6th Grade Math Essential Units of Study Year at a Glance

Transcription

1 6th Grade Math Essential Units of Study Year at a Glance 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Week of 8/27/07 9/3/07 9/10/07 9/17/07 9/24/07 10/1/07 10/8/07 10/15/07 10/22/07 10/29/07 11/5/07 11/12/07 11/19/07 11/26/07 12/3/07 12/10/07 12/17/07 12/24/07 12/31/07 1/7/08 1/14/08 1/21/08 1/28/08 2/4/08 2/11/08 2/18/08 2/25/08 3/3/08 3/10/08 3/17/08 3/24/08 3/31/08 4/7/08 4/14/08 4/21/08 4/28/08 5/5/08 5/12/08 5/19/08 5/26/08 6/2/08 Essential Unit of Study Problem Solving Number Theory & Algebraic Reasoning Data Analysis Rational Numbers Proportionality Probability Measurement Systems Geometry Measurement - Perimeter, Area, Volume TAKS Review & Test Post TAKS Testing Windows Administration Scantrons Due Assessment I November December 3 Authentic Assessment February 7 & 8 March 17 Assessment II February March 3 TAKS Test April 28 - May 2 Assessment III May June 2

2 (6.11) Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. (6.12) Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representation and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and (B) evaluate the effectiveness of different representations to communicate ideas. (6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships. Problem Solving Quick Planner Suggested Timing: 2 Weeks Common Performance Assessment: The Pool 1. State a problem solving task accurately using their own words How to synthesize information from a problem and rephrase it to show understanding Techniques for identifying and noting necessary information in a problem 2. Discriminate between relevant and irrelevant information in a problem situation How to synthesize information from a problem and rephrase it to show understanding Techniques for identifying and noting necessary information in a problem 3. Estimate and/or hypothesize solutions with appropriate justification How to synthesize information from a problem and rephrase it to show understanding Key words that indicate operations in word problems Methods for estimating solutions (rounding, compatible numbers, benchmarking, grouping, etc ) Justification requires the use of mathematical reasoning How to organize and consolidate their mathematical thinking through communication How to communicate their mathematical thinking coherently and clearly to peers, teachers, and others Correct mathematical terminology Mental math, estimation, and number sense skills Key words that indicate operations in word problems How to use appropriate mathematical properties and notation to solve a problem How to select the most efficient strategy for a problem situation Various problem solving strategies and how to apply them (draw a picture, look for a pattern, guess and check, act it out, make a table, work a simpler problem, work backwards, etc ) Efficient and appropriate use of manipulatives, paper/pencil, and technology Key words that indicate operations in word problems How to use appropriate mathematical properties and notation to solve a problem How to create a variety of visual representations (table, chart, graph, diagram, etc ) How to organize and consolidate their mathematical thinking through communication How to communicate their mathematical thinking coherently and clearly to peers, teachers, and others How to select the most efficient strategy for a problem situation Various problem solving strategies and how to apply them (draw a picture, look for a pattern, guess and check, act it out, make a table, work a simpler problem, work backwards, etc ) 6th Grade Math Solve and represent problem situations with numbers and/or symbols 5. Solve/communicate with appropriate visual representations

3 Problem Solving Quick Planner Suggested Timing: 2 Weeks Common Performance Assessment: The Pool 6. Create a clear, organized, and complete explanation of problem solving process (what was done & why) Justification requires the use of mathematical reasoning How to create a variety of visual representations (table, chart, graph, diagram, etc ) How to organize and consolidate their mathematical thinking through communication How to communicate their mathematical thinking coherently and clearly to peers, teachers, and others Correct mathematical terminology How to select the most efficient strategy for a problem situation Various problem solving strategies and how to apply them (draw a picture, look for a pattern, guess and check, act it out, make a table, work a simpler problem, work backwards, etc ) Correct mathematical terminology How to synthesize information from a problem and rephrase it to show understanding Methods for estimating solutions (rounding, compatible numbers, benchmarking, grouping, etc ) Justification requires the use of mathematical reasoning How to organize and consolidate their mathematical thinking through communication How to communicate their mathematical thinking coherently and clearly to peers, teachers, and others Methods for evaluating the reasonableness of a solution (compare to estimate, extend to similar situations, number sense, etc ) Mental math, estimation, and number sense skills How to synthesize information from a problem and rephrase it to show understanding Methods for estimating solutions (rounding, compatible numbers, benchmarking, grouping, etc ) How to create a variety of visual representations (table, chart, graph, diagram, etc ) Efficient and appropriate use of manipulatives, paper/pencil, and technology 7. Identify and use appropriate problem solving strategies 8. Arrive at and communicate answers appropriately in reference to problem situations 9. Evaluate a solution for reasonableness 10. Select tools such as real objects, manipulatives, paper/pencil, or technology to solve problems 6th Grade Math

