## Math

Ratio Fifth Grade Math Measurement Third Grade Math Geometric Proportions Seventh Grade Math Whole Numbers to Millions Fifth Grade Math Multiplication Third Grade Math Decimals/Fractions Fourth Grade Math Measurement Fourth 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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