Same Area, Different Perimeter

Same Area, Different Perimeter

Ages 8–11 · 7 minutes · Math

If rectangles have the same area, do they also have the same perimeter?

Students will look at situations where two rectangles have the same perimeter and determine whether or not they have the same area. This exploration will help them understand that perimeter and area are two seprate concepts, and the lesson will conclude with a real-world application problem about optimizing space.

Part of

Standards alignment

Common Core State Standards

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

Alabama

  • MA19.3.24 — Construct rectangles with the same perimeter and different areas or the same area and different perimeters.
  • MA19.3.25 — Solve real-world problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length of rectangles.
  • MA19.4.23 — Apply area and perimeter formulas for rectangles in real-world and mathematical situations.

Alaska

  • 3.MD.10 — Solve real world and mathematical problems involving perimeters of polygons, including: • finding the perimeter given the side lengths, • finding an unknown side length, • exhibiting rectangles with the same perimeter and different areas, • exhibiting rectangles with the same area and different perimeters.
  • 3.MD.9.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.
  • 4.MD.3 — 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.

Arizona

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.A.3 * — Apply the area and perimeter formulas for rectangles in mathematical problems and problems in real-world contexts including problems with unknown side lengths. See Table 2.
  • 3.MD.C.7.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.

Arkansas

  • 4.GM.7 — Apply the area and perimeter formulas for rectangles and figures composed of two or more rectangles in real-world situations.
  • 3.GM.7 — Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real- world and mathematical problems.

California

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.
  • MP7 — Look for and make use of structure.

Colorado

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

Connecticut

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

Delaware

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.A.3 — 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.
  • 3.MD.C.7.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.

Florida

  • MA.4.GR.2.1 — Solve perimeter and area mathematical and real-world problems, including problems with unknown sides, for rectangles with whole-number side lengths.
  • MA.4.GR.2.2 — Solve problems involving rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • MA.3.GR.2.3 — Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula.

Georgia

  • 3.GSR.8.1 — Determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Solve problems involving perimeters of polygons.
  • 3.GSR.8.2 — Investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same area can have different perimeters.
  • 3.GSR.7 — Identify area as a measurable attribute of rectangles and determine the area of a rectangle presented in real-life, mathematical problems.
  • 3.GSR.7.3 — Discover and explain how area can be found by multiplying the dimensions of a rectangle.

Hawaii

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7b — 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.
  • 4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Idaho

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

Illinois

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.
  • MP.8 — Look for and express regularity in repeated reasoning.

Indiana

  • 3.M.5 — Find the area of a rectangle with whole-number side lengths by modeling with unit squares, and show that the area is the same as would be found by multiplying the side lengths. Identify and draw rectangles with the same perimeter and different areas or with the same area and different perimeters. (E)
  • 3.M.6 — Find perimeters of polygons given the side lengths or given an unknown side length.
  • 4.M.4 — Apply the area and perimeter formulas for rectangles to solve real-world and other mathematical problems. Investigate the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems. (E)
  • PS.8 — Look for and express regularity in repeated reasoning.

Iowa

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.A.3 — 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.
  • 3.MD.C.7.b — Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems.
  • SMP1 — Make sense of problems and persevere in solving them.

Kansas

  • 3.MD.8.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.9 — 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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems explaining and justifying the appropriate unit of measure. 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.

Kentucky

  • KY.3.MD.8 — Solve real world and mathematical problems involving perimeters of polygons.
  • KY.3.MD.8.a — Find the perimeter given the side lengths of a polygon.
  • KY.3.MD.8.c — Draw rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • KY.3.MD.7.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.
  • KY.4.MD.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Louisiana

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.
  • MP7 — Look for and make use of structure.

Maine

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7b — 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.
  • 4.MD.A.3 — 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.

Maryland

  • 3.MD.C.7.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.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7 — Relate area to the operations of multiplication and addition.
  • 4.MD.A.3 — 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.

Massachusetts

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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. (Note: When finding areas of rectangular regions answers will be in square units. For example, the area of a 1 cm x 1 cm rectangular region will be 1 square centimeter (1 cm2 , students are not expected to use this notation.) When finding the perimeter of a rectangular region answers will be in linear units. For example, the perimeter of the region is: 1cm + 1cm + 1cm +1cm = 4 cm or 2(1cm) + 2(1cm) = 4 cm).

Michigan

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

Minnesota

  • 3.3.2.2 — Find the perimeter of a polygon by adding the lengths of the sides.
  • 4.3.2.4 — Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.

Mississippi

  • 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 (including, but not limited to: modeling, drawing, designing, and creating) rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • 3.MD.7.b — Multiply side lengths to find areas of rectangles with whole-number side lengths (where factors can be between 1 and 10, inclusively) in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
  • 4.MD.3 — 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.

Missouri

  • 3.GM.C.12 — Multiply whole-number side lengths to solve problems involving the area of rectangles.
  • 3.GM.D.15 — Solve problems involving perimeters of polygons.
  • 3.GM.D.16 — Understand that rectangles can have equal perimeters but different areas, or rectangles can have equal areas but different perimeters.
  • 4.GM.C.8 — Apply the area and perimeter formulas for rectangles to solve problems.

Montana

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.A.3 — 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.
  • 3.MD.C.7.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.

Nebraska

  • 4.G.3 — Area and Perimeter: Students will apply perimeter and area formulas for rectangles.
  • 4.G.3.a — Apply perimeter and area formulas for rectangles to solve authentic problems.
  • 3.G.2 — Area and Perimeter: Students will recognize perimeter and area as attributes of plane figures and understand concepts of area measurement.
  • 3.G.2.a — Solve authentic problems involving perimeters of polygons when given the side lengths or when given the perimeter and unknown side length(s).

