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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Planned Instruction for Math- Grade 6

 Code Standard Content - Benchmark P Time Materials/Strategies/Activities CET PSSA 2.8 A. Apply simple algebraic patterns to basic number theory and to spatial relations A. Create, describe and extend patterns. B. Discover, describe and generalize patterns, including linear, exponential and simple quadratic relationships. • Exponential graph of powers of 2 • Graph : y = x + 2 • Graph : y = x 2 + 2 B. Discover and graph linear patterns (Quadrant I). Understand that a linear function results from a constant rate of change. C. Create and interpret expressions, equations or inequalities that model problem situations. • Use algebra to simplify expressions. • Use algebra to evaluate expressions. • Use symbolic notation.. C. Solve one step equations that model problem situations. D. Use concrete objects to model algebraic concepts. • Tiles • Two-sided chips • Algebraic balances D. Use concrete objects to model algebraic concepts with one variable. • Algebraic balances • Blocks • Chips or counters • Number tiles E. Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy. • Solve any graph inequalities. E. Select and use a strategy to solve a one step equation. Check the solution for accuracy. • Use manipulatives. • Solve by using inverse operations • Solve by guess and check F. Solve and graph equations and inequalities using scientific and graphing calculators and computer spreadsheets. F. Solve equations using a scientific calculator (any calculator that does order of operations). G. Represent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules. G. Understand the concept of a variable. • Complete input/output tables. State the rule (using a variable) for input/output tables. H. Graph a linear function from a rule or table. H. Graph a linear pattern. I. Generate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions. I. Create input/output rule. Create a table from the rule. Graph the table values (Quadrant I only). J. Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities; explain how a change in one quantity determines another quantity in a functional relationship. J. Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities. • Use an algebraic balance to demonstrate that doubling both sides will keep the equation balanced. 2.9 A. Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software. A. Draw and label points, lines (perpendicular, intersecting, and parallel) and planes. Describe the relationships of points, lines and planes. Yes B. Draw, label, measure and list the properties of complementary, supplementary and vertical angles. B. Identify complementary and supplementary angles. Yes C. Classify familiar polygons as regular or irregular up to a decagon. C. Classify and compare polygons (up to decagon) according to sides and angles. Yes D. Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders. D. Identify and list the properties of squares, rectangles, parallelograms, and triangles . • Identify the relationship between two and threedimensional shapes. • Draw squares, rectangles and circles. Yes E. Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles). E. Identify and draw parallel lines. Yes F. Distinguish between similar and congruent polygons. F. Identify congruent polygons Yes G. Discover the ratio Π(pi) using measures of circumference and diameter with various real circles. G. Recognize the value Π. Yes H. Use simple geometric figures (e.g., triangles, squares) to create, through rotation, transformational figures in three dimensions. H. • Create a three dimensional shape or design by translating a polygon. • Pattern blocks can be used to model translations. Yes I. Generate transformations using computer software. I. Generate translations using computer software. Yes J. Analyze geometric patterns (e.g., tessellations, sequences of shapes) and develop descriptions of of the patterns. J. Draw translations using grid paper and describe the move. Yes K. Analyze objects to determine whether they illustrate tessellations, symmetry, congruence, similarity and scale. K. Analyze objects to determine whether they illustrate line symmetry or congruence Yes 2.10 A. Compute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships. A. Draw right triangles and measure lengths of legs and the hypotenuse. Discover that the hypotenuse needs to be the longest side. B. Solve problems requiring indirect measurement for lengths of sides of triangles. B. Identify similar triangles in real world situations. A. Analyze graphs of related quantities for minimum and maximum values and justify the findings. A. Identify least and greatest values represented in a variety of graphs. Compare numbers and real-life quantities using ordering symbols (>,<,≥,≤). 2.11 B. Describe the concept of unit rate, ratio and slope in the context of rate of change. B. Examine linear (constant) rates of change in real life situations using tables to organize and graphs to display the data. • Miles per hour. • Pay per hour. C. Continue a pattern of numbers or objects that could be extended infinitely. C. Continue patterns of numbers and objects. • Long division with repeating decimals. • Input/output tables. • Designs with pattern blocks.