Summary
Highlights
Miss Elliot introduces the lesson on calculating fractional distance on both a number line and a coordinate plane. She uses a story about meeting a friend halfway between two cities on a map to illustrate the concept. The lesson will also cover finding points at other fractional distances, like 2/3 of the way.
The first example demonstrates finding a point that is 2/37 of the distance from point P (coordinate 2) to point N (coordinate 16). The steps are: 1) Find the total distance (16 - 2 = 14). 2) Multiply the total distance by the fraction (14 * 2/37 = 6 units). 3) Add this calculated distance to the starting point's coordinate (2 + 6 = 8). The final coordinate is 8.
The second example on a number line involves finding the coordinate that is 2/11 of the distance from point I (coordinate 5) to point T (coordinate 60). Step 1: Total distance (60 - 5 = 55). Step 2: Multiply (55 * 2/11 = 10 units). Step 3: Add to the starting coordinate (5 + 10 = 15). The coordinate is 15.
Miss Elliot reviews the general steps for calculating fractional distance: 1) Find the total distance. 2) Multiply by the fraction. 3) Add or subtract (or count). She explains that for a coordinate plane, these steps are applied twice: once for the x-axis and once for the y-axis, unless it's a straight horizontal or vertical line.
This example finds the coordinate that is 2/3 of the distance from A (-4, 2) to N (2, 2). Since it's a horizontal line, only the x-coordinates change. Step 1: Total distance in X (2 - (-4) = 6). Step 2: Multiply (6 * 2/3 = 4 units). Step 3: Add to the starting x-coordinate (-4 + 4 = 0). The final coordinate is (0, 2).
This problem asks for the coordinate that is 3/5 of the distance from B (-3, 8) to Y (-3, -2). Since it's a vertical line, only the y-coordinates change. Step 1: Total distance in Y (8 - (-2) = 10). Step 2: Multiply (10 * 3/5 = 6 units). Step 3: Subtract from the starting y-coordinate (8 - 6 = 2) because moving towards Y is downwards. The final coordinate is (-3, 2).
The video moves to a more complex example with a slanted line, finding a point 3/4 of the distance from Ben's house (coordinates not explicitly stated but derived as (-2, -4)) to Kate's house (6, 4). Step 1: Find total distance for X (8 units) and Y (8 units) by counting on the graph. Step 2: Multiply each distance by 3/4 (8 * 3/4 = 6 units for both X and Y). Step 3: Add/subtract from Ben's starting coordinates (-2 + 6 = 4 for x) and (-4 + 6 = 2 for y). Plotting on the graph, the meeting point is (4, 2).
This example finds the coordinate that is 2/3 of the distance from A to T. The horizontal distance (X) is 8 units and the vertical distance (Y) is 6 units. Step 2: Multiply by 2/3. For X: 8 * 2/3 = 5.33 repeating. For Y: 6 * 2/3 = 4. Step 3: Counting from A, move 5.33 units horizontally and 4 units vertically. The final coordinate is (6 and 1/3, 7).
For a point that is 1/2 the distance (midpoint) from the mess hall to the cabins, Miss Elliot quickly eyeballs the solution by halving the total horizontal and vertical distances. The midpoint is found at (1, 1).
The final combined example asks for 1/3 of the distance from I to N. The difference in Y is 12, and the difference in X is 9. Step 2: Multiply by 1/3. For Y: 12 * 1/3 = 4. For X: 9 * 1/3 = 3. Step 3: From I, go down 4 units and over 3 units. The final coordinate is (3, 8).
Miss Elliot outlines the practice assignment, which involves further fractional distance problems, some using a midpoint formula. She guides the students through problem #4 on the practice sheet, finding a point 2/5 of the distance from A (3,2) to B (8,7), resulting in the coordinate (5,4). She explains that the solution corresponds to coloring a specific number on the provided coloring page for bonus points.