Nevada

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.A.3 — 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.
  • 3.MD.C.7.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.
  • MP7 — Look for and make use of structure.

New Hampshire

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

New Jersey

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.A.3 — 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.
  • 3.MD.C.7b — 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.

New Mexico

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

New York

  • NY-3.MD.8.a — Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths or finding one unknown side length given the perimeter and other side lengths.
  • NY-3.MD.8.b — Identify rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • NY-4.MD.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
  • NY-3.MD.7.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.

North Carolina

  • 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.
  • NC.3.MD.7 — Relate area to the operations of multiplication and addition. • 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. • Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning. • Use tiles and/or arrays to illustrate and explain that the area of a rectangle can be found by partitioning it into two smaller rectangles, and that the area of the large rectangle is the sum of the two smaller rectangles.
  • NC.3.MD.8 — Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length.

North Dakota

  • 3.GM.M.6 — Solve problems involving the perimeters of rectangles given the side lengths or when given the perimeter and unknown side length(s).
  • 4.GM.M.5 — Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.

Ohio

  • 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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.3 — Develop efficient strategies to determine the area and perimeter of rectangles in real-world situations and mathematical problems. For example, given the total area and one side length of a rectangle, solve for the unknown factor, and given two adjacent side lengths of a rectangle, find the perimeter.
  • 3.MD.7.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.
  • MP.7 — Look for and make use of structure.

Oklahoma

  • 3.GM.2.1 — Find the perimeter of a polygon, given whole number lengths of the sides, using a variety of models.
  • 3.GM.2.2 — Analyze why length and width are multiplied to find the area of a rectangle by decomposing the rectangle into one unit by one unit squares and viewing these as rows and columns to determine the area.

Oregon

  • 4.GM.B.6 — Apply the area and perimeter formulas for rectangles in authentic contexts and mathematical problems.
  • 3.GM.C.7 — Relate area to multiplication and addition. Use relevant representations to solve problems in authentic contexts.
  • 3.GM.D.8 — Solve problems involving authentic contexts for perimeters of polygons.
  • MP7 — Look for and make use of structure.

Pennsylvania

  • CC.2.4.3.A.5 — Determine the area of a rectangle and apply the concept to multiplication and to addition.
  • CC.2.4.3.A.6 — Solve problems involving perimeters of polygons and distinguish between linear and area measures.
  • Make sense of problems and persevere in solving them.

Rhode Island

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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. (Note: When finding areas of rectangular regions answers will be in square units. For example, the area of a 1 cm x 1 cm rectangular region will be 1 square centimeter (1 cm2, students are not expected to use this notation.) When finding the perimeter of a rectangular region answers will be in linear units. For example, the perimeter of the region is: 1cm + 1cm + 1cm +1cm = 4 cm or 2(1cm) + 2(1cm) = 4 cm).

South Carolina

  • 3.MDA.6 — 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 perimeter and different areas or with the same area and different perimeters.
  • 4.MDA.3 — Apply the area and perimeter formulas for rectangles.
  • 3.PS.7b — Recognize mathematical repetition in order to make generalizations.
  • 5.MDA.4 — Differentiate among perimeter, area and volume and identify which application is appropriate for a given situation.

South Dakota

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.
  • MP7 — Look for and make use of structure.

Tennessee

  • 3.MD.D.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 exploring rectangles with the same perimeter and different areas or with the same area and different perimeters.

Texas

  • 4.5D — solve problems related to perimeter and area of rectangles where dimensions are whole numbers.
  • 3.6C — determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row;
  • 3.7B — determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems;
  • 4.5C — use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l × w); and

Utah

  • 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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.7.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 wholenumber products as rectangular areas in mathematical reasoning.
  • 4.MD.3 — 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.

Vermont

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

Virginia

  • 4.MG.3b — Determine the area and perimeter of a rectangle when given the measure of two adjacent sides (in whole number units), with and without models.
  • 4.MG.3e — Identify and represent rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • 4.MG.3f — Solve contextual problems involving area and perimeter of rectangles and squares.
  • 4.MG.3c — Determine the area and perimeter of a square when given the measure of one side (in whole number units), with and without models.
  • 4.MG.3d — Use concrete materials and pictorial models to explore the relationship between area and perimeter of rectangles.

Washington

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 4.MD.A.3 — 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.
  • 3.MD.C.7.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.
  • MP8 — Look for and express regularity in repeated reasoning.

Washington, D.C.

  • 3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • 3.MD.C.7.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.
  • 4.MD.A.3 — 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.

West Virginia

  • M.3.25 — 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 perimeter and different areas or with the same area and different perimeters.
  • M.3.24 — 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 wholenumber products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a x b and ax c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive and find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.
  • M.4.21 — Apply the area and perimeter formulas for rectangles in real-world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor (e.g., find the width of a rectangular room given the area of the flooring and the length).

Wisconsin

  • M.3.MD.D.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 perimeter and different areas or with the same area and different perimeters.
  • M.3.MD.C.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. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.
  • M.4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

Wyoming

  • 3.MD.J.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 perimeter and different area or with the same area and different perimeter.
  • 3.MD.I.7.A — Find the area of a rectangle with whole-number side lengths (dimensions) by multiplying them. Show that this area is the same as when counting unit squares.
  • 3.MD.J — Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
  • 4.MD.I.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems.