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7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important, takes significant time and repeated efforts, and requires reflection. Essential Question - What are the specific strategies that have wide application in attacking problems and can help in problem solving? C.7.2 NO.3.7.2 Solve with and without appropriate with and without appropriate technology: mental computation Solve, with and without appropriate technology, multi-step problems using a *represent multi-step problems using technology technology, multi-step problems using a variety of methods and tools manipulatives (including 2 or more steps) Distributive Property variety of methods and tools Ex. *solve problems mentally rational numbers Ex. objects, mental computation, paper and *solve multi-step problems with paper and like terms objects, mental computation, paper and pencil pencil problem solving pencil strategy FIRST NINE WEEKS 1. Enduring Understanding - Real numbers are either rational or irrational. 1a. Essential Question - What kinds of numbers make up the set of real numbers? F.7.3 NO.1.7.6 Identify subsets of the real number system *demonstrate that natural numbers are real number system Recognize subsets of the real number (natural, whole, integers, rational, and counting numbers beginning with 1 and natural numbers system (natural, whole, integers, rational, irrational numbers) that they build on one another whole numbers and irrational numbers) *identify whole numbers as numbers integers whose value includes zero and all natural rational numbers numbers irrational numbers *integers are all whole numbers and their perfect square opposites square root *apply the definition of a rational number undefined fraction (any number that can be written as a/b where a is any integer and b is any integer except 0. Including any terminating decimals, repeating decimals and perfect squares) *recognize that a fraction whose denominator is zero is undefined *identify irrational numbers as numbers that have infinite but non-repeating decimal representations (Ex. π; any square root that is not a perfect square) *identify subsets of the real number system rev. 05-2009 1 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word Enduring Understanding - Successful problem solvers possess a set of core ways ofthat support numbers. 2. Enduring Understanding - Exponential and scientific notation are efficient beliefs expressing their work: problem solving is important, takes significant time and repeated efforts, and requires reflection. 2a. Essential Question - What is the purpose of exponents? F.7.3 NO.1.7.2 A. Demonstrate, with and without with and without appropriate technology: scientific notation Demonstrate, with and without appropriate technology, an understanding *write the number in expanded notation exponents appropriate technology, an understanding of place value using powers of 10 Ex. 103 = 10×10×10 place value of place value using powers of 10 and B. Write numbers greater than one in *multiply and divide by multiples of 10 expanded notation write numbers greater than one in scientific notation *demonstrate the value of a decimal when power scientific notation dividing or multiplying by a power base (multiple) of 10 *demonstrate that exponents are repeated multiplication *identify the whole number of a scientific notation number as a value ≥ 1 and < 10 F.7.3 1 NO.1.7.3 Convert between scientific notation and *multiply and divide by powers of ten to scientific notation Convert between scientific notation and standard notation using numbers greater convert between standard and scientific standard notation standard notation using numbers greater than one notation powers of ten than one 3. Enduring Understanding - Fractions, decimals, and percents can be used interchangeably. 3a. Essential Question - What determines an appropriate representation for a number? F.7.3 NO.1.7.5 Compare and represent integers, *locate integers on a number line integers Compare and represent integers, fractions, fractions, decimals and mixed numbers *locate fractions on a number line number line decimals and mixed numbers and find their and find their approximate location on a *locate decimals on a number line approximate location on a number line number line *locate mixed numbers on a number line *locate and compare the values of integers, fractions, decimals and mixed numbers on a number line F.7.1 M.13.7.6 A. Find the distance between two points *plot two points on a number line distance Find the distance between two points on a on a number line *find the distance between two points midpoint number line and locate the midpoint B. Locate the midpoint *average two numbers on a number line to number line locate the midpoint rev. 05-2009 2 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.1 NO.1.7.4 A. Find decimals for mixed numbers & *explain how a part relates to a whole decimal Enduring Understanding Find decimal and percent equivalents for - Successful problem solvers possess a set of core beliefs that support explain why they represent the same *restate a mixed number as a whole percent their work: value number + fraction mixed numbers and explain why they repeated efforts, denominator equivalents problem solving is important, takes significant time and*convert fractions by dividing and requires reflection. represent the same value B. Find percent equivalents of mixed convert numbers & explain why they represent the into numerator same value *write a decimal as a mixed number *express mixed numbers as percents > 100 *demonstrate that the percent can be found by finding the fraction-to-decimal equivalent and then multiply the decimal by 100 F.7.1 1 NO.1.7.1 A. Show with and without models and *explain how a part relates to a whole and part-to-part Relate, with and without models and pictures, pictures the concept of ratio including vice versa part-to-whole concepts of ratio, proportion, and percent, ratios <1 and >100 *match decimals and percents of the ratio including percents less than 1 and greater B. Show with