Connecticut State Department of Education
2005 Connecticut Mathematics Curriculum Framework
Grades PreK through 12 Matrix
Approved September 2005
CSDE Page 1 Approved September 2005
Fra mew ork by Content Standard – Grades PreK -12
Algebraic Reasoning: Patterns And Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.
How do patterns and functions help us describe data and physical phenomena and solve a variety of problems?
Students Grade 9-12
Pre-K Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9-12 Core
should… Extended
1.1 a. Sort and a. Sort and a. Examine a. Describe and a. Create and a. Classify a. Identify trends a. Identify a. Analyze a. Analyze a. Describe a. Model real-
Understand classify classify objects attributes of extend patterns. describe patterns patterns as and make relationships and physical physical relationships and world situations
and describe objects by an using attributes. objects and using different repeating or predictions based make phenomena and phenomena, make and make
patterns and attribute. describe the b. Analyze objects and growing. upon patterns and generalizations patterns to functions and generalizations generalizations
functional b. Identify a relationships. change in terms symbols. data displayed in through the use identify patterns to about patterns about
relationships. b. Describe pattern and of quantity and different formats. of patterns. relationships and identify and functions. mathematical
and extend describe the rule quality using make relationships and relationships
patterns using using the physical patterns. generalizations. make using a variety of
the attributes attributes or generalizations. patterns and
of various position of functions.
objects. objects in a
sequence.
1.2 a. Represent the a. Represent real- a. Identify a. Demonstrate a. Recognize that a. Represent and a. Describe the a. Describe the a. Represent and a. Relate the
Represent result of life situations mathematical the equivalence a change in one analyze effects of effects of analyze linear behavior of
and analyze counting, using number relationships as of both sides of variable may mathematical characteristics of characteristics of and nonlinear functions and
quantitative combining and sentences. equations. an equation. relate to a change relationships with mathematical linear functions and relations to
relationships separating sets of in another the help of tables, relationships on relationships on relations specific
in a variety objects using variable. graphs, equations the way the the way the symbolically and parameters and
of ways. number and inequalities. relationships are relationships are with tables and determine
sentences. represented. represented graphs. functions to
verbally and in model real-world
tables, graphs and situations.
equations.
1.3 a. Identify a. Represent a. Represent a. Represent a. Describe the a. Solve real- a. Solve problems a. Solve problems a. Manipulate a. Use and
Use quantities as quantities that quantities that possible values general world problems using a variety of using various equations, extend algebraic
operations, equivalent or have the same have the same using symbols. relationship using algebraic algebraic algebraic inequalities and concepts to
properties nonequivalent. value with an value with an between two sets methods. methods. methods and functions to solve include real and
and equal sign. equal sign. of data using an properties. problems. complex
algebraic equation or b. Demonstrate b. Maintain numbers, vectors
symbols to inequality. how to maintain equivalence in and matrices.
determine equivalence in equations to
equivalence equations. determine
and solve solutions.
problems.
CSDE Page 2 Approved September 2005
Fra mew ork by Content Standard – Grades PreK -12
Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.
How are quantitative relationships represented by numbers?
Students Grade 9-12 Grade 9-12
should… Pre-K Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8
Core Extended
2.1 a. Use a. Use a. Represent and a. Represent three-digit a. Represent numbers a. Extend whole a. Extend whole a. Relate whole a. Represent real- a. Compare and a. Extend the a. Extend
Understand numbers to numbers to order two-digit numbers as groups of in expanded and number place value number place value numbers, fractions, world situations order integers, understanding the
that a count, count, order, numbers as hundreds, tens and regrouped forms in patterns, models and patterns, models decimals and and solutions to powers and of number to understand-
order and compare, groups of tens ones in the base ten the base ten place notations to include and notations to integers to number problems using the roots using include ing of
variety of
compare. label, locate and ones in the place value system. value system. decimals, which are include decimals, lines, scales, the appropriate number lines integers, number to
numerical and measure. base ten place b. Represent fractions fractions that have which are fractions coordinate plane symbolic form and grids. rational include the
representa- b. Share value system. by sharing portions of b. Recognize that a denominators that that have and problem- (fractions, numbers and set of
tions can be equal parts b. Share equal b. Identify and equal size as parts of a fraction with the same are multiples of ten. denominators that solving situations. decimals or b. Extend the real numbers. complex
used to of a whole parts of an compare equal whole or parts of a set. numerator and b. Use models and are multiples of ten. b. Express place percents). understanding of numbers.
