Desoto County Schools Pacing Guide Seventh Grade Math

Transcription

1 1 st Nine Weeks Unit 21: Introduction and Probability (approx. 3 weeks) Recognize that probability is expressed as a number between 0 and 1 Recognize that a random event with a probability of ½ is equally likely to happen Recognize that as probability moves closer to 1 it is increasingly likely to happen Recognize that as probability moves closer to 0 it is decreasingly likely to happen Draw conclusions to determine that a greater likelihood occurs as the number of favorable outcomes approaches the total number of outcomes Determine relative frequency (experimental probability) is the number of times an outcome occurs divided by the total number of times the experiment is completed Determine the relationship between experimental and theoretical probabilities by using the law of large numbers Predict the relative frequency (experimental probability) of an event based on the (theoretical) probability Recognize uniform (equally likely) probability Develop a uniform probability model and use it to determine the probability of each outcome/event Use models to determine the probability of events Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process Analyze a probability model and justify why its uniform or explain the discrepancy if it is not Comparing and ordering integers, PA.1.b Adding integers, PA.1.b Subtracting integers, PA.1.b Multiplying and dividing integers, PA.1.b Unit 2: Fractions and Integer Addition (approx. 3 weeks) Identify that opposite quantities have the sum of zero (0) Add rational numbers (i.e. fractions, decimals, integers, etc.) Apply and extend calculating the sum of integers expressions utilizing the horizontal and vertical number line Identify and apply positive and negative real-world contexts Apply commutative, associative, and identity properties to add rational numbers Multiply rational numbers Convert a rational number to a decimal using long division Explain that the decimal form of a rational number either terminates in zero or repeats 7.NS.1a 7.NS.1b 7.NS.1b 7.NS.1b 7.NS.1d 7.NS.2d 7.NS.2d Unit 3: Arithmetic Properties Sections 3.1 and 3.2 Only (approx. 2 weeks) Subtract numbers (i.e. fractions, decimals, integers, etc.) Demonstrate the subtraction of rational number as applying the additive inverse Apply the principle that the distance between two points on a number line is the difference in their absolute values and apply this principle in real world contexts Apply commutative, associative, and identity properties to subtract (through additive inverse) rational numbers Multiply rational numbers Utilize the distributive property when multiplying signed numbers Interpret products of rational numbers by describing real-world context Apply properties (associative, distributive, identity, multiplicative inverse and commutative) to multiply and divide rational numbers Add, multiply, divide and subtract rational numbers Solve real-world rational number word problems 7.NS.1c 7.NS.1c 7.NS.1c 7.NS.1d 7.NS.2c Formatted: Bullets and Numbering Formatted: Bullets and Numbering

2 Approximately 8 weeks is allocated for instruction and assessment above. This allows one week of flexibility and to account for nine weeks tests. 2 nd Nine Weeks Unit 23: Arithmetic Properties Section 3.3 Only (approx. 1.5 weeks) Divide (with non-zero divisors) rational numbers with concentration on integers Interpret quotients of rational numbers by describing real-world contexts Add, multiply, divide and subtract rational numbers Solve real-world rational number word problems Comparing and ordering integers, PA.1.b Adding integers, PA.1.b Subtracting integers, PA.1.b Multiplying and dividing integers, PA.1.b Unit 4: Portions and Expressions (approx. 4 weeks) Recognize and write ratios as a comparison of two quantities written as a fraction, using a colon or the word to Distinguish the need to convert to common units of measure and write in simplest form Compute units to demonstrate the relationship to one (1) and with proper labeling Translate a proportion into a table to determine equivalency Graph ordered pairs on a coordinate plane Represent ratios as ordered pairs on the coordinate plane Recognize that ordered pairs are proportional if they form a straight line through the origin Translate a proportion into a table to determine equivalency Determine the constant of proportionality (unit rate). Translate a real world situation into an equation and create a table to demonstrate proportionality Explain what a point (x, y) on a graph of a proportional relationship means in terms of the situation Explain what the point (0, 0) means in context Explain what the point (1, r) means in context, where r is the unit rate Apply properties to expand expressions. For example: 2(x + 3) + 3(x 4) = 2x x 12 Identify and combine like terms utilizing commutative and associative properties Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients Identify corresponding parts of similar geometric figures Construct a proportion to solve for unknown quantities Unit 5: Probability Sections 5.1 and 5.2 Only (approx. 2.5 weeks) Convert between fractions, decimals, and percents Recognize that a percent is a proportional relationship out of 100 Determine relative frequency (experimental probability) is the number of times an outcome occurs divided by the total number of times the experiment is completed Determine the relationship between experimental and theoretical probabilities by using the law of large numbers Predict the relative frequency (experimental probability) of an event based on the (theoretical) probability Recognize uniform (equally likely) probability Develop a uniform probability model and use it to determine the probability of each outcome/event Use models to determine the probability of events Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process Analyze a probability model and justify why it s uniform or explain the discrepancy if it is not Define and describe a compound event Recognize that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs Identify the outcomes in sample space for an everyday event Find probabilities of compound events using organized lists, tables, tree diagrams, etc. and analyze the outcomes Choose the appropriate method such as organized lists, tables, and tree diagrams to represent sample spaces for compound events Design and use a simulation to generate frequencies for compound events 7.NS.2b 7.NS.2b 7.RP.1 7.RP.1 7.RP.1 7.RP.2b 7.RP.2b 7.RP.2c 7.EE.1 7.EE.1 7.EE.1 7.G.1 7.G.1 7.SP.8a 7.SP.8a 7.SP.8b 7.SP.8b 7.SP.8b 7.SP.8c