and without models and same value proportion than 100 pictures the concept of percent including *represent percents out of 100 percent percents <1 and >100 *describe a situation in which a percent C. Show with and without models & might be between 1 & 100 pictures proportion including proportions *draw a picture or model a number as a <1 and >100 decimal and percent D. Relate with and without models and pictures concepts of ratio, percent, and proportions including percents <1 and >100 F.7.3 NO.3.7.4 A. Apply factorization to solve problems *find multiples and factors of given prime numbers Apply factorization, LCM, and GCF to solve using more than two numbers and explain numbers composite numbers problems using more than two numbers the solution *find the prime factorization of a number prime factorization and explain the solution B. Apply LCM to solve problems using (Ex. tree diagram) LCM more than two numbers and explain the *identify numbers as prime or composite GCF solution *find the LCM and GCF of more than two C. Apply GCF to solve problems using numbers more than two numbers and explain the *apply and explain solutions solution rev. 05-2009 3 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.1 MC-1 NO.3.7.6 Solve, with and without appropriate with and without appropriate technology: technology OR-1 Enduring Understanding - Successful problem solvers possess a set of core beliefs that support Solve, with and without appropriate technology, real-world percent problems *solve percent problems percent their work: technology, real-world percent problems Ex. Ex. interest repeated efforts, problem solving is important, takes significant time andWhat number is 50% of 80? and requires reflection. Ex. I=PRT principal I=PRT (whole unknown) 80 is what percent of 50? rate 80 is 50% of what number? time *use fractions, decimals and percents interchangeably *apply knowledge of percent to real-world situations Ex. I = PRT 4. Enduring Understanding - Integers have magnitude and direction. 4a. Essential Question - How do operations with integers compare to operations with whole numbers? F.7.3 NO.2.7.4 A. Model and develop addition and *model addition and subtraction of positive integers Model and develop addition, subtraction, subtraction of integers and negative numbers using absolute value multiplication and division of integers B. Model and develop multiplication and manipulatives opposites division of integers *model multiplication and division of inverse operations positive and negative numbers using manipulatives F.7.3 2 NO.2.7.3 A. Apply rules (conventions) for order of *solve problems with integers using order order of operations Apply rules (conventions) for order of operations to integers including of operations integers operations to integers and positive rational parentheses, brackets or exponents *solve problems with positive rational rational numbers numbers including parentheses, brackets or B. Apply rules (conventions) for order of numbers using order of operations exponents exponents operations to positive rational numbers *use rules for order of operations grouping symbols including parentheses, brackets or including: (brackets, exponents •grouping symbols ( ), [ ] parentheses) •fraction bar •exponents •multiplication & division left to right •addition & subtraction left to right rev. 05-2009 4 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.3 NO.2.7.1 A. Apply the Distributive Property of *solve using Distributive Property to Distributive Property multiplication over addition or solvers simplify computations of core or Enduring Understanding - Successful problem subtraction possess a set with addition beliefs that support Apply the Distributive Property of integers their work: multiplication over addition or subtraction to to simplify computations with integers subtractions of integers solve problem solving is important, takes significant time and5(2+3) simplify computations with integers, fractions B. Apply the Distributive Property of repeated efforts, and requires reflection. 5(2+3) simplify and decimals multiplication over addition or subtraction 5(5) 5(2)+5(3) evaluate to simplify computations with fractions 25 10 + 15 decompose C. Apply the Distributive Property of 25 multiplication over addition or subtraction to simplify computations with decimals 5(3-2) 5(3-2) 5(3)-5(2) 5(1) 15-10 5 5 *solve using Distributive Property to simplify computations with addition or subtraction to solve problems with fractions 2(5 + 1/2) 2(5 - 1/2) 10 + 1 10 - 1 11 9 *solve using Distributive Property to simplify computations with addition or subtraction to solve problems with decimals 5.03 (3) 5(3) + .03(3) 15 + .09 15.09 *use subtraction to make multiplication of decimals easier (mental math) 5(10.98) 5(11) - 5(.02) 50+4.90 55 - .10 54.9 54.9 rev. 05-2009 5 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word Enduring Understanding - Successful representations generalize patterns and relationships. 5. Enduring Understanding - Algebraicproblem solvers possess a set of core beliefs that support their work: F.7.3 1 5a. Essential Question - Why are mathematical rulesand repeated efforts, and requires reflection. problem solving is important, takes significant time necessary? NO.3.7.1 Compute, with and without appropriate with and without appropriate technology: technology Compute, with and without appropriate technology, with integers and positive *solve word problems using addition of integers technology, with integers and positive rational numbers using real-world positive integers, decimals, and fractions positive rational rational numbers using real-world situations situations to solve problems (including mixed numbers) numbers to solve problems *solve word problems using subtraction of absolute value positive integers, decimals, and fractions (including mixed numbers) *solve word problems using multiplication of positive integers, decimals, and fractions (including mixed numbers) *solve word problems using division of positive integers, decimals, and fractions (including mixed numbers) *explain solution 6. Enduring Understanding - Computational estimations produce approximate results. 