Mathematics Grade Level
Considerations for Grades 3–5
Considerations for Grades 3–5
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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
for Grades 3–5
Words vs. Numerals
John had 9 red balloons
and 14 white balloons.
How many balloons
does he have in all?
19 + ____ = 35
10, 16, 22, 28, ?
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., 11 A.M., 12:30 P.M.)
– Ordered pairs and coordinates (e.g., (3,4))
Words vs. Numerals
Example 1:
Patty has 10 pennies and 3 nickels.
How much money does Patty have?
A.
13¢
B.
25¢
C.
40¢
D.
53¢
Example 2:
The table below shows the number
of cans two students collected.
Student
Number of Cans
Sara
87
Lorenzo
59
How many more cans did Sara
collect than Lorenzo? Show your
work or explain how you know.
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)
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)
Representing Missing Values
6 + ☐ = 11
3, 5, 7, 9, ?
5×7=?
Look at this equation:
3+6=?
Contexts
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Appropriate contexts:
– Sports familiar played
during physical
education (basketball,
soccer)
– School activities (class
trips, library, music,
children’s games)
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Inappropriate contexts:
– Skiing
– Backyard
swimming pools
– Earning money at a
part-time job or saving
to buy a car
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 3–5
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Operations and Algebraic Thinking
Number and Operations – Base 10
Number and Operations – Fractions
Measurement and Data
Geometry
Operations and Algebraic Thinking
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Grade 3: Understanding meaning of
multiplication and division
Grade 4: Applying understanding
Grade 5: Writing and interpreting
numerical expressions
Number and Operations – Base 10
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Grade 3: Using place value and
properties of operations to add and
subtract whole numbers
Grade 4: Multiplying and dividing
whole numbers
Grade 5: Solving problems with
decimals using the four operations
Number and Operations – Fractions
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Grade 3: Understanding of fractions as
numbers
Grade 4: Understand fraction equivalence
and operations with fractions
Grade 5: Solving problems involving the
four operations
Measurement and Data
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Grade 3: Measuring time, liquid volumes,
and masses of objects and solving simple
one-step word problems
Grade 4: Solving problems involving
measurement, representing and interpreting
data, and understanding angles
Grade 5: Understanding volume and
solving problems that involve estimating
and measuring volume
Geometry
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Grade 3: Understanding that shapes in
different categories may share attributes
and recognizing quadrilaterals
Grade 4: Classifying shapes based on properties
Grade 5: Graphing points on the coordinate
plane and understanding that attributes
belonging to a category of two-dimensional
shapes also belong to all subcategories of
that category
Claim 2 – Problem Solving
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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
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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
Elementary School Mathematics
Grade Level Considerations
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Vocabulary, style, context, and item difficulty
Claims from the Smarter Balanced
Mathematics Content Specifications