Standard #: MA.912.GR.4.4

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.GR.1.6 
• MA.912.GR.3.4 
• MA.912.T.1.2

 

Terms from the K-12 Glossary

• Area

 

Vertical Alignment

Previous Benchmarks

• MA.5.GR.2 
• MA.6.GR.2 
• MA.7.GR.1.1
• MA.7.GR.1.2 
• MA.8.GR.1.2 
• MA.912.AR.2.1

Next Benchmarks

• MA.912.C.5

 

Purpose and Instructional Strategies

In elementary grades, students are introduced to the concepts of perimeter and area, with a focus on rectangles. In middle grades, students expand their knowledge of areas of quadrilaterals and triangles. In Geometry, students solve mathematical and real-world problems involving areas of two-dimensional figures, including population density. In Calculus, students will use integrals to connect the concept of area to many other real-world and mathematical contexts. 

• Instruction includes reviewing units and conversions within and across different measurement systems (as this was done in middle grades). 
• Instruction includes discussing the convenience of answering with exact values (e.g., the simplest radical form or in terms of pi) or with approximations (e.g., rounding to the 22 nearest tenth or hundredth or using 3.14, $\frac{\text{22}}{\text{7}}$ or other approximations for pi). It is also 7 important to explore the consequences of rounding partial answers on the accuracy or precision of the final answer, especially when working in real-world contexts. 
• Instruction includes exploring the area of regular polygons and the formula based on the perimeter and the apothem ($A$ = $\frac{\text{1}}{\text{2}}$$a$$p$, where $a$ is the length of the apothem and $p$ is the perimeter). The apothem is the line segment from the center to the midpoint of on the sides of a regular polygon. In many cases, finding the length of the apothem will require the use of trigonometric ratios. 
• The population density based on area is calculated by the quotient of the total population and the total area. Have students practice finding the population density or the total population, given the dimensions of a two-dimensional figure. That is, part of their work includes finding the area based on the dimensions. (MTR.7.1) 
• Instruction includes exploring a variety of real-world situations where finding the area is relevant for different purposes. Problem types include components like percentages, cost and budget, constraints, comparisons and others. 
• Problem types include finding missing dimensions given the area of a two-dimensional figure or finding the area of composite figures.

 

Common Misconceptions or Errors

• Students may not be careful with units of measurement involving area, particularly when converting from one unit to another. 
  •  For example, since there are 100 centimeters in a meter, a student may incorrectly conclude that there are 100 square centimeters in a square meter.

 

Instructional Tasks

Instructional Task 1 (MTR.7.1) 

• In 2019, the population of Leon County was 293,582 and the population of Sarasota County was 433,742. The area of Sarasota County is 752 square miles, while the area of Leon County is 702 square miles. 
  •  Part A. Which county has a higher population density? 
  •  Part B. If the physical shape of the county identified in Part A was a rectangle, what are possible dimensions of the county if the length is greater than the width? 
  •  Part C. If the county identified in Part A was the physical shape of a right triangle, what are possible dimensions of the base and height of the county? 
  •  Part D. Does changing the shape of the tract of land change the population density of the county? 

Instructional Task 2 (MTR.3.1) 

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