## Math CCGPS/Unit Information

MATH CLASSES:

I am placing a link that will take you to the CCGPS (Common Core Georgia Performance Standards). You can also click on tab below the map for the CCGPS to see the standards. If you have any questions please feel free to contact me via e-mail and I will get back to you as soon as possible.

CCGPS 7^{th Grade }

The middle school standards specify the mathematics that all students should study in order to be high school ready. The middle school standards are listed in conceptual categories including Number Sense, Algebra, Expressions and Equations, Geometry, and Statistics and Probability.

In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two‐ and three‐dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics such as estimation, mental computation, and basic computation facts should be addressed on an ongoing basis. Ideas related to the eight practice standards should be addressed constantly as well. To assure that these units are taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under "Evidence of Learning" be reviewed early in the planning process. A variety of resources should be utilized to supplement these units. These units provide much needed content information, but excellent learning activities as well. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources.

Numbers and Number Systems.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

__MCC7.NS.1 __Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

__MCC7.NS.1a __Describe situations in which opposite quantities combine to make 0. *For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. *

** MCC7.NS.1b Understand 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. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real**‐

**world contexts.**

__MCC7.NS.1c __Understand subtraction of rational numbers as adding the additive inverse, ** p - q = p+(-q). 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.**

__MCC7.NS.1d __Apply properties of operations as strategies to add and subtract rational numbers.

__MCC7.NS.2 __Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

** MCC7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1) (-1) = 1and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real**‐

**world contexts.**

** MCC7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non**‐

**zero divisor) is a rational number. If p and q are integers then –(p/q) = (-p)/q = p / (-q). Interpret quotients of rational numbers by describing real**‐

**world contexts.**

__MCC7.NS.2c __Apply properties of operations as strategies to multiply and divide rational numbers.

__MCC7.NS.2d __Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

** MCC7.NS.3 Solve real**‐

**world and mathematical problems involving the four operations with rational numbers.**

Expressions.

Use properties of operations to generate equivalent expressions.

__MCC7.EE.1 __Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

__MCC7.EE.2 __Understand 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. *For example, a + 0.05a = 1.05a means that "increase by5%" is the same as "multiply by 1.05." *

Equations and inequalities.

** MCC7.EE.3 Solve multi**‐

**step real**‐

**life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.**

*For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.*

** MCC7.EE.4 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.**

__ __

__MCC7.EE.4a __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. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. *For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? *

** MCC7.EE.4b 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. Graph the solution set of the inequality and interpret it in the context of the problem.**

*For example, as a**salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.*

** **

Draw, construct, and describe geometrical figures and describe the relationships between them.

__MCC7.G.1 __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.

__MCC7.G.2 __Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

** MCC7.G.3 Describe the two**‐

**dimensional figures that result from slicing three**‐

**dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.**

__MCC7.G.4 __Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

** MCC7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi**‐

**step problem to write and solve simple equations for an unknown angle in a figure.**

** MCC7.G.6 Solve real**‐

**world and mathematical problems involving area, volume and surface area of two**‐

**and three**‐

**dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.**

** **

Use random sampling to draw inferences about a population.

__MCC7.SP.1 __Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

__MCC7.SP.2 __Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. *For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. *

Draw informal comparative inferences about two populations.

__MCC7.SP.3 __Informally assess the degree of visual overlap of two numerical data distributions with similar variability’s, measuring the difference between the centers by expressing it as a multiple of a measure of variability. *For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. *

** MCC7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh**‐

**‐**

*grade science book are generally longer than the words in a chapter of a fourth*

*grade science book.*

Investigate chance processes and develop, use, and evaluate probability models.

__MCC7.SP.5 __Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

** MCC7.SP.6 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.**

*For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.*__MCC7.SP.7 __Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

__MCC7.SP.7a __Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. *For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. *

__ __

** MCC7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open**‐

*end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?*__MCC7.SP.8 __Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

__MCC7.SP.8a __Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

__MCC7.SP.8b __Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

__ __

__MCC7.SP.8c __Design and use a simulation to generate frequencies for compound events. *For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? *

* *

https://www.georgiastandards.org/Common-Core/Pages/default.aspx