Standard

Recognize area as an attribute of plane figures and understand concepts of area measurement.

a. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Student language:

• "I can understand that the area of plane shapes can be measured in square units."

Explanation

About the Math, Learning Targets, and Rigor

This standards calls for students to explore the concept of covering a region with “unit squares,” which could include square tiles or shading on grid or graph paper.

Students can cover rectangular shapes with tiles and count the number of units (tiles) to begin developing the idea that area is a measure of covering. Area describes the size of an object that is two-dimensional. The formulas should not be introduced before students discover the meaning of area.

The area of a rectangle can be determined by having students lay out unit squares and count how many square units it takes to completely cover the rectangle completely without overlaps or gaps.

Note: Area should always be represented as square units (square centimeters, square feet, etc.) since:

• rectangles/squares are covered with square units
• rectangles/squares are two dimensional shapes (2 dimensions = length and width = square units)

Resources

Videos

• Khan Academy
  • scroll to 3.MD.5, click on a skill, watch videos on left side in each skill
• Learn Zillion
  • 3.MD.5a
  • 3.MD.5b
• Virtual Nerd

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 3rd grade at bottom, then 3.MD.7
• Common Core Sheets

Released Assessment Questions

PARCC

3.MD.5

Recognize area as an attribute of plane figures and understand concepts of area measurement.

a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Performance Indicators: 3.MD.5

Level 5: Exceeds Expectations

• Recognizes area as an attribute of plane figures.
• Understands area is measured using square units. Describes a visual model to show understanding that area that can be found by covering a plane figure without gaps or overlaps with unit squares and counting them.
• Connects counting squares to multiplication when finding area.
• Represents the area of a plane figure as “n” square units.

Level 4: Meets Expectations

• Recognizes area as an attribute of plane figures.
• With a visual model, understands area is measured using square units. Determines area by covering a plane figure without gaps or overlaps with unit squares and counting them.
• Represents the area of a plane figure as “n” square units.

Critiquing Standards

3.C.3-2

Base explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response).

(Content Scope: Knowledge and skills articulated in 3.MD.5, 3.MD.6, 3.MD.7)

• Tasks may include those with and without real-world contexts.
• Tasks with a context may present realistic or quasi-realistic images of a contextual situation (e.g., a drawing of a meadow). However, tasks do not provide the sort of abstract drawings that help the student to represent the situation mathematically (e.g., a tiling of the meadow).

Performance Indicators: 3.C.3-2

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on operations using concrete referents such as diagrams- -including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• an efficient and logical progression of steps with appropriate justification
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• determination of whether an argument or conclusion is generalizable
• evaluating, interpreting, and critiquing the validity of other’s responses, approaches, and reasoning, and providing a counterexample where applicable

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• a logical progression of steps
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluating, interpreting, and critiquing the validity of other’s responses, approaches, and reasoning.