Douglas County School District Sixth Grade Critical Content Checklist Math

Transcription

1 Teacher: Year: The Nevada ematics Standards and Douglas County s ematics Critical Content connect the Process and Content Standards. The Process Standards describe the process in which students should learn mathematics and engage in mathematical thinking. They are included on this checklist as a constant reminder of how our students should be supported in their mathematical thinking and embedded in every lesson. The Content Standards outline the big mathematical ideas that all students should know and be able to do. These are provided in the typical checklist format. Neither will develop mathematically proficient students when used in isolation. Grades 6-8 Process Standards Process Standard: Problem Solving Generalize solutions and apply previous knowledge to new problem solving situations Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem Apply problem solving strategies until a solution is found or it is clear that no solution exists Interpret and solve a variety of mathematical problems by paraphrasing Identify necessary and extraneous information Check the reasonableness of a solution Apply technology as a tool in problem solving situations Process Standard: ematical Communication Use formulas, algorithms, inquiry, and other techniques to solve mathematical problems Evaluate written and oral presentations in mathematics Identify and translate key words and phrases that imply mathematical operations Model and explain mathematical relationships using oral, written, graphic, and algebraic methods Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems Process Standard: ematical Reasoning Recognize and apply deductive and inductive reasoning Review and refine the assumptions and steps used to derive conclusions in mathematical arguments Justify answers and the steps taken to solve problems with and without manipulatives and physical models Process Standard: ematical Connections Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics Use manipulatives and physical models to explain the relationships between concepts and procedures Use the connections among mathematical topics to develop multiple approaches to problems Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science Identify, explain, and apply mathematics in everyday life Revised July 2008 Page 1 of 10

2 All Competencies/Standards listed are to be taught to mastery Note: Although these are mastery objectives, pacing of content is at the discretion of the teacher. Key: E = Enduring, I = Important, W = Worth being familiar with, S = Assessed at the state and local level, L= Assessed at the local level onlycontent Standard: Numbers, Number Sense, and Computation Place Value E/S Identify, read and write numbers to 100 billions Identify, read and write decimals to 10 thousandths Fractions I/S Houghton Mifflin : Ch: 1.1 pg. 4-5; 6-7 Ch: 1.1 pg. 4-5, 6-7 Ch: 1.3 pg 8-9 ematical Thinking Add and subtract fractions with unlike denominators Multiply and divide fractions with like and unlike denominators Add and subtract mixed numbers with regrouping Use models and drawings to identify, compare, add, and subtract fractions with unlike denominators Use models to translate among fractions, decimals, and percents Limit denominators up to 16. Items should use models of equivalent decimals, fractions, and percents. Equivalent percents limited to 1%, 5%, 10%, 20%, 25%, 50%, 75%, and 100% Houghton Mifflin : Ch: 5.2 pg Ch. 5.3 pg Ch: 5.4 pg Ch: 6.2 pg Ch: 6.3 pg Ch: 6.4 pg Ch: 6.5 pg Name That Portion Investigation 2; Session 3-9 Houghton Mifflin : Ch: 3.1 pg Ch: 3.2 pg Ch: 3.3 pg Ch: 3.4 pg ematical Thinking Investigation 2; Session 1-3 Name That Portion Houghton Mifflin : Ch: 16.1 pg Ch: 16.4 pg Ch: 17.2 pg Revised July 2008 Page 2 of 10

3 Comparing and Ordering I/S Read, write, compare and order groups of fractions, groups of decimals, and group of percents Percents must be 1% or greater, no improper fractions or mixed numbers Houghton Mifflin : Ch: 1.1 pg. 4-5; 6-7 Ch: 1.1 pg. 4-5, 6-7 Ch: 1.3 pg 8-9 ematical Thinking Facts E/S Identify equivalent expressions between and among fractions, decimals, and percents Identify fractions, decimals, and percents equivalent facts limited to ½, ¼, 1/5 and 1/10 Estimating and Estimation E/S Strategies Estimate and round using decimals, percents, and fractions Use estimation strategies in mathematical and practical situations Items may be written in context and may be multistep Name that Portion Computation I/S Houghton Mifflin : Ch: 5.1 pg Ch: 6.1 pg Ch: 17.4 pg Ch: 21.3 pg Name that Portion Calculate using fractions, decimals, and percents in mathematical and practical situations Use order of operations to evaluate expressions with integers Houghton Mifflin : Ch: 16.1 pg Ch: 16.4 pg Ch: 17.2 pg Ch: 1.7 pg Ch: 1.8 pg Ch: 2.7 pg 48-49, 53 Name that Portion Revised July 2008 Page 3 of 10

