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Chapter 1 Data Representation and Communication document sample
Instruction Period JEFFERSON COUNTY SCHOOLS Dates Taught Sixth Grade Mathematics TN Department of Education Student Performance Building blocks for the Essential Vocabulary Common Materials/ CONTENT STANDARD/ GLE Checks for Understanding Indicators (SPI) new standards *teacher word Assessment item Resources FIRST NINE WEEKS GLE 0606.1.2 Apply and 0606.1.6 Model SPI 0606.1.1 adapt a variety of appropriate situations by devising Make conjectures strategies to problem solving, and carrying out and predictions including estimation, and experiments and based on data. reasonableness of the solution. simulations. 1 (Introduced) (Introduced) (Introduced) Chapter 1 SPI 0506.3.2 Evaluate multi-step numerical expressions inolving fractions using order of operations. SPI 0506.3.1 evaluate algebraic expressions involving decimals and fractions using order of operations. * 0506.3.1 0606.3.3 Recognize Evaluate an the use of juxtaposition expression by (such as 3x, ab) to SPI 0606.3.2 Use substituting non- stand for multiplication, order of operations negative rational and the convention in and parentheses to number values for these cases of writing simplify expressions letter variables in 1 GLE 0606.3.3 numbers to include grouping symbols and exponents. Extend order of operationsbefore letters. and solve problems. the expression. Chapter 1 SPI 0506.2.3 Select a reasonable GLE 0606.3.2 Interpret and solution to a real- represent algebraic world division relationships with variables in problem in which expressions, simple equations the remainder must 1 and inequalities. be considered. Chapter 1 0606.1.5 Illustrate properties of operations by showing that two expressions are equivalent in a given SPI 0606.1.4 context (e.g., using an Select the area model for representation that distributive property, models one of the and grouping/set arithmetic properties models for (commutative, commutative and associative, or 1 associative properties). distributive). Chapter 1 SPI 0506.2.5 Solve addition and subtraction problems involving both fractions and decimals. * 0506.2.3 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. * 0506.2.5 Make reasonable estimates of fractions and decimal sums and differences. SPI 0506.2.4 Solve problems involving the division of two- and three-digit numbers by one- and two-digit whole SPI 0606.2.3 numbers. Solve problems *0506.2.7 involving the Understand addition, subtraction, placement of the multiplication, and decimal point in equation, solution, division of calculations of solving and equation, decimals.(Introduced) multiplication and defining the variable Chapter 1 SPI 0606.3.3 Write equations that correspond to given situations or represent a given GLE 0606.3.1 Write and mathematical term, sequence, solve two-step equations and relationship. arithmetic sequence, 1 inequalities. (Introduced) (Introduced) geometric sequence Chapter 1 statistics, data, frequency table, scale, interval, line graph, SPI 0606.3.7 scatter plot, line plot, Use algebraic cluster, outlier, range, expressions and measures of central properties to analyze tendency, mean, numeric and median, mode, stem- geometric patterns. and-leaf plot, stem, leaf, bar graph, 1 histogram Chapter 1 SPI 0506.5.3 Calculate measures of central tendency to analyze data. *05065.5 Evaluate how different measures of central tendencies describe data. *0506.5.6 Identify the outliers and determine their 0606.5.8 Connect effect on mean, data sets and their median, mode and graphical range. representations (such SPI 0506.5.2 Make as bar graphs, circle, predictions based graphs, and stem-and- on various data leaf plots). representations, including double 0606.5.9 Determine bar and line the sample space for a graphs. given situation. *0506.5.3 Design investigations to GLE 0606.5.2 Interpret 0606.5.11 Select the address a question representations of data from appropriate measure of and consider how surveys and polls, and describe center to describe a data collection sample bias and how data data set. methods affect the representations can be nature of the data misleading. set. Chapter 2 SPI 0506.2.1 Read an dwrite nimbers from millions to millionths in various contexts. *0506.2.10 Use exponential notation to represent repeated multiplication of whole numbers. SPI 0506.2.2 Write the prime factorization of numbers throush 50 using bother exponenial and standard notation. SPI 0606.1.3 Use *0506.2.1 Identify concrete, pictorial, prime numbers up and symbolic to 50. representation for *0506.2.2 Use the integers. prime factorization SPI of two whole 0606.2.7 Locate nujbers to positive rational determine greatest 0606.2.10 Explore numbers on the common factor, contexts that can be number line. least common GLE 0606.2.5 Develop described with negative SPI multiple. integer, graph, meaning for integers; represent numbers (such as 0606.2.8 Locate *0506.2.4 Use positive integer, and compare quantities with money, elevation, and integers on the divisibility rules to negative integer, 1 integers. temperature). number line. factor numbers. absolute value Chapter 3 0606.2.10 Explore SPI 0606.1.2 contexts that can be Judge the GLE 0606.2.5 Develop described with negative reasonableness of meaning for integers; represent numbers (such as the results of rational and compare quantities with money, elevation, and number estimates 1 integers. temperature). and/or computations. Chapter 3 0606.3.10 Understand that in an ordered pair (x, y), the x represents horizontal location and y represents vertical location. coordinate plane, coordinate grid, x- 0606.3.11 Identify the SPI 0606.3.9 axis, y-axis, quadrant of the Graph ordered pairs origin, ordered coordinate system in of integers in all four pair, x- GLE 0606.3.6 Understand which a point lies. quadrants of the coordinate, y- and use the Cartesian Cartesian coordinate coordinate, 1 coordinate system. system. quadrants Chapter 3 SPI 0606.1.3 Use concrete, pictorial, and symbolic representation for opposites, 1 integers. additive inverse Chapter 3 SPI 0606.1.3 Use concrete, pictorial, and symbolic representation for 1 integers. Chapter 3 0606.1.11 Model algebraic expressions with manipulatives, technology, and pencil and paper. SPI 0606.1.5 0606.3.7 Move fluently Model algebraic GLE 0606.3.1 Write and between different expressions using solve two-step equations and representations (such algebra tiles. inequalities. as verbal, tabular, SPI GLE numerical, algebraic, 0606.3.4 Rewrite 0606.3.4 Use expressions, and graphical) of expressions to equations and formulas to solve equations and represent quantities expression, zero 1 problems. expressions. in different ways. pairs Chapter 4 SPI 0506.3.3 Find the unknown in single-step equations involving fractions and mixed inverse numbers. operations, 0606.3.6 Use * 0506.3.2 Use Subtraction equations to describe variables Property of simple relationships appropriately to Equality, Addition shown in a table or SPI 0606.3.6 represent numbers Property of graph. Solve two-step linear whose values are Equality, equations using not yet known. coefficient, 0606.3.8 Represent number sense, *0506.3.3 Solve Division Property GLE 0606.3.1 Write and patterns using words, properties, and single-step linear of Equality, two- solve two-step equations and graphs, and simple inverse operations. equations using step equation, 1 inequalities. symbolic notation. inverse operations. inequality Chapter 4 SPI 0506.2.9 Compare whole numbers, decimals and fractions using the symbols <,>, and =. * 0506.2.9 Explore numbers less than 0 by extending the number line through familiar applications (e.g., temperatures, below zero, owing money, measuring elevation below sea levels. SPI 0506.3.4 Given a set fo values, identify those that make an inequality a true statement. * 0506.3.4 Solve single-step linear inequalities and terminating decimals, graph solutions on repeating decimals, GLE 0606.3.5 Use multiple SPI 0606.3.1 a number line. bar notation, ratio, representations including Represent on a * 0506.3.5 percent, common function, function symbolic algebra to model number line the Determine if a denominator, least table, domain, and/or solve contextual solution of a linear given value is a common denominator range, linear problems that involve linear inequality. solution to a linear (LCD), rational equation, ordered 1 relationships. equation/inequality. numbers pair Chapter 4 0606.2.1 Efficiently compare and order fractions, decimals and SPI 0606.2.3 percents; determine Solve problems their approximate involving the locations on a number addition, subtraction, line. multiplication, and division of decimals. 