8 th grade mathematics Team: T. Kisker, S. Miller, B. Ricks, B. Byland April 2012

Transcription

1 Compare and order all rational numbers including percents and find their approximate location on a number line. N.1.A.8 Number and Operations -Order positive rational numbers on a number line 1, 2, 5, 6, 7 1, 5, 10 August Which sign makes the sentence true? > < = Use fractions, decimals and percents to solve problems. N.1.B.8 Know that there are numbers that are not rational, and approximate them by rational numbers. Write - 9 -Write equivalent 20 as a decimal number. fractions -Convert fractions, to decimals, to percents 1, 2, 3, 5, 6, 7, 9 5, 10, 11, 12, 13, 22, 24, 25, 30, 58, 67 September

2 Recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including scientific notation. N.1.C.8 Work with radicals and integer exponents. Apply properties of operations to all rational numbers including order of operations and inverse operations. N.2.C.8 Work with radicals and integer exponents. How do you write 590,000 in scientific notation? = Multiply. Simplify your answer and write it as a proper fraction or as a whole or mixed number = -Use exponential notation to generate equivalent representations of numbers -Apply properties of operations to positive rational numbers 9,10, 11, 12, 13, 14, 15 1, 2, 7, 9 10, 23, 28, 46, 57 September 21, 31, 33, 36, 50

3 Generalize patterns represented graphically or numerically with words or symbolic rules, using explicit notation. A.1.B.8 Use functions to model relationships between quantities. Type the missing numbers in this sequence: 88, 85,, 79, 76, Kim put 36 empty cans in the first bin, 49 empty cans in the second bin, 64 empty cans in the third bin, and 81 empty cans in the fourth bin. What kind of sequence is this? Algebraic Relationships -Construct tables and graphs -Use words to represent patterns or rules 15, 16, January arithmetic geometric both neither Identify functions as linear or nonlinear from tables, graphs or equations. A.1.D.8 Define, evaluate, and compare functions. Does (0, 0) make the equation y = 5x true? Which equation gives the rule for this table? x y Equation of a line: y=mx+b -Find the slope of a line (rise over run) -Locate the y- intercept -Construct an x/y chart 11, 13, 14, 15, 16, 17 47, 56 November

4 y = x + 89 y = x + 25 y = x + 34 y = x + 29 Use symbolic algebra to represent and solve problems that involve linear relationships. A.2.A.8 Analyze and solve linear equations and pairs of simultaneous linear equations. This equation shows how the number of pages Sandra still has to read depends on the number of hours she spends on her book. P = - 30h + 63 The variable h represents the number of hours she has spent reading, and the variable p represents the number of pages left to read. After 2 hours of reading, how many pages will Sandra have left to read? -In one variable, first 1, 2 3, 4, 14 August pages Use properties to generate equivalent forms for simple algebraic expressions that include all rationals. A.2.B.8 Analyze and solve linear equations and pairs of simultaneous linear equations. Which property of addition is shown? M + 0 = m associative commutative Identity -Use properties to generate equivalent forms for algebraic expressions that include positive rationals - and include integers 9 38

5 Model and solve problems, using multiple representations such as graphs, tables, and linear equations. A.3.A.8 Use functions to model relationships between quantities. In the data set below, what are the lower quartile, the median, and the upper quartile? 1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12 -Model multiplication -Model addition -Model fractions 3, 5, 6, 9 47, 53, 62 November Describe, classify and generalize relationships between and among types of a)2-dimensional objects and b)3-dimensional objects using their defining properties including the Pythagorean Theorem. G.1.A.8 Understand and apply the Pythagorean Theorem. 8 cm 15 cm What is the length of the hypotenuse? Geometric and Spatial Relationships -Identify 2- dimensional crosssection of a 3- dimensional object c 9, 12, 15, 16 Investigation: The Pythagorean Theorem, Investigation: Classifying Quadrilaterals C = centimeters December

6 Use coordinate geometry to analyze properties of right triangles and quadrilaterals (including the use of the Pythagorean Theorem) G.2.A.8 Understand and apply the Pythagorean Theorem. a 2 + b 2 = c 2 Example: Solve this triangle. a 2 + b 2 = c 2 -Construct and identify geometric shapes on a coordinate plane -Identify and name properties of geometric shapes (segment, vertices, angle, etc) 5, 7, 9 Investigation: The Coordinate Plane, = c = c 2 September 169 = c 2 c 2 = 169 c = 169. Reposition shapes under formal transformations such as reflection, rotation and translation. G.3.A.8 Understand congruence and similarity using physical models, transparencies, or geometry software. c = 13 This graph illustrates a translation. True or False? -Vocabulary (flip, slide, turn) -Use manipulatives to model transformations -Model transformations on a coordinate plane 6, 7, 9 26

7 Describe the relationship between the scale factor and the area of the image using a dilation (stretching/shrinking). G.3.B.8 Understand congruence and similarity using physical models, transparencies, or geometry software. 6x = X = 1 ½ -Calculate scale factor -Calculate the scale factor and perimeter of an image as it stretches/shrinks 6, 7 19, 26 Solve problems of angle measure, including those involving triangles and parallel lines cut by a transversal. M.2.B.8 Understand congruence and similarity using physical models, transparencies, or geometry software. Supplementary Complementary Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Adjacent Angles Measurement -Use a protractor to measure angles to the nearest degree -Classify angles as acute, right, obtuse, straight, or reflex 6, 9 18 If angle 7 has a measure of 120º, what are the measures of the other angles?

8 Solve problems involving circumference and/or area of a circle and the surface area/volume of a rectangular or triangular prism, or cylinder. M.2.C.7 Solve real-world and mathematical problems involving angle measure, surface area, and volume. Analyze precision and accuracy in measurement situations and determine number of significant digits. M.2.D.8 The area of a circle is 78.5 square meters. What is the radius? Here are the basic rules for significant digits: 1) All nonzero digits are significant. 2) All zeroes between significant digits are significant. 3) All zeroes which are both to the right of the decimal point and to the right of all non-zero significant digits are themselves significant. Round 742,396 to four, three, and two significant digits: -Calculate the area of polygons -Calculate the perimeter of polygons -Round real numbers -Use estimation in real world problems 9 6, 7, 9, 13, 14, 16 8, 37, 39, 40, 42, 43 September Convert from one unit to another (capacity) and convert square or cubic units not the same system of measurement (English to metric and metric to English). M.2.E.7 (part) 742,400 (four significant digits) 742,000 (three significant digits) 740,000 (two significant digits) 37 in 2.54 cm 93.98cm 1 1 in -Calculate measures of conversion in the same unit of measurement 2, 9 52 January

9 Compare different representations of the same data and evaluate how well each representation shows important aspects of the data. D.2.B.8 Data and Probability -Collect data -Record data -Display data (graphs, charts, tables, diagrams) -Analyze data March Is this the best representation of the data? Is it misleading? If so, what aspect of it makes it misleading?