Mathematics Grade Level
Considerations for Grades 6-8
Considerations for Grades 6–8
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Vocabulary
Style Guide
Representation of numbers
Contexts
Item Difficulty
Assessment Targets
Vocabulary
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Items must be written so students can
easily understand the item or task.
Use vocabulary at or below grade-level.
Style
Overview of Mathematics Style Conventions
Specific to Middle School Grades
• Use variables to indicate missing
values in equations
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Use the product dot rather
than the multiplication symbol
except in scientific notation
2x + 4 = 16
2  12
a  2a
1.2 × 104 = 12,000
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In grade 8, use the terms
translate, reflect, and rotate
Use graphics or tables to present
information in order to reduce
the amount of reading
Translate
Reflect
Rotate
Words vs. Numerals
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Use numerals for
numbers that are used
to solve a problem
Sarah sold 9 adult tickets
for a total of $45.
What was the price of
each adult ticket?
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Use numerals for
numbers that appear
in equations
19 + x = 35
Words vs. Numerals
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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., 3 A.M., 12:30 P.M.)
– Ordered pairs and coordinates (e.g., (3,4))
Commas in Numbers
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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)
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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
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Appropriate contexts
– Popular sports
– Bicycle riding
– Making nominal
purchases
– Making and reading
maps and floor plans
– School related activities
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Inappropriate contexts
– Expensive or
regional sports
– Purchases that are
unusual for students
Item Difficulty
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Items should include a range of difficulty
Anticipated difficulty for sample items
Claim 1
Concepts and Procedures:
Students can explain and apply mathematical concepts
and interpret and carry out mathematical procedures
with precision and fluency.
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Selected Response
Constructed Response
Technology-Enhanced
Extended Response and Performance Tasks
Assessment Targets Measured in Grades 6–8
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Ratios and Proportional Relationships
The Number System
Expressions and Equations
Geometry
Statistics and Probability
Functions
Ratios and Proportional Relationships
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Grade 6: Ratios introduced
Grade 7: Extended to proportional
relationships
The Number System
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Grades 6 & 7: Rational numbers
Grade 8: Irrational numbers
Expressions and Equations
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Grade 6: Introduce algebraic expressions
Grade 7: Create expressions and equations
and use to solve problems
Grade 8: Analyze and solve more complex
problems
Geometry
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Grade 6: Area, surface area, and volume
Grade 7: Drawing and constructing figures
Grade 8: Congruence, similarity, and the
Pythagorean Theorem
Statistics and Probability
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Grade 6: Statistic and probability introduced
Grade 7: Sampling, inferences, and
probability
Grade 8: Associations in bivariate data
Functions
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Grade 8: Defining, evaluating, comparing,
and modeling functions
Claim 2 – Problem Solving
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Selected Response, Constructed Response,
Extended Response, and TechnologyEnhanced 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
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Constructed Response, Extended Response,
and Technology-Enhanced items and tasks
that focus on mathematical reasoning
Relevant verbs include:
– understand, explain, justify, prove, derive, assess,
illustrate, and analyze
Claim 4 – Modeling and Data Analysis
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Performance Tasks and collections of
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
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Assessment Targets for Claims
2, 3, and 4 are not divided into a
grade-by-grade description
A general set of assessment targets
applicable across grade levels
Middle School Mathematics
Grade Level Considerations
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Vocabulary, style, context, and item difficulty
Claims from the Smarter Balanced
Mathematics Content Specifications