6a. Essential Question - What determines a reasonable estimation for a given situation? F.7.3 1 NO.3.7.3 A. Determine when an estimate is *determine when an estimate is sufficient estimate Determine when an estimate is sufficient and sufficient *use estimation strategies to check for estimation use estimation to decide whether answers B. Use estimation to decide whether reasonableness of solutions reasonable are reasonable in problems including answers are reasonable in problems fractions and decimals including fractions and decimals rev. 05-2009 6 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word Enduring Understanding - Successful problem are related. 7. Enduring Understanding - Powers and roots solvers possess a set of core beliefs that support their work: 7a. Essential question - How are powers and roots related? problem solving is important, takes significant time and repeated efforts, and requires reflection. F.7.3 NO.3.7.5 A. Represent and solve problem situations with and without appropriate technology: absolute value Represent and solve problem situations that that can be modeled by and solved using *write and solve problems using the exponents can be modeled by and solved using concepts of absolute value with and concept of absolute value square roots concepts of absolute value, exponents and without appropriate technology *write and solve problems using perfect squares square roots (for perfect squares) with and B. Represent and solve problem situations exponents technology without appropriate technology that can be modeled by and solved using *write and solve problems using square concepts of exponents with and without roots appropriate technology C. Represent and solve problem situations that can be modeled by and solved using concepts of square roots (for perfect squares) with and without appropriate technology rev. 05-2009 7 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word SECOND NINE WEEKS Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: 1. Enduring Understanding - Patterns and relationships can be expressedand requires numerically, problem solving is important, takes significant time and repeated efforts, graphically, reflection. symbolically, and verbally. 1a. Essential Question - What can be learned from an identified pattern/function? F.7.3 MC-2 A.4.7.2 Identify and extend patterns in real-world *use skills in A.4.7.1 patterns OR-1 Identify and extend patterns in real-world situations *find missing terms and numbers in a term situations pattern or a function table arithmetic sequence *predict patterns in real-world situations geometric sequence *write a rule to extend a pattern to the nth term F.7.3 A.4.7.3 Interpret and write a rule for a two- *A.4.6.2 function table Interpret and write a rule for a two-operation operation function table *interpret and write the algebraic rule for function table Ex. one- and two-operation function tables Ex. multiply by 2, add 1 multiply by 2, add 1 F.7.3 A.4.7.1 Create and complete a function table *identify (x-value) as input and (y-value) function table Create and complete a function table (input/output) using a given rule with two as output input/output (input/output) using a given rule with two operations *apply a given rule with two operations to operations create and complete a function table F.7.3 A.6.7.3 Create and complete a function table *create and complete a function table function table Create and complete a function table (input/output) using a given rule with two using a given rule with two operations in input/output (input/output) using a given rule with two operations in real-world situations real-world situations operations in real-world situations F.7.1 A.7.7.1 Use, with and without appropriate *use tables to identify situations with technology Use, with and without appropriate technology, technology, tables and graphs to compare constant or varying rates of change (Ex.. rates tables and graphs to compare and identify and identify situations with constant or d=rt) constant rate of situations with constant or varying rates of varying rates of change *use graphs to identify situations with change change constant or varying rates of change varying rates of change rev. 05-2009 8 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word Enduring Understanding - Successful problem solvers possess a set of verbally, graphically, numerically, 2. Enduring Understanding - Functional relationships can be expressed core beliefs that support their work: and symbolicallyis important, takes significant time and repeated efforts, and requires reflection. problem solving and are used to solve real-world problems. 2a. Essential Question - How can a function be identified? F.7.3 A.6.7.1 A. Use tables to represent linear equations *use tables to represent the relationship in linear equations Use tables and graphs to represent linear by plotting, with and without appropriate a linear equation, with and without technology equations by plotting, with and without technology, points in a coordinate plane appropriate technology coordinate plane appropriate technology, points in a B. Graph linear equations by plotting, with *use graphs to represent the relationship x-axis coordinate plane and without appropriate technology, points in a linear equation on a coordinate plane, y-axis in a coordinate plane with and without appropriate technology ordered pairs origin 2b. Essential Question - What can be learned from studying functions? F.7.3 1 A.5.7.2 A. Solve simple linear equations using *solve linear equations linear equations Solve simple linear equations using integers *graph solution points on a coordinate integers integers and graph on a coordinate plane B. Graph simple linear equations in a plane using a T-chart coordinate plane Ex. coordinate plane quadrant use a T-chart x-axis y-axis origin F.7.1 G.10.7.1 Plot points in the coordinate plane *identify four quadrants on coordinate coordinate plane Plot points in the coordinate plane plane x-axis *identify x and y axis y-axis *use ordered pairs to plot points on ordered pairs coordinate plane quadrants origin F.7.3 1 A.6.7.2 Represent, with and without appropriate *same as A.6.7.1 with real-world technology Represent, with and without appropriate technology, linear equations by plotting applications linear equations technology, linear equations by plotting and and graphing points in the coordinate coordinate plane graphing points in the coordinate plane using plane using all four quadrants given data quadrants all four quadrants given data in a table from in a table from a real-world situation origin a real-world situation x-axis y-axis 3. Enduring Understanding - Algebraic representations generalize patterns and relationships. 