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Mathematics Grade Level Considerations for Grades 3–5
Considerations for Grades 3–5
• Vocabulary
• Style Guide
• Representation of numbers
• Contexts
• Item Difficulty
• Assessment Targets
Vocabulary
• 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
• 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
Patty has 10 pennies and 3 nickels. How much money does Patty have?
A. 13¢
B. 25¢
C. 40¢
D. 53¢
Example 1:The table below shows the number of cans two students collected.
How many more cans did Sara collect than Lorenzo? Show your work or explain how you know.
Example 2:
Student Number of Cans
Sara 87
Lorenzo 59
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)
3 + 6 = ?
Representing Missing Values
Look at this equation:
6 + ☐ = 11
3, 5, 7, 9, ?
5 × 7 = ?
Contexts
• Appropriate contexts:– Sports familiar played
during physical education (basketball, soccer)
– School activities (class trips, library, music, children’s games)
• Inappropriate contexts:– Skiing – Backyard
swimming pools– Earning money at a
part-time job or saving to buy a car
Item Difficulty
• Items should include a range of difficulty
• Anticipated difficulty for sample items
Claim 1
• Selected Response
• Constructed Response
• Technology-Enhanced
• Extended Response and Performance Tasks
Concepts and Procedures: Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.
Assessment Targets Measured in Grades 3–5
• Operations and Algebraic Thinking
• Number and Operations – Base 10
• Number and Operations – Fractions
• Measurement and Data
• Geometry
Operations and Algebraic Thinking
• Grade 3: Understanding meaning of multiplication and division
• Grade 4: Applying understanding
• Grade 5: Writing and interpreting numerical expressions
Number and Operations – Base 10
• 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
• 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
• 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
• 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
• 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, 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
• 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
• 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 MathematicsGrade Level Considerations
• Vocabulary, style, context, and item difficulty
• Claims from the Smarter Balanced Mathematics Content Specifications