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Seventh Grade Mathematics Instr Seq COS # Course of Study Objective Suggested Lesson Resources/Activities Lesson Plan (description, number, etc.) Date Implemented Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. (7-RP) 2 2 7.1 7.2 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7-RP1] Example: If a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Recognize and represent proportional relationships between quantities. [7-RP2] Intro/Writing ratios – 67182 (I), MA6812 (Q) Unit Rates – M7049 (I), M7050 (Q) Relationships M7051 (I), M7052 (P), M7053 (Q), M7053 (R), M7055 (P), M7056 (Q) Word Prob 67183 (I), MA6814 (Q) 2 7.2a. 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-RP2a] Tables M7057 (I), M7058 (Q) Constant Ratios M7059 (I), M7060 (Q) 2 7.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [7-RP2b] Scale M7073 (I), M7074 (P), M7075 (Q), M7076 (R), M7077 (P), M7078 (Q) Linear Graphs M7245 (I), M7246 (P), M7247 (Q), M7248 (R), M7249 (P), M7250 (Q) 2 7.2c. Represent proportional relationships by equations. [7-RP2c] Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the 2010 Alabama Course of Study Mathematics Ratio, Rates, Proportions 8076 (part I), 8118 (part 2), MA8ZZ35 (Q) 1 Seventh Grade Mathematics total cost and the number of items can be expressed as t = pn. 2 7.2d. 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-RP2d] Compass does not discuss points (0,0) or (1,r) in regard to proportional relationships Linear Graphs M7245 (I), M7246 (P), M7247 (Q), M7248 (R), M7249 (P), M7250 (Q) Basic Percent (is/of) MA6871 (I), MA6872 (Q) 8073, 8115, MA8ZZ32 (Q) 2 7.3 Use proportional relationships to solve multistep ratio and percent problems. [7-RP3] Examples: Sample problems may involve simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error. Increase/Decrease (incl. Sales tax) M7061 (I), M7062 (P), M7063 (Q), M7064 (R), M7065 (P), M7066 (Q) 76258 (part 1), 76259 (part 2), MA7ZZ06 (Q) 8074 (part 1), 8116 (part 2), MA8ZZ33 Q) 8075 (part1), 8117 (part 2), MA8ZZ34 (Q) The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 1 1 7.4 7.4a 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. [7-NS1] Describe situations in which opposite quantities combine to make 0. [7-NS1a] Example: A hydrogen atom has 0 charge because its two 2010 Alabama Course of Study Mathematics Student Activity # M7500 (for whole class instruction, use math toolkit and choose operations in the drop-down box in top-left corner) Add/subtract on Number Line M7085 (I), M7086 (P), M7087 (Q), M7088 (R), M7089 (P), M7090 (Q) Additive and Multiplicative Inverse – M7079 (I), M7080 (P), M7081 (Q), M7082 (R), M7083 (P), M7084 (Q) 2 Seventh Grade Mathematics constituents are oppositely charged. Additive and Multiplicative Inverse – M7079 (I), M7080 (P), M7081 (Q), M7082 (R), M7083 (P), M7084 (Q) Add/Subtract Integers 67203 (I) MA6534 (Q) 1 7.4b 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. [7-NS1b] 76238 (part 1), 79239 (part 2) MA7ZZ24 (Q) Fractions – like denominators MA64121 (I), MA64122 (Q) Fractions – unlike denominators MA64131 (I), MA64132 (Q) 76250 (I), MA7ZZ32 (Q) Mixed Numbers 76251 (I), MA7ZZ33 (Q) 1 7.4c 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-NS1c] Subtraction as “add the opposite” 67203 (I), MA6534 (Q) Add/Subtract Integers 76238 (part 1), 79239 (part 2) MA7ZZ24 (Q) 1 7.4d Apply properties of operations as strategies to add and subtract rational numbers. [7-NS1d] 1 7.5 Apply and extend previous understandings of multiplication 2010 Alabama Course of Study Mathematics Properties of Real Numbers M7105 (I), M7106 (Q) 3 Seventh Grade Mathematics and division and of fractions to multiply and divide rational numbers. [7-NS2] Distributive and Inverse Property MA6241 (I), MA6242 (Q) 1 7.5a 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 multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. [7-NS2a] Basic Mult/Div Rule with Integers (no fractions, decimals) MA6541 (I), MA654 (Q) Mult/Div with integers, fractions, decimals M7091 (I), M7092 (P), M7093 (Q), M7094 (R), M7095 (P), M7096 (Q) Dividing Whole Numbers 76230 (I), MA7ZZ21 (Q) Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. 