3a. Essential Question - Why are equations and inequalities useful? F.7.3 A.5.7.4 A. Write algebraic expressions using *write and solve algebraic expressions algebraic Write and evaluate algebraic expressions positive rational numbers with one or more variables using positive expressions using positive rational numbers B. Evaluate algebraic expressions using rational numbers rational numbers positive rational numbers variables rev. 05-2009 9 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.3 4 A.5.7.3 A. Translate phrases into algebraic *express word phrases using variables, algebraic positive numbers, rational core and expressions Enduring Understanding - Successful problem solvers possess a set of numbers,beliefs that support Translate phrases and sentences into expressions their work: algebraic expressions and equations B. Translate sentences into equations problem solving is important, takes significant time andoperations use of the Distributive requires reflection. including parentheses and positive and repeated efforts, and including parentheses, positive numbers *explain the equations rational numbers rational numbers and simplify algebraic and rational numbers Property to simplify like terms coefficient expressions by combining like terms C. Simplify algebraic expressions by *simplify algebraic expressions by constant combining like terms combining like terms variable F.7.3 A.5.7.1 A. Solve and graph one-step linear *identify phrases that indicate inequalities linear equations Solve and graph one-step linear equations equations using a variety of methods (Ex. in real-world situations inequalities and inequalities using a variety of methods hands-on, inverse operations, symbolic) *solve one-step linear equations and inverse operations (Ex. hands-on, inverse operations, symbolic) with real-world application with and inequalities, with and without appropriate technology with real-world application, with and without without appropriate technology technology, using a variety of methods variables appropriate technology B. Solve and graph one-step linear *graph one-step equations and inequalities using a variety of methods inequalities on a number line (Ex. hands-on, inverse operations, symbolic) with real-world application with and without appropriate technology F.7.3 1 NO.2.7.2 A. Apply the addition, subtraction, *know the properties of equality for equations Apply the addition, subtraction, multiplication multiplication and division properties of addition, subtraction, multiplication, and integers and division properties of equality to one-step equality to one-step equations with division and apply to one-step equations properties of equality equations with integers, fractions, and integers using integers inverse operations decimals B. Apply the addition, subtraction, *know the properties of equality for one-step equations multiplication and division properties of addition, subtraction, multiplication, and equality to one-step equations with division and apply to one-step equations fractions using fractions C. Apply the addition, subtraction, *know the properties of equality for multiplication and division properties of addition, subtraction, multiplication, and equality to one-step equations with division and apply to one-step equations decimals using decimals rev. 05-2009 10 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word THIRD NINE WEEKS Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: 1. Enduring Understanding - Graphical representations and statistical measures influence interpretations problem solving is important, takes significant time and repeated efforts, and requires reflection. and predictions about data. 1a. Essential Question - How can the results of a statistical investigation be used to support an argument? F.7.1 2 DAP.14.7.1 Identify different ways of selecting *develop appropriate questions for sample vs. Identify different ways of selecting samples samples and compose appropriate surveys population and compose appropriate questions questions *identify survey response, random sample, random sample Ex. Ex. representative sample & convenience survey response survey response, random sample, survey response, random sample, sample representative representative sample and convenience representative sample and convenience sample sample sample convenience sample F.7.1 DAP.14.7.2 A. Explain that line graphs are appropriate *identify that line graphs are used to graph line graph Explain which types of display are appropriate for graphing change over time change over time circle graph for various data sets (line graph for change B. Explain that circle graphs are *identify that circle graphs are used to part-to-whole over time, circle graph for part-to-whole appropriate for graphing part-to-whole graph part-to-whole comparisons comparison comparison, scatter plot for trends) comparisons *identify that scatter plots are used to scatter plot C. Explain that scatter plots are graph trends trends appropriate graphing trends F.7.3 1 DAP.15.7.2 A. Analyze, with and without appropriate with and without appropriate technology: technology Analyze, with and without appropriate technology, a set of data by using and *find the mean, median and mode for a central tendencies technology, a set of data by using and comparing measures of central tendencies set of data mean comparing