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KS.7.EE.Expressions and Equations
Expressions and Equations
Use properties of operations to generate equivalent expressions. 7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with integer coefficients. For example: apply the distributive property to the expression 24ݑ + 18Űݑ to produce the equivalent expression 6(4ưݑ +3Űݑ).
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, ݑ + 0.05ΰݑ = 1.05ΰݑ means that increase by 5%” is the same as “multiply by 1.05.”
Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 7.EE.3. Solve multi-step real-life and mathematical problems with rational numbers. 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 e Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct two-step equations and inequalities to solve problems by reasoning about the quantities. 7.EE.4a. Solve word problems leading to equations of the form pݑ+Űݑ =r, and p(ްݑ +Űݑ)=r where p, q, and r are specific rational numbers. Solve equations of these forms fluently (efficiently, accurately, and flexibly). Compare an algebraic solution to an arithmetic
7.EE.4b. Solve word problems leading to inequalities of the form pݑ + Űݑ>r or pްݑ + Űݑ0. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson
Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.1. Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Solve real-life and mathematical problems involving area, surface area, and volume. 7.G.4. Use the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Quiz, Flash Cards, Worksheet, Game & Study Guide Area Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
7.G.5. Investigate the relationship between three-dimensional geometric shapes; 7.G.5a. Generalize the volume formula for prisms and cylinders (ݑ = ɰݐբĎ where B is the base and h is the height). Quiz, Flash Cards, Worksheet, Game & Study Guide Volume
7.G.5b. Generalize the surface area formula for prisms and cylinders (ݑưݐ = 2ݐ +հݑâĎ where B is the area of the base, P is the perimeter of the base, and h is the height (in the case of a cylinder, perimeter is replaced by circumference)).
7.G.6. Solve real-world and mathematical problems involving area of two-dimensional objects and volume and surface area of three-dimensional objects including cylinders and right prisms. (Solutions should not require students to take square roots or cube roots. Quiz, Flash Cards, Worksheet, Game & Study Guide Area Quiz, Flash Cards, Worksheet, Game & Study Guide Volume
KS.7.NS.The Number System
Apply and extend previous understandings of operations with positive rational numbers to add, subtract, multiply, and divide all rational numbers. 7.NS.1. 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. Show that a number and its opposite have a sum of 0 (are additive inverses). For example, show zero-pairs with two-color counters.
7.NS.1b. Show p + q as the number located a distance |ݑ| from p, in the positive or negative direction depending on whether q is positive or negative.
7.NS.1c. Model subtraction of rational numbers as adding the additive inverse, p − ݑ=p + (ޢȒݑ).
7.NS.1d. Model subtraction as the distance between two rational numbers on the number line where the distance is the absolute value of their difference.
7.NS.1e. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2. Apply and extend previous understandings of multiplication and division of positive rational numbers to multiply and divide all rational numbers. 7.NS.2a. Describe how multiplication is extended from positive rational numbers to all 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
7.NS.2b. Explain 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. Leading to situations such that if p and q are integers, then –(p/q) = -p/q = p/-q.
7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.2d. Convert a rational number in the form of a fraction to its decimal equivalent using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
7.NS.3. Solve and interpret real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
KS.7.RP.Ratios and Proportional Relationships
Ratios and Proportional Relationships
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 or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/
7.RP.2. Recognize and represent proportional relationships between quantities: 7.RP.2b. Analyze a table or graph and recognize that, in a proportional relationship, every pair of numbers has the same unit rate (referred to as the “m”).
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.
KS.7.SP.Statistics and Probability
Statistics and Probability
Use random sampling to draw inferences about a population. 7.SP.1. Use statistics to gain information about a population by examining a sample of the population; 7.SP.1a. Know that generalizations about a population from a sample are valid only if the sample is representative of that population and generate a valid representative sample of a population.
7.SP.1b. Identify if a particular random sample would be representative of a population and justify your reasoning.
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 informally gauge the variation in estimates or predictions. For example, e
Investigate chance processes and develop, use, and evaluate probability models. 7.SP.5. Express the probability of a chance event as a number between 0 and 1 that represents 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 Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
7.SP.6. Collect data from a chance process (probability experiment). Approximate the probability by observing its long-run relative frequency. Recognize that as the number of trials increase, the experimental probability approaches the theoretical probability. C
7.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. 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.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.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.8a. Know 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.
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.