8th Grade Math Home > Teacher Resources > Mathematical Power for All Students K-12 > Part II - Content Strands

Content Strands

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 3

 A122: relative size of numbers (pp 41-42) A124: equivalent forms of numbers (p 49), includes A121 (names of numbers), A123 (concrete and symbolic representations of numbers) A221: place value concepts (p 55) A321: effects of operations on numbers (p 60) A322: appropriate operation to solve a specific problem (p 64) A323: appropriate methods of computing (p 68) A421: estimation strategies (p 72) - includes B321 (estimates of measurements) A521: basic number theory concepts including primes, composites, factors, and multiples (p 78)

 Number Sense, Concepts, and Operations

 B122: real-world problems involving length, weight, perimeter, area, capacity, volume, time, temperature, and angles (PP 82-83) B221: direct and indirect measures (p 90) B222: appropriate standard and nonstandard units of measurement (p 96) - includes B421 (which units to use with answers to real-world problems) B422: appropriate instruments and technology to measure in real-world situations (PP 101-102)

 Measurement

 C121: appropriate geometric vocabulary to draw and describe 2- and 3-D shapes (p 108) C221: spatial relationships, symmetry, reflections, congruency, and similarity (p 113), includes B122, C121, C321, (see chart) C222: flips, slides, and turns (p 119) C321: strategies, properties, and formulas to solve real-world problems involving 2- and 3-D shapes (PP 125-126), includes C221 (see chart) C322: positive ordered pairs in a rectangular coordinate system (PP 134-135)

 Geometry and Spatial Sense

 D121: patterns and relationships using models (PP 142-143) D221: represent a given simple problem situation (PP 156-157), includes D222 (see chart) D222: informal methods to solve equations and inequalities (p 163), includes D221 (see chart)

 Algebraic Thinking

 E121: generate, collect, organize, display, and analyze data to solve problems (PP 170-171) - includes E123 (analyzes real world data) E122: range, mean, median, and mode (p 183) - includes E123 (see E121) E221: display possible outcomes using models (p 189) E222: predict the likelihood of simple events occurring (p 194)

 Data Analysis and Probability

 All FCAT math items at Grade 3 are tested in multiple choice format PP - Test Item and Performance Task Specifications pages

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 4

 A122: relative size of numbers (PP 43-44) A124: equivalent forms of numbers (PP 50-51), includes A121 (names of numbers), A123 (concrete and symbolic representations of numbers) A221: place value concepts (p 56) A321: effects of operations on numbers (p 61) A322: appropriate operation to solve a specific problem (p 65) A323: appropriate methods of computing (p 69) A421: estimation strategies (p 73) - includes B321 (estimates of measurements) A521: basic number theory concepts including primes, composites, factors, and multiples (p 79)

 Number Sense, Concepts, and Operations

 B122: real-world problems involving length, weight, perimeter, area, capacity, volume, time, temperature, and angles (PP 84-85) B221: direct and indirect measures (p 91) B222: appropriate standard and nonstandard units of measurement (PP 97-98) - includes B421 (which units to use with answers to real-world problems) B422: appropriate instruments and technology to measure in real-world situations (PP 103-104)

 Measurement

 C121: appropriate geometric vocabulary to draw and describe 2- and 3-D shapes (p 109) C221: spatial relationships, symmetry, reflections, congruency, and similarity (p 114), includes B122, C121, C321, (see chart) C222: flips, slides, and turns (PP 120-121) C321: strategies, properties, and formulas to solve real-world problems involving 2- and 3-D shapes (PP 127-128), includes C221 (see chart) C322: positive ordered pairs in a rectangular coordinate system (p 136)

 Geometry and Spatial Sense

 D121: patterns and relationships using models (PP 144-145) D221: represent a given simple problem situation (p 158), includes D222 (see chart) D222: informal methods to solve equations and inequalities (PP 164-165), includes D221 (see chart)

 Algebraic Thinking

 E121: generate, collect, organize, display, and analyze data to solve problems (PP 172-173), includes E123 (analyzes real world data) E122: range, mean, median, and mode (PP 184-185) - includes E123 (see E121) E221: display possible outcomes using models (p 190) E222: predict the likelihood of simple events occurring (p 195)

 Data Analysis and Probability

 All FCAT math items at Grade 4 are tested in multiple choice format PP - Test Item and Performance Task Specifications pages