measures of central tendencies (mean, median, mode) *compare the mean, median, mode for a average (mean, median, mode) and measures of B. Analyze, with and without appropriate set of data median spread (range, quartile, interquartile range) technology, a set of data by using and *find measures of spread (range, quartile, mode comparing measures of spread (range, interquartile range) for a set of data measure of spread quartile, interquartile range) *compare measures of spread using a box- range and-whiskers plot quartile *analyze measures of central tendency interquartile range and measures of spread (including outliers outliers) for a set of data F.7.1 1 DAP.15.7.1 Analyze data displays, including ways that *identify data display composition: misleading Analyze data displays, including ways that they can be misleading •scale scale they can be misleading •data sample population techniques intervals •misuse of central tendencies central tendencies rev. 05-2009 11 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.1 MC-3 DAP.14.7.3 A. Construct and interpret circle graphs with and without appropriate technology: double bar graphs OR-1 Enduring Understanding - with and without appropriate solvers *circle Construct and interpret circle graphs, box- Successful problemtechnology possess a set of core beliefs that support circle graphs their work: and-whisker plots, histograms, scatter B. Construct and interpret box-and- problem solving is important, takes significant time and repeated efforts, and •explain part-to-whole correlation requires reflection. box-and-whisker plots and double-line graphs, with and without whisker plots with and without appropriate •demonstrate taking numbers from plots appropriate technology technology fractions to decimals to percents to histograms C. Construct and interpret histograms with degrees scatter plots and without appropriate technology •use a protractor to create angles double line graphs D. Construct and interpret scatter plots •construct circle graph technology with and without appropriate technology •interpret data correlation E. Construct and interpret double-line *box-and-whisker plots trend line graphs with and without appropriate •represent each quartile as 25% line of best fit technology •analyze and record the spread stem-and-leaf plots •interpret central tendencies Venn diagrams •find medians and extremes •construct box-and-whisker plot & identify outliers, if any *histogram •create a frequency table, place the frequency of occurency on y-axis & intervals of continuous data on x-axis •construct histogram (similar to a bar graph except bars touch) •compare independent variables to dependent variables •interpret data *scatter plot •determine dependent (y) variable & independent (x) variable •plot points (x,y) •decide the overall correlation •interpret data *double line graphs •determine dependent (y) & independent (x) variable •identify the data sets (2 or more) rev. 05-2009 12 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word •plot points & connect data set Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: independently compare changes over time problem solving is important, takes significant time and•evaluate andkey efforts, and requires reflection. repeated all graphs appropriately *title, label & 2. Enduring Understanding - Sampling affects the relationship between experimental and theoretical probability. 2a. Essential Question - How are experimental and theoretical probability related? F.7.1 1 DAP.17.7.1 Demonstrate that probability can take any *describe events that will not occur as probability Understand that probability can take any value between 0 and 1 (events that are probability 0 certainty value between 0 and 1 (events that are not not going to occur have probability 0, *describe events that will certainly occur outcome going to occur have probability 0, events events certain to occur have probability 1) as probability of 1 most likely certain to occur have probability 1) *create situations in which the probability least likely falls between 0 & 1 equally likely F.7.1 DAP.17.7.2 Design, with and without appropriate with and without appropriate technology: technology Design, with and without appropriate technology, an experiment to test a *create theoretical probabilities and test theoretical probability technology, an experiment to test a theoretical probability and explain how the them (experiment) experimental theoretical probability and explain how the results may vary *explain how results vary probability results may vary Ex. *formulate reasons why theoretical and Ex. suggested materials for simulations are experimental results vary suggested materials for simulations are: two- two-color counters, a number cube, and color counters, a number cube, and spinners spinners 3. Enduring Understanding - Linear relationships are characterized by a constant rate of change. 3a. Essential Question - Why are linear functions useful? F.7.1 1 DAP.16.7.1 A. Make, with and without appropriate *given a scatter plot determine a technology Make, with and without appropriate technology, conjectures of possible relationship between the dependent and conjectures technology, conjectures of possible relationships in a scatter plot independent variables scatter plot relationships in a scatter plot and B. Approximate the line of best fit (trend *make a conjecture about possible line of best fit approximate the line of best fit (trend line) line) relationships between variables trend line *construct a line of best fit to most dependent variable appropriately represent the "average" independent variable relationship between dependent and relationship independent variables rev. 05-2009 13 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word 4. Enduring Understanding - Selectionproblem solvers possess atools and units depends on real-world Enduring Understanding - Successful of standard measurement set of core beliefs that support their work: situations. problem solving is important, takes significant time and repeated efforts, and requires reflection. 