Recognize area as an attribute of plane figures and understand concepts of area measurement.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Area is the amount of flat surface a shape covers. Before any formulas, third graders build the idea of measuring it by tiling: covering a shape completely with identical squares, leaving no gaps and no overlaps, and counting them. A square with sides 1 unit long is called a unit square, and it has an area of 1 square unit. If a shape can be covered by 12 unit squares, its area is 12 square units.
This understanding guards against later confusion. Area is not the same as perimeter, which measures the distance around the edge, and it is not changed by moving or rearranging the pieces of a shape. Students learn that the unit matters too: a rug might measure 6 square feet or 864 square inches, and both describe the same surface. Hands-on covering with square tiles, sticky notes or grid paper gives students a mental image of area that makes the multiplication shortcut in 3.MD.C.7 feel sensible rather than mysterious.
Some students count the edges of the shape instead of the squares inside. Ask them to color the inside to show what area measures.
When covering a shape with mixed tiles, children may leave spaces or stack pieces. Emphasize the rule of no gaps and no overlaps.
Counting some big squares and some small squares together gives a meaningless total. All units must be the same size.
Students may write 12 inches instead of 12 square inches. Area is counted in square units.
A rectangle is covered exactly by unit squares in 3 rows with 5 squares in each row. What is its area?
Answer: The area is 15 square units.
Use color tiles, sticky notes and grid paper. Ask students to cover the same shape with two different units and compare the counts, which shows why units must be stated. Contrast area with perimeter early by having students trace around a shape with string and fill it with tiles.
Tests typically show a shape on a grid and ask for its area in square units, or ask which statement about area is true. Shapes that are not rectangles are useful to make sure students are counting, not just multiplying.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 9 (also accepted: 9 square units)
Area is the number of unit squares that cover the shape, so it is 9 square units.
Answer: D) one square unit
A unit square has side length 1 unit and an area of 1 square unit. Its perimeter is 4 units.
Answer: C) Part of the surface would not be counted
Area measures all the surface. A gap is surface that is not counted, so the measured area would be too small.
Answer: 24 (also accepted: 24 square units)
Count or skip count the squares: 6, 12, 18, 24. The area is 24 square units.
Answer: A) square inches
Area is measured in square units, such as square inches or square centimeters.
Answer: 8 (also accepted: 8 square units)
Area is additive: 5 + 3 = 8 square units.
Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
A full lesson with slides, activities and an exit ticket on understanding area and unit squares, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 3.MD.C.5 with an answer key, ready in about a minute.
Make a worksheet βTurn understanding area and unit squares into a quiz students answer online that marks itself, with a class summary for you.
Build a test βPart a defines the unit square and the square unit. Part b says a shape covered by n unit squares, without gaps or overlaps, has an area of n square units.
In 3.MD.C.7, after they understand area as counting unit squares. Grade 4 (4.MD.A.3) applies the area formula for rectangles in real-world problems.