### 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.).

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**3

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### 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.

### Instructional Tasks

*Instructional Task 1*

- a. What is the area of Kendra’s figure?
- b. Explain how you counted.

### Instructional Items

*Instructional Item 1*

- 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

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Expert

## STEM Lessons - Model Eliciting Activity

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

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

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.

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.

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.

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

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.

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

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.

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.

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 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.

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

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

## Original Student Tutorials

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

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

Type: Original Student Tutorial

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