Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
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, 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 ( = , where is the length of the apothem and 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 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
Instructional Task 2 (MTR.3.1)
- The area of a regular decagon is 24.3 square meters. Determine the side length, in meters, of
the regular decagon.
Instructional Item 1
- In 2019 the population for Siesta Key, FL, was 5,573 while Destin, FL, had a population of
13,702. Siesta Key is 3.475 square miles and Destin is 8.46 square miles. Which location has
a smaller population density?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.