Students compute area for rectangular regions using area = length × width in real-world problems (e.g., a rectangular plot 80 ft × 55 ft yielding 4,400 sq ft). Students also compute the area of a rectangular painting (16.9 in × 9.3 in = 157.17 sq in) on practice pages and are prompted to use multiplication to find area in the Wrapping Up section.

Students set up and compute area = length × width with fractional and mixed-number dimensions (e.g., Peter's room: 13 1/2 × 6 2/3 → 90 sq ft). Students complete quiz problems that ask for the area of rectangles with fractional side lengths and use area models (science poster board and grid overlap) to interpret fractional products. Multiple activities require converting mixed numbers to improper fractions and multiplying to find areas in real-world contexts.

Students are asked to compute area for rectangular shapes in word problems, e.g., Ian's rectangular stand (4 1/4 in by 2 1/2 in) and Kasey's canvas (2 1/2 ft by 1 2/3 ft), with worked answer keys showing multiplication of fractional side lengths to find area. Students are prompted to include correct units for questions requiring perimeter and area and complete perimeter problems for rectangles with fractional side lengths. Several activity pages require writing number sentences and solving real-world area problems using rectangles.

Students use the formulas A = s^2 and V = s^3 and evaluate those expressions (e.g., find the volume of a cube with side s = 5 cm and the area of a square with side s = 13 in.). The student activity pages include problems that require computing s^2 and s^3 and a real-world style challenge asking whether two square posters (10 in and 12 in) fit under a total area limit. Students practice applying exponents to evaluate area and volume for squares and cubes.

Students compute the area of combined rectangular regions using area models and algebraic expressions (e.g., (5×4)+(5×8) and 5(4+8)). Students write and manipulate expressions for rectangular areas with variables (e.g., 5(n+2), (5·n)+(5·2), and 5n+10) and match area diagrams to equivalent algebraic expressions. Students use substitution to evaluate expressions and confirm equivalence of original and simplified forms in real-world contexts (playground, pet display).

Students decompose and compose two-dimensional figures (rectangles, parallelograms, triangles, trapezoids, kites and other polygons) to compute areas using A = b·h, A = 1/2·b·h, and rectangle area. Students apply these formulas to real-world and mathematical problems (pool with a platform, sail areas, pavers/walkway, picture frame, gardens) and perform unit conversions when needed. Students also find areas on a coordinate grid by counting units or decomposing plotted polygons into triangles and rectangles.

Students compute scale factors and use them to find actual lengths (e.g., Mia's garden, architect blueprint, fort problem) and to reproduce scale drawings at different scales (Interactive Notebook, Drawing to Scale activities). Students calculate perimeters and areas for originals and scale drawings (Mrs. Yee chicken fence: perimeter and area comparisons, area = 48 → 192) and are explicitly taught that area changes by the square of the scale factor. Students practice area calculations for rectangles, triangles, and circles and convert scale-factor ratios to percentages.

Students compute areas of triangles, trapezoids, and parallelograms by decomposing figures (e.g., trapezoid area decomposition problems and parallelogram area in the quilt problem). Students apply area and circumference formulas for circles in real-world contexts (e.g., the fire ring with diameter 4 ft and answer key calculations). Students use scale factors to relate lengths, perimeters, and areas (scale drawing problems asking for perimeter and area scale factors and worked solutions).

Students are asked to create and solve "Real-Life Area Problem" activities that involve calculating the area of various shapes and to use visual models and drawings to represent those problems. The Parent Plan skills explicitly instruct students to apply area formulas and to find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. The "Decompose a Polygon" station directs students to physically cut and partition polygons into simpler shapes to determine area, and the station planning and creation steps require students to produce answer keys showing solutions for area tasks.

Students decompose a trapezoid into a rectangle and triangle to compute area, showing work with area of triangles and quadrilaterals. Students lay out nets, measure face dimensions, compute each face's area, and add the areas to find surface area for cubes, rectangular prisms, triangular prisms, and square pyramids. Students apply and use formulas SA = 2LW + 2LH + 2WH and SA = 6s^2 as well as area formulas for rectangles and triangles. Students solve real-world surface-area problems (wrapping a box, painting a pyramid-shaped roof) using these calculations.

