Download - 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010
![Page 1: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/1.jpg)
1
The Case of the Missing Coordinates
6th Grade AZ Math Standard
S4C3-PO2Carol Cherry/MPS/2010
![Page 2: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/2.jpg)
2
Just the Facts
To help you solve the case, we’ll
review some basic facts about
coordinates in the next few slides.
![Page 3: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/3.jpg)
3
Ordered PairsAlways start at the origin (0,0)
The first number tells how many units to go on the horizontal, or x-axis.
If the first number is positive, e.g. (3,4), go Right 3 units
If the first number is negative, e.g. (-3,4) go Left 3 units
€
y
€
x
€
(0, 0)
€
+
€
–
![Page 4: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/4.jpg)
4
The second number tells how many units to go on the vertical, or y-axis.
If the second number is positive, e.g. (3,4), go Up 4 units
If the second number is negative, e.g. (3,-4), go Down 4 units
€
y
€
x
€
(0, 0)
€
+
€
–
![Page 5: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/5.jpg)
5
To solve the mystery of the missing coordinates you need
to know the properties of some important polygons
![Page 6: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/6.jpg)
6
Clues that a polygon is a square
Number of sides: 4
Number of pairs of parallel sides: 2
Number of right angles: 4
Number of congruent sides: 4
![Page 7: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/7.jpg)
7
Clues that a polygon is a rectangle
4
Number of pairs of parallel sides: 2
Number of right angles: 4
Number of congruent sides: 2 pairs of opposite sidescongruent
Number of sides:
![Page 8: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/8.jpg)
8
Clues that a polygon is a parallelogram
Number of sides: 4
Number of pairs of parallel sides: 2
Number of right angles: 0
Number of congruent sides: 2 pairsopposite sidescongruent
![Page 9: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/9.jpg)
9
Clues that a polygon is an isosceles trapezoid
Number of sides: 4
Number of pairs of parallel sides: 1
Number of right angles: 0
Number of congruent sides: One pair of opposite sides congruent
![Page 10: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/10.jpg)
10
Here is an example of how a great detective would solve this case.
Goal:Find the missing coordinates of this parallelogram and justify your answer.
Properties to use as clues:Both pairs of sides are parallel, so the bottom line, or base, has to be parallel to the top line. That means the vertex will be on the same line as the vertex at (-6,1) so 1 is the second coordinate.The base has to be congruent to the top line, which is 6 units long. So start at the left vertex, -6, and go 6 units right. The X, or first coordinate is at X=0.
€
y
€
x
€
(−6,1)
€
(−4,6)
€
(2,6)
€
(0,1)
The missing coordinates are (0,1)
![Page 11: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/11.jpg)
11
Now you’re ready to find some missing coordinates!
![Page 12: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/12.jpg)
12
What are the missing coordinates
of this square?
The coordinates are:
(-1,-1)
Explain how you found them.
€
y
€
x
€
(−1,5)
€
(5,5)
1)- (5,
![Page 13: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/13.jpg)
13
Find the coordinates for the
fourth vertex of this rectangle.
Ordered pair:
(-6,4)
Explain how you found them.
€
y
€
x
€
(−6,−4)
(4,4)
€
(4,−4)
![Page 14: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/14.jpg)
14
Locate the missing coordinates in this
parallelogram
See the next slide for a tip
€
y
€
x
€
(-4,2)
€
(-1,7)
€
(3,2)
![Page 15: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/15.jpg)
15
Think of the parallelogram as a rectangle and
2 triangles
The triangles are congruent.
The left triangle has a base of 3 units.
Therefore, the base of the triangle on the right is 3 units.
Now you can find the missing coordinates: (6,7)
€
y
€
x
€
(-4,2)
€
(-1,7)
€
(3,2)
€
← 3 →
€
← 3 →
![Page 16: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/16.jpg)
16
Find the coordinates for the missing vertex of this parallelogram.
Coordinates:
(5,-2)
Justify your answer.
€
y
€
x
€
(-5, -8)
€
(-3, -2)
€
(3, -8)
![Page 17: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/17.jpg)
17
Think of this isosceles trapezoid as a square
plus 2 triangles.
Missing Coordinates:
(5,-1)
€
y
€
x
€
(−6,−1)
€
(−3,4)
€
(2,4)
Find the missing coordinates.
![Page 18: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/18.jpg)
18
One last chance to practice:Find the ordered pair for the missing vertex in this parallelogram.
Tell your partner which properties of a parallelogram helped you find your answer.
Ordered pair for the missing vertex:
(4,7)
€
y
€
x
€
(−6,2)
€
(1,2)
€
(−3,7)
![Page 19: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/19.jpg)
19
For more practice with ordered pairs, try these websites:
http://www.oswego.org/ocsd-web/games/BillyBug2/bug2.html
http://www.shodor.org/interactivate/activities/MazeGame/
http://funbasedlearning.com/algebra/graphing/default.htm
![Page 20: 1 The Case of the Missing Coordinates 6 th Grade AZ Math Standard S4C3-PO2 Carol Cherry/MPS/2010](https://reader035.vdocument.in/reader035/viewer/2022062404/5514dc1d55034640138b65eb/html5/thumbnails/20.jpg)
20
Thank you for
helping solve the
Case of the Missing
Coordinates. Now
you are ready to
solve your own
cases.