4 Expressions used to assess order of operations may contain parentheses, but not exponents. Limited to whole numbers only. Solving Problems and I/S Number Theory Use the concepts of number theory, including prime and composite numbers, factors, multiples, and the rules of divisibility to solve problems Determine the Least Common Multiple or Greatest Common Factor of two or three numbers. Content Standard 2: Patterns Functions, and Algebra Patterns E/S Houghton Mifflin : Ch: 3.1 pg Ch: 3.2 pg Ch: 3.3 pg Ch: 3.4 pg ematical Thinking Investigation 2; Session 1-3 Name That Portion Use and create tables and charts to extend a pattern in order to describe a rule for input/output tables and to find missing terms in a sequence Patterns must be repeated three times. Number patterns must use whole numbers only. Houghton Mifflin : Ch: 13.3 pg Patterns of Change Variables and Unknowns I/S Evaluate formulas and algebraic expressions using whole number values Solve and graphically represent equations and simple inequalities in one variable Number Sentences, I/L Expressions, and Polynomials Write simple expressions and equations using variables to represent mathematical situations Houghton Mifflin : Ch: 1.7 pg Ch: 1.8 pg Ch: 2.7 pg 48-49, 53 Houghton Mifflin : Ch: 12.1 pg Ch: 12.2 pg Revised July 2008 Page 4 of 10

5 Relations and Functions Use a rule to create a table and represent the ordered pairs on a coordinate grid Limited to linear relationships using whole numbers only I/S Houghton Mifflin : Ch: 13.3 pg Ch: 13.1 pg Content Standard 3: Measurement Comparison, Estimation, E/S and Conversion Estimate and compare corresponding units of measure for temperature, length, and weight/mass between customary and metric systems Customary units for length include: inch, foot, yard, and mile Metric units for length include: millimeter, centimeter, meter, and kilometer Customary units for weight include: ounce, pound, and ton Metric units for weight/mass include: milligram, gram, and kilogram Precision in Measurements E/S Given two measurements of the same object, select the one that is more precise Explain how the size of the unit of measure used effects precision Items are limited to constructed response only Formulas E/S Houghton Mifflin : Ch: 8.1 pg Ch: 8.4 pg Ch: 8.5 pg Ch: 13.5 pg Measurement Benchmarks Houghton Mifflin : Ch: 8.1 pg Ch: 8.4 pg Measurement Benchmarks Estimate, measure to the required degree of accuracy, derive, and apply formulas to find the perimeter, circumference, and surface area of plane figures Houghton Mifflin : Ch: 8.1 pg Ch: 8.4 pg Measurement Benchmarks Revised July 2008 Page 5 of 10

6 Items may use squares, triangles, rectangles and circles only Money E/S Compare and use unit cost Houghton Mifflin : in practical situations Ch: 16 pg Ratios and Proportions I/S Write and apply ratios in mathematical and practical problems involving measurement and monetary conversions Understand ratio, proportion, and percent including conversions of decimals, fractions and percents Ratios may use whole numbers only Houghton Mifflin : Ch: 16.1 pg Name that Portion Time E/S Use equivalent periods of time to solve practical problems with seconds/minutes/hours/days/ months/years Houghton Mifflin : 52B Content Standard 4: Spatial Relationships, Geometry, and Logic Two Dimensional Shapes E/S Measure angles using a protractor Identify, classify, compare, and draw regular and irregular quadrilaterals Identify, draw, and use central angles to represent fractions of a circle (the number of degrees represented by a central angle is limited to whole numbers) Congruence, Similarity, and I/S Transformations Determine actual measurements represented on scale drawings (i.e. maps, blueprints, house plans) Houghton Mifflin : Ch: 14.4 pg Ch: 14.6 pg Picturing Polygons Houghton Mifflin : Ch: 16.6 pg Revised July 2008 Page 6 of 10

