|
6.1
Number and Operations
|
-
6.1.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
-
6.1.1.A
Read, write and compare numbers
-
6.1.1.A.1
compare and order integers, positive rationals and percents, including finding their approximate location on a number line
-
6.1.1.B
Represent and use rational numbers
-
6.1.1.B.1
recognize and generate equivalent forms of fractions, decimals and percents
-
6.1.1.C
Compose and decompose numbers
-
6.1.1.C.1
recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including expanded notation
-
6.1.1.D
Classify and describe numeric relationships
-
6.1.1.D.1
use factors and multiples to describe relationships between and among numbers, including whole number common factors and multiples
-
6.1.2
Understand meanings of operations and how they relate to one another
-
6.1.2.B
Describe effects of operations
-
6.1.2.B.1
describe the effects of addition and subtraction on fractions and decimals
-
6.1.3
Compute fluently and make reasonable estimates
-
6.1.3.C
Compute problems
-
6.1.3.C.1
add and subtract positive rational numbers
-
6.1.3.D
Estimate and justify solutions
-
6.1.3.D.1
estimate and justify the results of addition and subtraction of positive rational numbers
-
6.1.3.E
Use proportional reasoning
-
6.1.3.E.1
solve problems using equivalent ratios
|
|
6.2
Algebraic Relationships
|
-
6.2.1
Understand patterns, relations, and functions
-
6.2.1.B
Create and analyze patterns
-
6.2.1.B.1
represent and describe patterns with tables, graphs, pictures, symbolic rules or words
-
6.2.1.C
Classify objects and representations
-
6.2.1.C.1
compare various forms of representations to identify a pattern
-
6.2.1.D
Identify and compare functions
-
6.2.1.D.1
identify functions as linear or nonlinear from a table or graph
-
6.2.2
Represent and analyze mathematical situations and structures using algebraic symbols
-
6.2.2.A
Represent mathematical situations
-
6.2.2.A.1
use variables to represent unknown quantities in expressions
-
6.2.2.B
Describe and use mathematical manipulation
-
6.2.2.B.1
recognize equivalent forms for simple algebraic expressions (associative, distributive properties)
-
6.2.3
Use mathematical models to represent and understand quantitative relationships
-
6.2.3.A
Use mathematical models
-
6.2.3.A.1
model and solve problems, using multiple representations such as graphs, tables, expressions and equations
-
6.2.4
Analyze change in various contexts
-
6.2.4.A
Analyze change
-
6.2.4.A.1
compare situations with constant or varying rates of change
|
|
6.3
Geometric and Spatial Relationships
|
-
6.3.1
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
-
6.3.1.A
Describe and use geometric relationships
-
6.3.1.A.1
identify the properties of 1- 2- and 3-dimensional shapes using the appropriate geometric vocabulary
-
6.3.1.B
Apply geometric relationships
-
6.3.1.B.1
describe relationships between the corresponding angles and the length of corresponding sides of similar triangles (whole number scale factors)
-
6.3.2
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
-
6.3.2.A
Use coordinate systems
-
6.3.2.A.1
use coordinate geometry to construct geometric shapes
-
6.3.3
Apply transformations and use symmetry to analyze mathematical situations
-
6.3.3.A
Use transformations on objects
-
6.3.3.A.1
describe the transformation from a given pre-image to its image using the terms reflection/flips, rotation/turn and translation/slide
-
6.3.3.C
Use symmetry
-
6.3.3.C.1
create polygons and designs with rotational symmetry
-
6.3.4
Use visualization, spatial reasoning and geometric modeling to solve problems
-
6.3.4.A
Recognize and draw three-dimensional representations
-
6.3.4.A.1
use spatial visualization to identify isometric representations of mat plans
-
6.3.4.B
Draw and use visual models
-
6.3.4.B.1
draw or use visual models to represent and solve problems
|
|
6.4
Measurement
|
-
6.4.1
Understand measurable attributes of objects and the units, systems and processes of measurement
-
6.4.1.A
Determine unit of measurement
-
6.4.1.A.1
identify and justify an angle as acute, obtuse, straight or right
-
6.4.1.C
Tell and use units of time
-
6.4.1.C.1
solve problems involving elapsed time (hours and minutes)
-
6.4.2
Apply appropriate techniques, tools and formulas to determine measurements
-
6.4.2.A
Use standard or non-standard measurement
-
6.4.2.A.1
estimate a measurement using either standard or nonstandard unit of measurement
-
6.4.2.B
Use angle measurement
-
6.4.2.B.1
select and use benchmarks to estimate measurements of 0-, 45-, 90-, 180-, 360- degree angles
-
6.4.2.C
Apply geometric measurements
-
6.4.2.C.1
describe how to solve problems involving the area or perimeter of polygons
-
6.4.2.E
Use relationships within a measurement system
-
6.4.2.E.1
convert from one unit to another within a system of measurement (mass and weight)
|
|
6.5
Data and Probability
|
-
6.5.1
Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them
-
6.5.1.A
Formulate questions
-
6.5.1.A.1
formulate questions, design studies and collect data about a characteristic
-
6.5.1.C
Represent and interpret data
-
6.5.1.C.1
interpret circle graphs; create and interpret stem-and-leaf plots
-
6.5.2
Select and use appropriate statistical methods to analyze data
-
6.5.2.A
Describe and analyze data
-
6.5.2.A.1
find the range and measures of center, including median, mode and mean
-
6.5.2.B
Compare data representations
-
6.5.2.B.1
compare different representations of the same data and evaluate how well each representation shows important aspects of the data
-
6.5.3
Develop and evaluate inferences and predictions that are based on data
-
6.5.3.A
Develop and evaluate inferences
-
6.5.3.A.1
use observations about differences between 2 samples to make conjectures about the populations from which the samples were taken
-
6.5.4
Understand and apply basic concepts of probability
-
6.5.4.A
Apply basic concepts of probability
-
6.5.4.A.1
use a model (diagrams, list, sample space, or area model) to illustrate the possible outcomes of an event
|
|
