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