4 Number Theory And Algebraic Reasoning Quick Planner Suggested Timing: 3-4 Weeks Common Performance Assessment: The Factor Game Focus TEKS (6.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (D) write prime factorizations using exponents; (E) identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers; (6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (C) use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates; (ratios and rates will appear in later unit of study) (D) estimate and round to approximate reasonable results and to solve problems where exact answers are not required; (E) use order of operations to simplify whole number expressions (without exponents) in problem solving situations. (6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity c (A) use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area (6.5) Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in an equation. The student is expected to: formulate equations from problem situations described by linear relationships 1. Apply divisibility rules to positive whole numbers How to recognize even and odd numbers 2. Multiply whole numbers (no more than two digits by three digits without technology) How to multiply and divide by multiples of Divide whole numbers (no more than two digit divisor into a four digit dividend) expressing remainders as whole numbers, fractions, and decimals How to multiply and divide by multiples of 10 How to divide by two using the distributive property That the mathematical situation determines the type of remainder that is appropriate 4. Estimate and solve application problems involving whole number operations How to multiply and divide by multiples of 10 That the mathematical situation determines the type of remainder that is appropriate Key words that indicate operations in word problems (sum, difference, product, quotient, each, etc ) The difference between estimating and rounding Strategies to estimate solutions (rounding, compatible numbers, benchmarking, grouping, etc ) 5. List factors of a positive whole number How to divide by two using the distributive property Different strategies for finding factors (T-chart, rainbow, list, prime factorization, L-method, etc ) 6. Use a factor tree to find the prime factorization of a number How to divide by two using the distributive property Different strategies for finding factors (T-chart, rainbow, list, prime factorization, L-method, etc ) Operation and grouping symbols (the dot, asterisk, slash, fraction bar, parenthesis, etc ) How to tell the difference between prime and composite 7. Write prime factorization using exponential and expanded form interchangeably How to divide by two using the distributive property Exponents represent repeated multiplication Operation and grouping symbols (the dot, asterisk, slash, fraction bar, parenthesis, etc ) How to tell the difference between prime and composite p. 650 p. 658 p p , p , th Grade

5 Number Theory And Algebraic Reasoning Quick Planner Suggested Timing: 3-4 Weeks Common Performance Assessment: The Factor Game Focus TEKS 8. Evaluate exponential expressions Exponents represent repeated multiplication Operation and grouping symbols (the dot, asterisk, slash, fraction bar, parenthesis, etc ) The difference between an expression and an equation 9. Use the order of operations to simplify whole number expressions (with and without exponents) Exponents represent repeated multiplication Operation and grouping symbols (the dot, asterisk, slash, fraction bar, parenthesis, etc ) Create a function table and write a function rule 1-6 Explore, 1-6 Operation and grouping symbols (the dot, asterisk, slash, fraction bar, parenthesis, etc ) p How to set up a table to organize data (title, column and row headings, etc ) That variables represent unknown quantities in an algebraic expression or equation That mathematical situations can be represented in multiple ways (four corners) A function rule must be true for all sets of data in a table The difference between an expression and an equation 11. Write equations with variables to represent problem situations 1-5, 1-8 Key words that indicate operations in word problems (sum, difference, product, quotient, each, etc ) Operation and grouping symbols (the dot, asterisk, slash, fraction bar, parenthesis, etc ) That variables represent unknown quantities in an algebraic expression or equation That mathematical situations can be represented in multiple ways (four corners) The difference between an expression and an equation 12. Match corresponding verbal, algebraic, and tabular representations 1-9 Explore Operation and grouping symbols (the dot, asterisk, slash, fraction bar, parenthesis, etc ) How to set up a table to organize data (title, column and row headings, etc ) That variables represent unknown quantities in an algebraic expression or equation That mathematical situations can be represented in multiple ways (four corners) A function rule must be true for all sets of data in a table The difference between an expression and an equation 6th Grade