0606.2.8 Recognize that a terminating SPI 0606.2.5 decimal equals a Transform numbers fraction with a from one form to denominator that is a another (fractions, SPI 0506.2.7 power of ten. decimals, percents, Recognize GLE 0606.2.3 Understand and mixed numbers). equivalent and use ratios, rates and 0606.2.9 Recognize representations for percents. (Introduced) that the decimal form of SPI 0606.2.6 the same number. a rational number Solve problems SPI 0506.2.8 GLE 0606.2.4 Understand either terminates or involving ratios, rates Write terminating and convert between fraction, repeats. and percents. decimals in the decimal, and percent forms of form of fractions or 1 rational numbers. mixed numbers. Chapter 5 Compatable numbers, GCF (Greatest Common Factor), multipliative inverse, reciprocal, Multiplication Property 2 SECOND NINE WEEKS of Equality SPI 0606.2.1 Solve problems involving the multiplication and division of fractions. SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and GLE 0606.1.2 Apply and division of mixed adapt a variety of appropriate numbers. strategies to problem solving, SPI including estimation, and 0606.3.6 Solve reasonableness of the solution. two-step linear GLE 0606.1.2 Recognize equations using 0606.3.4 Use expressions, when an estimate is number sense, SPI 0506.2.6 Add equations and formulas to solve more appropriate than properties, and and subtract proper perimeter, formula, problems. an exact answer in a inverse operations. and improper area, circle, center, variety of problem fractions as well as circumference, 2 situations. mixed numbers diameter, pi, raidius Chapter 6 SPI 0506.4.2 Decompose irregular shapes to find perimeter and area. * 0506.4.2 Find the area of a convex polygon by decomposing it into triangles/rectangles. SPI 0506.4.6 Record measurements in context to 0606.4.11 Relate the reasonable degree circumference of a of accuracy using circle with the perimeter decimals and/or of a polygonal figure. fractions. *0506.4.9 Correctly 0606.4.12 Derive the interpret significant meaning of Pi using digits in the concrete models and/or accuracy of appropriate technology. measurements and associated 0606.4.16 Solve calculations. contextual problems *0506.4.10 involving area and Recognize that circumference of measurements are equivalent ratios, ratio, circles, surface areas never exact. rate, unit rate, and volumes of prisms, SPI 0606.4.4 * 0506.4.11 proportion, cross pyramids, cones, and Calculate with Understand the product, scale, scale cylinders. circumferences and usefulness of drawing, scale factor, 2 areas of circles. approximations. scale model Chapter 6 0606.2.4 Understand ratio as a fraction used to compare two quantities by division. 0606.2.5 Recognize a:b, a/b, and “a to b” as notations for ratios. 0606.2.6 Recognize common percentages as ratios based on fractions whose denominators are 2, 3, 4, 5, or 10. 0606.2.7 Connect ratio and rate to SPI 0606.2.6 multiplication and Solve problems division. involving ratios, rates percent, percent and percents. proportion, part, base, 2 (continued) percent equation 0606.2.1 Efficiently compare and order fractions, decimals and percents; determine their approximate survey, random locations on a number sample, population, line. SPI 0606.2.4 percent of change, Solve multi-step percent of increase, 0606.2.2 Use area arithmetic problems percent of decrease, models to represent using fractions, sales tax, discount, multiplication of mixed numbers, and simple interest, 2 fractions. decimals. principle, discount Chapter 7 and 8 SPI 0506.5.1 Depict data using various representations, including decimal and/or fractional SPI 0606.5.1 data. 0606.5.9 Determine Determine the *0506.5.1 Construct the sample space for a theoretical probability and analyze double given situation. of simple and bar and line compound events in graphs. *0506.5.2 0606.5.10 Distinguish familiar contexts. Represent data between a random and using ordered pairs nonrandom sample. in the first quadrant of the coordinate SPI 0606.5.3 system. *0506.5.4 0606.5.12 Predict the Determine whether Recognize the characteristics of a or not a sample is differences in population based on biased. representing the analysis of sample categorical and 2 data. numerical data. Chapter 8 outcomes, simple, event, probability, random, complementary events, fair game, tree diagram, sample space, Fundamental Counting Principal, compound event, independent event, permutation, combinations, experimental probability, theoretical, probabality,dependent 3 THIRD NINE WEEKS event 0606.5.1 Understand that the probability of an event is a number between zero and one that expresses the likelihood of its occurrence. 0606.5.2 6.5.2 Identify the probability of an event as the ratio of the number of its actual occurrences to the total number of its possible occurrences. 0606.5.3 Express probabilities in different ways. 0606.5.4 Understand the difference between probability and odds. 0606.5.5 Analyze a situation that involves probability of an independent event. GLE 0606.5.1 Understand the 0606.5.6 Estimate meaning of probability and how the probability of simple 3 it is expressed. and compound events Chapter 9 0606.3.10 Understand that in an ordered pair (x, y), the x represents horizontal location and y represents vertical location. 