# MA.3.GR.2.1

Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares.

### Clarifications

Clarification 1: Instruction emphasizes the conceptual understanding that area is an attribute that can be measured for a two-dimensional figure. The measurement unit for area is the area of a unit square, which is a square with side length of 1 unit.

Clarification 2: Two-dimensional figures cannot exceed 12 units by 12 units and responses include the appropriate units in word form (e.g., square centimeter or sq.cm.).

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Rectangular Array

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is to provide the foundation for students to understand area measurement. In Grades 1 and 2, students learned about linear measurement using number lines, rulers, and calculating perimeter. In Grade 3, students build on their knowledge of measurement and multiplicative reasoning to explore and understand area measurement. Instruction emphasizes that area is a two-dimensional measurement, therefore it is measured in units that are also two-dimensional – unit squares with side lengths that measure one unit. Area is calculated using unit squares that cover a shape without gaps or overlap (MTR.5.1).
• The expectation of this benchmark is for students to calculate area of rectangles by counting unit squares (MTR.2.1).
• Instruction allows for students to draw conclusions about connections to arrays and to determine more efficient counting strategies for calculation, leading to the use of a multiplication formula in 3.GR.2.2 (MTR.4.1, MTR.5.1).

### Common Misconceptions or Errors

• Students may miscount unit squares when they are laid out in a figure. Encourage students to mark unit squares as they are counted.
• Students can confuse why area is measured in “square units.” Use this exploratory benchmark for students to relate area measurement to the counting of squares. This benchmark provides the opportunity for students to build vocabulary necessary for area measurement.

### Strategies to Support Tiered Instruction

• Instruction includes modeling how to number the unit square tiles, so students do not miscount when finding area.
• For example, the teacher provides students with figures created with squares and has them number each square as they count.

• Instruction includes creating figures with no gaps or overlaps that have a given area. Students mark each unit square with a number as they count to check that the area of the figure they create has the correct area.
• For example, the teacher provides students with grid paper and ask them to create a figure with an area of 24 square units. Student count and label 24 connected squares on the grid paper and then shade in the entire figure (see example below).

• Instruction includes measuring the area of given figures by covering them with 1-inch square tiles, leaving no gaps or overlaps. Students count the total number of squares it takes to completely cover the figure and explain how that number represents the area in square units of the figure.
• For example, the teacher provides a sheet with figures that can be covered perfectly using the square tiles. Students tile the figure and count the square tiles to identify the area.
• Instruction includes students creating their own figures by connecting square tiles with no gaps or overlaps and counting the tiles.
• For example, the teacher provides a set of 1-inch tiles and asks students to build a figure with an area of 18 square inches. After students have created the figure, they will count and number each tile to ensure they have an area of 18 square inches.

Kendra used unit squares with 1-centimeter side lengths to find the area of the rectangle below. She started, but then stopped for a lunch break.
• a. What is the area of Kendra’s figure?
• b. Explain how you counted.

### Instructional Items

Instructional Item 1

Alex put the tiles shown on his floor.
• Part A. What is the area in square feet of the portion that Alex has covered?
• Part B. What is the area in square feet of the entire floor?
• Part C. The area of Alex’s floor is 30 square feet. Select all the floors that could be Alex’s.

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.3.GR.2.AP.1: Explore area as an attribute of a two-dimensional figure that can be measured by covering the figure with unit squares without gaps or overlaps.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Complete the Rectangle:

Students are given a rectangle with one column and one row of unit squares (same size squares) drawn. Students are asked to complete and then find the total number of same size squares in the partition.

Type: Formative Assessment

How Many Units?:

Students are given a rectangle with some columns and rows partially constructed. Students are asked to find how many same-size squares are in the rectangle.

Type: Formative Assessment

Construct Rows and Columns:

Students are given a rectangle with tick marks drawn horizontally on one side of the rectangle and vertically on the bottom of the rectangle. Students are asked to partition the rectangle into columns and rows and then determine how many unit squares (same-size squares) are in the rectangle.

Type: Formative Assessment

Partition the Rectangle Into Unit Squares:

Students are given a rectangle with one unit square (same size square) drawn in the corner of the rectangle. Students are asked to draw the remaining unit squares and then find the total number of unit squares in the rectangle.

Type: Formative Assessment

Using Tiles of Different Sizes:

Students consider whether tiling a rectangle with different sized tiles is appropriate when calculating area.

Type: Formative Assessment

Unit Square:

Students are asked to explain how the area of a rectangle can be calculated and their responses are examined for references to the unit square as the unit of measurement.

Type: Formative Assessment

Overlapping Tiles:

Students are asked to evaluate another student's area calculation that involves overlapping tiles.

Type: Formative Assessment

Calculating Area:

Students discuss the meaning of area and are asked about the kinds of figures for which area can be calculated.

Type: Formative Assessment

Dawn’s Vegetable Garden:

Students are given a diagram showing a garden shaped like an irregular hexagon and are asked to find the area by counting the number of unit squares the figure contains.

Type: Formative Assessment

Area of a Right Trapezoid:

Students determine the area of a right trapezoid.

Type: Formative Assessment

How Many Square Units?:

Students determine the area of a right triangle.

Type: Formative Assessment

Fenced Dog Run:

Students are given a diagram showing a rectangular dog run and asked to find its area.