6 (6.10) Probability and statistics. The student uses statistical representations to analyze data. The student is expected to: (A) select and use an appropriate representation for presenting and displaying different graphical representations of the same data including line plot, line graph, bar graph, and stem and leaf plot; (B) identify mean (using concrete objects and pictorial models), median, mode, and range of a set of data; (C) sketch circle graphs to display data; and (D) solve problems by collecting, organizing, displaying, and interpreting data Data Analysis Quick Planner Suggested Timing: 2-3 Weeks Common Performance Assessment: Wacky Weather 1. Read and interpret various types of graphical representations (line plot, line graph, bar graph, double bar graph, stem and leaf plot, circle graph) Vocabulary related to Data Analysis How to recognize the approximate relationship between parts of a whole in all graphical representations 2. Create graphical representations to display data (line plot, line graph, bar graph, double bar graph, stem and leaf plot) 2-2, 2-3, 2-5 p , , 2-2, 2-2 Extend, 2-4, 2-5 Vocabulary related to Data Analysis How to organize a graphical representation (titles, labels, axes, key, scale, interval, etc ) Purposes of various graphical representations How to recognize the approximate relationship between parts of a whole in all graphical representations Different methods of data collection (survey, list, frequency table, etc ) 3. Sketch circle graphs, without the use of protractors 7-2 Vocabulary related to Data Analysis How to organize a graphical representation (titles, labels, axes, key, scale, interval, etc ) Purposes of various graphical representations How to recognize the approximate relationship between parts of a whole in all graphical representations Different methods of data collection (survey, list, frequency table, etc ) 4. Select and use appropriate graphical representations to display a given 2-8 set of data Vocabulary related to Data Analysis p. 15 Purposes of various graphical representations How to recognize the approximate relationship between parts of a whole in all graphical representations 5. Select multiple, appropriate representations for the same set of data 2-8 Vocabulary related to Data Analysis Purposes of various graphical representations p Identify measures of central tendency using concrete and pictorial models 2-6 Vocabulary related to Data Analysis p. 6-11, That pictures and concrete models can be use to represent mathematical relationships 7. Calculate mean, median, mode, and range 2-7 Vocabulary related to Data Analysis That pictures and concrete models can be used to represent mathematical relationships Basic operations with whole numbers (by hand and with calculators) 8. Solve problems by collecting, organizing, displaying, and interpreting data 2-1, 2-8 Extend Vocabulary related to Data Analysis How to recognize the approximate relationship between parts of a whole in all graphical representations Basic operations with whole numbers (by hand and with calculators) Different methods of data collection (survey, list, frequency table, etc )

7 Focus TEKS will (6.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (A) compare and order nonnegative rational numbers; (B) generate equivalent forms of rational numbers including whole numbers, fractions, and decimals (E) identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers; (F) identify multiples of a positive integer and common multiples and the least common multiple of a set of positive integers (6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (A) model addition and subtraction situations involving fractions with objects, pictures, words, and numbers; (B) use addition and subtraction to solve problems involving fractions and decimals; (D) estimate and round to approximate reasonable results and to solve problems where exact answers are not required Rational Numbers Quick Planner Suggested Timing: 5-7 Weeks Common Performance Assessment: Poor Geppetto will need to know 1. Compare and order decimals (with and without models) Decimal place value through the thousandths place The position of a digit, in relationship to the decimal point, determines its value in a number Decimals have a value less than one and greater than zero How to represent decimals in word form, standard form, and expanded form How to use a number lines and other manipulatives to represent fraction and decimal values 2. Estimate and solve for sums and differences with decimals Decimal place value through the thousandths place The position of a digit, in relationship to the decimal point, determines its value in a number How to round decimals and fractions 3. Find common factors and the greatest common factor of two or more numbers How to identify factors of a positive whole number Strategies to find the Greatest Common Factor (Factor Towers, L-method, Venn diagram, prime factorization, lists, etc ) 3-1, 3-2 p , , 3-4, 3-5 Explore, 3-5 p. 216, th Grade The practical meaning of the numerator and denominator (the denominator tells how many parts in the whole) How to simplify fractions How to generate equivalent fractions How to find common denominators (with and without models) Fractions and decimals can represent the same values in different forms That the fraction bar represents division Identify multiples of a positive whole number 5. Find common multiples and the least common multiple for a set 4-5 of positive whole numbers p Strategies to find the Least Common Multiple (L-method, Venn diagram, lists, prime factorization, etc ) 6. Compare and order fractions (with and without models) 4-6 How to use a number lines and other manipulatives to represent fraction and p decimal values The practical meaning of the numerator and denominator (the denominator tells how many parts in the whole) How to simplify fractions How to convert between improper fractions and mixed numbers How to generate equivalent fractions How to find common denominators (with and without models) 7. Convert between fractions and decimals (and vice versa) 4-7, 4-8 Decimal place value through the thousandths place p , The position of a digit, in relationship to the decimal point, determines its value 228 in a number Decimals have a value less than one and greater than zero

