Standard #: MA.3.GR.2.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.3.NSO.2.2

 

Terms from the K-12 Glossary

• Rectangular Array

 

Vertical Alignment

Previous Benchmarks

• MA.2.AR.3.2 
• MA.2.GR.2.1

 

Next Benchmarks

• MA.4.GR.2.1 
• MA.4.GR.2.2

 

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 

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.