Primary Skills and Concepts – Number Sense
Students will read, write, count and model whole numbers 010,000, developing an understanding of place value for ones, tens,
hundreds, thousands and ten thousands
Students will apply multiple representations (e.g., drawings,
manipulatives, base-10 blocks, number lines, expanded form,
symbols) to describe and compare whole numbers and fractions
(e.g., halves, thirds, fourths) in mathematical and real-world
problems
Students will order groups of objects according to quantity
Students will order, compare and understand the relative
magnitude of numbers from 0-10,000, using the symbols <, >, =,
including the use of physical and visual models for smaller numbers
Students will develop beginning fractional concepts (e.g., dividing
an object into equal parts and naming the equal parts [e.g., halves,
thirds, fourths])
Students will expand fraction concepts (e.g., whole to part and part
to whole; one-half is larger than one-fourth) be introduced to and
use decimals to represent money
Grade 4 Skills and Concepts – Number Sense
Students will apply multiple representations (e.g., drawings,
manipulatives, base-10 blocks, number lines, expanded form,
symbols) to represent whole numbers (0 to 1,000,000)
Students will read, write and model whole numbers from 0 to
1,000,000, developing place value for hundred thousands and
millions
Students will order and compare numbers to 1,000,000 and
understand their relative magnitude
Students will investigate and apply multiple representations of
commonly used and equivalent fractions through twelfths (e.g.,
1/2=3/6) and decimals through thousandths with manipulatives
(e.g., drawings, manipulatives, base-10 blocks, number lines,
expanded form, symbols)
Students will explore the use of simple ratios to describe problem
situations
Students will explore the relationship between fractions, decimals
and percents
Students will apply whole numbers, commonly used fractions and
decimals to represent real-world problems
Students will explain how the base 10 number system relates to
place value
Students will develop equivalent relationships between commonly
used fractions, decimals and whole numbers (e.g., 1/2=0.5, 4/2=2,
2=2.0)
Students will graph a whole number, commonly used fraction or
decimal on a number line
Grade 5 Skills and Concepts – Number Sense
Students will read, write, model, order, compare (using relative
magnitude) and apply multiple representations of whole numbers
Students will compare and apply the relative sizes of common and
mixed fractions
Students will investigate multiple representations of equivalent
fractions (e.g., 21  36 , 112  32 ) with manipulatives, drawings and
fractional notation
Students will explore the use of simple ratios to describe problem
situations
Students will explore, investigate, compare, relate and apply
relationships among whole numbers, fractions, decimals and
percents
Students will read, write, identify and compare decimals through
ten-thousandths
Grade 6 Skills and Concepts – Number Sense
Students will continue to develop number sense using fractions,
decimals and percents, including percents greater than 100% and
improper fractions
Students will extend applications of operations ( ,,, ) to include
fractions and decimals
Students will develop place value of large and small numbers,
including decimals
Students will explore positive integral exponents (e.g. squares,
cubes)
Students will compare, order and convert between whole numbers,
fractions, decimals and percents using concrete materials,
drawings or pictures and mathematical symbols (e.g., ,,,,, ,
order on a number line)
Grade 7 Skills and Concepts – Number Sense
Students will extend number sense for percents and integers
Students will extend applications of operations ( ,,, ) to include
integers
Students will develop number sense for π (pi) as one example of
an irrational number

Students will use whole number exponents to represent/express
numbers
Students will compare, order and determine equivalent
relationships among fractions, decimals and percents
Students will provide examples of and use models, diagrams and
symbols (e.g., number lines, 10 by 10 grids, rectangular arrays,
number sentences) to describe and write equivalent forms of
integers, fractions, decimals, percents, square roots and π
Grade 8 Skills and Concepts – Number Sense
Students will continue to develop number sense to include irrational
numbers (e.g., square roots, cube roots, π)
Students will provide examples of, describe and compare irrational
and rational numbers (e.g., magnitude, order on a number line,
scientific notation, very large and very small integers, numbers close
to zero)
Students will describe and provide multiple representations of
numbers (rational, square roots, cube roots
and π) in a variety of equivalent forms using models, diagrams and
symbols based on real-world and/or mathematical situations
High School Skills and Concepts – Number Sense
Students will compare real numbers using order relations
Students will locate the position of a real number on the number
line, find its distance from the origin (absolute value/magnitude) and
find the distance between two numbers on the number line (the
absolute value of their difference)
Students will determine the relative position on the number line of
real numbers, including very large and very small numbers, and the
relative magnitude of numbers expressed in fractional form, in
decimal form, as roots or in scientific notation
Students will explore vectors and matrices as systems that have
some of the properties of the real number system
Students will compare and contrast number systems, including
complex numbers as solutions to quadratic equations that do not
have real solutions