Survivor Math

Everyone has their own opinions on how to teach math to young children. I am going to tell you exactly how I feel. If they don’t know why, they will never remember how!!!  Conceptual teaching of mathematics is the way to go. If children can explain in their own words why something works, it is so much more meaningful. In this section of the website, I am going to share conceptual ways of teaching math and lots of fun ideas for the classroom. These conceptual ideas are nothing new- just something that should be brought to the forefront again. 

Again- if you like what you see, let me hear from you. I am more than happy to share! Here is a glimpse into my world:

SURVIVOR MATH (This is an excerpt from 6th grade Math- It also assumes that you have access to internet and subscriptions to www.discoveryeducation.com and/or www.brainpop.com)

Survivor Math is a 20 countdown before End of Grade Testing!  It is available for grades 3-7. DISCLAIMER: Figures used in Survivor Math will NOT show up on the website unless downloaded.

DAY 11: COORDINATE GEOMETRY 6th Grade

RETEACH GOAL 3:01 & 3:04

3.01
Identify and describe the intersection of figures in a plane.
3.04
Solve problems involving geometric figures in the coordinate plane.

Coordinate Geometry

The coordinate planeis made up of a horizontal number line, the x-axis, and a vertical number line, y-axis. The x-axis and y-axis intersect at the origin, or point (0,0). Points in the coordinate plane are identified by combining the x coordinate of the point and the y coordinate of the point, (x,y). This is called an ordered pair and it is important to note that the x-coordinate always comes before the y-coordinate when writing a point as an ordered pair.When solving geometry problems on a coordinate plane, remember that the gridlines and intervals of the coordinate plane will provide the information needed to solve the problem.

Example:

 

What is the perimeter of the object on the coordinate plane above?

Solution: 20 units

Explanation:

The perimeter is the distance around an object. Use the grid to measure the length of each side of the figure.

The object has six sides, with lengths of 6, 4, 3, 3, 3, and 1.

Add up the lengths of each side to find the perimeter:

6 + 4 + 3 + 3 + 3 + 1 = 20 units.

Coordinate Geometry

When two figures intersect, we can often use the properties of one figure to determine the properties of the other figure.

Example:

 

Study the coordinate plane above. If a circle were drawn in such a way that it intersected the red square at points (4,5), (6,3), (6,7), and (8,5), then what would be the length of the diameter of the circle?

The diameter of a circle is the line segment that joins two points on the circumference of circle and passes through the center of the circle.

In this case, the circle to be drawn shares exactly one point with each side of the red square. So the distance across the circle, or diameter, will have the same length as any side of the square.

Using the coordinate plane, you can see that a side of the square is 4 units long.

Therefore, the length of the diameter of the circle is 4.

GAME: Coordinate Plane Game

 PRACTICE:               Ordered Pairs

      

Tell what point is located at each ordered pair.

1. (3,-2) ______                 2. (2,3) ______                  3. (-5,5) ______

4. (-7,-8) ______               5. (-4,4) ______                 6. (-5,0) ______

 

Write the ordered pair for each given point.

7. E ____________                      8. M ____________                    9. P ____________

10. G ____________       11. Q ____________       12. N ____________

 

Plot the following points on the coordinate grid.

13. S (-6,-3)                                     14. T (2,-4)                           15. U (5,8)

 

VIDEO: Coordinate Grid

 CHALLENGE:

Coordinate Geometry

1. 

 

Study the coordinate plane above. A square is to be drawn around the blue circle in such a way that it intersects the circle at points (3,4), (5,2), (5,6), and (7,4). Which of the following could be the coordinates for one of the vertices of the square?

 
 

A.

(7,6)
 

B.

(4,3)
 

C.

(7,5)
 

D.

(3,4)

2. 

 

Study the coordinate plane above. If a circle were drawn in such a way that it intersected the purple square at points (2,11), (7,6), (7,16), and (12,11), then what would be the length of the diameter of the circle?

 

A.

8
 

B.

9
 

C.

12
 

D.

10

3. 

 

What is the area of the figure shown on the coordinate plane above?

 

A.

26 square units
 

B.

21 square units
 

C.

30 square units
 

D.

23 square units

4. 

 

What is the area of the figure shown on the coordinate plane above?

 

A.

17 square units
 

B.

18 square units
 

C.

23 square units
 

D.

15 square units

5. 

 

What is the perimeter of the figure shown on the coordinate plane above?

 

A.

35
 

B.

28
 

C.

31
 

D.

27

6. 

 

Study the coordinate plane above. If a circle were drawn in such a way that it intersected the orange square at points (4,9), (7,6), (7,12), and (10,9), then what would be the length of the diameter of the circle?

 

A.

6
 

B.

4
 

C.

3
 

D.

12

7. 

 

Study the coordinate plane above. If a circle were drawn in such a way that it intersected the blue square at points (2,5), (4,3), (4,7), and (6,5), then what would be the length of the diameter of the circle?

 

A.

5
 

B.

1
 

C.

4
 

D.

8

8. 

 

What is the perimeter of the figure shown on the coordinate plane above?

 

A.

16
 

B.

12
 

C.

8
 

D.

15

9. 

 

What is the area of the figure shown on the coordinate plane above?

 

A.

15 square units
 

B.

13 square units
 

C.

14 square units
 

D.

24 square units

10. 

Consider the intersection of a circle and a quadrilateral in a plane. What is the maximum number of points of intersection for these two figures?
 

A.

5
 

B.

12
 

C.

10
 

D.

8

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