4a. Essential Question - Why are scientific units and tools used to measure different attributes? F.7.2 1 M.12.7.1 For real-world problems to the required *state the common standard units customary Understand, select and use the appropriate degree of accuracy: *apply the prefixes of the metric system measurement units and tools (metric and customary) to A. Select and use the appropriate units *select the appropriate tool to measure in hours to minutes measure length, weight, mass and volume to and tools (metric and customary) to applicable units (Ex. ruler, meter stick, feet to inches the required degree of accuracy for real-world measure length gallon, liter, grams, pound, tons, quarts to gallons problems B. Select and use the appropriate units protractor, degrees, etc.) benchmark prefixes: and tools (metric and customary) to *apply the appropriate tool to measure milli-, centi-, kilo- Note: Use the appropriate tool to measure measure weight length, weight, mass, and volume of a length degrees of angles. Students are given a C. Select and use the appropriate units variety of real-world objects weight protractor to use on the Benchmark test. and tools (metric and customary) to *use a variety of measurement tools mass There have been test questions concerning measure mass (graduated cylinder, triple beam balance, volume the use of the protractor. D. Select and use the appropriate units meter stick, protractor and others) degree and tools (metric and customary) to metric units measure volume gram/liter/meter E. Select and use the appropriate tool to pounds measure angle degrees (protractor) gallons yards capacity protractor C.7.1 M.13.7.2 A. Draw and measure distance to the *know measuring begins with the first tic accurately Draw and measure distance to the nearest nearest 1/16 inch accurately mark precision millimeter and 1/16 inch accurately. B. Draw and measure distance to the *be able to record distance to the nearest tic mark/origin nearest millimeter accurately 1/16 inch *be able to draw a line to the nearest 1/16 inch *be able to record distance to the nearest millimeter *be able to draw a line to the nearest millimeter rev. 05-2009 14 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.1 2 M.12.7.2 Compare units within the same system *compare standard units Enduring Understanding - Successful problem solvers possess a set of Understand relationships among units within core beliefs that support their work: *compare metric units the same system seconds↔minutes↔ problem solving is important, takes significant time and repeated efforts, and requires reflection. hours↔days inches↔feet↔ yards↔miles ounces↔cups↔ pints↔ quarts↔gallons benchmark prefixes kilo-↔deci-↔centi- ↔milli- grams liters meters C.7.1 M.13.7.1 A. Solve real-world problems involving two *explain time concepts (clock and elapsed time Solve real-world problems involving two or or more elapsed times, counting forward calendar; Ex. number of days in each more elapsed times, counting forward and and backward on a calendar month) in the context of counting forward backward (calendar and clock) B. Solve real-world problems involving two and backward or more elapsed times, counting forward *solve real-world situations involving two and backward on a clock or more elapsed times 5. Enduring Understanding - Relationships exist among the angles, sides, lengths, perimeters, areas, and volumes of geometric figures. 5a. Essential Question - How are interior angles and the number of sides of the polygon related? C.7.1 OR-1 G.8.7.4 A. Use paper or physical models to *fold/cut paper to make physical models of interior angles Use paper or physical models to determine the sum of the measures of quadrilaterals & triangles quadrilaterals determine the sum of the measures of interior angles of triangles *demonstrate that the measures of the triangles interior angles of triangles and B. Use paper or physical models to sum of the interior angles of quadrilaterals non-overlapping quadrilaterals determine the sum of the measures of is 360º overlapping interior angles of quadrilaterals *demonstrate that the measures of the diagonals sum of the interior angles of triangles is 180º *find a missing angle given two angles in a triangle *find a missing angle given three angles in a quadrilateral rev. 05-2009 15 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word Enduring Understanding - Successful problem can change position and maintain the same attributes work: 6. Enduring Understanding - Geometric figures solvers possess a set of core beliefs that support their on a coordinate plane. important, takes significant time and repeated efforts, and requires reflection. problem solving is 6a. Essential Question - How does the movement of a geometric figure affect its attributes? F.7.1 G.10.7.2 Plot points that form the vertices of a *identify vertices of polygons vertices Plot points that form the vertices of a geometric figure and draw, identify and *replicate (draw) polygons on a coordinate faces geometric figure and draw, identify and classify the figure plane using ordered pairs edges classify the figure *classify figures according to number of vertices C.7.1 1 G.9.7.2 A. Perform translations of two-dimensional *fold/cut paper to perform translations of 2- rotation Perform translations and reflections of two- figures using a variety of methods (paper dimensional figures translation dimensional figures using a variety of folding, tracing, graph paper) *trace to perform translations of 2- reflection methods (paper folding, tracing, graph paper) B. Perform reflections of two-dimensional dimensional figures two-dimensional figures using a variety of methods (paper *use graph paper to perform translations figure folding, tracing, graph paper) of 2-dimensional figures *fold/cut paper to perform reflections of 2- dimensional figures *trace to perform reflections of 2- dimensional figures *use graph paper to perform reflections of 2-dimensional figures 7. Enduring Understanding - Relationships exist among angles, sides and triangles. 