8 Rational Numbers Quick Planner Suggested Timing: 5-7 Weeks Common Performance Assessment: Poor Geppetto 8. Use bar notation to represent repeating decimals Decimal place value through the thousandths place The position of a digit, in relationship to the decimal point, determines its value in a number Decimals have a value less than one and greater than zero Fractions and decimals can represent the same values in different forms That the fraction bar represents division 9. Memorize decimal equivalencies for fractions with denominators of 2, 3, 4, 5, 8, 10, and 100 Decimal place value through the thousandths place The position of a digit, in relationship to the decimal point, determines its value in a number Decimals have a value less than one and greater than zero The practical meaning of the numerator and denominator (the denominator tells how many parts in the whole) Fractions and decimals can represent the same values in different forms That the fraction bar represents division 10. Compare and order fractions and decimals within the same set Decimal place value through the thousandths place The position of a digit, in relationship to the decimal point, determines its value in a number Decimals have a value less than one and greater than zero How to use a number lines and other manipulatives to represent fraction and decimal values The practical meaning of the numerator and denominator (the denominator tells how many parts in the whole) How to simplify fractions How to convert between improper fractions and mixed numbers How to generate equivalent fractions How to find common denominators (with and without models) Fractions and decimals can represent the same values in different forms That the fraction bar represents division 11. Model addition and subtraction of fractions with objects, pictures, words, and numbers How to use a number lines and other manipulatives to represent fraction and decimal values Strategies to find the Least Common Multiple (L-method, Venn diagram, lists, prime factorization, etc ) The practical meaning of the numerator and denominator (the denominator tells how many parts in the whole) How to simplify fractions How to convert between improper fractions and mixed numbers How to generate equivalent fractions How to find common denominators (with and without models) How to rename a whole number as a fraction and vice versa (a number over itself is one whole) 5-4, Explore 5-5, 5-5, 5-6, 5-7 p ,

9 Rational Numbers Quick Planner Suggested Timing: 5-7 Weeks Common Performance Assessment: Poor Geppetto 12. Estimate and solve for sums and difference with fractions and 5-1, 5-2, 5-4, mixed numbers (with like and unlike denominators, with and without Explore 5-5, 5-5, 5- regrouping) 6, 5-7 How to round decimals and fractions p , Strategies to find the Greatest Common Factor (Factor Towers, L-method, Venn diagram, prime factorization, lists, etc ) Strategies to find the Least Common Multiple (L-method, Venn diagram, lists, prime factorization, etc ) The practical meaning of the numerator and denominator (the denominator tells how many parts in the whole) How to simplify fractions How to convert between improper fractions and mixed numbers How to generate equivalent fractions How to find common denominators (with and without models) How to rename a whole number as a fraction and vice versa (a number over itself is one whole) 13. Apply addition and subtraction of fractions and decimals to real 5-1, 5-2, 5-4, world problem situations Explore 5-5, 5-5, 5-6, 5-7 Decimal place value through the thousandths place The position of a digit, in relationship to the decimal point, determines its value in a number Decimals have a value less than one and greater than zero Strategies to find the Greatest Common Factor (Factor Towers, L-method, Venn diagram, prime factorization, lists, etc ) Strategies to find the Least Common Multiple (L-method, Venn diagram, lists, prime factorization, etc ) The practical meaning of the numerator and denominator (the denominator tells how many parts in the whole) How to simplify fractions How to convert between improper fractions and mixed numbers How to generate equivalent fractions How to find common denominators (with and without models) Fractions and decimals can represent the same values in different forms How to rename a whole number as a fraction and vice versa (a number over itself is one whole) Key words that indicate operations in word problems (sum, difference, product, quotient, each, etc ) 14. Justify solutions to problems involving fractions and decimals Key words that indicate operations in word problems (sum, difference, product, quotient, each, etc ) How to justify the selection of operations in a problem through oral or written explanation p ,

