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6.4.1
Number and Numerical Operations
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6.4.1.6 A
Number Sense
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6.4.1.6 A.1
Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well).
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6.4.1.6 A.1.a
All integers
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6.4.1.6 A.1.b
All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers
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6.4.1.6 A.1.c
All decimals
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6.4.1.6 A.2
Recognize the decimal nature of United States currency and compute with money.
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6.4.1.6 A.3
Demonstrate a sense of the relative magnitudes of numbers.
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6.4.1.6 A.4
Explore the use of ratios and proportions in a variety of situations.
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Geometry: Find side lengths of similar figures (Sixth grade - Y.15)
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Ratios, proportions, and percents: Write a ratio to describe objects in a picture (Sixth grade - Z.1)
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Ratios, proportions, and percents: Equivalent ratios (Sixth grade - Z.2)
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Ratios, proportions, and percents: Proportions (Sixth grade - Z.3)
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Ratios, proportions, and percents: Unit rates and equivalent rates (Sixth grade - Z.4)
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Ratios, proportions, and percents: Scale drawings (Sixth grade - Z.5)
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6.4.1.6 A.5
Understand and use whole-number percents between 1 and 100 in a variety of situations.
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Consumer math: Which is the better coupon? (Sixth grade - G.1)
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Consumer math: Percents - calculate tax, tip, mark-ups, and more (Sixth grade - G.5)
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Consumer math: Simple interest (Sixth grade - G.6)
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Ratios, proportions, and percents: Percents of numbers and money amounts (Sixth grade - Z.9)
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Ratios, proportions, and percents: Percents of numbers: word problems (Sixth grade - Z.10)
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Ratios, proportions, and percents: Find what percent one number is of another (Sixth grade - Z.12)
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Ratios, proportions, and percents: Find what percent one number is of another: word problems (Sixth grade - Z.13)
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6.4.1.6 A.6
Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.
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6.4.1.6 A.7
Develop and apply number theory concepts in problem solving situations.
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6.4.1.6 A.7.a
Primes, factors, multiples
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6.4.1.6 A.7.b
Common multiples, common factors
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6.4.1.6 A.7.c
Least common multiple, greatest common factor
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6.4.1.6 A.8
Compare and order numbers.
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6.4.1.6 B
Numerical Operations
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6.4.1.6 B.1
Recognize the appropriate use of each arithmetic operation in problem situations.
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6.4.1.6 B.2
Construct, use, and explain procedures for performing calculations with fractions and decimals with:
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6.4.1.6 B.2.a
Pencil-and-paper
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6.4.1.6 B.2.b
Mental math
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6.4.1.6 B.2.c
Calculator
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6.4.1.6 B.3
Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.
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6.4.1.6 B.4
Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.
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6.4.1.6 B.5
Find squares and cubes of whole numbers.
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6.4.1.6 B.6
Check the reasonableness of results of computations.
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6.4.1.6 B.7
Understand and use the various relationships among operations and properties of operations.
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6.4.1.6 B.8
Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses.
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6.4.1.6 C
Estimation
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6.4.1.6 C.1
Use a variety of strategies for estimating both quantities and the results of computations.
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6.4.1.6 C.2
Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.
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6.4.1.6 C.3
Determine the reasonableness of an answer by estimating the result of operations.
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6.4.1.6 C.4
Determine whether a given estimate is an overestimate or an underestimate.
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6.4.2
Geometry and Measurement
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6.4.2.6 A
Geometric Properties
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6.4.2.6 A.1
Understand and apply concepts involving lines and angles.
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6.4.2.6 A.1.a
Notation for line, ray, angle, line segment
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6.4.2.6 A.1.b
Properties of parallel, perpendicular, and intersecting lines
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6.4.2.6 A.1.c
Sum of the measures of the interior angles of a triangle is 180°
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6.4.2.6 A.2
Identify, describe, compare, and classify polygons and circles.
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6.4.2.6 A.2.a
Triangles by angles and sides
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6.4.2.6 A.2.b
Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi
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6.4.2.6 A.2.c
Polygons by number of sides.
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6.4.2.6 A.2.d
Equilateral, equiangular, regular
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6.4.2.6 A.2.e
All points equidistant from a given point form a circle
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6.4.2.6 A.3
Identify similar figures.
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6.4.2.6 A.4
Understand and apply the concepts of congruence and symmetry (line and rotational).
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6.4.2.6 A.5
Compare properties of cylinders, prisms, cones, pyramids, and spheres.
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6.4.2.6 A.6
Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives.
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6.4.2.6 A.7
Identify a three-dimensional shape with given projections (top, front and side views).
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6.4.2.6 A.8
Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape).