1 7.5b p p p . If p and q are integers, then q q q Interpret quotients of rational numbers by describing real-world contexts. [7-NS2b] Divide Decimal Numbers 76246 (part 1) 76247 (part 2), MA7ZZ30 (Q) Divide Whole # by Fractions 76253 (part 1), 76254 (part 2), MA7ZZ35 (Q) Divide Fractions 76255 (I), MA7ZZ36 (Q) Divide Mixed Numbers 8067 (part 1), 8110 (part 2), MA8ZZ28 (Q) 1 1 7.5c Apply properties of operations as strategies to multiply and divide rational numbers. [7-NS2c] 7.5d 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. [7-NS2d] 2010 Alabama Course of Study Mathematics Basic Intro 67187 (worksheet available) 4 Seventh Grade Mathematics Fractions, Decimals, Percents M7027 (I), M7028 (P), M7029 (Q), M7030 (R), M7031 (P), M7032 (Q) 1 7.6 Solve 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.) [7-NS3] Order of Operations M7015 (I), M7016 (P), M7017 (Q), M7018 (R), M7019 {P), M7020 (Q) Other topics covered in activities listed above. Expressions and Equations Use properties of operations to generate equivalent expressions. Evaluate Expressions M7103 (I), M7104 (Q) 4 7.7 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7-EE1] Simplify by Adding Like Terms 67205 Simplify with Like Terms and Distributive Property M7115 (I), M7116 (P), M7117 (Q), M7118 ®, M7119 (P), M7120 (Q) Factoring Polynomials by GCF and by Grouping A11011 (I), A11012 (Q) 1 7.8 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. [7-EE2] Example: a + 0.05a = 1.05a means that ―increase by 5%‖ is the same as ―multiply by 1.05.‖ Intro to Variables and Translating Verbal to Numerical M7107 (I), M7108 (P), M7109 (Q), M7110 (R), M7111 (P), M7112 (Q) Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 3 7.9 Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form 2010 Alabama Course of Study Mathematics 5 Seventh Grade Mathematics (whole numbers, fractions, and decimals), using tools strategically. 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. [7-EE3] Examples: If a woman making $25 an hour gets a 10% raise, she will make an additional of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 inches long in the center of a door that is 27 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. 1 10 34 12 Basic Multi-step Problems M7213 (I), M7214 (P), M7215 (Q), M7216 (R), M7217 (P), M7218 (Q) Multi-step Problems with Tables, Fractions, % M8063 (I), M8064 (P), M8065 (Q), M8066 (R), M8067 (P), M8068 (Q) Multi-step Problems with Ratios, Rates, Proportions M8069 (I), M8070 (P), M8071 (Q), M8072 (R), M8073 (P), M8074 (Q) Advanced Multi-step Problems M8075 (I), M8076 (P), M8077 (Q), M8078 (R), M8079 (P), M8080 (Q) Assessing Reasonableness/Justifying Solutions MA61031 (I), M61032 (Q) 4 4 7.10 7.10a 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-EE4] 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. [7-EE4a] Example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 2010 Alabama Course of Study Mathematics Intro to Variables and Translating Verbal to Numerical M7107 (I), M7108 (P), M7109 (Q), M7110 (R), M7111 (P), M7112 (Q) Writing Equations from Word Problems M8101 (I), M8102 (Q) Basic Multi-step Problems M7213 (I), M7214 (P), M7215 (Q), M7216 (R), M7217 (P), M7218 (Q) Multi-step Problems with Tables, Fractions, % M8063 (I), M8064 (P), M8065 (Q), M8066 (R), M8067 (P), M8068 (Q) 6 Seventh Grade Mathematics Multi-step Problems with Ratios, Rates, Proportions M8069 (I), M8070 (P), M8071 (Q), M8072 (R), M8073 (P), M8074 (Q) Advanced Multi-step Problems M8075 (I), M8076 (P), M8077 (Q), M8078 (R), M8079 (P), M8080 (Q) Exploring Graphs of Linear Inequalities M7504 4 7.10b 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. [7-EE4b] 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. Solving Inequalities of One Variable M8111 (I), M8112 (P), M8113 (Q), M8114 (R), M8115 (P), M8116 (Q) Graphing Inequalities incl. Word Problems M8195 (I), M8196 (P), M8197 (Q), M8198 (R), M9199 (Q) Geometry Draw, construct, and describe geometrical figures and describe the relationships between them. Solve Problems with Scales on Maps 67242 (I), MA6844 (Q) 2 7.11 11. 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-G1] 2010 Alabama Course of Study Mathematics Scale with Geometry 67241 (I), MA6842 (Q) Scale with maps, geometry, etc. M7073 (I), M7074 (P), M7075 (Q), M7076 (R), M7077 (P), M7078 (Q) 7 Seventh Grade Mathematics Drawing/Measuring Angles with Protractor GE132 Theorems for Angle Measures in Triangles AL120 3 7.12 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. [7-G2] 67253 (I), MA6926 (Q) Classifying Triangles AL123 Determine Angle Measures of Specific Triangles (Isosceles, Right, etc) M7127 (I), M7128 (P)), M7129 (Q), M7130 (R), M7131 (P), M7132 (Q) 3 7.13 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-G3] 67236 (student worksheet available) 67238 (student worksheet available) Solve real-world and mathematical problems involving angle measure, area, surface area, and volume. Radius, Diameter, Circumference 67160 (I), MA69122 (Q) 3 7.14 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-G4] Radius, Diameter, Area 67224 (I), MA69132 (Q) Circumference and Area M7143 (I), M7144 (Q) 76273, MA7ZZ44 (Q) 8087 (part 1), 8129 (part 2), MA8ZZ17 (Q) 2010 Alabama Course of Study Mathematics 8 Seventh Grade Mathematics Angles from Parallel Lines and Transversals 67218 (I), MA69210 (Q) 76267 (I), MA7ZZ41 (Q), student worksheet 3 7.15 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. [7-G5] Interior and Exterior Angles in Triangles M7125 (I), M7126 (Q) Suppl/ Compl/Corr/Vert/Adj Angles M7151 (I), M7152 (P), M7153 (Q), M7154 (R), M7155 (P), M7156 (Q) Apply to Real World Problems M7157 (I), M7158 (Q) Area 67208 (I), MA6282, worksheet Surface Area 67225 (I), MA69152 (Q), worksheet 4 7.16 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-G6] M7179 (I), M7180 (P), M7181 (Q), M7182 (R), M7183 (P), M7184 (Q) 76274 (part 1), 76275 (part 2), lesson quiz Volume 67226 (I), MA69162 (Q), worksheet M8145 (I), M8146 (P), M8147 (Q), M8148 (R), M8149 (P), M8150 (Q) Statistics and Probability Use random sampling to draw inferences about a population. 