Type: Formative Assessment

## Lesson Plans

Area Architects, Lesson 1:

In this unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area. Using all five lessons will allow the students to discover, explore and eventually relate area to multiplication and addition. This lesson is the first lesson of the unit. In Lesson 1, students will develop strategies for finding area by counting square units. Students will learn the importance of accurately measuring area by exploring the concepts of area in realistic applications.

Type: Lesson Plan

Best Vegetable Garden:

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

Type: Lesson Plan

Rectangles Rule! (Lesson 1 of 2):

In this lesson students will use rulers to measure the side lengths of rectangles and use 1-inch square tiles to cover the rectangles. Students will count the total number of square units to find the area and explore relationships between the lengths of the sides and the total number of tiles.  In # 66132 Rectangles Rule! Team Challenge (Lesson 2 of 2), students will expand their understanding of tiling to find area to connect area to a multiplication formula.

Type: Lesson Plan

Same Perimeter, Different Area:

In this lesson, students are presented with a problem that requires them to create rectangles with the same perimeter but different areas.  Students also search for relationships among the perimeters and areas of different rectangles and find which characteristics produce a rectangle with the greatest area.

Type: Lesson Plan

Which Rectangle is Bigger?:

Students will learn how to partition rectangles into equal parts and write equations to represent the parts. They will gain a basic understanding of area from the book Bigger, Better, BEST! by Stuart J. Murphy.

Type: Lesson Plan

Count Those Square Units:

Students count unit squares to find the area of rectangles and play a matching game for practice.

Type: Lesson Plan

Playground Protection:

Students will decide which type of protective surface should be put in under a new playground unit. They will consider many factors before ranking their decisions about the best surface.

Type: Lesson Plan

Make A Mighty Monster: Practice with Area and Perimeter:

In this lesson, students will use their knowledge of area and perimeter to create a "Mighty Monster”. Given specific criteria related to area and perimeter, students will make their monster on centimeter grid paper and calculate both the area and perimeter of each body part to explore the differences between the two types of measurement.

Type: Lesson Plan

Area Designers:

This hands-on lesson makes a real-world connection for students in measuring area by counting square units. Students become area designers during an activity that illustrates area, and then make a real-world connection with area when they are shown a residential blueprint. Students gain practice determining the area and recording the area of rectangular rooms in square units.

Type: Lesson Plan

Area Isn't Just for Squares:

This lesson helps students make the connections between area and multiplication using square tiles.

Type: Lesson Plan

## Original Student Tutorials

Ariana Explores Area:

Ariana explores Area as she plants vegetables in her rectangular garden boxes. Help Ariana cover rectangles with unit squares without gaps or overlaps and count the squares to find the area with this interactive tutorial.

Type: Original Student Tutorial

Building a Square Garden:

Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

Type: Original Student Tutorial

Techies Talk Area:

Discover how square units can be used to cover the interior of a rectangle and measure its area of a rectangle in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

## STEM Lessons - Model Eliciting Activity

Best Vegetable Garden:

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

Playground Protection:

Students will decide which type of protective surface should be put in under a new playground unit. They will consider many factors before ranking their decisions about the best surface.

## MFAS Formative Assessments

Area of a Right Trapezoid:

Students determine the area of a right trapezoid.

Calculating Area:

Students discuss the meaning of area and are asked about the kinds of figures for which area can be calculated.

Complete the Rectangle:

Students are given a rectangle with one column and one row of unit squares (same size squares) drawn. Students are asked to complete and then find the total number of same size squares in the partition.

Construct Rows and Columns:

Students are given a rectangle with tick marks drawn horizontally on one side of the rectangle and vertically on the bottom of the rectangle. Students are asked to partition the rectangle into columns and rows and then determine how many unit squares (same-size squares) are in the rectangle.

Dawn’s Vegetable Garden:

Students are given a diagram showing a garden shaped like an irregular hexagon and are asked to find the area by counting the number of unit squares the figure contains.

Fenced Dog Run:

Students are given a diagram showing a rectangular dog run and asked to find its area.

How Many Square Units?:

Students determine the area of a right triangle.

How Many Units?:

Students are given a rectangle with some columns and rows partially constructed. Students are asked to find how many same-size squares are in the rectangle.

Overlapping Tiles:

Students are asked to evaluate another student's area calculation that involves overlapping tiles.

Partition the Rectangle Into Unit Squares:

Students are given a rectangle with one unit square (same size square) drawn in the corner of the rectangle. Students are asked to draw the remaining unit squares and then find the total number of unit squares in the rectangle.

Unit Square:

Students are asked to explain how the area of a rectangle can be calculated and their responses are examined for references to the unit square as the unit of measurement.

Using Tiles of Different Sizes:

Students consider whether tiling a rectangle with different sized tiles is appropriate when calculating area.

## Original Student Tutorials Mathematics - Grades K-5

Ariana Explores Area:

Ariana explores Area as she plants vegetables in her rectangular garden boxes. Help Ariana cover rectangles with unit squares without gaps or overlaps and count the squares to find the area with this interactive tutorial.

Building a Square Garden:

Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

Techies Talk Area:

Discover how square units can be used to cover the interior of a rectangle and measure its area of a rectangle in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Ariana Explores Area:

Ariana explores Area as she plants vegetables in her rectangular garden boxes. Help Ariana cover rectangles with unit squares without gaps or overlaps and count the squares to find the area with this interactive tutorial.

Type: Original Student Tutorial

Building a Square Garden:

Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

Type: Original Student Tutorial

Techies Talk Area:

Discover how square units can be used to cover the interior of a rectangle and measure its area of a rectangle in this interactive tutorial.

Type: Original Student Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.