7th Grade Topic Alignment Topic Code Indicators Strategies Adding and Subtracting Fractions

Transcription

1 Adding and Subtracting Fractions Adding and Subtracting Mixed Numbers Algebraic Expressions (Evaluating and Writing) Areas of Parallelograms, Triangles, and Other Figures Circle Graphs Circles Circumferences and Areas of Circles Congruent Figures Various computer activities with fractions. 7P7 Justify that two forms of an algebraic expression are equivalent, and 7N4 Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals. Area and Perimeter meter/index.html (Computer Application) 7M2 Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters 7M6 Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms. 7M7 Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors. 7D1 Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate. 7D2 Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph 7G2 Determine sufficient (not necessarily minimal) properties that define a 7G2a Determine when one set of figures is a subset of another; e.g., all 7G2b Develop a set of properties that eliminates all but the desired figure; 7N4 Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals. 7M7 Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors. 7G4 Determine necessary conditions for congruence of triangles. 7G5 Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 1

2 Constructing Bisectors 7G2 Determine sufficient (not necessarily minimal) properties that define a Constructing Bisectors Data Analysis to Persuade 7G2 7D2 7D4 Determine when one set of figures is a subset of another; e.g., all Develop a set of properties that eliminates all but the desired figure; Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph. Construct opposing arguments based on analysis of the same data, using different graphical representations. 7D6 Identify misuses of statistical data in articles, advertisements, and other media. Decimal Operations 7N1 Demonstrate an understanding of place value using powers of 10 and Dividing Fractions and Mixed Numbers write large numbers in scientific notation. Divisibility Tests 7N6 Simplify numerical expressions involving integers and use integers to Draw a Diagram and Look for a Pattern 7M5 Analyze problem situations involving measurement concepts, select 7P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. 7P2 Generalize patterns by describing in words how to find the next term. Draw a Diagram and Solve a Simpler Problem Equations (From Words to Symbols) Equations (Solving by Adding or Subtracting) Equations (Solving by Multiplying or Dividing) 7P4 Create visual representations of equation-solving processes that model the use of inverse operations. 7P7 Justify that two forms of an algebraic expression are equivalent, and 7P4 Create visual representations of equation-solving processes that model the use of inverse operations. Data Analysis and Probability/various virtual manipulatives matti.usu.edu/nlvm/nav/category_g_3_t_5. html Using Pascal's triangle for divisibility cal1.html and cal2.html Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 2

3 Equations (Solving with Multiple Steps) 7P7 7N6 Justify that two forms of an algebraic expression are equivalent, and Simplify numerical expressions involving integers and use integers to 7P7 Justify that two forms of an algebraic expression are equivalent, and Equations (Writing Equations from Patterns) Equations (Writing Equations using Percents) Equations (Writing Equations using Percents) Equations With Fractions Estimating Length and Area 7M3 Estimate a measurement to a greater degree of precision than the tool provides. Estimating With Fractions and Mixed Numbers Estimation Strategies Exponents and Order of Operation 7N1 7M3 7N4 Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation. Estimate a measurement to a greater degree of precision than the tool provides. Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals. 7N9 Represent and solve problem situations that can be modeled by and (for perfect squares) Fractions (Comparing and Ordering) Fractions (Mixed Numbers and Improper Fractions) Fractions (Multiplying Fractions and Mixed Numbers) Website with 40 different printable Solving Equations worksheets with answer keys ath10/unita/a1/a1worksheetoutline.htm Worksheet/Basic Equations/change the number of problems html Various computer activities with fractions. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 3

4 Fractions (Simplifying) Fractions and Decimals Frequency 7N3 7D1 Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and others (irrational) as non terminating and non repeating decimals Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate. Create your own worksheet to practice simplifying actions.html 7D2 Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph 7D3 Analyze a set of data by using and comparing combinations of Functions using Tables, Rules, and Graphs 7P1 measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. 7P10 Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another. Graphing and Writing Inequalities 7P6 Represent inequalities on a number line or a coordinate plane. Graphing Linear Equations 7P5 Represent linear equations by plotting points in the coordinate plane. Activity which students have to match graphs, descriptions, table of values son/fmpro?-db=cs.fp5&-lay=web&- format=lesson.html&-recid=47&-find 7P10 Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another. Graphing Points in Four Quadrants 7G8 Perform translations, reflections, rotations and dilations of twodimensional figures using a variety of methods (paper folding, tracing, graph paper) Inequalities (Solving by Adding or Subtracting) 7P6 Represent inequalities on a number line or a coordinate plane. Inequalities (Solving by Multiplying or Dividing) 7P6 Represent inequalities on a number line or a coordinate plane. Integers (Comparing and Ordering) Integers Operations 7N5 Explain the meaning and effect of adding, subtracting, multiplying and dividing integers; e.g., how adding two integers can result in a lesser value 7N6 Simplify numerical expressions involving integers and use integers to 7N9 Represent and solve problem situations that can be modeled by and (for perfect squares) 7P6 Represent inequalities on a number line or a coordinate plane. 7N5 Explain the meaning and effect of adding, subtracting, multiplying and dividing integers; e.g., how adding two integers can result in a lesser value Print-offs for rules Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 4

