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An Overview of
Mathematics 6
DRAFT May 2014
Number (N)
In Mathematics 6, we
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read, write, represent, and describe numbers greater than one million and less than one-thousandth
using symbols, expressions, expanded notation, decimal notation, and place-value charts
explore place value (greater than one million and less than one-thousandth)
use place-value patterns to understand numbers greater than one million and less than onethousandth
compare and order whole numbers and decimal numbers in a variety of ways
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represent, interpret, and model proper fractions ( ), improper fractions ( ), and mixed numbers
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( 2 ) using concrete materials, pictures, and symbols
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compare and order a set of fractions on a number line
rename a mixed number as an improper fraction, and an improper fraction as a mixed number
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recognize and find factors of numbers (numbers that can be multiplied together to make a specific
number) by creating rectangles using tiles or grid paper
identify the factors of a given number (e.g., the factors of 16 are 1, 2, 4, 8, and 16)
identify multiples of a given number (e.g., some multiples of 4 are 4, 8, 12, 16, 20, …)
solve problems involving factors and multiples
discover the difference between prime and composite numbers and their relationship to factors
explain why 0 and 1 are neither prime nor composite numbers
represent ratios concretely, pictorially, and symbolically
identify and describe ratios
solve problems involving ratios
determine equivalent ratios using concrete materials
understand the relationship between ratio and percent
represent percent concretely, pictorially, and symbolically
express a percent as a fraction and as a decimal
solve percent problems using benchmarks of 25%, 50%, 75%, and 100%
describe, represent, and record integers (negative numbers like those on a thermometer)
identify real-life situations in which integers are used
compare and order integers
Overview of Mathematics 6
DRAFT May 2014
1
Number (N) continued
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create and solve addition, subtraction, multiplication, and division problems involving whole
numbers, and addition and subtraction of decimal numbers
estimate and calculate sums, differences, products, and quotients of whole numbers using an
appropriate method (mental mathematics, paper and pencil, or technology)
estimate and calculate sums and differences involving decimal numbers using an appropriate
strategy (mental mathematics, paper and pencil, or technology)
represent, concretely, pictorially, and symbolically, the multiplication and division of decimal
numbers by a one-digit whole number
solve and create story problems involving the multiplication and division of decimal numbers by a
one-digit whole number
estimate the products and quotients (answers) involving the multiplication and division of decimal
numbers by a one-digit whole number
use personal strategies to calculate products and quotients (answers) involving the multiplication
and division of decimal numbers by a one-digit whole number
demonstrate and explain why there is a need to have a standard order of operations
apply the order of operations to solve problems
Overview of Mathematics 6
DRAFT May 2014
2
Patterns and Relations (PR)
In Mathematics 6, we
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describe and use pattern rules to continue a pattern and to complete a table of values
represent pattern rules using an expression
use pattern rules to describe the relationship within a column and between the columns of a table
of values
identify errors and missing terms within a pattern or table of values
create tables of values to solve problems
use a pattern to create a table of values and graph the values
create a table of values from a pattern or a graph
describe the relationship shown on a graph
solve a variety of problems that involve patterns
use letter variables to show the commutative property of addition and multiplication
(e.g., a + b = b + a or a × b = b × a)
model and explain the preservation of equality using balances and pictures (If I add three cubes to
one side of the balance, I must add three cubes to the other side of the balance in order to preserve
equality.)
write equivalent forms of a given equation (3n = 12 is the same as 3n + 5 = 12 + 5 or 2n = 7 is the
same as 3(2n) = 3(7)
solve simple equations that have a missing number or that use a letter to represent the missing
number(s) (e.g., 3 × ___ = 12 or 3 × a = 12)
develop a formula for finding the perimeter of any regular polygon
develop a formula for finding the area of any rectangle
Overview of Mathematics 6
DRAFT May 2014
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Measurement (M)
In Mathematics 6, we
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describe angles as a measure of rotation (turn)
identify and classify angles as acute, obtuse, right, straight, or reflex
estimate the measure of an angle using a referent
sketch angles without using a protractor
measure angles using a protractor
draw angles using a protractor
explain, using models, that the sum of the interior angles of any triangle is 180˚
explain, using models, that the sum of the interior angles of any quadrilateral is 360˚
explain, using models, how the perimeter of any polygon (2-D shape) can be determined
generalize a formula for calculating perimeter (distance around the outside)
explain, using models, how the area (inside space) of any rectangle can be determined
generalize a formula for calculating area of rectangles
explain, using models, how the volume (the amount of space occupied by a 3-D object) of any
rectangular prism can be determined
generalize a formula for calculating volume of rectangular prisms
solve measurement problems that involve perimeter, area, and/or volume
Overview of Mathematics 6
DRAFT May 2014
4
Geometry (G)
In Mathematics 6, we
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sort triangles based on the length of sides (scalene, isosceles, and equilateral) and on the measure
of interior angles (acute, obtuse, and right) and explain our sorting rules
describe triangles according to their side lengths and angle measures
draw specified triangles
show that two given triangles are congruent
sort 2-D shapes as polygons and non-polygons and explain the sorting rule
sort polygons as regular or irregular and explain the sorting rule
identify and describe regular and irregular polygons in the environment
demonstrate congruence (sides to sides; angles to angles) of regular polygons
show that a 2-D shape and its transformation image (flip, slide, or turn) are congruent
model, identify, and describe a combination of transformations (flips, slides, or turns) on 2-D shapes
predict or draw what happens when we combine transformations
analyze a design and describe the original shape and the transformations used to create this design
create a design using transformations
describe why a shape will or will not tessellate (create a tiling pattern with no gaps or overlap)
create and describe tessellations
find examples of tessellations in the real world
plot points on the first quadrant of the Cartesian plane using ordered pairs
match points on the first quadrant of the Cartesian plane with the corresponding ordered pairs
draw shapes/designs on the first quadrant of the Cartesian plane when given ordered pairs
create shapes/designs on the first quadrant of the Cartesian plane and identify the ordered pairs
used to create them
identify the ordered pairs of the vertices (corners) of any 2-D shape placed on the first quadrant of
the Cartesian plane
perform transformations (flips, slides, and turns) on the first quadrant of the Cartesian plane and
identify the ordered pairs of the original shape and its image
describe the change in the position of the vertices of a 2-D shape after a transformation has
occurred
Overview of Mathematics 6
DRAFT May 2014
5
Statistics and Probability (SP)
In Mathematics 6, we
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read and interpret line graphs
create line graphs from a table of values or a set of data
explain the difference between discrete data (data that has finite values and can be counted, such
as the number of pets) and continuous data (data that includes an infinite number of values
between two points, such as plant growth over time)
determine whether a set of data is continuous and can be represented with a line graph or is
discrete and can be represented by a series of points
determine the most appropriate type of graph (pictographs, line plots, bar graphs, double bar
graphs, and line graphs) for displaying a set of data
solve problems by graphing data and interpreting graphs
select an appropriate method for collecting data to answer a question
design and use questionnaires for collecting data and answering questions
identify various ways that data can be collected
explain when it is appropriate to use a database to collect data
gather data using electronic media
make observations about everyday probability situations
identify the possible outcomes for a given probability experiment
predict and determine the theoretical probability of a certain outcome occurring
design and conduct probability experiments and analyze the information that is collected
explain the difference between experimental probability and theoretical probability
compare experimental probability with theoretical probability from a probability experiment
explain that as the number of trials in a probability experiment increases, the experimental
probability approaches theoretical probability for an outcome
Overview of Mathematics 6
DRAFT May 2014
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