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“Which is perimeter…is that the outside, or the inside?!...is this where you multiply, or add?...”

Sound familiar? It’s hard to keep them straight, especially when the Grade 3 teaching sequence often includes perimeter and area in proximity to each other.

However, when students see that a rectangle of a given area can take more than one shape, therefore different lengths and widths, and therefore different perimeters, they learn to distinguish between the two. These problems are intended to address this issue. Students also get a look at some of the patterns that can be found in the different combinations of dimensions (factors) that can produce a given area, all of which will also produce different perimeters.

There are 3 types of problems here:

(a) Find all rectangles with a given area and identify length, width, and perimeter of each.

(b) Find all rectangles with a given perimeter, and identify length, width, and area of each.

(c) Given 2 of the 4 numbers related to the size of a rectangle (length, width, area, perimeter), find the other two, e.g., “A rectangle is 4 feet wide and has a perimeter of 28 feet. What is its area?”

All of the first two types of problems are accompanied by a 1-centimeter grid large enough to accommodate real-size drawings of the rectangles. A page of 1-cm grid paper is also included.

Common Core Standards:

3.MD.6: Measure areas by counting unit squares (square cm, square m, square

in, square ft, and improvised units).

3.MD.7: Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

3.MD.8: “Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with….the same area and different perimeters….”

Subjects: Math, Geometry, Measurement

Level: Grades 3-4

Duration: 10 pages, many problems, 2-4 days

Answer Key: Yes

A Smartboard 14 file is also included.

Sound familiar? It’s hard to keep them straight, especially when the Grade 3 teaching sequence often includes perimeter and area in proximity to each other.

However, when students see that a rectangle of a given area can take more than one shape, therefore different lengths and widths, and therefore different perimeters, they learn to distinguish between the two. These problems are intended to address this issue. Students also get a look at some of the patterns that can be found in the different combinations of dimensions (factors) that can produce a given area, all of which will also produce different perimeters.

There are 3 types of problems here:

(a) Find all rectangles with a given area and identify length, width, and perimeter of each.

(b) Find all rectangles with a given perimeter, and identify length, width, and area of each.

(c) Given 2 of the 4 numbers related to the size of a rectangle (length, width, area, perimeter), find the other two, e.g., “A rectangle is 4 feet wide and has a perimeter of 28 feet. What is its area?”

All of the first two types of problems are accompanied by a 1-centimeter grid large enough to accommodate real-size drawings of the rectangles. A page of 1-cm grid paper is also included.

Common Core Standards:

3.MD.6: Measure areas by counting unit squares (square cm, square m, square

in, square ft, and improvised units).

3.MD.7: Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

3.MD.8: “Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with….the same area and different perimeters….”

Subjects: Math, Geometry, Measurement

Level: Grades 3-4

Duration: 10 pages, many problems, 2-4 days

Answer Key: Yes

A Smartboard 14 file is also included.

Total Pages

10 pages

Answer Key

Included

Teaching Duration

3 days