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MD.MA.7.EE.Expressions and Equations (EE)
Expressions and Equations (EE)
Use properties of operations to generate equivalent expressions.
7.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 by 5%” is the same as “multiply by 1.05.”
7.EE.2.1. Ability to utilize Properties of Operations in order to rewrite expressions in different forms.
Solve real-life mathematical problems using numerical and algebraic expressions and equations.
7.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 to calculate with numbers in any form; c
7.EE.3.1. See the skills and knowledge that are stated in the Standard.
7.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.
7.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
7.EE.4b.1. Ability to develop correct usage of all four inequality symbols and related terminology (at least, no more than, etc.).
Draw, construct, and describe geometrical figures and describe the relationships between them.
7.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.
7.G.1.1. Ability to describe and identify ratios and proportions (see 7.RP.1 and 7.RP.2).
7.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.
7.G.3.2. Ability to differentiate between the characteristics of right rectangular prisms and right rectangular pyramids.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.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.
7.G.4.1. Ability to identify and apply the vocabulary for a circle – radius, diameter, chord, circumference, center, pi (π)≈3.14159 and 22/7.
7.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 (SC 7).
7.G.5.1. Ability to explore the relationship between the angles of intersecting lines and figures.
Quiz, Flash Cards, Worksheet, Game & Study GuideFinding Volume
7.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.
7.G.6.1. See the skills and knowledge that are stated in the Standard.
Quiz, Flash Cards, Worksheet, Game & Study GuideVolume
MD.MA.7.NS.The Number System (NS)
The Number System (NS)
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, and represent addition and subtraction on a horizontal or vertical number line diagram.
7.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.
7.NS.1a.1. Ability to build on prior experience with positive and negative rational numbers (see 6.NS.5).
7.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 numbe
7.NS.1b.1. Ability to build on prior experience with absolute value (see 6.NS.7).
7.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.
7.NS.1c.1. See the skills and knowledge that are stated in the Standard.
7.NS.1d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.1d.1. Ability to identify and apply the following properties: Commutative Property of Addition; Associative Property of Addition; Identity Property of Addition.
7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational number.
7.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) = 1 and the rules for
7.NS.2a.1. Ability to identify and apply the following properties: Multiplicative Inverse; Commutative Property of Multiplication; Associative Property of Multiplication; Identity Property of Multiplication; Recognize that rules for multiplying signed numbers remain
7.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 de
7.NS.2b.2. Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to extend to multiplication and division.
Quiz, Flash Cards, Worksheet, Game & Study GuideUsing Integers
7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.2c.1. Ability to identify and apply the following properties: Distributive Property; Associative Properties; Commutative Properties; Identity Properties.
Quiz, Flash Cards, Worksheet, Game & Study GuideUsing Integers
7.NS.2d. Convert a rational number to a decimal using long division; and know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NS.2d.1. Ability to recognize that when rational numbers in fractional form are converted to decimals, they either terminate or repeat.
7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
7.NS.3.2. Ability to apply knowledge of Order of Operations.
Quiz, Flash Cards, Worksheet, Game & Study GuideUsing Integers
MD.MA.7.RP.Ratios and Proportional Relationships (RP)
Ratios and Proportional Relationships (RP)
Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like and or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fractio
7.RP.1.2. Ability to recognize the difference(s) between a unit rate and a ratio (see 7.G.1).
7.RP.2. Recognize and represent proportional relationships between quantities.
7.RP.2a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
7.RP.2a.1. Ability to recognize in a given proportional situation that the two “between ratios” and the two “within ratios” are the same.
7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships.
7.RP.2b.1. Ability to express unit rates using a variety of representations, given a contextual situation.
7.RP.2c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number of n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
7.RP.2c.1. Ability to recognize that multiplicative relationships are proportional.
7.RP.2d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7.RP.2d.1. Ability to identify that a proportional relationship intersects (0,0).
7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
7.RP.3.1. Ability to build on prior experience with equivalent fractions to solve multi-step problems with ratio and percent (see 6.RP.3c).
Investigate chance processes and develop, use, and evaluate probability models.
7.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 indi
7.SP.5.1. Ability to devise models where outcomes are equally likely versus not equally likely.
Quiz, Flash Cards, Worksheet, Game & Study GuideProbability
7.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
7.SP.6.1. See the skills and knowledge that are stated in the Standard.
7.SP.7. Develop a probability model and use it to find probabilities of events; compare probabilities from a model to observed frequencies; and if the agreement is not good, explain possible sources of the discrepancy.
7.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 t
7.SP.7a.1. See the skills and knowledge that are stated in the Standard.
7.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 d
7.SP.7b.1. Ability to describe and identify possibility versus probability.
7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
7.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 (SC 7).
7.SP.8a.1. Ability to compare simple events with compound events.
7.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 (SC
7.SP.8b.1. See the skills and knowledge that are stated in the Standard.
Use random sampling to draw inferences about a population.
7.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 rand
7.SP.1.1. Ability to describe and identify population, sample of a population, random sampling, validity, reliability, invalid, inferences.
7.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
7.SP.2.1. See the skills and knowledge that are stated in the Standard.
Draw informal comparative inferences about two populations.
7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, mean height of players on
7.SP.3.1. Ability to describe and identify deviation, standard deviation, absolute deviation, measures of central tendency, measures of variability.