Download Reading Math Standards PowerPoint

New Math Standards
2010
Mathematical Practices
1.
2.
3.
4.
5.
6.
7.
8.
Attend to precision
Construct viable arguments and critique the reasoning
of others
Make sense of problems and persevere in solving them
Look for and make use of structure
Look for and express regularity in repeated reasoning
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
K-8 Overview
K
1
2
3
4
Counting
and Cardinality
5
6
7
8
Ratios and
Proportional Relationships
Operations and Algebraic Thinking
The Number
System
Number and Operations in Base Ten
Expressions and
Equations
Number and Operations
Fractions
Functions
Statistics and
Probability
Measurement and Data
Geometry
Overview of the Mathematics Standards
Grades 6-8
6
Ratio and
Proportional
Relationships
The Number
System
Expressions and
Equations
7
• Ratio concepts and use ratios to
solve problems
•Analyze proportional
relationships
• Fractions
•Multi-digit numbers, common
factors, multiples
• The system of rational numbers
•Add, subtract, multiply, and
divide rational numbers
•Know there are numbers
which are not rational, and
approximate them by rational
numbers
• Algebraic expressions
•Equations and inequalities
•Quantitative relationships
between variables
•Generate equivalent
expressions
•Solve problems using
expressions and equations
•Radicals and integer
exponents
•Proportional relationships,
lines, and linear equations
•Linear equations and systems
•Define, evaluate, compare
functions
•Model relationships with
functions
Functions
•Solve problems involving area,
surface area, and volume
•Geometric figures
•Solve problems involving angle
measure, area, surface area, and
volume
•Congruence and similarity
•Pythagorean Theorem
•Volume of cylinders, cones,
and spheres
• Statistical variability
•Summarize and describe
distributions
•Random sampling to draw
inferences about a population
•Comparative inferences about
two populations
•Patterns of association in
bivariate data
Geometry
Statistics and
Probability
8
Grade 6 Overview
Ratios and Proportional Relationships
• Understand ratio concepts and use
ratio reasoning to solve problems.
The Number System
• Apply and extend previous understandings
of multiplication and division to divide
fractions by fractions.
• Compute fluently with multi-digit
numbers and find common factors and
multiples.
• Apply and extend previous understandings
of numbers to the system of rational
numbers.
Expressions and Equations
• Apply and extend previous understandings
of arithmetic to algebraic expressions.
• Reason about and solve one-variable
equations and inequalities.
• Represent and analyze quantitative
relationships between dependent and
independent variables.
Geometry
• Solve real-world and mathematical
problems involving area, surface area,
and volume.
Statistics and Probability
• Develop understanding of statistical
variability.
• Summarize and describe distributions.
Grade 7 Overview
Ratios and Proportional Relationships
• Analyze proportional relationships and
use them to solve real-world and
mathematical problems.
The Number System
• Apply and extend previous
understandings of operations with
fractions to add, subtract, multiply, and
divide rational numbers.
Expressions and Equations
• Use properties of operations to generate
equivalent expressions.
• Solve real-life and mathematical
problems using numerical and
algebraic expressions and equations.
Geometry
• Draw, construct and describe
geometrical figures and describe the
relationships between them.
• Solve real-life and mathematical
problems involving angle measure,
area, surface area, and volume.
Statistics and Probability
• Use random sampling to draw inferences
about a population.
• Draw informal comparative inferences
about two populations.
• Investigate chance processes and
develop, use, and evaluate probability
models.
Grade 8 Overview
The Number System
• Know that there are numbers that are not
rational, and approximate them by
rational numbers.
Expressions and Equations
• Work with radicals and integer
exponents.
• Understand the connections between
proportional relationships, lines, and
linear equations.
• Analyze and solve linear equations and
pairs of simultaneous linear equations.
Functions
• Define, evaluate, and compare functions.
• Use functions to model relationships
between quantities.
Geometry
• Understand congruence and similarity
using physical models, transparencies,
or geometry software.
• Understand and apply the Pythagorean
Theorem.
• Solve real-world and mathematical
problems involving volume of
cylinders, cones and spheres.