7 Convert actual measurements to scale All conversions should result in whole number measurements. Scale factors should be whole numbers only. Coordinate Geometry and I/S Lines of Symmetry Using a coordinate grid, identify coordinates for a given point and locate points of given coordinates Plot geometric shapes in all four quadrants. Geometric shapes are limited to triangles, rectangles, and squares Item is limited to constructed response Three Dimensional Figures I/L Make a model of a threedimensional prism from a two-dimensional drawing Measurement Benchmarks Houghton Mifflin : Ch: 13.1 pg Picturing Polygons Containers and Cubes Make a two-dimensional drawing of a threedimensional prism Algebraic Connections I/L Model slope (pitch, angle of inclination) using concrete objects and practical examples Lines, Angles, and their I/S Properties Houghton Mifflin : Ch: 13.4 pg , 345 Draw complementary and supplementary angles Identify and find measures of complementary and supplementary angles using arithmetic and geometric methods Houghton Mifflin : Ch: 14.2 pg Picturing Polygons Triangles I/L Determine the measure of missing angles of triangles based on the Triangle Sum Theorem Sum of the angles equals 180 º Houghton Mifflin : Ch: 15.1 pg 383 Ch: 14.5 pg Revised July 2008 Page 7 of 10

8 Constructions W/L Construct circles, angles, and triangles based on given measurements using a variety of methods and tools including compass, straight edge, paper-folding, and technology Logic I/L Houghton Mifflin : Circles pg 532 Angles Pg 360 Triangles pg 364 Identify counterexamples to disprove a conditional statement If-Then statements Between Never and Always, Sessions 1 and 2 Likelihood Content Standard 5: Data Analysis Data Collection and Organization I/S Pose questions that guide the collection of data Organize and represent data using a variety of graphical representations including circle graphs, bar graphs, line graphs, histograms, pictographs, stem-and-leaf plot, tree diagrams, boxand-whisker plots, scatter plots, and tables Data displays may include all previously assessed types of data displays, plus circle graphs and scatter plots Data: Kids, Cats, and Ads Houghton Mifflin : Pg Collect and organize data to construct simple tables to show patterns and relationships with and without technology Central Tendency and Data I/S Distribution Select and apply the measures of central tendency to describe data, including mean, median, mode, range, and outliers Data: Kids, Cats, and Ads Houghton Mifflin : Pg , 235, 246, 268 Revised July 2008 Page 8 of 10

9 Interpretation of Data I/S Analyze the effect a change of graph type has on the interpretation of a set of data Interpret data and make predictions using circle graphs and scatter plots Analyzing the effect of a change in graph type is for constructed response only Permutations and E/S Combinations Houghton Mifflin Grade 5: Ch: pg Grade 6 Ch: 10.8 pg Find the number of outcomes for a specific event by constructing sample spaces and tree diagrams Items limited to 16 outcomes Compute total number of outcomes by using the fundamental counting principle Experimental and I/S Theoretical Probability Find experimental probability using concrete materials Use of simple probability experiments with up to 2 events and limited to 16 outcomes Represent the results of simple probability experiments as fractions, decimals, percents, and ratios to make predictions about future events Statistical Inferences I/S Analyze various representations of a set of data to draw conclusions and make predictions Describe the limitations of various graphical representations. Explain the appropriateness of a data display. Houghton Mifflin : Pg 486 Houghton Mifflin : Pg 495, 504 Between Never and Always Houghton Mifflin ; Pg 208, 221,226 Houghton Mifflin : Grade 4 Ch: 15.5 pg Data; Kids, Cats and Ads Revised July 2008 Page 9 of 10

10 Items are limited to constructed response only. Revised July 2008 Page 10 of 10