7th Grade STAAR Math Reference Sheet & Formula Chart
Official Texas TEA formulas for circles, lateral/total surface area, volume of prisms and pyramids, and linear rates for Grade 7 Mathematics.
Linear & Proportional Rates (TEKS 7.4A)
Constant of proportionality and direct variation relationships.
| Mathematical Concept | Standard Formula | Key Notes & Meaning |
|---|---|---|
| Constant of Proportionality | y = kx | k = y / x | Where k represents the constant unit rate, passing through the origin (0, 0). |
Circumference & 2D Area Formulas (TEKS 7.5B, 7.8C, 7.9B)
Standard 2D boundary and surface equations provided on the reference sheet.
| Measurement | Geometric Figure | Formula | Calculation Strategy |
|---|---|---|---|
| Circumference | Circle | C = 2πr or C = πd | Distance around a circle (π ≈ 3.14 or 22/7). |
| Area | Circle | A = πr² | Pi times the radius squared (r × r). |
| Triangle | A = ½bh | Half of base times perpendicular height. | |
| Rectangle / Parallelogram | A = bh | Base times perpendicular height. | |
| Trapezoid | A = ½(b₁ + b₂)h | Average of parallel bases multiplied by height. |
Surface Area & Volume of 3D Solids (TEKS 7.9A, 7.9D)
Formulas for prisms and pyramids (where P = perimeter of base, B = area of base, h = height, l = slant height).
| Measurement | Solid Shape | Formula | Variables & Meaning |
|---|---|---|---|
| Lateral Surface Area | Prism | S = Ph | Perimeter of base P times prism height h. |
| Pyramid | S = ½Pl | Half of base perimeter P times slant height l. | |
| Total Surface Area | Prism | S = Ph + 2B | Lateral area plus area of 2 bases (2B). |
| Pyramid | S = ½Pl + B | Lateral area plus area of 1 base (B). | |
| Volume | Prism | V = Bh | Base area B times vertical height h. |
| Pyramid | V = ⅓Bh | One-third of base area B times vertical height h. |
Test Your Skills with 7th Grade STAAR Math Practice
Solve authentic Texas TEKS circle area, surface area, and pyramid volume problems with instant step-by-step rationales.
7th Grade STAAR Math Reference Sheet FAQs
Essential answers regarding 7th-grade circle formulas, surface area equations, and pyramid volume questions.
What circle formulas are on the 7th Grade STAAR Math reference sheet?
The 7th-grade reference chart provides formulas for both circumference (C = 2πr or C = πd) and area of a circle (A = πr²). It also specifies standard approximations for pi: π ≈ 3.14 or π ≈ 22/7.
How do 7th graders distinguish between lateral and total surface area on STAAR?
Lateral surface area includes only the sides (faces) around the solid and excludes the top and bottom bases (Prism: S = Ph; Pyramid: S = 1/2 Pl, where P is perimeter of the base, h is prism height, and l is slant height). Total surface area includes the lateral faces plus the bases (Prism: S = Ph + 2B; Pyramid: S = 1/2 Pl + B, where B is the base area).
What is the constant of proportionality formula on the Grade 7 formula chart?
Under TEKS 7.4A, the constant of proportionality is written as y = kx, with k = y / x. This relationship represents direct variation through the origin (0, 0), where k is the unit rate or constant slope.
How is pyramid volume calculated using V = 1/3 Bh on the 7th grade exam?
A pyramid occupies exactly one-third the volume of a prism with an identical base and height. Students first determine the base area B (using A = lw for a rectangular base, or A = 1/2 bh for a triangular base), multiply by the perpendicular height h, and divide the result by 3.