Essential Questions: What is perimeter? How does knowing the attributes of plane figures help find the perimeter of an identified plane figure? What methods are used to measure perimeter/area? How does knowing the attributes of plane figures help find the area of a figure? How is area related to multiplication and addition? What is the difference between area and perimeter? How can the area of rectilinear figures be calculated? Lesson Plans and Seeds Lesson Plan C.7a: Using Tiling to Find Area Lesson Seed C.5: Covering the Shapes Lesson Seed C.7c: Using the Distributive Property to Find the Area Lesson Seed C.7d: Area Rectilinear Download Seeds, Plans, and Resources (zip) Unit Overview Content Emphasis By Clusters in Grade 3 Progressions from Common Core State Standards in Mathematics Send Feedback to MSDE’s Mathematics Team
Lesson Plan C.7a: Using Tiling to Find Area
Lesson Seed C.5: Covering the Shapes
Lesson Seed C.7c: Using the Distributive Property to Find the Area
Lesson Seed C.7d: Area Rectilinear
Unit Overview
Content Emphasis By Clusters in Grade 3
Progressions from Common Core State Standards in Mathematics
Send Feedback to MSDE’s Mathematics Team
Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.
For an in-depth discussion of the overarching, “big picture” perspective on student learning of content related to this unit, see:
Vertical Alignment: Vertical curriculum alignment provides two pieces of information: (1) a description of prior learning that should support the learning of the concepts in this unit, and (2) a description of how the concepts studied in this unit will support the learning of additional mathematics.
Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the over-arching unit standards from within the same cluster. The table also provides instructional connections to grade-level standards from outside the cluster.
Overarching Unit Standards
Supporting Standards within the Domain
Instructional Connections outside the Cluster
3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
3.MD.C.5a A square with side length 1 unit, called a “unit square,” is said to have “one square unit” of area, and can be used to measure area.
3.MD.C.5b A plane figure which can be covered without gaps or overlaps by n unit square is said to have an area of n unit squares.
3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
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.
3.MD.C.7a 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.
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.
3.MD.C.7C 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.
3.MD.C.7d 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.
3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.
3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3.OA.B.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known.(Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.)
3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Connections to the Standards for Mathematical Practice: This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. These proficiencies correspond to those developed through the Literacy Standards. The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the Content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.
In this unit, educators should consider implementing learning experiences which provide opportunities for students to:
Content Standards with Essential Skills and Knowledge Statements and Clarifications: The Content Standards and Essential Skills and Knowledge statements shown in this section come directly from the Maryland State Common Core Curriculum Frameworks. Clarifications were added as needed. Educators should be cautioned against perceiving this as a checklist. All information added is intended to help the reader gain a better understanding of the standards.
Standard
Essential Skills
and Knowledge
Clarification
Ability to apply experience with partitioning rectangles into rows and columns to count the squares within
See the skills and knowledge that are stated in the Standard.
Students develop understanding of using square units to measure area by:
An interactive whiteboard would allow students to see that square units can be used to cover a plane figure.
Knowledge that area is the measure of total square units inside a region or how many square units it takes to cover a region
To illustrate the relationship between area and length and width, students may fold or cut square grid paper in order to solve problems (e.g., If the length and width were cut in half, what would happen to the area?).
Ability to explain the relationship of multiplication arrays and area
Ability to justify the understanding of area by comparing tiling and counting with repeated addition/multiplication
Students should be given opportunities to find the area of a given shape given the dimensions. They should also have opportunities to provide the dimensions of a given shape when given the area. For example, students should tile a rectangle then multiply the side lengths to show it is the same.
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Ability to apply the formula for area of a rectangle to solve word problems
Students should solve real-world mathematical problems.
3.MD.C.7c 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.
Joe and John made a poster that was 4’ by 3’. Mary and Amir made a poster that was 4’ by 2’. They placed their posters on the wall side-by-side so that that there was no space between them. How much area will the two posters cover?
This is an extension of 3.MD.7c.
What are a few ways this figure could be decomposed to find the area?