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 5

 A122: relative size of numbers (MC, GR) PP 45-47 A124: equivalent forms of numbers (MC, GR) PP 52-53, includes A121 (names of numbers), A123 (concrete and symbolic representations of numbers) A221: A221: place value concepts (GR) PP 57-58 A321: A321: effects of operations on numbers (MC) p 62 A322: A322: appropriate operation to solve a specific problem (MC) p 66 A323: A323: appropriate methods of computing (MC, GR) p 70 A421: A421: estimation strategies (SR) PP 74-76, includes B321 (estimates of measurements) A521: A521: basic number theory concepts including primes, composites, factors, and multiples (MC) p 80

 Number Sense, Concepts, and Operations

 B122: real-world problems involving length, weight, perimeter, area, capacity, volume, time, temperature, and angles (MC, GR) PP 86-88 B221: direct and indirect measures (MC, GR) PP 92-94 B222: appropriate standard and nonstandard units of measurement (MC) p 99, includes B421 (which units to use with answers to real-world problems) B422: appropriate instruments and technology to measure in real-world situations (MC) PP 105-106

 Measurement

 C121: appropriate geometric vocabulary to draw and describe 2- and 3-D shapes (SR) PP 110-111 C221: spatial relationships, symmetry, reflections, congruency, and similarity (MC, ER) PP 115-117, includes B122, C121, C321, (see chart) C222: flips, slides, and turns (MC) PP 122-123 C321: strategies, properties, and formulas to solve real-world problems involving 2- and 3-D shapes (MC, SR) PP 129-132, includes C221 (see chart) C322: positive ordered pairs in a rectangular coordinate system (MC, SR) PP 137-140

 Geometry and Spatial Sense

 D121: patterns and relationships using models (MC, GR) PP 146-148 D122: generalize pattern, relation, or function to explain cause-and-effect (SR) PP 152-154, includes D121 (see chart) D221: represent a given simple problem situation (MC, SR) PP 159-161, includes D222 (see chart) D222: informal methods to solve equations and inequalities (MC, GR) PP 166-168, includes D221 (see chart)

 Algebraic Thinking

 E121: generate, collect, organize, display, and analyze data to solve problems (MC, GR, ER) PP 174-181, includes E123 (analyzes real world data) E122: range, mean, median, and mode (MC, GR) PP 186-187, includes E123 (see E121) E221: display possible outcomes using models (SR) PP 191-192 E222: predict the likelihood of simple events occurring (MC) p 196 E321: collect, organize, analyze, and display data (MC, SR) PP 200-203, includes E322 (uses data to make predictions)

 Data Analysis and Probability

 MC - multiple choice, GR - gridded response, SR - short response, ER - extended response PP - Test Item and Performance Task Specifications pages

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 6

 A122: relative size of numbers (MC) p 42 A134: equivalent forms of numbers (MC, GR) PP 47-48, includes A131 (verbal and word names for numbers), A133 (concrete and symbolic representations of numbers) A231: exponential and scientific notation (MC, GR) PP 54-55 A331: effects of operations on numbers (MC) p 61 A332: order of operations (MC, GR) PP 65-66 A333: appropriate methods of computing (MC, GR) PP 72-73 A431: estimation strategies (MC) p 79, includes A421 (reasonableness of results), B231 (direct and indirect measurement), B331 (estimates of measurements)

 Number Sense, Concepts, and Operations

 B131: derive formulas for perimeter, area, surface area, circumference, or volume (MC, GR) PP 84-86, includes B122 (grades 3-5, real world measurement problems), B231 (see A431) B132: derive formulas for rate, distance, time, angle measures (MC, GR) p 96, includes B122 (see B131), B231 (see A431) B133: impact of change in one dimension on other measurements (MC, GR) PP 103-105, includes C231 (see chart) B134: real-world problems involving scale drawings (MC, GR) PP 113-115, includes B231 (see A431) B232: real-world problems involving conversions within the metric or customary system (MC, GR) PP 122-123

 Measurement

 C131: relationships and properties among regular and irregular shapes (MC, GR) PP 129-131, includes C121 (grades 3-5, draw or describe 2- and 3-dimensional shapes) C231: symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations (MC) PP 139-140, includes B133 (see chart), C121 (see C131), C131 (see chart), C331 (see chart) C331: real-world and mathematical problems involving geometric properties and relationships (MC) PP 153-154, includes C231 (see chart) C332: rectangular coordinate system and simple properties of lines (MC) PP 163-164

