Students are given and use the formulas C = πd, C = 2πr, and A = πr^2 in the Things to Know section and repeatedly in practice problems (Activities 2, 4, 5, and practice pages). Students measure die-cut circles, compute C/d ≈ 3.14, and solve multiple circumference and area problems using the formulas. Students cut a circle into wedges, rearrange them into a rectangle to see that area = (1/2 · C) · r (Activity 3), and then substitute C = 2πr to derive A = πr^2 algebraically in Activity 4. The activities require students to compute numerical circumference and area values and compare the rectangle area to the circle area as evidence of the informal derivation.

Students are asked to compute radius, circumference, and area for paired circles on a student activity page that asks them to fill a table with radius, circumference, and area for original and scale drawings. Students use numeric examples with circles (e.g., radii 2 and 8) in the answer key where circumference and area values are listed and used to compare scaling effects. Students also solve problems that require converting circle sizes (a problem lists two circles with diameters 10 in and 4 in and asks for ratios and percents), giving practice applying circle measures in scale contexts.

Students are explicitly asked to find the circumference and area of circles in multiple word problems (e.g., a fire ring with diameter 4 ft and a fountain with diameter 6 m), and the answer key shows use of formulas C = πd (or 2πr) and A = πr^2 to compute numeric answers. The unit summary and parent plan list "Know the formulas for the area and circumference of a circle and use them to solve problems," and practice items require computing circumference and area and using those results to find counts (sand bags, paint cans).

The lesson explicitly asks "How can we find the area of a polygon or circle?" in the Ideas to Think About section and includes a Student Activity Page titled "Real-Life Area Problem" where students create and solve problems that include calculating the area of various shapes. The Parent Plan lists as a skill: "Apply area formulas in the context of solving real-world and mathematical problems," and the activities require students to decompose shapes and use area formulas for triangles, quadrilaterals, and polygons. The stations planning and answer-key tasks require students to construct and solve area problems and record solutions on answer cards.

The Basic Skills Review includes Problem 9 asking students to "Find the circumference and area of the circle" with radius 6 mm, and the Answer Key shows the formulas C = 2πr and A = πr^2 and uses them to compute numeric values. The wrapping-up section also states that students "have learned how to measure area, circumference, surface area, and volume," indicating students practice using the circle formulas in review work.

Problem 5 on the Basic Skills Review #15 asks students to find both the circumference and the area of a circle given a 10 cm radius. The provided answer key shows students use C = 2πr and A = πr^2 and compute numeric values using π ≈ 3.14 (giving 62.8 for circumference and 314 for area). This requires students to recall and apply the standard formulas and perform calculations with a given radius.

The Parent Plan explicitly lists "Know the formulas for the area and circumference of a circle and use them to solve problems." The Circles and Scale Drawings activity gives two problems (radius 5 cm and diameter 4 ft) that ask students to find circumference and area. The answer key displays and applies C = 2πr and A = πr^2 (using π ≈ 3.14) to compute numeric answers.

In Task 1: Drop Zone Radius students are instructed to calculate a drop zone radius using the formula A = πr^2. The Student Activity Page explicitly shows the area formula A = πr^2 and provides tables where students compute radius (and then area) and total cost for each location. The provided answer key lists computed radii and costs (e.g., 17.83 m, 15.95 m, 18.71 m), indicating students solve area equations and apply those results to real problems.

The lesson explicitly presents the area formula A = πr^2 in the Getting Started section and records it on the Student Activity "Volume Notes" page. Students use that area formula as the base area in multiple activities (e.g., deriving V = πr^2h for cylinders by treating a cylinder as a stack of circles and plugging A = πr^2 into volume calculations). The materials also have students identify radius and diameter and use π ≈ 3.14 in computations, reinforcing the area formula in worked examples and practice problems.

Problems 18 and 19 ask students to find the volume of a round pencil cup (cylinder) and a snow cone (cone) given radius and height, with instruction to use 3.14 for pi. To solve these volume problems students must compute πr^2 (and 1/3·πr^2 for the cone), which requires using the area formula for a circle in a problem-solving context.