Students calculate volume of right rectangular prisms by counting unit cubes and by using V = l × w × h, including practice with fractional edge lengths by packing with 1/2- and 1/4-inch cubes and multiplying fractional dimensions (Activity 1 and Activity 2). Students apply the formula V = B × h by finding the area of triangular bases and then multiplying by prism height to find volumes of triangular prisms, and they use V = s^3 for cubes (Activity 3). Students solve multiple real-world and mathematical word problems (aquarium, mailing boxes, packaging cubes, tent) and complete quiz problems that require computing surface area and volume of prisms, a square pyramid, cubes, and rectangular solids.

Students calculate volume and surface area in real-world contexts such as Archie's mugs: they find the volume of one boxed mug (80 in^3), multiply to get total volume (640 in^3), compare net dimensions of candidate shipping boxes (Boxes A, B, C) and compute each box's volume to choose an appropriate box. Students compute surface area for the chosen box (SA = 528 in^2) and use that to determine how many packages of mailing paper are needed. Student activities require computing volumes and surface areas for cubes, right rectangular prisms, triangular prisms, a pentagonal prism (travel kennel), and a square pyramid, and include finding areas of triangular faces and cross sections.

Students compute surface area and volume for cubes and rectangular prisms using provided formulas (SA = 6s^2, SA = 2LW+2LH+2WH, V = l×w×h, V = B×h) in multiple problems (e.g., cube SA/volume, rectangular prism SA/volume, Problems 9–12, 11–12). Students solve real-world tasks that require surface area or volume (Kareem painting a storage box, decorative paper for boxes, soap factory prism length, butter slices, cereal box net) and practice with nets and cross sections (matching nets to solids, sketching nets, naming 2D cross-section shapes). The review explicitly includes right prisms, triangular bases, polygons (hexagon base slices), fractional edge lengths, and composite solids for which students calculate area, surface area, and volume.

Students select three full-size pre-printed nets (cube, rectangular prism, triangular prism, square pyramid) and calculate surface area for each and volume for the cube, rectangular prism, and triangular prism (Step 3). Area and volume formulas (A = l × w, Atriangle = 1/2 bh, SA = 2lw + 2lh + 2wh, V = l × w × h, V = B × h, s^3, etc.) are provided on the activity sheets and used in calculations. The answer key shows worked calculations for surface area and volume of the cube, rectangular prism, triangular prism, and square pyramid, and students measure nets using graph paper and round measurements to the nearest half unit.

Students are asked to find the volume of a rectangular prism (Activity: Basic Skills Review problem with a 6 cm by 4 cm by 3 cm prism) and to compute the area and circumference of a circle (Basic Skills Review problem with a 10 cm radius). The Basic Skills Review instructs students to include unit labels and to use the volume formula V = l × w × h for the prism. These items require students to apply area and volume formulas to solve numeric problems.

Students solve for area of a parallelogram (A = base × height) in Basic Skills Review #16 using the given base 14 cm and height 4 cm to find 56 cm2. Students also work with a cube in Basic Skills Review #16: they use the given volume 27 ft3 to find the side length (s = 3) and then compute the surface area (SA = 6s2 = 54). These tasks require students to compute area, use volume to find dimensions, and compute surface area for a cube.

Students solve a real-world area problem for a rectangular rug with fractional side lengths (6 2/3 ft by 3 1/2 ft) and compute its area (70/3 = 23 1/3 sq ft). Students also practice multiplying mixed numbers and fractions in several exercises (e.g., 2 5/6 × 4 4/5 and other fraction multiplication problems) that support computing area via multiplication of side lengths. The Mario wage problem requires multiplying a fractional total hours value by a unit rate, showing application of fractional multiplication to real-world contexts.

