Age group: 6t h Grade Virginia - Mathematics Standards of Learning (2009): 6.3 a Fairfax County Public Schools Program of Studies: 6.3.a.3, 6.3.a.

Size: px

Start display at page:

Download "Age group: 6t h Grade Virginia - Mathematics Standards of Learning (2009): 6.3 a Fairfax County Public Schools Program of Studies: 6.3.a.3, 6.3.a."

Eugenia Chandler
6 years ago
Views:

1 1 Lesson Plan Plotting and Read ing Negative Numbers on a Coord inate Grid Age group: 6t h Grade Virginia - Mathematics Standards of Learning (2009): 6.3 a Fairfax County Public Schools Program of Studies: 6.3.a.3, 6.3.a.4 Online resources: T ake t he H e at Opening Teacher present s Students pract ice Math Pract ice Closing M at h Obj ect ives E xpe ri e nc e a real-world example of a function using negative numbers P rac t i c e reading values from a graph Learn to plot points in Quadrant III De vel o p strategies for converting units Ope ni ng 8

2 2 Distribute a handout with a 4-quadrant grid, such as the following, to each student. Ask the students to number from -10 to +10 on both axe s. When the students are done, display a numbered grid so they can correct their work. Ask: Where on the grid are both the x- and y- c o o rdi nat e s positive? The x- and y-coordinates are both positive in Quadrant ant I, the upper right-hand quadrant. Ask: Where on the grid is the x-coordinate positive, but the y- coordinate negative? In Quadrant ant I V, the lower right-hand quadrant, the x-coordinate is positive and the y-coordinate is negative. Ask: Where on the grid are both the x- and y-coordinates negative? The x- and y-coordinates are both negative in Quadrant ant I I I, the

3 3 lower left-hand quadrant. Ask: In which quadrant is the point (-3, 6)? The point (-3, 6) is in Quadr ant I I, the upper left-hand quadrant. Ask: How do we plot the point (-2, -5)? We start at the o ri gi n and move 2 spaces left. Then we move down 5 spaces and plot our point. Say: In today s episode, we will practice plotting points when both coordinates are negative. T e ac he r prese nt s M at h game : T ake t he H e at - N e gat i ve N umbe rs 12 Present Matific s episode T ake t he H e at - N e gat i ve N umbe rs to the class, using the projector. The goal of the episode is to practice plotting points in Quadrant III by pairing negative Celsius temperatures with their equivalent Fahrenheit temperatures.

4 Say: Please read the instructions. Students can respond based on the episode. Say: Look at the graph. What is the horizontal label? What is the vertical label?

4 4 Say: Please read the instructions. Students can respond based on the episode. Say: Look at the graph. What is the horizontal label? What is the vertical label? The horizontal label is degrees Fahrenheit. The vertical label is degrees Celsius. Say: Look at the numbers for the Celsius temperatures. Why is -90 on the bottom and -20 on the top? Where is 0? The temperatures are increasing as we move up. Since -90 is smaller than -20, it is lower. We cannot see 0 degrees Celsius it is above -20 and does not appear in the episode. Say: We are looking at only part of the coordinate grid. What

5 5 portion of the coordinate grid are we looking at? We are looking at part of Quadrant III (and a small part of Quadrant IV on the right). Say: We can see the y-axis, but we cannot see the x-axis. The x-axis is further up on the grid it is not shown in the episode. Let s turn our attention to the task. How do we plot the value that is given in the instructions? Students should describe how to move horizontally to find the appropriate Fahrenheit temperature and vertically to find the appropriate Celsius temperature and then how to follow the grid lines to see where the two coordinates meet. Follow the students instructions on where to place the point and click. If the point is correct, the episode will proceed to instruct you to place another point. If the point is incorrect, the instructions and the point will wiggle. The episode will ask you to plot a total of two points. Then a line will be drawn through the two points. The episode will proceed to ask four questions about the line and the relationship between Fahrenheit and Celsius. St ude nt s prac t i c e M at h game : T ake t he H e at - N e gat i ve N umbe rs 10 Have the students play T ake t he H e at - N e gat i ve N umbe rs on their personal devices. Circulate, answering questions as necessary.

6 M at h P rac t i c e : N e gat i ve N umbe rs o n a Co o rdi nat e Gri d Wo rkshe e t 14 Run the episode, plotting the first two points, so that the line is drawn. Display the line.

6 6 M at h P rac t i c e : N e gat i ve N umbe rs o n a Co o rdi nat e Gri d Wo rkshe e t 14 Run the episode, plotting the first two points, so that the line is drawn. Display the line. For example: On the board, draw the following table: Ask the students to copy the table into their notebooks. Ask them to fill in the table with five points that they find from the line displayed in the episode. Distribute graph paper and rulers. Ask the students to: 1. Draw a 4-quadrant grid. 2. Label the axes from -100 to +100, counting by tens. 3. Plot 3 points from their table.

7 7 4. Draw a line through the 3 points. 5. Answer the following questions in their notebooks: a. Where does the line cross the x-axis? The y-axis? b. What do we learn from the places where the line crosses the axes? c. Are there positive Fahrenheit temperatures that have equivalent Celsius temperatures that are negative? Are there positive Celsius temperatures that have equivalent Fahrenheit temperatures that are negative? How can you tell? Circulate, answering questions as necessary. When the students are done working, share. Say: Name some points that are on the graph. Responses will vary. Ask: Where does the line cross the x-axis? Where does it cross the y-axis? Responses may not be completely accurate due to the imprecision of the students graphs. The exact answers are: The graph crosses the x-axis at (32, 0) and crosses the y-axis at. Ask: What do we learn from the places where the line crosses the axes? We learn that 0 degrees Celsius is equal to 32 degrees Fahrenheit and that 0 degrees Fahrenheit is equal to degrees Celsius. Ask: Are there positive Fahrenheit temperatures that have equivalent Celsius temperatures that are negative? Are there positive Celsius temperatures that have equivalent Fahrenheit

8 8 temperatures that are negative? How can you tell? There are some positive Fahrenheit temperatures that are equivalent to negative Celsius temperatures, but no positive Celsius temperatures that are equivalent to negative Fahrenheit temperatures. We can tell because the line goes through Quadrant IV but not Quadrant II. In Quadrant IV, the x-coordinates are positive and the y-coordinates are negative. Since Fahrenheit has been plotted on the x-axis and Celsius on the y-axis, then the portion of the graph that goes through Quadrant IV shows positive Fahrenheit temperatures that are equivalent to negative Celsius temperatures.

9 9 Cl o si ng 3 Distribute a small piece of paper with a 4-quadrant grid. Ask the students to: 1. Plot (-2, -5) and (-4, -1). 2. Draw a line through the two points that extends beyond them. 3. Find the y-value on the line when x = Find the x-value on the line when y = -7. Collect the papers to review later. 1 & 2: 3: y = -3 4: x = -1

Возрастная группа: 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 3.4, 4.4 d,

1 План урока Estimating Quotients (2-Digit Divisor) Возрастная группа: 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 3.4, 4.4 d, 5.5 a Virginia - Mathematics Standards of Learning (2016):