describe object. object. parts of a whole. c. Recognize that the denominator pictures to reveal b. Classify numbers value patterns b. Understand the scientific b. Interpret
quantitative c. Partition a set denominator of a represents the whole patterns about by their factors. using exponents to use of scientific notation to very and represent
relation- c. Share a set of objects into fraction tells how many object or an entire set. equivalent fractions c. Express numbers write powers of notation as related small numbers. large sets of
ships. of objects that smaller groups equal parts an object or and ratios. as equivalent ten. to powers of ten as numbers with
is divided into with equal a set has been divided c. Use fractions to c. Use fractions to fractions, decimals c. Interpret and an efficient method the aid of
groups with amounts. into, and the numerator measure and to represent a ratio or a or percents. connect fraction for writing and technologies.
equal d. Describe indicates how many of represent points on a division problem. d. Represent ratios notation to comparing very
amounts. relationships the parts are being ruler or number line. d. Make and proportions and division. large numbers.
between considered. comparisons and solve problems d. Compare c. Use percents to
quantities using d. Describe describe quantitative using models and quantities and make comparisons
ratios. relationships between relationships using pictures. solve problems between groups of
quantities using ratios. ratios. using ratios, rates unequal size.
and percents.
2.2 c. Count, a. Count, a. Count by a. Develop fact a. Use strategies that a. Use place value a. Estimate and a. Solve problems a. Extend the a. Solve a. Develop a.
Use adding one adding one groups, add one families of basic facts involve place value concepts and compute using using a variety of operations of problems strategies for Investigate
numbers more to the more to the more to the using the inverse patterns and algebraic commutative and models and computational addition, involving computation mathemat-
previous previous grouping and relationship of addition properties to estimate, associative pictures. strategies, subtraction, fractions, and ical
and their
amount. number and compare values and subtraction. add and subtract. properties to including the use multiplication and decimals, ratios estimation properties
properties group and of groups. b. Approximate estimate and of calculators. division to and percents. using and
to compute count by ones b. Explore the solutions to problems compute. negative numbers. b. Make properties of operations
flexibly and and tens. b. Add by relationship of involving computation b. Use number b. Describe when generalizations number related to
fluently, counting and multiplication and through the use of patterns, basic facts, products or about operations systems to objects that
and to combining and division through a efficient methods. rectangular arrays, quotients with with very large solve are not
reasonably subtract by variety of methods. c. Solve multiplication place value models fractions and and very small problems. numbers.
estimate separating, and division problems and the distributive decimals can yield numbers.
measures comparing or c. Identify and use using rectangular property to multiply a larger or smaller c. Connect the b. Solve
counting on. equivalent arrays, number and divide. result than either exponential proportional
and
representations of patterns, skip counting c. Add and subtract factor. growth and reasoning
quantities. numbers to estimate and repeated addends. fractions and mixed decay models to problems.
and compute. d. Compare fractions, numbers with like repeated
identify equivalent and unlike multiplication
fractions, add and denominators using by the same
subtract fractions with models, pictures and factor.
like and unlike number sentences.
denominators using
models and pictures.
CSDE Page 3 Approved September 2005
Fra mew ork by Content Standard – Grades PreK -12
Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.
How do geometric relationships and measurements help us to solve problems and make sense of our world?
Students Grade 9-12
Pre-K Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9-12 Core
should… Extended
3.1 a. Identify and a. Identify and a. Classify a. Identify a. Classify and a. Describe a. Use geometric a. Classify a. Describe and a. Explore the a. Investigate a. Use methods
Use properties sort shapes and sort shapes and shapes and solids shapes as the compare geometric relationships to polygons classify polygons relationships relationships of deductive and
and solids by solids by by common same when there polygons and properties of describe polygons according to according to among sides, among plane and inductive
characteristics of physical physical characteristics. are changes in solids using polygons and and solids. their properties. their angles, solid geometric reasoning to
two- and three- characteristics. characteristics. position. various solids. transformational perimeters, figures using make, test and
dimensional attributes. b. Recognize that b. Examine the properties. areas, surface geometric validate
shapes and changes in the relationships areas and models, geometric
geometric perimeter of a between the volumes of constructions conjectures.
theorems to polygon may measures of area congruent and and tools.
describe affect its area, of 2-dimensional similar polygons b. Develop and b. Explore non-
relationships, and changes in objects and and solids. evaluate Euclidean
communicate area may affect volumes of 3- mathematical geometries.
ideas and solve the perimeter. dimensional arguments using
problems. objects. reasoning and
proof.