Students complete multiple problems finding area of triangles, parallelograms, rectangles, trapezoids, and squares (including decomposing a trapezoid into triangles and a rectangle). The Parent Plan explicitly lists the skill to "Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms." Activity 2 directs students to complete a linked quiz titled "Surface Area and Volume" to practice solving surface area and volume problems.

Students solve real-world problems that require using square roots to find side lengths from area (for example, the square tile floor with area 225 ft^2 leading to √225 = 15). Students use cube roots to find dimensions from volumes (answer key and problems include ∛1000 = 10, ∛512 = 8, and ∛343 = 7). The Real-World Problems student page explicitly asks students to decide when to use exponents or roots to calculate length, area, and volume and to use a calculator when needed.

Students solve problems that involve area and volume of basic square and cubic shapes: they find the side length of a square garden given area 144 and 169, and they find the side length of cubic boxes given volumes 27 and 64. Several items ask for interpreting area and volume in context (e.g., square-shaped park, cubic container) so students practice reversing area and volume formulas to find dimensions.

Students calculate area when they compute the drop zone using the formula A = πr^2 and then multiply area by a cost to find the total build cost (Part 2, Task 1). Students work with cubes in the backup-fuel task: each fuel cell is given as a cube with side length (4 ft) and area (16 ft²), and students compute how many fuel-cell cubes are needed and the room area or storage volume required (Part 1, Task 3). The tasks require converting and using volume/space units (storage needed in m³ or ft²) and calculating how many three-dimensional fuel-cell units fit into a storage area.

Students calculate perimeter of rectangles in multiple ways and set up equations to solve for missing side lengths using P = 2(l + w). Students solve area problems for rectangles (A = l × w) and for triangles (A = 1/2 × b × h), including finding a missing width from area = 150 cm² and finding a triangle's height from a given area. Students translate word problems into algebraic equations (e.g., 150 = 15 × w; 60 = (1/2) × 10 × h) and solve these real-world and mathematical area problems.

Students record and use formulas for the volumes of cylinders (V = πr²h), cones (V = 1/3 πr²h), and spheres (V = 4/3 πr³). Students solve real-world and mathematical problems using those formulas (e.g., volumes of a pencil cup, paint can, traffic cone, tennis ball) and work backward algebraically to find missing heights or radii. Students apply volume calculations in a design challenge where they choose realistic dimensions for a cylinder, sphere, and cone and compute capacities.

Students work on multiple problems that require computing volumes of cylinders, cones, and spheres (e.g., find the height of a cylinder given volume and radius; find the radius of a cone given volume and height; find the radius from a sphere's volume). The skills list and answer keys explicitly state that students should "Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres" and "Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems." Students also apply the Pythagorean Theorem in numerical problems, which supports solving some three-dimensional measurement tasks.

Students measure dimensions and calculate volumes for three solid parts (cylinder, sphere, cone) using formulas and π = 3.14 on the "3D Sculpture Volume Worksheet." They record individual volumes and compute a total sculpture volume; an answer key provides example calculations and numeric results. Students also apply measurement procedures (find diameter → radius) and round answers to the nearest inch as part of a real-world sculpture-building task.

Students solve volume problems for cylinders, cones, and spheres: they write and apply V = πr²h, V = (1/3)πr²h, and V = (4/3)πr³, compute numeric volumes (e.g., cylinder with r=4, h=10; cone with r=3, h=14), and solve for a radius given a sphere's volume. Students also use the Pythagorean Theorem to find missing side lengths and the distance between points on a coordinate plane. The lesson includes an external practice link explicitly for volume of pyramids and cones.

Students compute volumes of three-dimensional objects in Problems 18 and 19: they calculate the volume of a round pencil cup (a cylinder) using radius and height and the volume of a snow cone (a cone) using radius and height, with answers given using pi. Students also solve right-triangle numerical problems (Problem 17 finds the hypotenuse) and compute distances between points (Problem 16), which show work with triangle side lengths. The answer key provides numeric volume results (≈113.04 and ≈25.12) demonstrating students carry out volume calculations.