3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area
measurement.
a. 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.
b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to
have an area of n square units.

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.
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 × b and a × c. Use area models to represent the
distributive property in mathematical reasoning.
d. Recognize area as additive. Find the 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.

2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers,
yardsticks, meter sticks, and measuring tapes.

2.MD.2 Measure the length of an object twice, using length units of different lengths for the two
measurements; describe how the two measurements relate to the size of the unit chosen.

2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total
number of them.

2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5
rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

MP.2 Reason abstractly and quantitatively. Students build toward abstraction, starting with tiling a
rectangle, and then gradually move to finish incomplete grids and drawing grids of their own.
Students then eventually work purely in the abstract, imagining the grid as needed.

MP.3 Construct viable arguments and critique the reasoning of others. Students explore their
conjectures about area by cutting to decompose rectangles and then recomposing them in
different ways to determine if different rectangles have the same area. When solving area
problems, students learn to justify their reasoning and determine whether they have found all
possible solutions, when multiple solutions are possible.

MP.6 Attend to precision. Students precisely label models and interpret them, recognizing that the
unit impacts the amount of space a particular model represents, even though pictures may
appear to show equal-sized models. They understand why, when side lengths are multiplied,
the result is given in square units. 

MP.7 Look for and make use of structure. Students relate previous knowledge of the commutative
and distributive properties to area models. They 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.

MP.8 Look for and express regularity in repeated reasoning. Students use increasingly
sophisticated strategies to determine area throughout the course of the module. As students
analyze and compare strategies, they eventually realize that area can be found by multiplying
the number in each row by the number of rows.

3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b
equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line
diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as
the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and
that the endpoint of the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0.
Recognize that the resulting interval has size a/b and that its endpoint locates the
number a/b on the number line.

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about
their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same
point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain
why the fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole
numbers. Examples: Express 3 in the form of 3 = 3/1; recognize that 6/1 = 6; locate 4/4
and 1 at the same point of a number line diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning
about their size. Recognize that comparisons are valid only when the two fractions refer
to the same whole.