NC.4.MD.3

Solve problems with area and perimeter.

Find areas of rectilinear figures with known side lengths.
Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas.
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Step 1: Lesson Standards & Learning Goals

Unpacking Clarification

Students will determine the area of a rectilinear figure.

A rectilinear figure is a polygon that has all right angles.

Students will decompose rectilinear figures into rectangles, determine the area of the rectangles, and use the areas of the rectangles to determine the area of the rectilinear figure.

Students will solve problems that involve the relationship between the perimeter and the area in a rectangle using models and strategies.

Given a fixed area, students will determine all of the possible dimensions of the rectangle.
Given a fixed perimeter, students will determine all possible areas.

Students learn to apply these understandings and formulas to the solution of real-world and mathematical problems. Note that “apply the formula” does not mean write down a memorized formula and put in known values.

Sample Essential Questions

What do area and perimeter mean and how can each be found?

How can I determine the area and perimeter of a rectangular figure?

How are area and perimeter alike and different?

How can I determine the missing measure of a rectangle when given the area or perimeter?

Vocabulary

Area
Formula
Dimension
Length
Perimeter
Rectangle
Square
Square units
Width

Students will be able to...

Find the perimeter of a rectangular figure.
Find the area of a rectangular figure.
Measure area in square units by covering a figure with unit squares
Decompose a composite figure to find the total area.
Solve perimeter problems with an unknown length when the total perimeter is given.
Solve areas problem with an unknown dimension when the total area is given.

Students will know...

The concepts of area and perimeter as attributes of plane figures.
Area is measured in square units.
The dimensions of a rectangle are length and width.
Two rectangles can have the same perimeter and different areas or have the same area and different perimeters.

Step 2: Assessment