Students develop an understanding of areas as how much two-dimensional space a figure takes up, and relate it to their work with multiplication from Units 2 and 3.
In Unit 4, students understand area as how much two-dimensional space a figure takes up and relate it to their work with multiplication in Units 2 and 3.
In early elementary grades, students may have informally compared area, seeing which of two figures takes up more space. In Grade 2, students, partitioned a rectangle into rows and columns of same-sized squares and counted to find the total number of them, including skip-counting and repeated addition to more efficiently do so (2.G.2, 2.OA.4).
Students begin their work in this unit by developing an understanding of area as an attribute of plane figures (3.MD.5) and measure it by counting unit squares (3.MD.6). After extensive work to develop students’ spatial structuring, students connect area to the operation of multiplication of length and width of the figure (3.MD.7a, b). Lastly, students connect the measure of area to both multiplication and area, seeing with concrete cases that the area of a rectangle with whole-number side lengths $$a$$ and $$b + c$$ is the sum of $$a\times b$$ and $$a\times c$$ (3.MD.7c), and using the more general idea that area is additive to find the area of composite figures (3.MD.7d). Thus, the unit serves as a way to link topics and thinking across units, providing coherence between the work with multiplication and division in Units 2 and 3 (3.OA) with the work of area in this unit (3.MD.C).
Students will engage with many mathematical practices deeply in the unit. For example, students “use strategies for finding products and quotients that are based on the properties of operations; for example, to find [the area of a rectangle by multiplying] $$4\times 7$$, they may recognize that $$7 = 5 + 2$$ and compute $$4 \times 5 + 4 \times 2$$. This is an example of seeing and making use of structure (MP.7). Such reasoning processes amount to brief arguments that students may construct and critique (MP.3)” (PARCC Model Content Frameworks for Mathetmatics, p. 16). Further, students make use of physical tiles, rulers to relate side lengths to physical tiles, and later in the unit, the properties of operations themselves in order to find the area of a rectangle (MP.5). Additionally, “to build from spatial structuring to understanding the number of area-units as the product of number of units in a row and number of rows, students might draw rectangular arrays of squares and learn to determine the number of squares in each row with increasingly sophisticated strategies, such as skip-counting the number in each row and eventually multiplying the number in each row by the number of rows (MP.8)” (GM Progression, p. 17).
In future grades, students will rely on the understanding of area to solve increasingly complex problems involving area, perimeter, surface area, and volume (4.MD.3, 5.MD.3—5, 6.G.1—4). Students will also use this understanding outside of their study of geometry, as multi-digit multiplication problems in Grade 4 (4.NBT.5), fraction multiplication in Grade 5 (5.NF.4), and even polynomial multiplication problems in Algebra (A.APR.1) rely on an area model.
Pacing: 16 instructional days (13 lessons, 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 3rd Grade Scope and Sequence Recommended Adjustments.
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area | square unit |
length and width | unit square |
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Intellectual Prep for All Units
Unit-Specific Intellectual Prep
This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
3.MD.C.5
3.MD.C.6
Understand that area is an attribute of plane figures that is measured in square units. Find the area of a figure using pattern blocks, which can be used as concrete non-standard units.
3.MD.C.5
3.MD.C.6
Find the area of a figure using square-inch and square-centimeter tiles, which can be used as concrete standard units.
3.MD.C.5
3.MD.C.6
Find the area of a rectangle by counting unit squares or units on grids.
3.MD.C.5
3.MD.C.6
3.MD.C.7.A
Find the area of a rectangle by making unit squares inside of them to form a grid, connecting the side length of a rectangle with the number of tiles on a side.
3.MD.C.6
3.MD.C.7.A
Find the area of a rectangle with incomplete information about its rows and columns of square units.
3.MD.C.6
3.MD.C.7.A
Find the area of a rectangle that has been superimposed over a grid.
3.MD.C.6
3.MD.C.7.A
Find the area of a rectangle through multiplication of the side lengths.
3.MD.C.7.B
Solve word problems involving area.
3.MD.C.7.C
Compose and decompose rectangles, seeing and making use of the idea that the sum of the areas of the decomposed rectangles is equal to the area of the composed rectangle.
3.MD.C.7.C
Apply the distributive property as a strategy to find the total area of a large rectangle.
3.MD.C.7.D
Recognize area as additive. Find the area of composite figures as shown on grids or with all side lengths labeled.
3.MD.C.7.D
Recognize area as additive. Find areas of composite figures when not all dimensions are given.
3.MD.C.7.D
Recognize area as additive. Find the area of complex composite figures.
Key: Major Cluster Supporting Cluster Additional Cluster
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