Students build and name rectangular arrays (e.g., create a 6×4 array with counters) and physically break them into two smaller arrays, then write the corresponding multiplication sentences and add them (e.g., (2×4)+(4×4)). Students are prompted to picture and break a 12×5 array into two smaller rectangular arrays (5×5 and 7×5 or 10×5 and 2×5), compute each product, and add to get the original product. The Student Activity Page shows a 5×6 grid decomposed to 5×2 and 5×4 and records 5×6 = 5×2 + 5×4, modeling decomposition and addition of the parts.

Students count and fill shapes with one-inch tiles to determine area (e.g., filling a 6 by 4 box to get 24 square inches) and are asked to find areas of other rectangles by tiling. Students create shapes from a given number of unit tiles (e.g., using 15 tiles to make different shapes) and note each shape has the same area because it uses the same number of unit squares. Students use a grid and dice to draw and record rectangles (e.g., 2 across by 3 down → 6 sq cm) and use the PhET Area Builder to create and count areas of given shapes.

Students build rectangles on an interactive grid, count unit squares, and then find area by multiplying side lengths (several guided examples: 3×4, 5×6, 2×6). The Skills list explicitly includes "Relate area to the operations of multiplication and addition." Students also make shapes with unit squares and pipe cleaners and write number sentences for the areas, and they measure real-world rectangles (sidewalk/driveway or household objects) and compute their areas in square units.

Students are given an explicit definition that to find the area of a composite shape you add the areas of each separate shape and the Skills list states they should "find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas." In Activity 2 and multiple worksheets (Finding Composite Areas, Composite Shapes Review) students cut, arrange, and decompose L- and T-shaped composite figures into rectangles, compute each rectangle's area by multiplying side lengths, and add those areas to find totals. In the "Design Your Garden" activity students divide a garden into two rectangles, find each area, and add them, providing an applied/real-world use of the decomposition-and-addition technique.

The lesson's Skills list explicitly includes: "Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts." In Activity 3 (My Own Creature) students trace creature body parts on a centimeter grid, calculate area and perimeter for six body parts, and then compute the creature's total area and perimeter. In Activity 1 (Measuring My Name) students fill whole grid squares for letters and compute area by counting squares and record total area, practicing additive combination of parts.

Students are prompted to break a rectangle into smaller rectangles to compute area using the distributive property (for example, 15×3 is split into (8×3)+(7×3)=24+21=45). The Food Court activity asks students to compute areas and then combine stands (e.g., "If Carly and Sally combine their stands, what will the resulting area be? (45 sq. units)"), requiring addition of areas. The robot activity has students draw and cut parts with specified areas and paste them together to build a robot, which involves composing and comparing areas of multiple parts.

The Skills list explicitly states students should "Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts." The Unit Review prompts students to describe how to find the area of a composite shape by dividing it into simple shapes, finding those areas, and then adding them together. Problems 19 and 20 present L-shaped (rectilinear) figures with dimensions and ask students to calculate the total area.

The Basic Skills Review includes a real-world area question: students determine whether a rectangular rug with sides 7 and 9 feet fits in a room of area 60 sq. ft., which requires computing 7×9 and comparing to 60. The review also contains multiplication equations (e.g., 60×b=360) that give students practice with multiplication facts relevant to computing rectangular area.

The Basic Skills Review #21 includes a real-world rug problem in which students compute a square rug's area using multiplication (7×7=49) and compare it to the room area (42 sq. ft.) to decide if the rug will fit. The review also contains multiplication word problems (e.g., 5×8=40, a×8=400) that practice the multiplication operation used to find areas of rectangles and squares.

Students draw a 3×4 rectangle, find its area by multiplying and by counting 12 unit squares, and then divide that rectangle into halves, thirds, and fourths to find the area of each part (6, 4, and 3 sq cm respectively). Students divide complex L-shaped and stepped figures on grid paper into equal parts and shade specified fractions, and they use tiles to create shapes and partition them into equal-area parts. The Basic Skills item about the rug asks students to compare areas in a real-world context (6×6 = 36 sq ft vs. room area 42 sq ft).

Students use a laminated grid and geoboard to draw a 6 by 6 square and divide it into halves and fourths, and they create a 2 cm by 6 cm rectangle and divide it into thirds. The Skills list states students will "Partition shapes into parts with equal areas" and "Express the area of each part as a unit fraction of the whole." The unit test problems ask students to divide grid-based rectangles into equal parts, shade specified parts, and state the fraction of the whole that is shaded.

Students draw a rectangle of area 15 square centimeters (3 by 5) on grid paper and partition it into thirds, shading one-third and showing two-thirds so they work with equal-area parts. Students are asked to find another way to divide the same rectangle into thirds, ensuring each part has five 1-cm^2 squares, and they repeat similar partition tasks with a 16-cm^2 square (one-fourth) and a 9-cm^2 square (two-thirds). Students use unit squares to count area and create partitions that are equal in area.