 Geometry and Spatial Sense

 D131: patterns, relationships, and functions (MC, GR) PP 176-178, includes A531 (number sequences) D132: cause-and-effect relationships (MC, GR) PP 185-186, includes A531 (see D131) D231: algebraic expressions, equations, and inequalities (MC) p 197, includes A133 (see A134) D232: linear equations and inequalities (MC, GR) PP 203-204

 Algebraic Thinking

 E131: different ways of presenting data leading to different interpretations (MC, GR) PP 210-212, includes E133 (analyze and organize data in a quality display) E132: measures of central tendency and range (MC, GR) PP 225-227, includes E133 (see E131) E231: experimental results compared with mathematical expectations (MC) PP 235-236 E232: odds for and odds against a given situation (MC) p 243, includes E222 (grades 3-5, predicts likelihood of simple events occurring) E331: inferences and conclusions based on statistics (MC) PP 248-249, includes E332 (common uses and misuses of statistics)

 Data Analysis and Probability

 All FCAT math items at Grade 6 are tested in multiple choice (MC) or gridded response (GR) format PP - Test Item and Performance Task Specifications pages

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 7

 A132: relative size of numbers (MC) p 43 A134: equivalent forms of numbers (MC, GR) PP 49-50, includes A131 (verbal and word names for numbers), A133 (concrete and symbolic representations of numbers) A231: exponential and scientific notation (MC, GR) PP 56-57 A331: effects of operations on numbers (MC) p 62 A332: order of operations (MC, GR) PP 67-68 A333: appropriate methods of computing (MC, GR) PP 74-75 A431: estimation strategies (MC) p 80, includes A421 (reasonableness of results), B231 (direct and indirect measurement), B331 (estimates of measurements)

 Number Sense, Concepts, and Operations

 B131: derive formulas for perimeter, area, surface area, circumference, or volume (MC, GR) PP 87-89, includes B122 (grades 3-5, real world measurement problems), B231 (see A431) B132: derive formulas for rate, distance, time, angle measures (MC, GR) PP 97-99, includes B122 (see B131), B231 (see A431) B133: impact of change in one dimension on other measurements (MC, GR) PP 106-108, includes C231 (see chart) B134: real-world problems involving scale drawings (MC, GR) PP 116-117, includes B231 (see A431) B232: real-world problems involving conversions within the metric or customary system (MC, GR) PP 124-125

 Measurement

 C131: relationships and properties among regular and irregular shapes (MC, GR) PP 132-134, includes C121 (grades 3-5, draw or describe 2- and 3-dimensional shapes) C231: symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations (MC) p 141, includes B133 (see chart), C121 (see C131), C131 (see chart), C331 (see chart) C232: patterns involving tessellations (MC) p 150 C331: real-world and mathematical problems involving geometric properties and relationships (MC) PP 155-156, includes C231 (see chart) C332: rectangular coordinate system and simple properties of lines (MC) PP 165-166

 Geometry and Spatial Sense

 D131: patterns, relationships, and functions (MC, GR) PP 179-181, includes A531 (number sequences) D132: cause-and-effect relationships (MC, GR) PP 187-189, includes A531 (see D131) D231: algebraic expressions, equations, and inequalities (MC) p 198, includes A133 (see A134) D232: linear equations and inequalities (MC, GR) PP 205-206

 Algebraic Thinking

 E131: different ways of presenting data leading to different interpretations (MC, GR) PP 213-215, includes E133 (analyze and organize data in a quality display) E132: measures of central tendency and range (MC, GR) PP 228-230, includes E133 (see E131) E231: experimental results compared with mathematical expectations (MC) PP 237-238 E232: odds for and odds against a given situation (MC) p 244, includes E222 (grades 3-5, predicts likelihood of simple events occurring) E331: inferences and conclusions based on statistics (MC) p 250, includes E332 (common uses and misuses of statistics)

 Data Analysis and Probability

 All FCAT math items at Grade 7 are tested in multiple choice (MC) or gridded response (GR) format PP - Test Item and Performance Task Specifications pages

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 8

 A132: relative size of numbers (MC) PP 44-45 A134: equivalent forms of numbers (MC, GR) PP 51-52, includes A131 (verbal and word names for numbers), A133 (concrete and symbolic representations of numbers) A231: exponential and scientific notation (MC, GR) PP 58-59 A331: effects of operations on numbers (MC) p 63 A332: order of operations (MC, GR) PP 69-70 A333: appropriate methods of computing (MC, GR) PP 76-77 A431: estimation strategies (SR) PP 81-82 , includes A421 (reasonableness of results), B231 (direct and indirect measurement), B331 (estimates of measurements)

