### the PowerPoint Presentation

```Mathematics Grade Level
Considerations for High School
Considerations for High School
•
•
•
•
•
•
Vocabulary
Style Guide
Representation of numbers
Contexts
Item Difficulty
Assessment Targets
Vocabulary
•
•
Items must be written so students can easily
Use vocabulary at or below grade-level.
Style
Words vs. Numerals
•
Use numerals for
numbers that are used
to solve a problem
for a total of \$45.
What was the price of
•
Use numerals for
numbers that appear
in equations
19 + x = 35
Words vs. Numerals
•
•
•
Use words for a number that is the first word in a sentence
Use words for numbers zero through nine
Use numerals for:
– Numbers 10 and above
– Numbers that precede abbreviated units of measure (e.g., 10 cm, 8 sq. ft.)
– Numbers that precede or follow symbols such as the percent sign or
dollar sign (e.g., 5%, \$9.32)
– Dates and years (e.g., July 4)
– Time of day that appears before A.M. and P.M. (e.g., 11 A.M., 12:30 P.M.)
– Ordered pairs and coordinates (e.g., (3,4))
Commas in Numbers
•
•
Use commas in numbers:
– With five or more digits (e.g., 90,000)
– With four digits if the number appears with numbers
of five or more digits (e.g., 1,000 + 5,000 + 10,000)
– Written as words
(e.g., seventy-three thousand, one hundred)
Do not use commas in:
– Numbers with four digits if all numbers with which it appears
contain four or less digits (e.g., 50 + 200 + 1000)
– compound measures (e.g., 5 feet 9 inches tall)
Contexts
•
Appropriate contexts:
– Sports familiar played
during physical
soccer)
– School activities (class
trips, library, music,
children’s games)
fruit, or drinks
•
Inappropriate contexts:
– Skiing
– Backyard
swimming pools
– Paying a mortgage or
using retirement funds
Item Difficulty
•
•
Items should include a range of difficulty
Anticipated difficulty for sample items
High School Standards
•
•
Know and be able to do to be college
high school
High School Conceptual Categories
•
•
•
•
•
•
Number and Quantity
Algebra
Functions
Modeling
Geometry
Statistics and Probability
Number and Quantity
•
•
Kindergarten through Middle School:
– Extend understanding of numbers
High School:
– Extend understanding of quantity
– Model wider variety of units
Algebra
•
Middle School
– Algebraic expressions, equations, and inequalities
•
High School:
– Solve equations and manipulate formulas of
increasing complexity
Functions
•
– Define, evaluate and compare functions
– Use functions to model relationships
•
High School:
– Function notation
– Concepts of domain and range
– Model real-world situations
Modeling
•
Modeling: Choosing and using appropriate
mathematics and statistics to:
– Analyze empirical situations
– Understand situations
– Improve decisions
Geometry
•
High School:
– Euclidean Geometry
– Increasingly precise definitions
– Developing formal proofs
– Congruence, similarity, and symmetry
– Geometry of right triangles and circles
Statistics and Probability
•
•
Study of how to use data to make decisions
and predictions
High School:
– Gather, display, and examine data to
inform decisions
– Randomization
High School Common Core State Standards
•
for advance courses such as Calculus
and Statistics
Appendix A
•
Organize standards into model pathways to
Claim 1
Concepts and Procedures:
Students can explain and apply mathematical concepts
and interpret and carry out mathematical procedures
with precision and fluency.
•
•
•
•
Selected Response
Constructed Response
Technology-Enhanced
Number and Quantity
Assessment Targets
A. Extend the properties of exponents to
rational exponents
B. Use properties of rational and irrational
numbers
C. Reason quantitatively and use units to
solve problems
Algebra
Assessment Targets
D. Interpret the structure of expressions
E. Write expressions in equivalent forms to solve problems
F. Perform arithmetic operations on polynomials
G. Create equations that describe numbers or relationships
H. Understand solving equations as a process of reasoning
and explain reasoning
I.
Solve equations and inequalities in one variable
J.
Represent and solve equations and inequalities graphically
Functions
Assessment Targets
K. Understand the concept of a function and
use function notation
L. Interpret functions that arise in applications
in terms of a context
M. Analyze functions using different
representations
N. Build a function that models a relationship
between two quantities
Geometry
Assessment Targets
O. Prove geometric theorems
Statistics and Probability
Assessment Targets
P. Summarize, represent, and interpret data on
a single count or measurement variable
Claim 2 – Problem Solving
•
•
•
Selected Response, Constructed Response,
Extended Response, and Technology-Enhanced
items that focus on problem solving
Items and tasks require students to construct
their own pathway to the solution
Relevant verbs include:
– understand, solve, apply, describe, illustrate,
interpret, and analyze
Claim 3 – Communicating Reasoning
•
•
Constructed Response, Extended Response,
that focus on mathematical reasoning
Relevant verbs include:
– understand, explain, justify, prove, derive,
assess, illustrate, and analyze
Claim 4 – Modeling and Data Analysis
•
•
•
•
Extended Response items
Real world problems
Draw upon knowledge and skills articulated
in the progression of standards up to the grade
being assessed
Relevant verbs include:
– model, construct, compare, investigate, build,
interpret, estimate, analyze, summarize, represent,
solve, evaluate, extend, and apply
Claims 2, 3, and 4
•
•
Assessment Targets for Claims
2, 3, and 4 are not divided into a
A general set of assessment targets