Formulas: 3D Shapes [TEKS Tools Grade 7]

This post specifically looks at how formulas can be used solve problems involving volume and surface area. Read more about TEKS Tools and their rationale here.

Formulas

Formulas account for around 22% of each 7th grade STAAR test. These formulas are applied to solve problems related to volume, surface area, composite figures, linear relationships, and composite figures.

The main function of a formula is to understand the relationship between quantities. In fourth grade, students were first introduced to the formulas for area and perimeter of squares and rectangles. In fifth grade, they were introduced to the formula for volume of a rectangular prism. In sixth grade, the formulas for area of a triangle, parallelogram, and trapezoid are explored. For the first time in 7th grade, students are introduced to circle geometry, exploring π (pi), circumference, and area.

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Surface Area

Both lateral surface area, which excludes the bases of a 3D shape, and total surface area are first introduced in 7th grade without the use of specific formulas. Instead, students use nets and treat the shape as a composite figure.

7.9D - solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net

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2023-24: a net was given, students had to solve for the lateral surface area

2024-27: a net was given, students had to solve for the total surface area

2025-35: a net was given, students had to solve for the total surface area

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Volume

First introduced in 5th grade, volume continued in 6th grade restricted to right rectangular prisms. In 7th grade, the concept expands to include triangular prisms and two types of pyramids.

7.9A - solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids

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2023-17: the side length and height of a square pyramid were given, students had to solve for the volume

2023-34: the volume and base of a rectangular prism were given, students had to solve for the height

2024-4: the area of the base and height of a triangular pyramid were given, students had to solve for the volume

2025-5: the base and height of the triangular base, and the height of the prism, were shown for a triangular prism, students had to solve for the volume

2025-26: the base and height of the rectangular base, and the height of the pyramid, were shown for a rectangular pyramid, students had to solve for the volume