 Number Sense, Concepts, and Operations

 B131: derive formulas for perimeter, area, surface area, circumference, or volume (GR, SR) PP 90-94, includes B122 (grades 3-5, real world measurement problems), B231 (see A431) B132: derive formulas for rate, distance, time, angle measures (GR, SR) p 100-101, includes B122 (see B131), B231 (see A431) B133: impact of change in one dimension on other measurements (MC, GR) PP 109-111, includes C231 (see chart) B134: real-world problems involving scale drawings (MC, GR) PP 118-120, includes B231 (see A431) B232: real-world problems involving conversions within the metric or customary system (MC, GR) PP 126-127

 Measurement

 C131: relationships and properties among regular and irregular shapes (MC, GR) PP 135-137, includes C121 (grades 3-5, draw or describe 2- and 3-dimensional shapes) C231: symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations (MC, GR, ER) PP 142-147, includes B133 (see chart), C121 (see C131), C131 (see chart), C331 (see chart) C232: patterns involving tessellations (MC) p 151 C331: real-world and mathematical problems involving geometric properties and relationships (MC, SR) PP 157-161, includes C231 (see chart) C332: rectangular coordinate system and simple properties of lines (MC, SR) PP 167-174

 Geometry and Spatial Sense

 D131: patterns, relationships, and functions (MC, GR) PP 182-183, includes A531 (number sequences) D132: cause-and-effect relationships (MC, GR, SR) PP 190-195, includes A531 (see D131) D231: algebraic expressions, equations, and inequalities (MC, SR) p 199-201, includes A133 (see A134) D232: linear equations and inequalities (MC, GR) PP 207-208

 Algebraic Thinking

 E131: different ways of presenting data leading to different interpretations (MC, GR, ER) PP 216-223, includes E133 (analyze and organize data in a quality display) E132: measures of central tendency and range (MC, GR) PP 231-233, includes E133 (see E131) E231: experimental results compared with mathematical expectations (SR) PP 239-241 E232: odds for and odds against a given situation (MC, GR) p 245-246, includes E222 (grades 3-5, predicts likelihood of simple events occurring) E331: inferences and conclusions based on statistics (MC, SR) PP 251-253, includes E332 (common uses and misuses of statistics)

 Data Analysis and Probability

 MC - multiple choice, GR - gridded response, SR - short response, ER - extended response PP - Test Item and Performance Task Specifications pages

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 9

 A142: relative size of numbers (MC) p 40 A144: equivalent forms of numbers (MC, GR) PP 44-45, includes A141 (verbal and word names for numbers), A143 concrete and symbolic representations of numbers A341: effects of operations on numbers (MC, GR) PP 49-50, includes A242 (real number system) A342: properties of numbers as operational shortcuts (MC, GR) PP 54-55, includes A242 (see A341) A343: appropriate methods of computing (MC, GR) PP 58-59, includes A242 (see A341) A441: estimation strategies in complex situations (MC) PP 63-64, includes B341 (estimates of measurements)

 Number Sense, Concepts, and Operations

 B141: derive formulas for perimeter, area, surface area, circumference, or volume (MC, GR) PP 69-71, includes B122 (grades 3-5, real-world problems involving other common units of measure) B142: derive formulas for rate, distance, time, angle measures, or arc lengths (MC, GR) PP 77-78, includes B122 (see B141) B143: real-world problems involving similarity and proportionality (MC, GR) PP 84-86 B241: direct and indirect measurement (MC, GR) PP 89-90 B242: real-world problems involving rated measures (mph, fps) (MC, GR) PP 94-95, includes B232 (grades 6-8, problems and conversions within the metric or customary systems)

 Measurement

 C141: formal and informal proofs (MC, GR) PP 100-101, includes C121 (grades 3-5, describes/draws 2- and 3-D shapes), C131 (grades 6-8, basic properties of 2- and 3-D shapes) C241: perpendicularity, parallelism, tangency, congruency, similarity, reflections, symmetry, and transformations (MC, GR) PP 109-111, includes B143, C141, C341 (see chart) C341: ratio, proportion, right triangle geometry (MC) PP 124-126, includes C241 (see chart) C342: algebraic properties in a rectangular coordinate system (MC, GR) PP 133-135, includes C332 (grades 6-8, ordered pairs and simple properties of lines), D241 (sequences and series)