7a. Essential question - How can properties of triangles be applied to solve problems? F.7.1 G.8.7.6 Develop the properties of similar figures *categorize shapes similar figures Develop the properties of similar figures (ratio of sides and congruent angles) *explain the concept of similarity and scale congruent angles (ratio of sides and congruent angles) *identify similar figures according to ratio properties of sides and angles scale F.7.1 MC-1 M.13.7.5 Apply properties (scale factors, ratio, and *identify corresponding parts of triangles scale factors OR-1 Apply properties (scale factors, ratio, and proportion) of congruent or similar *set up proportion formulas (scale factors, ratio proportion) of congruent or similar triangles to solve problems involving ratios) using variables to find a missing proportion triangles to solve problems involving missing lengths and angle measures length of a triangle congruent missing lengths and angle measures *apply correlation properties to find a similar missing angle of a triangle correlation rev. 05-2009 16 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word FOURTH NINE WEEKS Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: 1. Enduring Understanding - Constructions are time and repeated efforts, and requires reflection. problem solving is important, takes significant based on properties of geometric figures. 1a. Essential Question - How are geometric properties used in constructions? F.7.2 2 G.8.7.1 A. Identify, draw, classify and compare 2- *identify and model 2-dimensional regular polygon Identify, draw, classify and compare D geometric figures using models and real- geometric figures including regular and irregular polygon geometric figures using models and real- world examples irregular polygons two-dimensional world examples B. Identify, draw, classify and compare 3- *classify 2-dimensional geometric figures figures D geometric figures using models and real- *compare 2-dimensional geometric figures three-dimensional world examples using real-world examples figures (pyramid, *draw 2-dimensional geometric figures cone, sphere, *identify and model 3-dimensional figures cylinder, cube, prism) *classify geometric 3-dimensional figures quadrilaterals *compare geometric 3-dimensional figures (rectangle, square, using real-world examples parallelogram, *draw 3-dimensional geometric figures trapezoid, rhombus) circle ellipse triangles (scalene, isosceles, equilateral, right, acute, obtuse) pentagons, hexagons, octagon, decagon, n-gon F.7.2 3 G.8.7.2 Investigate geometric properties and their *draw convex and concave polygons one-dimensional Investigate geometric properties and their relationships in one-, two-, and three- *compare and contrast the characteristics model relationships in one-, two-, and three- dimensional models, including convex and of one-, two-, and three-dimensional two-dimensional dimensional models, including convex and concave polygons models to see relationships among them model concave polygons three-dimensional model angles convex polygon concave polygon classification of polygons by sides classification of polygons by angles rev. 05-2009 17 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.2 G.8.7.3 A. Identify the pairs of angles formed and *identify vertical angles and know that they angles Enduring Understanding - Successful between the solvers are congruent Recognize the pairs of angles formed and the relationship problemangles of two possess a set of core beliefs that support right angle their work: the relationship between the angles intersecting lines (vertical, adjacent, linear *identify supplementary angles and know acute angle problem solving is important, takes significant time andthat they are congruent to 180º pair, supplementary, perpendicular) repeated efforts, and requires reflection. obtuse angle including two intersecting lines and parallel lines cut by a transversal (vertical, B. Identify the pairs of angles formed and *identify complementary angles and know intersecting lines supplementary, complementary, the relationship between parallel lines cut that they are congruent to 90º transversal corresponding, alternate interior, alternate by a transversal (vertical, supplementary, *identify corresponding angles and know vertical angles exterior angles and linear pair) corresponding, alternate interior, alternate that they are congruent supplementary exterior angles and linear pair) *identify alternate interior angles/alternate angles C. Identify the pairs of angles and the exterior angles and know that they are complementary relationship that exists to form congruent angles complementary angles *identify linear pairs and adjacent angles corresponding *identify the relationship of the angles angles formed by a transversal and parallel lines alternate interior angles alternate exterior angles linear pair alternate pair parallel lines interior exterior adjacent congruent rev. 05-2009 18 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word 2. Enduring Understanding - Relationships exist among the angles, sides, lengths, perimeters, and two- Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: dimensional areas. important, takes significant time and repeated efforts, and requires reflection. problem solving is 2a. Essential Question - How are the areas of rectangles, parallelograms, triangles, trapezoids, and circles related? F.7.2 M.13.7.3 A. Develop and use strategies to solve *use a variety of strategies to solve for trapezoid Develop and use strategies to solve problems problems involving area of a trapezoid area of a trapezoid altitude/height involving area of a trapezoid and B. Develop and use strategies to solve *apply formula for area of trapezoid base 1, base 2 circumference and area of a circle problems involving circumference of a *use a variety of strategies to solve for circumference circle finding the circumference of a circle area of a circle C. Develop and use strategies to solve *apply the formula for circumference of a radius problems involving area of a circle circle pi (π) *use a variety of strategies to solve for finding the area of a circle *apply the formula