Overview of 5th - 8th grade Common Core State Standards. Changes from the GLCEs are shown in red italics.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
5. Use appropriate tools strategically.
2. Reason abstractly and quantitatively.
6. Attend to precision.
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure
4. Model with mathematics.
8. Look for and express regularity in repeated reasoning.
5TH GRADE
6TH GRADE
7TH GRADE
8TH GRADE
Number and Operations in Base
Ten
Understand the place value system.
The Number System - Operations
with integers and decimals
Fluently divide multi-digit numbers.
NEW from 5th grade.
Fluently add, subtract, multiply, and
divide multi-digit decimals.
The Number System
Add, subtract, multiply, and divide
signed numbers and interpret in realworld contexts.
NEW: Operations with integers is now
introduced in 7th grade. Students learn
the meaning of integers in 6th grade,
but not how to operate with them.
> Square root and cube root have
moved to 8th grade.
The Number System
Know that there are numbers that are
not rational, and approximate them by
rational numbers.
Work with radicals and integer
exponents, including scientific
notation.
NEW: rounding of decimals.
Perform operations with multi-digit
whole numbers and with decimals to
hundredths.
> Whole number exponential notation
has moved to 6th grade.
Find common factors and multiples.
Write and evaluate numerical
expressions involving whole-number
exponents. NEW from 5th grade.
Understand the meaning of negative
numbers and graph rational numbers
on number lines and coordinate grids.
> Operations with integers begins in
7th grade.
> Integer exponents and scientific
notation has moved to 8th grade.
Number and Operations—
Operations with Fractions
Add and subtract fractions.
Multiply a fraction by a fraction;
divide a whole number by a fraction
or a fraction by a whole number.
> Percents are no longer in 5th grade
The Number System— Operations
with Fractions
Divide fractions by fractions to solve
word problems, using visual fraction
models and equations to represent the
problem.
The Number System—Fractions
Add, subtract, multiply, and divide
rational numbers to solve problems.
Convert a fraction to a decimal using
long division. NEW from 8th grade.
(see 6.RP.3c)
> Prime factorization is no longer in
5th grade.
> Ratios are no longer in 5th grade.
Ratios and Proportional
Relationships
Understand and solve problems with
ratios and rates.
Ratios and Proportional
Relationships
Compute unit rates.
Use proportional relationships to solve
real-world and mathematical problems
including multistep ratio and percent
problems such as simple interest, tax,
markups and markdowns, gratuities
and commissions, fees, percent
increase and decrease, percent error.
(see Functions below)
> Working with derived quantities
(e.g. density) has moved to high
school geometry.
Operations and Algebraic Thinking
Write and interpret numerical
expressions. NEW from 6th grade
Expressions and Equations
Write, read, and evaluate expressions
with whole number exponents.
Write, read, and evaluate expressions
with variables; identify and generate
equivalent expressions.
Solve one-variable single-step
equations with positive coefficients.
Represent solutions of inequalities of
the form x > c or x < c on number
lines and relate to real-world
problems. NEW: previously
inequalities started in 8th grade.
Analyze patterns and relationships.
NEW, including graphing ordered
pairs, from 6th grade
Expressions and Equations
Use properties of operations to add,
subtract, factor and expand
expressions.
Expressions and Equations
Analyze and solve linear equations
involving rational number
coefficients.
Solve multi-step real-life and
mathematical problems using
numerical and algebraic expressions,
equations and inequalities with
positive and negative rational
numbers. NEW: Inequalities, moved
from 8th grade.
Analyze and solve pairs of
simultaneous linear equations.
> Factoring quadratic expressions
and solving quadratic equations is
moved to Algebra I.
Assess the reasonableness of answers
using mental computation and
estimation strategies.
Express relationships between
dependent and independent variables
in tables, graphs and equations.
Represent proportional relationships
with equations and graphs.
Identify the constant of proportionality
(unit rate) in tables, graphs, equations,
2
Functions
Understand the connections between
proportional relationships, lines, and
linear equations; understand slope and
diagrams, and verbal descriptions of
proportional relationships.
use the equations y = mx and y = mx +
b.
> The term “slope” is not introduced
until 8th grade, although the concept is
presented here. Interpreting the
intercepts of graphs of linear
functions has also moved out of 7th
grade.
Use linear functions to model
relationships between quantities.
Compare properties of linear functions
represented algebraically, graphically,
numerically in tables, or by verbal
descriptions
> Inversely proportional relationships
are not explicitly contained in the
CCSS.
Define, evaluate, and compare
functions. (Function notation is not
required in 8th grade.)
> Quadratic expressions, equations
and functions are not addressed until
high school. Exponential functions are
not addressed formally until high
school.
Measurement …
Convert like measurement units within
a given measurement system.
Geometric measurement: understand
concepts of volume and relate volume
to multiplication and to addition.
… and Data
Represent and interpret data using line
plots.
Statistics and Probability
Develop understanding of statistical
variability.
Statistics and Probability
Use random sampling to draw
inferences about a population.
> Mean/mode are no longer in 5th
grade (see 6.SP.5c)
Display, summarize and describe data
sets.
Draw informal comparative inferences
about two populations.
th
th
NEW from 4 grade: median; from 5
grade: mean; from 7th grade:
interquartile range.
> Probability has moved to 7th grade.
Investigate chance processes and
develop, use, and evaluate probability
models. NEW from 6th and 8th grades.
> Represent and interpret data using
graphs has moved to 6th grade.
> Scatter plots and line of best fit has
moved to 8th grade.
3
Statistics and Probability
Investigate patterns of association in
bivariate data. NEW from 7th grade
and Algebra I
> Probability is no longer addressed
in 8th grade – see 7.SP.6-8
> Measures of central tendency is now
in 6th grade; bias in presentation of
data is in high school.
Geometry
Graph points on the coordinate plane
to solve real-world and mathematical
problems. NEW from 6th grade
Classify two-dimensional figures into
categories based on their properties.
> Area of rectangles, triangles and
parallelograms is no longer in 5th
grade (see 6.G.1)
Geometry
Solve real-world and mathematical
problems involving area of triangles,
special quadrilaterals and other
polygons (NEW from 5th grade),
surface area, and volume.
> Transformations and congruence
has moved to 8th grade.
> Problems involving angle measure
has moved to 7th grade.
> Informal paper-folding
constructions has moved to high
school geometry.
Geometry
Solve real-life and mathematical
problems involving angle measure,
area, surface area (not cones or
spheres), and volume. (Problems
involving angle measure is new from
6th grade.)
Geometry
Understand and solve problems
involving congruence and similarity
using physical models, transparencies,
or geometry software. This is the first
time that transformations are
addressed.
Know the formulas for the area and
circumference of a circle and use them
to solve problems. NEW from 8th gr.
Draw, construct and describe
geometrical figures and describe the
relationships between them.
Understand and apply the Pythagorean
Theorem.
> Formal compass and straight-edge
constructions has moved to high
school geometry.
4
Solve real-world and mathematical
problems involving volume of
cylinders, cones, pyramids and
spheres. Not surface areas of cones or
spheres. Circles moved to 7th grade.
> Sketching 2-D views of solids is no
longer in 8th grade.