3 Define simulation Approximately 8 weeks is allocated for instruction and assessment above. This allows one week of flexibility and to account for semester exams. 7.SP.8c

4 3 rd Nine Weeks Unit: Word Problems Section 5.3 Only (approx. 1.5 weeks) Calculate multi-step word problems with rational numbers in any form Convert between whole numbers, fractions, and decimals as appropriate Assess the reasonableness of answers using mental computation and estimations Apply properties of operations to calculate with numbers in any form Comparing and ordering integers, PA.1.b Adding integers, PA.1.b Subtracting integers, PA.1.b Multiplying and dividing integers, PA.1.b Unit 6: Solving Inequalities and Equations (approx. 4 weeks) Calculate multi-step word problems with rational numbers in any form Convert between whole numbers, fractions, and decimals as appropriate Assess the reasonableness of answers using mental computation and estimations Apply properties of operations to calculate with numbers in any form Solve one-step equations Create one-step equations from real-world situations Solve two-step equations Create two-step equations from real-world situations Solve multi-step equations with the distributive property Construct multi-step equations from real-world situations Solve one-step inequalities Create one-step inequalities from real-world situations Solve two-step inequalities Create two-step inequalities from real-world situations Solve multi-step inequalities with the distributive property Construct multi-step inequalities from real-world situations Graph the solution set of an inequality Interpret the solution in the context of the problem Unit 7: Proportions and Percents (approx. 3 weeks) Explain what a point (x, y) on a graph of a proportional relationship means in terms of the situation Explain what the point (0, 0) means in context Recognize that a percent is a proportional relationship out of 100 Substitute into and apply the simple interest formula Solve multi-step ratio and percent problems to calculate tax, markups and markdowns, gratuities, commissions, fees, percent increase and decrease and percent error Analyze, investigate, and justify real-world rational number word problems Create real-world rational number word problems Write equivalent expressions with fractions, decimals, percents, and integers Rewrite an expression in an equivalent form in order to provide insight about how quantities are related in a problem context Calculate multi-step word problems with rational numbers in any form Convert between whole numbers, fractions, and decimals as appropriate Assess the reasonableness of answers using mental computation and estimations Apply properties of operations to calculate with numbers in any form Solve multi-step equations with rational coefficients 7.EE.2 7.EE.2

5 Construct multi-step equations with rational coefficients from real-world situations Recall formulas and substitute information given to solve for the unknown Approximately 8.5 weeks is allocated for instruction and assessment above. This allows half a week of flexibility and to account for nine weeks tests.

6 4 th Nine Weeks Unit 28: Statistics and Angle Relationships (approx. 3 weeks) Recognize the attributes of triangles Construct a triangle (freehand, with a ruler, protractor, and technology) Analyze given conditions based on the three measures of angles or sides of a triangle to determine wen there is a unique triangle, more than one triangle, or no triangle Recognize and identify angles as supplementary, complementary, vertical, or adjacent Determine unknown angle measures by writing and solving multi-step equations based on relationships between angles Solve for the missing measure using angle relationships (complementary, supplementary, adjacent and vertical). Recognize statistics terms such as population, sample, sample size, random sampling, generalizations, valid, biased, and unbiased Generalize a population from a sample as a valid only if the sample is representative of that population Apply statistics to gain information about a population from a sample of the population Generalize that random sampling tends to produce representative samples and support valid inferences Define random sample Identify an appropriate sample size Analyze and interpret 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 determine the variation in estimates or predications by comparing and contrasting the samples Identify measures of central tendency (mean, medina, and mode) in a data distribution Identify measures of variation including upper quartile, lower quartile, upper extreme maximum, lower extreme minimum, range, inter-quartile range, and mean absolute deviation (i.e. box-and-whisker plots, line plots, dot plots, etc.) Compare two numerical data distributions on a graph by visually comparing data displays, and assessing the degree of visual overlap Compare the differences in the measure of central tendency in two numerical data distributions by measuring the difference between the centers and expressing it as a multiple of a measure of variability Find measures of central tendency (mean, median, and mode), and measures of variability (range, interquartile range, mean absolute deviation, etc.) Analyze and interpret data using measures of central tendency and variability Draw informal comparative inferences about two populations from random samples Comparing and ordering integers, PA.1.b Adding integers, PA.1.b Subtracting integers, PA.1.b Multiplying and dividing integers, PA.1.b Unit 9: Circles and Volume (approx. 3 weeks) Reproduce a scale drawing at a different scale Identify the two-dimensional figures that make up a three-dimensional figure, specifically, right-rectangular prisms and rightrectangular pyramids Name the shape of the cross sections in a three-dimensional figure Identify the formulas for circumference and area of a circle Solve equations involving area and circumference when given either the diameter or the radius Solve for the circumference of a circle when given the area and visa versa Justify that π can be derived from the circumference and diameter of a circle Recall and deconstruct the formula for area for two-dimensional objects composed of triangles, quadrilaterals, and polygons Recall and deconstruct the formula for surface area of three-dimensional objects composed of cubes, and right prisms Recall and deconstruct the formula for volume three-dimensional objects composed of cubes, and right prisms Substitute into formulas and solve for unknown quantities 7.G.2 7.G.2 7.G.2 7.G.5 7.G.5 7.G.5 7.SP.4 7.SP.4 7.SP.4 7.G.1 7.G.3 7.G.3 Approximately 6 weeks is allocated for instruction and assessment above. This allows three weeks of flexibility and to account for state tests and semester exams.

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