for area of a circle F.7.3 M.12.7.3 A. Find different areas for a given *given a perimeter, solve for area of linear units Find different areas for a given perimeter perimeter various shapes volume and find a different perimeter for a given B. Find a different perimeter for a given *label using appropriate units perimeter area area *given an area, identify all perimeter area combinations using whole numbers square units *label using appropriate units rev. 05-2009 19 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word 3. Enduring Understanding - Generalizations can be made to represent the relationship between area and Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: volume. solving is important, takes significant time and repeated efforts, and requires reflection. problem 3a. Essential Question - How do the dimensions of a geometric figure affect area, surface area, and volume? F.7.2 2 M.13.7.4 A. Derive and use formulas for surface *use the formulas for finding the areas of surface area Derive and use formulas for surface area and area of prisms and justify them using common shapes: circles, squares, volume volume of prisms and cylinders and justify geometric models and common materials triangles and rectangles prisms them using geometric models and common B. Derive and use formulas for surface *draw nets and use them to find the cylinders materials area of cylinders and justify them using formula for the surface area of a prism nets geometric models and common materials *use the formula to find the surface area derived formula C. Derive and use formulas for volume of of a prism prisms and justify them using geometric *use real world items to compare to nets models and common materials *apply appropriate units to surface area D. Derive and use formulas for volume of *draw nets and use them to find the cylinders and justify them using geometric formula for the surface area of a cylinder models and common materials *use the formula to find the surface area of a cylinder *use manipulatives to find a formula for the volume of rectangular prisms *apply the derived formula of volume to a variety of rectangular prisms (including common item i.e., matchbox, tissue box, shoebox, etc.) *identify the surface area parts of a cylinder as a rectangle attached to two circles at each end *use manipulatives to find a formula for the volume of cylinders *apply the derived formula of volume to a variety of cylinders (paper towel roll, soup can, etc.) rev. 05-2009 20 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word 3b. Essential Question - How can formulas be developed using models?core beliefs that support their work: Enduring Understanding - Successful problem solvers possess a set of F.7.2 M.13.7.7 Estimate and compute the area of more *apply the formulas for finding the areas of regular two- problem solving is of more complex or significant time Estimate and compute the areaimportant, takes irregular two-dimensional and repeated efforts, and requires reflection. basic shapes: circles, quadrilateral, dimensional shapes complex or irregular two-dimensional shapes by dividing them into more basic triangles irregular two- shapes by dividing them into more basic shapes *divide irregular/complex figures into basic dimensional shapes shapes 2-dimensional shapes area *find the area of basic shapes and complex combine these areas to find the area of the irregular figure F.7.2 G.8.7.5 Model and develop the concept that pi (π) *measure the radius and diameter pi (π) Model and develop the concept that pi (π) is is the ratio of the circumference to the *measure the circumference of circle ratio the ratio of the circumference to the diameter diameter of any circle *discover a relationship between the circumference of any circle diameter and circumference (known as pi) diameter *apply the formula for finding the radius circumference of a circle chord 4. Enduring Understanding - Geometric relationships exist between two-dimensional and three-dimensional figures. 4a. Essential Question - How are two-dimensional and three-dimensional figures related? F.7.2 1 G.11.7.1 Build three-dimensional solids from two- *match 2-dimensional patterns to 3- rectangular prism Build three-dimensional solids from two- dimensional patterns (nets) dimensional solids pyramids dimensional patterns (nets) *build 3-dimensional solids from a given 2- cylinders dimensional pattern (net) cones 3-dimensional solids 2-dimensional patterns nets F.7.2 1 G.11.7.2 Construct a building out of cubes from a *practice visualization skills using sets of cubes Construct a building out of cubes from a set of views (front, top, side) cubes (front, back, right side, left side and set of views (front, top, side) top) *construct buildings using cubes rev. 05-2009 21 of 22 7th Grade Math Arch Ford/Northwest Arkansas Instructional Alignment Seventh Grade Mathematics AR Department of Education NCTM Focal # of Essential Materials/ Point or Times CONTENT STANDARD/ Student Learning Objective Task Analysis Vocabulary Resources Connector Tested Expectations (SLE) *teacher word F.7.1 1 G.9.7.1 Examine the congruence, similarity, and *describe transformations-translations, congruence Enduring Understanding - Successful symmetry of solvers possess arotations core beliefs that support Examine the congruence, similarity, and line line or rotationalproblem objects reflections, and set of similarity their work: or rotational symmetry of objects using using transformations *identify symmetrical objects using line symmetry repeated problem solving is important, takes significant time andtransformations efforts, and requires reflection. transformations rotational symmetry *identify congruence/similarity in transformations relationship to transformations translations reflections rotations rev. 05-2009 22 of 22 problem solving is important, takes significant time andtransformations efforts, and requires reflection. transformations rotational symmetry *identify congruence/similarity in transformations relationship to transformations translations reflections rotations rev. 05-2009 22 of 22