4.MD.A.3
*This standard is part of a supporting cluster
Standard
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor .
Unpacked
In third grade students learned to consider perimeter and area of rectangles more abstractly. Based on work on previous grades with multiplication, spatially structuring arrays, and area, they abstract the formula for the area of a rectangle A=l x w
The formula is a generalization of the understanding, that, given a unit of length, a rectangle whose sides have length w units and l units, can be partitioned into w rows of unit squares with l squares in each row. The product l x w gives the number of unit squares in the partition, thus the area measurement is square units. These square units are derived from the length unit.
The area of a rectangle is the region inside the rectangle. The formula for area is A = l x w. Students can find a missing side if they know the length of one side and the area for the figure. Students need to use the relationship between multiplication and division to solve problems involving finding the missing side. The perimeter of a rectangle is the distance around it. The formula for finding perimeter is P = l + w + l + w or P = 2 l + 2 w.
Students can find the missing side using the perimeter and the known side. Students need to remember that there are two sides that have the same length or width. Focus for instruction should be understanding the concepts of area and perimeter and not just knowing the formulas.
Questions to check for understanding/ increase the rigor:

A rectangular figure has a perimeter of 35cm. What could the lengths of the sides be? Give two possibilities.

The floorplan of a building has an area 1200 square feet. How many rooms could the building have, and what would the area of each room be?
Construct blueprint for your building. Explain how you created the blueprint.

A construction worker laid 54 square feet of hardwood in the rectangular family room of a new house. What could possible perimeters of the room be? Construct blueprint for your building. Explain how you created the blueprint.


The areas of two shapes are each 40 square inches, but the perimeters are very different. Sketch the two shapes and calculate the perimeters. Justify your thinking.

Imagine a rectangle with an area of 28 square centimeters. If the length of the rectangle is 3 centimeters shorter than the width, find the dimensions of the rectangle.

A rectangle has a length of 3 cm and a width of 2 cm, with an area of 6 sq.cm. Double the length and width. What is the area of this rectangle?
How does that affect the area? Try doubling the side lengths again and
 describe the pattern you see.
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Solve for area and perimeter using the formulas, for rectangles in real world and mathematical problems, using key words from a word bank.
Solve for area and perimeter using the formulas, for rectangles in real world and mathematica l problems, using key
Solve for area and perimeter using the formulas, for rectangles in real world and mathematical problems, using simple sentences.
Level 4
Expanding
Solve for area and perimeter using the formulas, for rectangles in real world and mathematical problems, using complex sentences.
Level 5
Bridging
Solve for area and perimeter using the formulas, for rectangles in real world and mathematica l problems, using simple phrases from a word bank.
and complex sentences.
ELD Standard #3: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of
Mathematics.