1. (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. 7.4A Generating Formulas to Solve Problems

2. In math, formulas are often used to solve problems. Formulas use different variables to show the relationship between quantities. Often the value of all but one of the variables is given. EXAMPLE: Write a formula that can be used to find the diameter when given the circumference of a circle. The formula for the circumference of a circle in the Grade 7 Mathematics Chart is C = πd. The formula is useful in this form if you know the diameter of the circle and want to find the circumference. If you know the circumference and want to find the diameter, you can rewrite the formula. Write the formula so that the variable representing the diameter, d, is on one side of the equal sign, and everything else is on the other side of the equal sign.

3. Start with the formula for the circumference of a circle. Divide both sides of the equation by π. ππ C π d = The formula can be used to find the diameter when given the circumference of a circle. π C d =

4. 7.4A/7.4B STUDENT ACTIVITY #1 Write a formula that could be used to find the radius of a circle, r, given the circumference of the circle, C. The formula in the Grade 7 Mathematics Chart that relates the radius of a circle to its circumference is C = ______. Rewrite the formula so that it gives r in terms of C. To do so, divide both sides of the equation by _______. C 2πr ── = ─── The new formula can be used to find the _____________ of a circle when given the _______________________ of a circle. C ── = r 2π2π C 2πr2πr 2π2π 2π2π 2π2π 2π2π radius circumference

5. (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling. 7.4B Using Table and Graphs to Interpret Formulas

6. A formula like P = 4s expresses a relationship between a pair of values. For every value of s, there will be a corresponding value of P. Tables and graphs can also express a relationship between pairs of values. Information given in a table or graph can be used to see the relationship between the quantities in a formula more clearly. EXAMPLE: The formula gives r, the length of the radius of a circle, in relationship to the circumference of the circle. The formula means that the circumference of a circle divided by 2π equals the length of the radius. C ── = r 2π2π

7. You can use this formula to build a table. For each value of r, there is a corresponding value of C. The table below shows the relationship between circumference and radius. The radius data in the table is approximate because π is an approximation. By considering the number pairs in the table as ordered pairs, you can also graph this relationship on a coordinate grid. C ── = r 2π2π

8. Graph the ordered pairs (6, 0.96), (12,1.95), (18, 2.87), (24, 3.8), and (30, 4.78). The graph shows the same relationship between circumference and radius that the table shows.

9. This graph shows the relationship between the length of a diameter of a circle and the circumference of a circle. Build a table that represents the data in the graph. Write the coordinates of the four points plotted on the graph. (____, ____), (____, ____), (____, ____) The x-coordinates of the points represent ______________. The y-coordinates of the points represent ______________. Fill in the table so that it shows the same relationship between the length of the diameter and the circumference of a circle. 2 6 4 12 6 188 24 diameter circumference 2 6 4 12 6 188 24