5 Interest (Simple and Compound Interest) Interpreting Graphs Lines and Planes 7N6 Simplify numerical expressions involving integers and use integers to Simple Interest Worksheet 7D1 Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate. 7D2 Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph 7G2 Determine sufficient (not necessarily minimal) properties that define a 7G2a Determine when one set of figures is a subset of another; e.g., all 7G2b Develop a set of properties that eliminates all but the desired figure; Make a Table and a Graph 7P5 Represent linear equations by plotting points in the coordinate plane. Make an Organized List and Simulate a Problem 7D7 Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists tree diagrams and area models 7D8 Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results and explain differences Mean, Median, and Mode 7D3 Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures. Measuring and Classifying Angles 7G2 Determine sufficient (not necessarily minimal) properties that define a Determine when one set of figures is a subset of another; e.g., all Develop a set of properties that eliminates all but the desired figure; Create and Analyze Box Plots plot1/index.html plot2/index.html "Mystery Data Game" Given certain criteria, students must come up with a data set to match a mean, median, mode, etc. son/fmpro?-db=cs.fp5&-lay=web&- format=lesson.html&-recid=79&-find Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 5

6 Measuring in Metric Units 7N1 Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation. 7M3 Estimate a measurement to a greater degree of precision than the tool provides. Measuring in Metric Units Nonlinear Relationships Number Sense to Solve Equations Number Sequences Order of Operations and the Distributive Property 7P3 Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1, 3, 5, 7... is linear and 1, 3, 4, 8, is 7P10 Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another. 7P7 Justify that two forms of an algebraic expression are equivalent, and 7P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. 7P2 Generalize patterns by describing in words how to find the next term. 7P3 Recognize and explain when numerical patterns are linear or 7N4 nonlinear progressions; e.g., 1, 3, 5, 7... is linear and 1, 3, 4, 8, is Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals. 7N6 Simplify numerical expressions involving integers and use integers to Patterns and Graphs 7P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. Patterns and Tables 7P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. 7P2 Generalize patterns by describing in words how to find the next term. 7P10 Analyze linear and simple nonlinear relationships to explain how a Percent Application Percent of a Number Percent of Change change in one variable results in the change of another. 7N4 Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals. Print off conversion worksheet rintoffs/snap1.html Several activities for Consumer Math (percent markup, discount, etc.) Look under Consumer Math Topic. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 6

7 Percent Problems Using Proportions or Equations Percent Problems Using Proportions or Equations Percents Percents Greater than 100 or Less than 1 7M4 Solve problems involving proportional relationships and scale factors; 7N8 7N8 Develop and analyze algorithms for computing with percents and Develop and analyze algorithms for computing with percents and Percents, Fractions, and Decimals Permutations and Combinations 7N6 Simplify numerical expressions involving integers and use integers to Precision 7M3 Estimate a measurement to a greater degree of precision than the tool provides. Prime Factorization 7N6 Simplify numerical expressions involving integers and use integers to Probability (Including Experimental Probability) 7D8 Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results and explain differences Problem-Solving Plan 7N6 Simplify numerical expressions involving integers and use integers to Proportional Reasoning Pythagorean Theorem 7M4 7P9 Solve problems involving proportional relationships and scale factors;. Recognize a variety of uses for variables; e.g., placeholder for an 7P11 Use graphing calculators or computers to analyze change; e.g., distance-time relationships. 7N9 Represent and solve problem situations that can be modeled by and (for perfect squares). Print-off crossnumber worksheet s/cross2.html "How much do you weigh in outerspace?" Find the Missing Side pyth2/index.html **Computer Application 7G3 Use and demonstrate understanding of the properties of triangles. For Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 7