3.2 a. Use positional a. Use positional a. Describe, a. Recognize and a. Represent a. Find possible a. Identify, a. Construct a. Understand a. Model a. Verify a. Use a variety
Use spatial language to language to name and use geometric location on pathways describe and similar polygons how 3- geometric geometric of coordinate
reasoning, describe describe interpret relationships to simple maps. between two build nets for on coordinate dimensional relationships in a relationships systems and
location and location, location, direction and solve problems. points using maps solid figures and grids. objects can be variety of ways. using algebra, transformations
geometric direction and direction and position of that are based on objects. represented in 2 coordinate to solve
relationships to position of position of objects. the rectangular dimensions using geometry, and geometric
solve problems. objects. objects. coordinate b. Determine base plans transformations. problems in 2
system. geometric (footprints), and 3 dimensions
relationships orthogonal using appropriate
through spatial views, nets and tools and
visualization. isometric technologies.
drawings.
3.3 a. Sequence a. Use calendars a. Plan and a. Estimate and a. Plan events a. Recognize that a. Solve problems a. Solve a. Solve a. Use a variety a. Solve a variety a. Approximate
Develop and events during a and clocks to sequence events. measure the and make patterns exist in the measure of problems geometric and of concrete of problems measurements
apply units, limited time measure and length of time to schedules. between time and in involving measurement methods, involving 1-, 2- that cannot be
systems, period. record time. b. Estimate complete measurements of converting units measurement problems including and 3- directly
formulas and length, area, activities and b. Determine and length, perimeter of length in the through the use through the use displacement, to dimensional determined with
appropriate tools b. Use b. Use volume, weight tasks. use different and area of customary and of a variety of of a variety of find volumes of measurements some degree of
to estimate and nonstandard nonstandard and temperature tools and units squares and metric systems tools, techniques tools, techniques solids. using geometric precision using
measure. units to estimate units to estimate using b. Measure appropriate for rectangles. using specific and strategies. and strategies. relationships and appropriate tools,
measures of measures of nonstandard through direct specific ratios. b. Use specific b. Solve trigonometric techniques and
length, area and length, area, units. comparison and measurement b. Make precise ratios to convert problems ratios. strategies.
capacity. temperature, through tasks. measurements between involving
weight and c. Use standard repetition of and use measures of measurement
capacity. units of measure units. benchmarks to length, area, through the use
to communicate estimate volume, mass of appropriate
measurement in measures. and capacity in tools, techniques
a universal the customary and strategies.
manner. and metric
systems.
CSDE Page 4 Approved September 2005
Fra mew ork by Content Standard – Grades PreK -12
Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.
How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions?
Students Grade 9-12 Grade 9-12
should… Pre-K Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8
Core Extended
4.1 a. Make a. Visualize a. Collect, a. Construct a. Design a. Organize and a. Differentiate a. Display and a. Select the a. Construct a. Create the a. Model real
Collect, comparisons from information and organize, record graphs from surveys for the analyze between compare sets of appropriate appropriate appropriate data graphically
organize information make and describe data, then make collection of categorical and numerical and data using visual representations visual or using
and display displayed in real comparisons data. comparisons and data and justify numerical data. categorical data various representation of of data based on graphical appropriate
graphs. about draw conclusions and their systematic or data based on the size and kind representation of tools,
data using information conclusions. drawn from the appropriate graphical the kind of data of data set and real data. technologies and
appropriate displayed in real data. representations. representations. collected and the the purpose for strategies.
statistical and picture purpose for their their use.
and graphs. use.
graphical
methods.
4.2 a. Extend a. Organize data a. Determine a. Analyze data a. Describe what a. Examine a. Describe the a. Understand a. Make and a. Analyze real- a. Describe and
Analyze different types in tables and patterns and to identify a is “average” different data shape of data that measures of evaluate world problems analyze sets of
data sets to of patterns and graphs and make make typical element about the collection sets using the central tendency statistical claims using statistical data using
make comparisons of predictions from or event. characteristics in methods and measures of and spread can and justify techniques. statistical
form
predictions. the data. data displayed in a data set. their effects. spread and be used to conclusions with models.
hypotheses tables and central describe data evidence.
and make graphs. tendency. sets and justify
predictions. conclusions.
4.3 a. Determine when a. Observe the a. Determine the a. Analyze data a. Use samples a. Determine a. Relate the a. Understand a. Compare and a. Determine a. Understand a. Solve
Understand events are likely to frequency of likelihood of gathered from and simulations fair situations likelihood of an that probabilities determine possible and apply the problems using
and apply happen again. real-world certain events experiments and to determine and good event to a are more reliable experimental outcomes using principles of the methods of
basic events and through simple identify the probability, and choices based numerical value. to use as and theoretical a variety of probability in a discrete
identify the experiments and likelihood of to make and test upon the predictors when probabilities. counting variety of mathematics.
concepts of likelihood of observations of future events. predictions. likelihood of an there is a large techniques. situations.
probability. future events. games. occurrence. number of trials. b. Make
statistical
b. Express inferences
probability through the use
using various of probability.
numerical
representations.
CSDE Page 5 Approved September 2005