10 (6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (C) use multiplication and division of whole numbers to solve problems Including situations Involving equivalent ratios and rates (6.3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to: (A) use ratios to describe proportional situations (B) represent ratios and percents with concrete models, fractions, and decimals; and (C) use ratios to make predictions in proportional situations (6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to: (A) use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area Proportionality Quick Planner Suggested Timing: 3-4 Weeks Common Performance Assessment: Towering Pizzas 1. Express ratios and rates in a variety of forms to describe proportional situations That there is a difference between ratios and fractions fractions represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships The difference between ratios and rates 2. Determine whether two ratios are proportional That there is a difference between ratios and fractions fractions represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships How to simplify ratios Strategies to determine whether ratios are proportional (common denominators, simplifying, cross products, etc ) 3. Use tables to determine equivalent ratios and solve problems That there is a difference between ratios and fractions fractions represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships How to generate equivalent ratios How to simplify ratios How to organize tables of data That variables represent unknown quantities in proportions and equations 6-1, 6-1 Extend 6-1, 6-2 p , 6-2 Extend p Solve proportions with whole number scale factors 6-3, 6-4 That there is a difference between ratios and fractions fractions p represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships How to generate equivalent ratios How to simplify ratios How to organize tables of data That variables represent unknown quantities in proportions and equations 5. Set up and solve proportions from word problem situations, 6-4, 6-7, 6-7 including making predictions Extend That there is a difference between ratios and fractions fractions represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships How to generate equivalent ratios How to simplify ratios That variables represent unknown quantities in proportions and equations How to set up proportions by matching corresponding quantities and units How to recognize a proportional situation in word problems

11 Proportionality Quick Planner Suggested Timing: 3-4 Weeks Common Performance Assessment: Towering Pizzas 6. Model percents with objects and pictures (100s grid, circle graphs, percent bars, fraction models, etc ) That there is a difference between ratios and fractions fractions represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships How to generate equivalent ratios How to use manipulatives to represent fraction, decimal, and percent values 7. Convert between fractions, decimals, and percents That there is a difference between ratios and fractions fractions represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships How to generate equivalent ratios How to simplify ratios That variables represent unknown quantities in proportions and equations Fractions, decimals, and percents represent the same values in different forms 8. Memorize percent equivalencies for fractions with denominators of 2, 3, 4, 5, 8, 10, and 100 That there is a difference between ratios and fractions fractions represent part to whole relationships, ratios can represent part to part, part to whole, or whole to part relationships How to generate equivalent ratios Fractions, decimals, and percents represent the same values in different forms 9. Use tables to find patterns in arithmetic sequences How to organize tables of data That variables represent unknown quantities in proportions and equations How to recognize patterns and relationships in sets of numbers 10. Use a table to write an equation to describe a proportional situation How to organize tables of data That variables represent unknown quantities in proportions and equations How to recognize patterns and relationships in sets of numbers 7-1 Explore, , 4-8, 7-1, 7-3 p , , 6-7 Extend

12 Probability Quick Planner Suggested Timing: 1-2 Weeks Common Performance Assessment: Put On Your Dancin' Clothes Focus TEKS (6.9) Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to: (A) construct sample spaces using lists and tree diagrams. (B) find the probabilities of a simple event and its complement and describe the relationship between the two. 1. Find the probability of a simple event and its complement Vocabulary related to Probability All probabilities fall between 0 and 1 Probabilities can be written as fractions, decimals, or percents The sum of probability of a simple event and its complement is 1 How to set up the probability formula/ratio (number of favorable outcomes over the total number possible outcomes) 2. Describe the relationship between the probability of a simple event and its complement Vocabulary related to Probability All probabilities fall between 0 and 1 Probabilities can be written as fractions, decimals, or percents The sum of probability of a simple event and its complement is 1 3. Construct sample spaces using lists and tree diagrams Vocabulary related to Probability Strategies for creating a sample space (tree diagram, list, table, etc..) 4. Make predictions based on experimental and theoretical probability Vocabulary related to Probability How to apply proportions to make predictions All probabilities fall between 0 and 1 Strategies for creating a sample space (tree diagram, list, table, etc..) Probabilities can be written as fractions, decimals, or percents How to set up the probability formula/ratio (number of favorable outcomes over the total number possible outcomes) The difference between experimental and theoretical probability 7-4 Exolore, Explore, p

