Students build and count arrays on the abacus (for example, showing a 4 by 5 array, creating 3 rows of 5, and 10 groups of 4) and write multiplication sentences that correspond to those arrays. Students color beads on abacuses and complete worksheets matching arrays to multiplication facts and finding products. Students use rows and columns of beads as concrete representations of multiplication and check products by counting or trading beads.

Students build concrete arrays (for example a 6×4 array using counters) and physically break the array into two smaller arrays using a straw, then write multiplication sentences such as (2×4)+(4×4)=6×4 to show equality. Students picture and draw arrays for problems like 8×9 and rewrite them as 8×4 + 8×5, then add the two products to get 72. An illustrated area-model (6×9 broken into 6×(4+5) → (6×4)+(6×5) → 24+30=54) and student activity pages with grids (e.g., 5×6 = 5×2 + 5×4) show the distributive property using area/array models.

The lesson explicitly tells students to use the distributive property to break a multiplication into two smaller multiplications (Activity 5: "Remind him that multiplication is repeated addition and that he can also use what he knows about the distributive property… For example, 6×11 can become (6×5)+(6×6). Similarly, a problem like 7×12 can become (7×6)+(7×6)"). The skills list also includes "Apply properties of operations as strategies to multiply and divide," and multiple activities have students practice breaking factors apart and using repeated addition.

Students are asked to treat the Snail Parade picture as an array and reason that a 5 by 5 array equals 25 then subtract 3 to get 22, showing use of arrays to represent multiplication and subtraction. The Chinese Checkerboard activity has students group dots into equal groups (e.g., 10×12+1=121) and multiply groups then add extras, which uses grouping and area-like counting. A word problem example shows the sum of products written explicitly as (5×4)+(3×4) for counting legs, which presents multiplication distributed across groups.

Students draw groups of ten rods to model problems such as 3×40 and count the rods by tens to get 120. Students rewrite 40 as 4×10 (expanded form) and write equivalent expressions like 3×4×10 and (3×4)×10, using the associative property to simplify. Students are asked to draw 7 groups of 3 ten rods to model 7×30 and to explain their thinking aloud.

The Student Activity Pages include an explicit distributive-property equation: 9 × 8 = (9 × 4) + (9 × 4), and a multiple-choice question (Question 7) that asks which equation shows the distributive property, with an option of the form 6 × q = (6 × 5) + (6 × 4). The materials ask students to draw pictures or create arrays to solve problems (e.g., Carly's pepperoni problem asks students to "Draw a picture to show your work"), and the Multiplication Properties Review has students match multiplication sentences to the distributive property example.

The lesson explicitly tells students they may use the distributive property to break down numbers when planning food, and gives the example of drawing packages of 15 plates to figure how many packages are needed for 60 people. Students are asked to draw pictures and use a whiteboard to keep track of computations while solving multiplication and packaging problems. In the optional seating activity students color, cut out, and lay out images (blankets and tables) on blank paper to create seating arrangements and compute whether configurations allow for 60 people.

Students fill rectangles with one-inch tiles to find areas (for example, filling a 6 by 4 box with 24 tiles) and count unit squares to determine area. Students roll two dice and color a by b rectangles on grid paper, then state and write the area (e.g., 4 across and 6 down gives 24 square centimeters). Students use an interactive Area Builder to create shapes from unit squares and to practice creating and counting given rectangular areas.

Students use an interactive grid (Area Builder) to create rectangles with whole-number side lengths, count unit tiles, and then multiply side lengths to find area. The skills list and multiple activities (chalk/ tape rectangles, "Make These Areas!" with unit squares and pipe cleaners) require students to tile, draw area models, and write number sentences such as 2×5=10 and 3×4=12. Several tasks ask students to measure whole-number side lengths and compute areas by multiplication.

Students draw and shade shapes on centimeter grid paper and count unit squares to find areas (Activities 1, 3, and Design Your Garden). They decompose composite figures into non-overlapping rectangles, compute each rectangle's area by multiplying side lengths, and add those areas to get the whole (Activities 4, 5, and Finding Composite Areas). A web activity has students tile composite shapes by clicking and dragging colored unit squares to cover parts of a shape, then write corresponding numerical area equations (Activity 3).

Students draw block-letter names and creatures on centimeter grid paper, filling whole unit squares (tiling) and then count squares to find area and trace edges to find perimeter. The skills list tells students to multiply side lengths to find areas of rectangles with whole-number side lengths and to find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas. Activity 3 requires students to compute area and perimeter for six body parts and then compute the total area by adding the areas of those parts.

Students draw and trace rectangles on centimeter grid paper and count unit squares to find areas, providing a concrete tiling model. Activity 1 explicitly instructs students to break a 15×3 rectangle into two smaller rectangles and shows the computation (8×3)+(7×3)=24+21=45, naming this approach as the distributive property. Skills and activities also direct students to decompose rectilinear figures into non-overlapping rectangles and add their areas, reinforcing area-model reasoning.

Students receive laminated grid paper and are asked to draw rectangles and squares on grid paper and to draw shapes with specified perimeters and areas (e.g., draw an area of 25 as 5 by 5, draw an area of 28 as 4 by 7). The unit asks students to decompose composite (L-shaped) figures into non-overlapping rectangles and add the areas of the parts, and the Skills list explicitly includes relating area to multiplication and addition. The Unit Review and Activity pages include grid tasks and an Area Builder web link that use unit squares/tiles to build areas.

Day 2 Activity 3 asks students to draw three rectangles that are each 4 by 2 and to divide and shade them into 2 halves, 4 fourths, and 8 eighths so the colored regions look the same. Students partition identical rectangles and shade corresponding numbers of parts to show that 1/2 = 2/4 = 4/8, using rectangular area representations. Several other activities have students draw and match fraction parts on shapes (fraction strips, circles, and dominoes), reinforcing area-based fraction models.

Students draw a 3×4 rectangle on grid paper and find its area by multiplying side lengths (3×4=12) or by counting 1 cm squares, and they use colored tiles to find half, third, and fourth portions of that rectangle. Students divide the rectangle into multiple equal-area partitions (halves, thirds, fourths) on the grid without using diagonal lines and produce multiple area-preserving partitions. Students also build shapes with 10, 12, and 15 tiles and practice dividing those tiled shapes into equal parts.

Students watch a video on properties of multiplication and complete a cut-and-glue organizer that includes a section for the distributive property. The provided answer key explicitly shows distributive examples such as 6 × 9 = (6 × 4) + (6 × 5) and 8 × 12 = (8 × 2) + (8 × 10). Students practice identifying and producing examples that break a product into a sum of products.

Students draw rectangles on grid paper and create a 3-by-5 rectangle made up of 15 one-centimeter squares, then partition that rectangle into three equal parts each of five squares. Students also divide a 4-by-4 square into fourths and a 3-by-3 square into thirds, using the tiled grid to show equal-area parts. The activities require students to use tiling and area models (counting unit squares) to represent and partition areas.