§111.22. Mathematics, Grade 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 non-negative rational numbers;  2003 Problem 7  2003 Problem 16  2004 Problem 31  2008 Obj 1 Sample 1  2009 Problem 25  Daily Challenge 11

(B)  generate equivalent forms of rational numbers including whole numbers, fractions, and decimals;  2003 Problem 20  2004 Problem 28  2009 Problem 17

(C)  use integers to represent real-life situations;  2003 Problem 36  2006 Problem 14  Daily Challenge 13

(D)  write prime factorizations using exponents;  2003 Problem 14  2004 Problem 39  2006 Problem 3  2008 Obj 1 Sample 2  2009 Problem 36

(E)  identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers; and  2003 Problem 38  2004 Problem 17  2004 Problem 29  2006 Problem 15  2009 Problem 3  Daily Challenge 14

(F)  identify multiples of a positive integer and common multiples and the least common multiple of a set of positive integers.  2008 Obj 1 Sample 3  2009 Problem 15

(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;  2003 Problem 12  2004 Problem 11  2006 Problem 29  2008 Obj 1 Sample 4  2009 Problem 20  Daily Challenge 16

(B)  use addition and subtraction to solve problems involving fractions and decimals;  2003 Problem 42  2004 Problem 21   2004 Problem 45   2006 Problem 21  2008 Obj 1 Sample 5  2009 Problem 11  Daily Challenge 15  Daily Challenge 17

(C)  use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates;  2003 Problem 32  2006 Problem 4  2004 Problem 15   2006 Problem 11  2009 Problem 19  Daily Challenge 1  Daily Challenge 18

(D)  estimate and round to approximate reasonable results and to solve problems where exact answers are not required; and  2003 Problem 44  2004 Problem 5  2006 Problem 17  2009 Problem 32  Daily Challenge 2

(E)  use order of operations to simplify whole number expressions (without exponents) in problem solving situations.  2009 Problem 30

(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;  2003 Problem 24  2003 Problem 35  2004 Problem 26  2006 Problem 7  2008 Obj 2 Sample 1  2009 Problem 31  2009 Problem 44  Daily Challenge 4  Daily Challenge 19

(B)  represent ratios and percents with concrete models, fractions, and decimals; and  2004 Problem 14  2003 Problem 18  2004 Problem 42   2006 Problem 16  2006 Problem 18  2008 Obj 2 Sample 2  2009 Problem 9  2009 Problem 27  Daily Challenge 20  Daily Challenge 21

(C)  use ratios to make predictions in proportional situations.  2003 Problem 15  2003 Problem 10  2004 Problem 9  2004 Problem 37  2006 Problem 26  2008 Obj 2 Sample 3  2009 Problem 40  Daily Challenge 8  Daily Challenge 22

(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; and  2003 Problem 28  2006 Problem 25  2006 Problem 27  2009 Problem 35

(B)  use tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc.  2003 Problem 37  2004 Problem 25  2004 Problem 34  2006 Problem 31  2009 Problem 6  2009 Problem 23

(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.  2003 Problem 29  2003 Problem 45  2004 Problem 19  2006 Problem 2  2008 Obj 2 Sample 4  2009 Problem 12

(6)  Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to:

(A)  use angle measurements to classify angles as acute, obtuse, or right;  2003 Problem 4  2003 Problem 5  2004 Problem 2  2004 Problem 44  2008 Obj 3 Sample 1  2009 Problem 7  2009 Problem 42  Daily Challenge 25

(B)  identify relationships involving angles in triangles and quadrilaterals; and  2003 Problem 30  2003 Problem 40  2004 Problem 12  2004 Problem 40  2006 Problem 9  2008 Obj 3 Sample 2  2009 Problem 21  2009 Problem 39  Daily Challenge 26  Daily Challenge 28

(C)  describe the relationship between radius, diameter, and circumference of a circle.  2003 Problem 27  2004 Problem 23  2004 Problem 10  2006 Problem 13  2008 Obj 3 Sample 3   2009 Problem 2  2009 Problem 28

(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.  2003 Problem 39  2003 Problem 43  2004 Problem 1   2004 Problem 41  2008 Obj 3 Sample 4  2009 Problem 46  Daily Challenge 23

(8)  Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to:

(A)  estimate measurements (including circumference) and evaluate reasonableness of results;  2003 Problem 34  2004 Problem 30  2006 Problem 24  2008 Obj 4 Sample 1  2009 Problem 37  Daily Challenge 3

(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;  2003 Problem 21  2003 Problem 23  2004 Problem 16  2004 Problem 32  2006 Problem 28  2008 Obj 4 Sample 2  2009 Problem 8  2009 Problem 13  Daily Challenge 27  Daily Challenge 29

(C)  measure angles; and  2004 Problem 7  2003 Problem 19  2006 Problem 30  2008 Obj 4 Sample 3  2009 Problem 29  Daily Challenge 12  Daily Challenge 24

(D)  convert measures within the same measurement system (customary and metric) based on relationships between units.  2003 Problem 9  2004 Problem 46  2009 Problem 10  Daily Challenge 30

(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; and  2003 Problem 22  2004 Problem 43  2006 Problem 6  2009 Problem 1

(B)  find the probabilities of a simple event and its complement and describe the relationship between the two.  2003 Problem 25  2004 Problem 35  2006 Problem 23  2008 Obj 5 Sample 1  2009 Problem 18  Daily Challenge 31

(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;  2004 Problem 4   2009 Problem 5  Daily Challenge 9

(B)  identify mean (using concrete objects and pictorial models), median, mode, and range of a set of data;  2003 Problem 1  2003 Problem 26  2004 Problem 13  2006 Problem 10  2008 Obj 5 Sample 2  2009 Problem 33  Daily Challenge 10

(C)  sketch circle graphs to display data; and  2003 Problem 46  2004 Problem 22  2006 Problem 1  2009 Problem 41

(D)  solve problems by collecting, organizing, displaying, and interpreting data.  2003 Problem 6  2004 Problem 20  2006 Problem 20  2008 Obj 5 Sample 3  2009 Problem 43

(11)  Underlying processes and mathematical tools. The student applies Grade 6 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;  2003 Problem 3  2003 Problem 33  2004 Problem 36  2006 Problem 8  2008 Obj 6 Sample 1  2009 Problem 34  2009 Problem 38  Daily Challenge 32

(B)  use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;  2003 Problem 13  2003 Problem 41  2004 Problem 18  2004 Problem 33  2006 Problem 5  2009 Problem 22  2009 Problem 45  Daily Challenge 33

(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  2003 Problem 2 2004 Problem 6  2004 Problem 8  2004 Problem 24  2006 Problem 12  2006 Problem 19  2008 Obj 6 Sample 2  2009 Problem 16  2009 Problem 26

(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.

(12)  Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, 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  2003 Problem 11  2003 Problem 31  2004 Problem 27  2004 Problem 38  2006 Problem 22  2008 Obj 6 Sample 3  2009 Problem 24  Daily Challenge 5

(B)  evaluate the effectiveness of different representations to communicate ideas.

(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  2004 Problem 3  2003 Problem 17  2008 Obj 1 Sample 4  2009 Problem 4

(B)  validate his/her conclusions using mathematical properties and relationships.  2003 Problem 8  2009 Problem 14

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