13 (6.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (C) use integers to represent real-life situations (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles (covered in Geometry Unit of Study). The student is expected to: (A) estimate measurements (including circumference) and evaluate reasonableness of results; (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight; (D) convert measures within the same measurement system (customary and metric) based on relationships between units Measurement Systems Quick Planner Suggested Timing: 1-2 Weeks Common Performance Assessment: 1. Measure length, capacity, weight in the customary system How to use measurement tools (ruler, scale, thermometer, clock, etc ) The appropriate units for each type of measurement The differences between the customary and metric systems Measurement benchmarks (ex. an inch is the width of a quarter, a millimeter is the thickness of a dime, water freezes at 32ºF and 0º Celsius) How to apply proportions to measurement systems How to use the TAKS Chart as a reference and measurement tool 2. Estimate length, capacity, weight in the customary system and check for reasonableness The appropriate units for each type of measurement The differences between the customary and metric systems Measurement benchmarks (ex. an inch is the width of a quarter) How to apply proportions to measurement systems How to use the TAKS Chart as a reference and measurement tool 3. Convert between units in the customary system The appropriate units for each type of measurement The differences between the customary and metric systems Measurement benchmarks (ex. an inch is the width of a quarter) How to apply proportions to measurement systems How to use the TAKS Chart as a reference and measurement tool 8-1 p p Measure length, capacity, weight in the metric system 8-3 Explore, 8-4 How to use measurement tools (ruler, scale, thermometer, clock, etc ) The appropriate units for each type of measurement The differences between the customary and metric systems Measurement benchmarks (ex. an inch is the width of a quarter) How to apply proportions to measurement systems How to use the TAKS Chart as a reference and measurement tool How decimal place value applies to the metric system 5. Estimate length, capacity, weight in the metric system and 8-3, 8-4 check for reasonableness p The appropriate units for each type of measurement The differences between the customary and metric systems Measurement benchmarks (ex. an inch is the width of a quarter) How to apply proportions to measurement systems How to use the TAKS Chart as a reference and measurement tool How decimal place value applies to the metric system

14 Measurement Systems Quick Planner Suggested Timing: 1-2 Weeks Common Performance Assessment: 6. Convert between units in the metric system 8-6 The appropriate units for each type of measurement p The differences between the customary and metric systems Measurement benchmarks (ex. an inch is the width of a quarter) How to apply proportions to measurement systems How to use the TAKS Chart as a reference and measurement tool How decimal place value applies to the metric system How to multiply and divide by powers of Add and subtract to find elapsed time 8-7 How to use measurement tools (ruler, scale, thermometer, clock, etc ) p. 229 The appropriate units for each type of measurement Measurement benchmarks (ex. an inch is the width of a quarter) How to use the TAKS Chart as a reference and measurement tool How to regroup units of time 8. Choose and estimate reasonable temperatures 8-8 How to use measurement tools (ruler, scale, thermometer, clock, etc ) The appropriate units for each type of measurement Measurement benchmarks (ex. an inch is the width of a quarter) How to use the TAKS Chart as a reference and measurement tool What a negative sign means How negative numbers are arranged on a number line 9. Use integers to represent real-life situations 2-9 Measurement benchmarks (ex. an inch is the width of a quarter) What a negative sign means How negative numbers are arranged on a number line Key words that indicate positive and negative numbers (above/below sea level, loss/gain, deposit/withdrawal, etc..)

15 (6.6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. (A) use angle measurements to classify angles as acute, obtuse, or right; (B) identify relationships involving angles in triangles and quadrilaterals; (C) describe the relationship between radius, diameter, and circumference of a circle. (6.7) Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. The student is expected to locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, capacity, weight, and angles. (C) Measure Angles; Geometry Quick Planner Suggested Timing: 1-2 Weeks Common Performance Assessment: 1. Locate and name points on a coordinate plane (quadrant one only) Vocabulary related to Geometry How a coordinate plane is organized How ordered pairs are related to movement on a coordinate plane (you move on the x-axis first and the y-axis second, just like it is set up in ordered pairs) 2. Classify angles as acute, obtuse, or right Vocabulary related to Geometry How to name angles by their endpoints How to estimate angle measurements based on benchmark angles 3. Measure angles with a protractor Vocabulary related to Geometry How to use and read a protractor How to name angles by their endpoints How to estimate angle measurements based on benchmark angles 4. Sketch angles based on given measurements Vocabulary related to Geometry How to name angles by their endpoints How to estimate angle measurements based on benchmark angles Vocabulary related to Geometry How to name angles by their endpoints How to estimate angle measurements based on benchmark angles That the sum of the interior angles in a triangle is 180 degrees That the sum of the interior angles in a quadrilateral is 360 degrees The angles opposite congruent sides are congruent That hash marks represent congruent parts of geometric figures How to name geometric figures by their vertices, ΔABC Quad TUVW Vocabulary related to Geometry That relationship between the circumference and diameter is approximately 3 (pi) Find missing angle measurements in triangles and quadrilaterals 9-4 Explore, 9-4, 9-5 Explore, 9-5, 6. Describe the relationship between radius, diameter, and circumference of a circle 9-1, Explore, 10-2