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6.4.2.6 B
Transforming Shapes
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6.4.2.6 B.1
Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.
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6.4.2.6 B.2
Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.
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6.4.2.6 C
Coordinate Geometry
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6.4.2.6 C.1
Create geometric shapes with specified properties in the first quadrant on a coordinate grid.
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6.4.2.6 D
Units of Measurement
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6.4.2.6 D.1
Select and use appropriate units to measure angles, area, surface area, and volume.
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6.4.2.6 D.2
Use a scale to find a distance on a map or a length on a scale drawing.
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6.4.2.6 D.3
Convert measurement units within a system (e.g., 3 feet = ___ inches).
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6.4.2.6 D.4
Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).
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6.4.2.6 D.5
Use measurements and estimates to describe and compare phenomena.
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6.4.2.6 E
Measuring Geometric Objects
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6.4.2.6 E.1
Use a protractor to measure angles.
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6.4.2.6 E.2
Develop and apply strategies and formulas for finding perimeter and area.
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6.4.2.6 E.2.a
Triangle, square, rectangle, parallelogram, and trapezoid
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6.4.2.6 E.2.b
Circumference and area of a circle
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6.4.2.6 E.3
Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders.
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6.4.2.6 E.4
Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa.
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6.4.2.6 E.5
Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).
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6.4.3
Patterns and Algebra
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6.4.3.6 A
Patterns
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6.4.3.6 A.1
Recognize, describe, extend, and create patterns involving whole numbers and rational numbers.
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6.4.3.6 A.1.a
Descriptions using tables, verbal rules, simple equations, and graphs
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6.4.3.6 A.1.b
Formal iterative formulas (e.g., NEXT = NOW 3)
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6.4.3.6 A.1.c
Recursive patterns, including Pascal's Triangle (where each entry is the sum of the entries above it) and the Fibonacci Sequence: 1, 1, 2, 3, 5, 8,... (where NEXT = NOW + PREVIOUS)
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6.4.3.6 B
Functions and Relationships
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6.4.3.6 B.1
Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).
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6.4.3.6 C
Modeling
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6.4.3.6 C.1
Use patterns, relations, and linear functions to model situations.
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6.4.3.6 C.1.a
Using variables to represent unknown quantities
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6.4.3.6 C.1.b
Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities
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6.4.3.6 C.2
Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.
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6.4.3.6 C.2.a
Changes over time
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6.4.3.6 C.2.b
Relations between quantities
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6.4.3.6 C.2.c
Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)
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6.4.3.6 D
Procedures
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6.4.3.6 D.1
Solve simple linear equations with manipulatives and informally.
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6.4.3.6 D.1.a
Whole-number coefficients only, answers also whole numbers
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6.4.3.6 D.1.b
Variables on one or both sides of equation
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6.4.3.6 D.2
Understand and apply the properties of operations and numbers.
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6.4.3.6 D.2.a
Distributive property
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6.4.3.6 D.2.b
The product of a number and its reciprocal is 1
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6.4.3.6 D.3
Evaluate numerical expressions.
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6.4.3.6 D.4
Extend understanding and use of inequality.
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6.4.3.6 D.4.a
Symbols (greater than or equal to, not equal to, less than or equal to)
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6.4.4
Data Analysis, Probability, and Discrete Mathematics
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6.4.4.6 A
Data Analysis
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6.4.4.6 A.1
Collect, generate, organize, and display data.
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6.4.4.6 A.1.a
Data generated from surveys
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6.4.4.6 A.2
Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.
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6.4.4.6 A.2.a
Bar graph, line graph, circle graph, table, histogram
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6.4.4.6 A.2.b
Range, median, and mean
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6.4.4.6 A.2.c
Calculators and computers used to record and process information
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6.4.4.6 A.3
Respond to questions about data, generate their own questions and hypotheses, and formulate strategies for answering their questions and testing their hypotheses.
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6.4.4.6 B
Probability
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6.4.4.6 B.1
Determine probabilities of events.
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6.4.4.6 B.1.a
Event, complementary event, probability of an event
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6.4.4.6 B.1.b
Multiplication rule for probabilities
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6.4.4.6 B.1.c
Probability of certain event is 1 and of impossible event is 0
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6.4.4.6 B.1.d
Probabilities of event and complementary event add up to 1
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6.4.4.6 B.2
Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag).
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6.4.4.6 B.2.a
Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked
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6.4.4.6 B.2.b
Given data obtained experimentally, what is the likely distribution of items in the bag
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6.4.4.6 B.3
Explore compound events.
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6.4.4.6 B.4
Model situations involving probability using simulations (with spinners, dice) and theoretical models.
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6.4.4.6 B.5
Recognize and understand the connections among the concepts of independent outcomes, picking at random, and fairness.
