (CCSS: 7.SP.8a)

###### 7.3.2.d.ii. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. (CCSS: 7.SP.8b)

### CO.7.4. Shape, Dimension, and Geometric Relationships

#### 7.4.1. Modeling geometric figures and relationships leads to informal spatial reasoning and proof. Students can:

##### 7.4.1.a. Draw construct, and describe geometrical figures and describe the relationships between them. (CCSS: 7.G)

###### 7.4.1.a.i. 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. (CCSS: 7.G.1)

#### 7.4.2. Linear measure, angle measure, area, and volume are fundamentally different and require different units of measure. Students can:

##### 7.4.2.a. State the formulas for the area and circumference of a circle and use them to solve problems. (CCSS: 7.G.4)

##### 7.4.2.b. Give an informal derivation of the relationship between the circumference and area of a circle. (CCSS: 7.G.4)

##### 7.4.2.c. Use properties of supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (CCSS: 7.G.5)

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