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U n t er r i ch t spl a n
Pl o t t ing and R e ad ing Ne g at ive
Numb e rs o n a Co o rd inat e Grid
Altersgruppe: 6t h Gr ade
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-Ressourcen: T ake t he H e at
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
8
12
10
14
3
min
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e a real-world example of a function using negative
numbers
P r ac t i c e reading values from a graph
L e ar n to plot points in Quadrant III
De v e l o p strategies for converting units
Ope ni ng | 8 min
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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 ax e s .
When the students are done, display a numbered grid so they can
correct their work.
A sk : Where on the grid are both the x - and y- c o o r di nat e s
positive?
The x- and y-coordinates are both positive in Quadr ant I , the
upper right-hand quadrant.
A sk : Where on the grid is the x-coordinate positive, but the ycoordinate negative?
In Quadr ant I V , the lower right-hand quadrant, the x-coordinate
is positive and the y-coordinate is negative.
A sk : Where on the grid are both the x- and y-coordinates negative?
The x- and y-coordinates are both negative in Quadr ant I I I , the
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lower left-hand quadrant.
A sk : In which quadrant is the point (-3, 6)?
The point (-3, 6) is in Quadr ant I I , the upper left-hand quadrant.
A sk : How do we plot the point (-2, -5)?
We start at the o r i gi n and move 2 spaces left. Then we move
down 5 spaces and plot our point.
S ay : In today’s episode, we will practice plotting points when both
coordinates are negative.
T e ac he r pr e se nt s M at h game : T ake t he H e at - N e gat i v e
N umbe r s | 12 min
Present Matific ’s episode T ake t he H e at - N e gat i v e
N umbe r s 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.
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S ay : Please read the instructions.
Students can respond based on the episode.
S ay : 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.
S ay : 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.
S ay : We are looking at only part of the coordinate grid. What
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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).
S ay : 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.
S t ude nt s pr ac t i c e M at h game : T ake t he H e at - N e gat i v e
N umbe r s | 10 min
Have the students play T ake t he H e at - N e gat i v e N umbe r s
on their personal devices. Circulate, answering questions as
necessary.
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M at h P r ac t i c e : N e gat i v e N umbe r s o n a C o o r di nat e Gr i d
W o r kshe e t | 14 min
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.
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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. S ay : Name some points
that are on the graph.
Responses will vary.
A sk : 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
.
A sk : 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.
A sk : Are there positive Fahrenheit temperatures that have
equivalent Celsius temperatures that are negative? Are there
positive Celsius temperatures that have equivalent Fahrenheit
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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.
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C l o si ng | 3 min
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 = -3.
4. Find the x-value on the line when y = -7.
Collect the papers to review later.
1 & 2:
3: y = -3
4: x = -1
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