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6.4.4.6 C
Discrete Mathematics-Systematic Listing and Counting
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6.4.4.6 C.1
Solve counting problems and justify that all possibilities have been enumerated without duplication.
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6.4.4.6 C.1.a
Organized lists, charts, tree diagrams, tables
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6.4.4.6 C.1.b
Venn diagrams
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6.4.4.6 C.2
Apply the multiplication principle of counting.
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6.4.4.6 C.2.a
Simple situations (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).
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6.4.4.6 C.2.b
Number of ways a specified number of items can be arranged in order (concept of permutation)
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6.4.4.6 C.2.c
Number of ways of selecting a slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21)
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6.4.4.6 C.3
List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person's hand once).
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6.4.4.6 D
Discrete Mathematics-Vertex-Edge Graphs and Algorithms
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6.4.4.6 D.1
Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions.
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6.4.4.6 D.2
Analyze vertex-edge graphs and tree diagrams.
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6.4.4.6 D.2.a
Can a picture or a vertex-edge graph be drawn with a single line? (degree of vertex)
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6.4.4.6 D.2.b
Can you get from any vertex to any other vertex? (connectedness)
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6.4.4.6 D.3
Use vertex-edge graphs to find solutions to practical problems.
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6.4.4.6 D.3.a
Delivery route that stops at specified sites but involves least travel
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6.4.4.6 D.3.b
Shortest route from one site on a map to another
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6.4.5
Mathematical Processes
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6.4.5 A
Problem Solving
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6.4.5 A.1
Learn mathematics through problem solving, inquiry, and discovery.
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6.4.5 A.2
Solve problems that arise in mathematics and in other contexts.
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6.4.5 A.2.a
Open-ended problems
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6.4.5 A.2.b
Non-routine problems
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6.4.5 A.2.c
Problems with multiple solutions
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6.4.5 A.2.d
Problems that can be solved in several ways
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6.4.5 A.3
Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.
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6.4.5 A.4
Pose problems of various types and levels of difficulty.
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6.4.5 A.5
Monitor their progress and reflect on the process of their problem solving activity.
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6.4.5 A.6
Distinguish relevant from irrelevant information, and identify missing information.
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6.4.5 B
Communication
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6.4.5 B.1
Use communication to organize and clarify their mathematical thinking.
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6.4.5 B.1.a
Reading and writing
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6.4.5 B.1.b
Discussion, listening, and questioning
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6.4.5 B.2
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.
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6.4.5 B.3
Analyze and evaluate the mathematical thinking and strategies of others.
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6.4.5 B.4
Use the language of mathematics to express mathematical ideas precisely.
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6.4.5 C
Connections
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6.4.5 C.1
Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).
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6.4.5 C.2
Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).
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6.4.5 C.3
Recognize that mathematics is used in a variety of contexts outside of mathematics.
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6.4.5 C.4
Apply mathematics in practical situations and in other disciplines.
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6.4.5 C.5
Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).
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6.4.5 C.6
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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6.4.5 D
Reasoning
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6.4.5 D.1
Recognize that mathematical facts, procedures, and claims must be justified.
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6.4.5 D.2
Use reasoning to support their mathematical conclusions and problem solutions.
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6.4.5 D.3
Select and use various types of reasoning and methods of proof.
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6.4.5 D.4
Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.
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6.4.5 D.5
Make and investigate mathematical conjectures.
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6.4.5 D.5.a
Counterexamples as a means of disproving conjectures
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6.4.5 D.5.b
Verifying conjectures using informal reasoning or proofs.
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6.4.5 D.6
Evaluate examples of mathematical reasoning and determine whether they are valid.
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6.4.5 E
Representations
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6.4.5 E.1
Create and use representations to organize, record, and communicate mathematical ideas.
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6.4.5 E.1.a
Concrete representations (e.g., base-ten blocks or algebra tiles)
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6.4.5 E.1.b
Pictorial representations (e.g., diagrams, charts, or tables)
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6.4.5 E.1.c
Symbolic representations (e.g., a formula)
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6.4.5 E.1.d
Graphical representations (e.g., a line graph)
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6.4.5 E.2
Select, apply, and translate among mathematical representations to solve problems.
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6.4.5 E.3
Use representations to model and interpret physical, social, and mathematical phenomena.
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6.4.5 F
Technology
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6.4.5 F.1
Use technology to gather, analyze, and communicate mathematical information.
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6.4.5 F.2
Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.
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6.4.5 F.3
Use graphing calculators and computer software to investigate properties of functions and their graphs.
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6.4.5 F.4
Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).
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6.4.5 F.5
Use computer software to make and verify conjectures about geometric objects.
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6.4.5 F.6
Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).
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