 Geometry and Spatial Sense

 D141: relationships, patterns, and functions (MC, GR) PP 143-144 D142: impact when changing parameters of functions (MC, GR) PP 151-153 D242: systems of linear equations and inequalities (MC, GR) PP 158-160, includes D241 (see C342)

 Algebraic Thinking

 E141: interpret data from charts, tables, and plots (MC, GR) PP 169-171, includes E131 (grades 6-8, different ways of presenting data, leading to different interpretations), E143 (use of statistics to make predictions) E142: measures of central tendency and dispersion (MC, GR) PP 182-184, includes E143 (see E141) E241: probability, including permutations and combinations (MC, GR) PP 188-190, includes E242 (probability for simple and compound events) E341: interpret data that results from statistical experiments (MC, GR) PP 195-197, includes E331 (grades 6-8, inferences and conclusions based on statistics), E342 (limitations of statistical techniques and data in making inferences)

 Data Analysis and Probability

 All FCAT math items at Grade 9 are tested in multiple choice (MC) or gridded response (GR) format PP - Test Item and Performance Task Specifications pages

 SUMMARY OF BENCHMARKS ASSESSED ON FCAT - GRADE 10

 A142: relative size of numbers (MC) PP 41-42 A144: equivalent forms of numbers (MC, GR) PP 46-47, includes A141 (verbal and word names for numbers), A143 concrete and symbolic representations of numbers A341: effects of operations on numbers (MC, GR) PP 51-52, includes A242 (real number system) A342: properties of numbers as operational shortcuts (MC) p 56, includes A242 (see A341) A343: appropriate methods of computing (MC, GR) PP 60-61, includes A242 (see A341) A441: estimation strategies in complex situations (SR) PP 65-67, includes B341 (estimates of measurements)

 Number Sense, Concepts, and Operations

 B141: derive formulas for perimeter, area, surface area, circumference, or volume (GR, SR) PP 72-75, includes B122 (grades 3-5, real-world problems involving other common units of measure) B142: derive formulas for rate, distance, time, angle measures, or arc lengths (MC, SR) PP 79-82, includes B122 (see B141) B241: direct and indirect measurement (MC) PP 91-92 B242: real-world problems involving rated measures (mph, fps) (MC, GR) PP 96-98, includes B232 (grades 6-8, problems and conversions within the metric or customary systems)

 Measurement

 C141: formal and informal proofs (MC, GR, SR) PP 102-107, includes C121 (grades 3-5: describes/draws 2- and 3-D shapes), C131 (grades 6-8, basic properties of 2- and 3-D shapes) C241: perpendicularity, parallelism, tangency, congruency, similarity, reflections, symmetry, and transformations (MC, GR, ER) PP 112-118, includes B143 (similarity and proportionality), C141, C341 (see chart) C242: planar cross sections (MC) PP 121-122 C341: ratio, proportion, right triangle geometry (MC, SR) PP 127-131, includes C241 (see chart) C342: algebraic properties in a rectangular coordinate system (MC, GR, SR) PP 136-141, includes C332 (grades 6-8, ordered pairs and simple properties of lines), D241 (sequences and series)

 Geometry and Spatial Sense

 D141: relationships, patterns, and functions (MC, GR) PP 145-149 D142: impact when changing parameters of functions (SR) PP 154-156 D242: systems of linear equations and inequalities (MC, GR, SR) PP 161-167, includes D241 (see C342)

 Algebraic Thinking

 E141: interpret data from charts, tables, and plots (MC, GR, SR) PP 172-180, includes E131 (grades 6-8, different ways of presenting data, leading to different interpretations), E143 (use of statistics to make predictions) E142: measures of central tendency and dispersion (MC, GR) PP 185-186, includes E143 (see E141) E241: probability, including permutations and combinations (MC, GR) PP 191-193, includes E242 (probability for simple and compound events) E341: interpret data that results from statistical experiments (MC, GR, SR) PP 198-202, includes E331 (grades 6-8, inferences and conclusions based on statistics), E342 (limitations of statistical techniques and data in making inferences)

 Data Analysis and Probability

 MC - multiple choice, GR - gridded response, SR - short response, ER - extended response PP - Test Item and Performance Task Specifications pages

 8th Grade Math Home > Teacher Resources > Mathematical Power for All Students K-12 > Part II - Content Strands