2010 Alabama Course of Study Mathematics 9 Seventh Grade Mathematics Intro 67228 (I), MA6692, worksheet 3 7.17 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. [7-SP1] Differentiate Sampling Techniques M8233 (I), M8234 (Q) M8235 (I), M8236 (Q) Sample Bias M8237 (I), M8238 (P), M8239 (Q), M8240 (R), M8241 (P), M8242 (Q) Mean, Median, Mode, Range, Outliers 67229 (I), MA6682 (Q), worksheet 3 7.18 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. [7-SP2] 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. Data Analysis (what if the data changes…) MA6683 (I), MA6684 (Q), worksheet Mean, Median, Mode from Charts, Graphs, etc M7271 (I), M7272 (P), M7273 (Q), M7274 (R), M7275 (P), M7276 (Q) Apply Mean, Median, Mode M7277 (I), M7278 (Q) Interpreting Statistical Graphs M7279 (I), M7280 (Q) Draw informal comparative inferences about two populations. 3 7.19 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. [7-SP3] Example: The mean height of players on the basketball team is 2010 Alabama Course of Study Mathematics 10 Seventh Grade Mathematics 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. 3 7.20 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7-SP4] Example: Decide whether the words in a chapter of a seventhgrade 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. 4 4 7.21 7.22 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. [7-SP5] Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 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. [7-SP6] 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. AL071 (I) Lesson Quiz follows, worksheet available Overview incl. Compound Events M7253 (I), M7254 (P), M7255 (Q), M7256 (R), M7257 (P), M7258 (Q) Experimental Results (Frequency Charts) M7251 (I), M7252 (Q) Independent Events 76286 (part 1), 76287 (part 2), lesson quiz Dependent Events 76288 (part 1), 76289 (part 2), lesson quiz 4 7.23 Develop a probability model and use it to find probabilities of 2010 Alabama Course of Study Mathematics 11 Seventh Grade Mathematics events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7-SP7] 4 7.23a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. [7-SP7a] 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. 4 7.23b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. [7-SP7b] 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? 4 7.24 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7-SP8] 7.24a 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. [7-SP8a] 7.24b 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 4 4 2010 Alabama Course of Study Mathematics Using Probability MA61061 (I), MA61062 (Q) Simulation Activities M7507 (Choose type in drop down box – coin, spinner, number cube, marbles) Using Probability MA61061 (I), MA61062 (Q) Simulation Activities M7507 (Choose type in drop down box – coin, spinner, number cube, marbles) Overview incl. Compound Events M7253 (I), M7254 (P), M7255 (Q), M7256 (R), M7257 (P), M7258 (Q) 8099 (part 1), 8173 (part 2), lesson quiz, worksheet 12 Seventh Grade Mathematics event. [7-SP8b] 4 7.24c Design and use a simulation to generate frequencies for compound events. [7-SP8c] 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? Simulation Activities (single events) M7507 (Choose type in drop down box – coin, spinner, number cube, marbles) Ratios and Proportional Relationships [RP] • Analyze proportional relationships and use them to solve real-world and mathematical problems. The Number System [NS] • Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Expressions and Equations [EE] • Use properties of operations to generate equivalent expressions. • Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Geometry [G] • Draw, construct, and describe geometrical figures and describe the relationships between them. • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Statistics and Probability [SP] • Use random sampling to draw inferences about a population. • Draw informal comparative inferences about two populations. • Investigate chance processes and develop, use, and evaluate probability models. 2010 Alabama Course of Study Mathematics 13