0606.4.1 Investigate the sum of the angles in a triangle and a quadrilateral using various methods. SPI 0606.4.1 ü 0606.4.2 Identify, define or Relate the sum of the describe geometric angles in a triangle to shapes given a the sum of the angles visual representation in polygons. or a written description of its 0606.4.3 Verify the properties. basic properties of triangles and SPI 0606.4.2 Find quadrilaterals using a a missing angle protractor and ruler. measure in problems involving 0606.4.4 Classify interior/exterior triangles by side angles and/or their lengths (scalene, sums. isosceles, and equilateral) and angle SPI 0606.4.3 measure (acute, right, Solve problems GLE 0606.4.1 Understand obtuse, isosceles and using the Triangle and use basic properties of equiangular). Inequality Theorem. triangles, quadrilaterals, and 3 other polygons. Chapter 10 3 similar 0606.4.8 Understand scaling, dilation and their relation to similarity. 0606.4.9 Analyze the differences between congruence and similarity. 3 Chapter 10 SPI 0606.4.3 0606.4.5 Model and Solve problems use the Triangle using the Triangle 3 Inequality Theorem. Inequality Theorem. Not in book 0606.4.7 Work with transformations in a plane and explore their meanings through drawings and manipulatives. GLE 0606.4.2 Use the 0606.4.10 Describe concepts of translation, the effect of a rotation, reflection, and transformation on a 2- symmetry to understand dimensional figure and 3 congruence in the plane. the resulting symmetry. Chapter 10 SPI 0606.4.1 Identify, define or SPI 0506.4.1 Solve describe geometric contextual shapes given a problems that visual representation require calculating or a written the area of description of its triangles and GLE 0606.4.3 Develop and properties. parallelograms. use formulas to determine the * 0506.4.1 circumference and area of SPI 0606.4.2 Find Develop the circles, and the area of a missing angle formula for the are trapezoids, and develop measure in problems af a triangle by strategies to find the area of 0606.4.14 Relate the involving relating it to the composite shapes. area of a trapezoid to interior/exterior area of a the area of a angles and/or their parallelogram or 3 parallelogram. sums. rectangle. Chapter 11 *0506.4.7 Understand, select and use units of appropriate size and type to measure angles, lengths/distances, area, surface area and volume. SPI 0506.4.3 Identify a three- 0606.4.15 Find lengths dimentional object given areas or from two- volumes, and vice dimentional versa. representations of that object and vice 0606.4.17 Use versa. manipulatives to * 0506.4.3 Build, discover the volume of SPI 0606.4.5 draw, and work with a pyramid is one-third Determine the prisms in the volume of the surface area and orthogonal views, related prism (the volume of prisms, projective views heights and base areas pyramids and and nets. are equal). cylinders. *0506.4.6 Decompose prisms GLE 0606.4.4 Develop and 0606.4.18 Use SPI 0606.4.6 to calculate surface use formulas for surface area manipulatives to Given the volume of area/volume. and volume of 3-dimensional discover the volume of a cone/pyramid, find SPI 0506.4.4 Solve figures. a cone is one-third the the volume of the problems involving volume of the related related cylinder/prism surface area and cylinder (the heights or vice versa. volume of and base areas are rectangular prisms 3 equal). and polyhedral 3 ALL YEAR LONG GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning. GLE 0606.1.2 Apply and adapt a variety of appropriate strategies to problem solving, 0606.1.3 Recognize including estimation, and errors generated by reasonableness of the solution. rounding. GLE 0606.1.3 Develop 0606.1.4 Describe independent reasoning to how changes in one communicate mathematical quantity or variable ideas and derive algorithms result in changes in and/or formulas. another. GLE 0606.1.4 Move flexibly 0606.1.7 between concrete and abstract Formulate questions, representations of design studies, and mathematical ideas in order to collect real world data. solve problems, model mathematical ideas, and 0606.1.8 Determine communicate solution an appropriate sample strategies. to test an hypothesis. GLE 0606.1.5 Use 0606.1.9 Use age- mathematical ideas and appropriate books, processes in different settings stories, and videos to to formulate patterns, analyze convey ideas of graphs, set up and solve mathematics. problems and interpret