8 Use Pythagorean Theorem to solve problems involving right triangles. Quadrilaterals and other Polygons 7P8 7G2 Use formulas in problem-solving situations. Determine sufficient (not necessarily minimal) properties that define a Determine when one set of figures is a subset of another; e.g., all Develop a set of properties that eliminates all but the desired figure; Random Samples and Surveys 7D5 Compare data from two or more samples to determine how sample Rational Numbers Ratios Sample Spaces and Compound Events Scale Drawings and Maps Scatter Plots 7N3 7M2 selection can influence results. Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and others (irrational) as non terminating and non repeating decimals Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters 7M4 Solve problems involving proportional relationships and scale factors; 7D7 Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists tree diagrams and area models 7D8 Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results and explain differences 7M4 Solve problems involving proportional relationships and scale factors; 7G6 Determine and use scale factors for similar figures to solve problems using proportional reasoning. 7D1 Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate. 7D3 Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures. Find polygons in triangle grid **Computer application Write ratios in lowest terms Data Analysis and Probability/ various virtual manipulatives matti.usu.edu/nlvm/nav/category_g_3_t_5. html Create & Analyze Stem and Leaf Plots mleaf/index.html **Computer Application Scientific Notation 7N1 Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation. Practice Problems dosxx.colorado.edu/~atlas/math/problems/ problems1.html Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 8

9 Similar Figures Slope of a Line Solve a Simpler Problem and Look for a Pattern Spreadsheets and Data Display Square Roots and Irrational Numbers Surface Areas of Prism and Cylinders 7N2 Explain the meaning of exponents that are negative or 0. 7N9 Represent and solve problem situations that can be modeled by and (for perfect squares) 7M4 Solve problems involving proportional relationships and scale factors;. 7G1 Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. 7G5 Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures. 7G6 Determine and use scale factors for similar figures to solve problems 7P8 7P11 using proportional reasoning. Use formulas in problem-solving situations. Use graphing calculators or computers to analyze change; e.g., distance-time relationships. 7N9 Represent and solve problem situations that can be modeled by and (for perfect squares) 7P2 7P11 Generalize patterns by describing in words how to find the next term. Use graphing calculators or computers to analyze change; e.g., distance-time relationships. 7D1 Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate. 7D3 Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures 7D5 7N3 7N9 7M4 Compare data from two or more samples to determine how sample selection can influence results. Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and others (irrational) as non terminating and non repeating decimals Represent and solve problem situations that can be modeled by and (for perfect squares) Solve problems involving proportional relationships and scale factors; 7M6 Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms. 7M8 Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas 7M9 Describe what happens to the surface area and volume of a threedimensional object when the measurements of the object are Create a scale model of a balsa wood plane. Website for guide regentsprep.org/regents/math/scale/tdino.htm They use a dinosaur model, but a plane works well. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 9

10 Symmetry, Reflections, and Rotations Three-Dimensional Figures 7G7 7G8 Identify the line and rotation symmetries of two-dimensional figures to solve problems. Perform translations, reflections, rotations and dilations of twodimensional figures using a variety of methods (paper folding, tracing, graph paper) 7G2 Determine sufficient (not necessarily minimal) properties that define a 7G2a Determine when one set of figures is a subset of another; e.g., all 7G2b Develop a set of properties that eliminates all but the desired figure; 7G9 Draw representations of three-dimensional geometric objects from different views. Transforming Formulas Translations 7G8 Perform translations, reflections, rotations and dilations of twodimensional figures using a variety of methods (paper folding, tracing, Triangles Two-Step Problems graph paper) 7G2 Determine sufficient (not necessarily minimal) properties that define a 7G2a Determine when one set of figures is a subset of another; e.g., all 7G2b Develop a set of properties that eliminates all but the desired figure; 7G3 Use and demonstrate understanding of the properties of triangles. For 7G3a Use Pythagorean Theorem to solve problems involving right triangles. Use triangle angle sum relationships to solve problems. 7G3b 7N6 Simplify numerical expressions involving integers and use integers to 7P7 Justify that two forms of an algebraic expression are equivalent, and Unit Rates and Proportional Reasoning 7M1 Select appropriate units for measuring derived measurements; e.g., miles per hour, revolutions per minute. Unit Rates and Proportional Reasoning 7M4 Solve problems involving proportional relationships and scale factors; Volumes of Rectangular Prisms and Cylinders 7M4 Solve problems involving proportional relationships and scale factors; Computer Game with Pythagoras as host wave/games/bathroom.html "Million Dollar Giveaway" Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 10

11 7M6 Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms. 7M8 Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas 7M9 Describe what happens to the surface area and volume of a three- dimensional object when the measurements of the object are changed; e g length of sides are doubled Computer Demonstration ault.html Shows Surface Area& Volume Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 11