Lesson 5: Geometric Formulas
Duration of Days: 2
Lesson Objective
Using evaluating expressions, students will use geometric formulas to evalutate.
How can we use Geometric Formulas to evaluate and find Volume, side of a right triangle?
How are geometric formulas similar to other expressions/equations we evaluate?
Pythagorean Theorem
A.SSE.2
2. HSA-SSE.A.2
Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
A.SSE.1a
A. Interpret the structure of expressions
Lesson Description: This section introduces students to the most common geometric formulas used in algebra. The focus is not just on memorization, but on the substitution and evaluation of these formulas.
Key topics include: Perimeter and Circumference: Calculating the distance around polygons and circles (P = 2l + 2w, C = 2pi r).Area: Measuring the surface space of squares, rectangles, triangles, and circles (A = lw, A = frac1/2bh, A = pi r^2).Volume: Finding the capacity of rectangular solids and cylinders ($V = lwh).Working with pi: Understanding the difference between an "exact answer" (leaving the result in terms of $\pi$) and an "approximate answer" (using 3.14).
Purpose: The purpose of this section is to demonstrate the utility of variables. By using geometric formulas, students see that: Variables like l, w, b, and h represent specific physical dimensions. Algebra allows us to solve for a missing dimension if the total (like Area or Perimeter) is already known.Dimensional consistency is vital (e.g., ensuring length and width are in the same units before multiplying).DOK Level: 1 & 2Level 1 (Recall & Reproduction): Students will identify the correct formula for a given shape and perform simple substitutions to find a missing value.
Level 2 (Skills & Concepts): Students will solve problems where they must first manipulate the "story" of the formula—for example, finding the radius of a circle when given the circumference, or finding the height of a triangle given its area and base.
Classwork and online work
"you try" on page 40 and practice problems