16 Measurement - Perimeter, Area, Volume Quick Planner Suggested Timing: 1-2 Weeks Common Performance Assessments: Tiling the Kitchen Chance and the Dice Factory Focus TEKS (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles (covered in Geometry Unit of Study). The student is expected to: (A) estimate measurements (including circumference) and evaluate reasonableness of results; (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight; (6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to: (A) use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area (B) use tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc. 1. Estimate and solve for the perimeter/circumference of geometric figures Vocabulary related to Measurement Which formula to apply to a given situation Know how to read and use the TAKS Chart What the variables in each formula represent How to substitute values into formulas Different ways to represent multiplication (dot, asterisks, parenthesis, variable variable (bh), number variable (4s), etc..) How to apply the order of operations to formulas The appropriate units for labeling measurements in a given situation Two dimensional figures have length and width 2. Estimate, model, and solve for the area of geometric figures (squares, rectangles, parallelograms, triangles, circles-estimate only) Vocabulary related to Measurement Which formula to apply to a given situation Know how to read and use the TAKS Chart What the variables in each formula represent How to substitute values into formulas Different ways to represent multiplication (dot, asterisks, parenthesis, variable variable (bh), number variable (4s), etc..) How to apply the order of operations to formulas The appropriate units for labeling measurements in a given situation Two dimensional figures have length and width 3. Solve for the perimeter and area of composite figures (combined shapes, shaded region, shapes within a shape, etc ) Vocabulary related to Measurement Which formula to apply to a given situation Know how to read and use the TAKS Chart What the variables in each formula represent How to substitute values into formulas Different ways to represent multiplication (dot, asterisks, parenthesis, variable variable (bh), number variable (4s), etc..) How to apply the order of operations to formulas The appropriate units for labeling measurements in a given situation How to separate composite figures into simpler figures for which a formula is known Two dimensional figures have length and width 10-1 Explore, 10-1, 10-2 Explore, 10-2 p Explore, 10-1, 10-2, 10-3, 10-4 Explore, 10-4 p. 182

17 Measurement - Perimeter, Area, Volume Quick Planner Suggested Timing: 1-2 Weeks Common Performance Assessments: Tiling the Kitchen Chance and the Dice Factory Focus TEKS 4. Estimate, model, and solve for the volume of rectangular prisms 10-6 Vocabulary related to Measurement Which formula to apply to a given situation Know how to read and use the TAKS Chart What the variables in each formula represent How to substitute values into formulas Different ways to represent multiplication (dot, asterisks, parenthesis, variable variable (bh), number variable (4s), etc..) How to apply the order of operations to formulas The appropriate units for labeling measurements in a given situation Three dimensional figures (rectangular prisms) have length, width, and height 5. Use tables to represent and describe relationships such as unit conversions, perimeter, and area Vocabulary related to Measurement Which formula to apply to a given situation Know how to read and use the TAKS Chart What the variables in each formula represent Different ways to represent multiplication (dot, asterisks, parenthesis, variable variable (bh), number variable (4s), etc..) How to set up tables to organize data 6. Use tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc. Vocabulary related to Measurement Which formula to apply to a given situation Know how to read and use the TAKS Chart What the variables in each formula represent Different ways to represent multiplication (dot, asterisks, parenthesis, variable variable (bh), number variable (4s), etc..) How to set up tables to organize data p , , , Explore, 10-1, 10-2, 10-3, 10-4 Explore, 10-4 p Explore, 10-1, 10-2, 10-3, 10-4 Explore, 10-4 p. 182