Statistics and Probability
• Investigate patterns of association in
bivariate data.
Overview of the Mathematics Standards
High School
 Number and Quantity
 Algebra
 Functions
 Modeling
 Geometry
 Statistics and Probability
Overview of the Mathematics Standards
High School
 Number and Quantity
 The Real Number System
 Quantities
 The Complex Number System
 Vector and Matrix Quantities
 Algebra
 Seeing Structure in Expressions
 Arithmetic with Polynomials and Rational Functions
 Creating Equations
 Reasoning with Equations and Inequalities
Overview of the Mathematics Standards
High School
 Functions
 Interpreting Functions
 Building Functions
 Linear, Quadratic, and Exponential Models
 Trigonometric Functions
 Modeling
Modeling is best interpreted not as a collection of isolated
topics but rather in relation to other standards. Making
mathematical models is a Standard for Mathematical
Practice, and specific modeling standards appear throughout
the high school standards indicated by a star symbol (*).
Overview of the Mathematics Standards
High School
 Statistics and Probability
 Interpreting Categorical and Quantitative Data
 Making Inferences and Justifying Conclusions
 Conditional Probability and the Rules of Probability
 Using Probability to Make Decisions
 Geometry
 Congruence
 Similarity, Right Triangles, and Trigonometry
 Circles
 Expressing Geometric Properties with Equations
 Geometric Measurement and Dimension
 Modeling with Geometry
How to Read Grade Level Standards
p. 42
How to Read Grade Level Standards
Ratios and Proportional Relationships 6.RP
Ratios
1. Understand the concept of a ratio and use ratio language to describe a
ratio relationship between two quantities. For example, “The ratio of
wings to beaks in the bird house at the zoo was 2:1, because for every 2
wings there was 1 beak.” “For every vote candidate A received,
candidate C received nearly three votes.”
2. Understand the concept of a unit rate a/b associated with a ratio a:b
with b ≠ 0, and use rate language in the context of a ratio relationship.
For example, “This recipe has a ratio of 3 cups of flour to 4 cups of
sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75
for 15 hamburgers, which is a rate of $5 per hamburger.”1
1Expectations
for unit rates in this grade are limited to non-complex fractions.
Ratios and Proportional Relationships 6.RP
Ratios
3. Use ratio and rate reasoning to solve real-world and mathematical
problems, e.g., by reasoning about tables of equivalent ratios, tape
diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number
measurements, find missing values in the tables, and plot the pairs of
values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and
constant speed. For example, if it took 7 hours to mow 4 lawns, then at
that rate, how many lawns could be mowed in 35 hours? At what rate
were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity
means 30/100 times the quantity); solve problems involving finding
the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and
transform units appropriately when multiplying or dividing quantities.
How to Read
Grade Level Standards
p. 64
Arithmetic with Polynomials and Rational Expressions A-APR
Perform arithmetic operations on polynomials
1. Understand that polynomials form a system analogous to the integers, namely,
they are closed under the operations of addition, subtraction, and
multiplication; add, subtract, and multiply polynomials.
Understand the relationship between zeros and factors of
polynomials
2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number
a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is
a factor of p(x).
3. Identify zeros of polynomials when suitable factorizations are available, and use
the zeros to construct a rough graph of the function defined by the polynomial.
Arithmetic with Polynomials and Rational Expressions A-APR
Use polynomial identities to solve problems
4. Prove polynomial identities and use them to describe numerical relationships.
For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be
used to generate Pythagorean triples.
5. (+) Know and apply the Binomial Theorem for the expansion of (x+ y)n in
powers of x and y for a positive integer n, where x and y are any numbers,
with coefficients determined for example by Pascal’s Triangle.1
PLUS SIGN—
All standards without a (+) symbol should be in the common mathematics
curriculum for all college and career ready students. Standards without a
(+) symbol may also appear in courses intended for all students.
More info
 Brennon Sapp
(Director of Secondary)
 Jenny Barrett
(Secondary Math Consultant)
 Sara Callahan
(Elementary Curriculum & Instructional Consultant)
http://www.corestandards.org/