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Mathematics Grade Level Considerations for Grades 3–5

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Mathematics Grade Level Considerations for Grades 3–5

- Vocabulary
- Style Guide
- Representation of numbers
- Contexts
- Item Difficulty
- Assessment Targets

- Items must be written so students can easily understand the item or task.
- Use vocabulary at or below grade-level.

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))

Example 1:

Example 2:

Patty has 10 pennies and 3 nickels. How much money does Patty have?

13¢

25¢

40¢

53¢

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.

- 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)

6 + ☐ = 11

3, 5, 7, 9, ?

5 × 7 = ?

3+6 = ?

Look at this equation:

- 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

- Items should include a range of difficulty
- Anticipated difficulty for sample items

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

Extended Response and Performance Tasks

Operations and Algebraic Thinking

Number and Operations – Base 10

Number and Operations – Fractions

Measurement and Data

Geometry

Grade 3: Understanding meaning of multiplication and division

Grade 4: Applying understanding

Grade 5: Writing and interpreting numerical expressions

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

Grade 3: Understanding of fractions as numbers

Grade 4: Understand fraction equivalenceand operations with fractions

Grade 5: Solving problems involving the four operations

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

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

- 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

- 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

- Performance Tasks and collections ofExtended Response items
- Real world problems
- Draw upon knowledge and skills articulatedin the progression of standards up to the gradebeing assessed
- Relevant verbs include:
- model, construct, compare, investigate, build, interpret, estimate, analyze, summarize, represent, solve, evaluate, extend, and apply

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

Vocabulary, style, context, and item difficulty

Claims from the Smarter Balanced Mathematics Content Specifications