Mathematics grade level considerations for grades 3 5
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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.

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Mathematics Grade Level Considerations for Grades 3–5

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Mathematics grade level considerations for grades 3 5

Mathematics Grade Level Considerations for Grades 3–5


Considerations for grades 3 5

Considerations for Grades 3–5

  • Vocabulary

  • Style Guide

  • Representation of numbers

  • Contexts

  • Item Difficulty

  • Assessment Targets


Vocabulary

Vocabulary

  • Items must be written so students can easily understand the item or task.

  • Use vocabulary at or below grade-level.


Style

Style


Overview of mathematics style conventions for grades 3 5

Overview of Mathematics Style Conventions for Grades 3–5

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


Words vs numerals

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 numerals1

Words vs. Numerals

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.


Commas in numbers

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)


Representing missing values

Representing Missing Values

6 + ☐ = 11

3, 5, 7, 9, ?

5 × 7 = ?

3+6 = ?

Look at this equation:


Contexts

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

Item Difficulty

  • Items should include a range of difficulty

  • Anticipated difficulty for sample items


Claim 1

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

Extended Response and Performance Tasks


Assessment targets measured in grades 3 5

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

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

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

Number and Operations – Fractions

Grade 3: Understanding of fractions as numbers

Grade 4: Understand fraction equivalenceand operations with fractions

Grade 5: Solving problems involving the four operations


Measurement and data

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

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

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

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

Claim 4 – Modeling and Data Analysis

  • 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


Claims 2 3 and 4

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 mathematics grade level considerations

Elementary School MathematicsGrade Level Considerations

Vocabulary, style, context, and item difficulty

Claims from the Smarter Balanced Mathematics Content Specifications


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