Example 6: Solve: Solution: Students understand that in geometry the square root of the area is the length of the side of a square and a cube root of the volume is the length of the side of a cube. Students use this information to solve problems, such as finding the perimeter. Example 7: What is the side length of a square with an area of 49 ft2? Solution: = 7 ft. The length of one side is 7 ft. 8.EE.3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. 8.EE.3 Students use scientific notation to express very large or very small numbers. Students compare and interpret scientific notation quantities in the context of the situation, recognizing that if the exponent increases by one, the value increases 10 times. Likewise, if the exponent decreases by one, the value decreases 10 times. Students solve problems using addition, subtraction or multiplication, expressing the answer in scientific notation. Example 1: Write 75,000,000,000 in scientific notation. Solution: 7.5 x 1010 Example 2: Write 0.0000429 in scientific notation. Solution: 4.29 x 10-5 4, 5, 6 Mini unit
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Example 1: Plant A and Plant B are on different watering schedules. This affects their rate of growth. Compare the growth of the two plants to determine when their heights will be the same. Solution: Let W = number of weeks Let H = height of the plant after W weeks Based on the coordinates from the table, graph lines to represent each plant. Solution: 3. Write an equation that represents the growth rate of Plant A and Plant B. Solution: Plant A H = 2W + 4 Plant B H = 4W + 2 4. At which week will the plants have the same height? Solution: 2W + 4 = 4W + 2 Set height of Plant A equal to height of Plant 2W – 2W + 4 = 4W – 2W+ 2 Solve for W 4 = 2W + 2 4 – 2 = 2W + 2 – 2 = 1 = W c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
example, the pre-image coordinates of a triangle are A(4, 5), B(3, 7), and C(5, 7). The image coordinates are A(-4, 5), B(-3, 7), and C(-5, 7). What transformation occurred? 8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 8.G.4 Similar figures and similarity are first introduced in the 8th grade. Students understand similar figures have congruent angles and sides that are proportional. Similar figures are produced from dilations. Students describe the sequence that would produce similar figures, including the scale factors. Students understand that a scale factor greater than one will produce an enlargement in the figure, while a scale factor less than one will produce a reduction in size. Example1: Is Figure A similar to Figure A’? Explain how you know. Solution: Dilated with a scale factor of . then reflected across the x-axis, making Figures A and A’ similar. Students need to be able to identify that triangles are similar or congruent based on given information. Example 2: Describe the sequence of transformations that results in the transformation of Figure A to Figure A’. Solution: 90° clockwise rotation, translate 4 right and 2 up, dilation of .. In this case, the scale factor of the dilation can be found by using the horizontal distances on the triangle (image = 2 units; pre-image = 4 units) 3, 2 Geometry Unit