Special Education Compliance Training Overview

This overview provides information on the special education monitoring process, self-assessment activities, and resources for assistance. Explore the steps, required activities, and timelines for self-assessment in Missouri.

• Special Education
• Compliance
• Training
• Missouri
• Monitoring

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Uploaded on Mar 02, 2025 | 0 Views

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1. How Close?

2. How Close? How close is the line passing through points ? and ? to point ?? 4 64 1 62= 60 63= 20 Gradient,? = 21 4 = 20 ? =104 1 + ? 21 ? 62,64 21 Eqn of line: 21? + 20? = 104 ? 1,4 (not to scale) ? 20, 5

3. How Close? How close is the line passing through points ? and ? to point ?? Perpendicular gradient, ? =21 21? + 20? = 104 20 5 =21 20 20 + ? ? = 16 ? 62,64 Eqn of perpendicular line: 20? 21? = 320 ? 1,4 (not to scale) ? 20, 5

4. How Close? How close is the line passing through points ? and ? to point ?? To find intersection, solve: 21? + 20? = 104 20? 21? = 320(1) 21? + 20? = 104(2) ? 62,64 515 29,106 29 20? 21? = 320 ? 1,4 (not to scale) ? 20, 5

5. How Close? Determine the hypotenuse, , of the triangle: 2 2 2= 20 515 6 29 + 5 10 29 2 2 2= 1414 + 156 515 29,106 29 29 29 2= 441 = 21 20, 5

6. How Close? How close is the line passing through points ? and ? to point ?? ALTERNATIVELY, having determined the equation of the line translate it and point ? such that ? now lies at the origin. That is, translate by vector 20 5 Eqn of line is now: 21 ? 5 + 20 ? 20 = 104 or: . 29 21? + 20? = 609 Find the ? and ? intercepts: 309 20

7. How Close? How close is the line passing through points ? and ? to point ?? 9 Hypotenuse of triangle with sides 29 and 30 20 is: 2 292+ 309 = 421 29 20 20 Area of the triangle gives: 1 229 309 =1 421 20 2 20 = 21 309 20

8. How Close? How close is the line passing through points ? and ? to point ?? You could even find the intersection of the line and the circle centred on ?. 21? + 20? = 104 Solve the simultaneous equations: (1) (2) 21? + 20? = 104 ? + 52+ ? + 202= ?2 (not to scale) ? 20, 5

9. How Close? (1) 21? + 20? = 104 ? + 52+ ? + 202= ?2 (2) ? = 20 21? +104 21 (1) 2 20 21? +104 21+105 + ? + 202= ?2 (2) 21 2 20 21? +209 + ? + 202= ?2 21 20? + 2092+ 21? + 4202= 212?2 841?2+ 9280? + 220081 = 441?2 841?2+ 9280? + 220081 441?2= 0 For a single root (tangent) the discriminant must equal zero. So, 92802= 4 841 220081 441?2 25600 = 220081 441?2 441?2= 194481 (not to scale) ? = 21 ? 20, 5

11. Note to Teacher(1) Not all of the lines are the same task A-H task I-L task M-P 4? + 3? = 10 24? + 7? = 10 20? + 21? = 104 3.2,7.6 0.16,0.88 515 29,10 6 29 But the shortest distance to 20, 5 is 21 for all. The coordinates of the closest point on the lines are given on the right, above. You could also have a discussion about how it was possible to get integer value coordinates for all the tasks.

12. Note to Teacher(2) Clearly, all of the lines are tangential to the circle, radius 21 with centre 20, 5 . The trick now is to find points on a unit circle that have rational coordinates. You can then scale the circle up to achieve integer coordinates (you will have tangents with rational gradients by default). This is how you do it: Draw a line from 1,0 to meet the unit circle If the gradient is rational (i.e. ? and ? are integers) then the coordinates of ?,? will be rational. ? 1 ?,? ? I am grateful to Tim Pattison (my HoD) for bringing this result to my attention. ? ? 1 1 ?2 ?2 ?2+ ?2, 2?? ?2+ ?2 ?,? = ?2 ?2 2?? ?2+?2 2?? Equation of tangent: ? = ? +

13. RESOURCES

14. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 5,10 ? 1,2 (not to scale) ? 20, 5 A

15. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 4, 2 ? 10, 10 (not to scale) ? 20, 5 B

16. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 8,14 ? 7, 6 (not to scale) ? 20, 5 C

17. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 5,10 ? 10, 10 (not to scale) ? 20, 5 D

18. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 14,22 ? 11,18 (not to scale) ? 20, 5 E

19. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 2,6 ? 1,2 (not to scale) ? 20, 5 F

20. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 8,14 ? 5,10 (not to scale) ? 20, 5 G

21. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 14,22 ? 13, 14 (not to scale) ? 20, 5 H

22. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 1, 2 ? 15, 50 (not to scale) ? 20, 5 I

23. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 6, 22 ? 8, 26 (not to scale) ? 20, 5 J

24. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 20,70 ? 15, 50 (not to scale) ? 20, 5 K

25. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 13,46 ? 8, 26 (not to scale) ? 20, 5 L

26. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 1,4 ? 22, 16 (not to scale) ? 20, 5 M

27. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 62,64 ? 20,24 (not to scale) ? 20, 5 N

28. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 41,44 ? 1,4 (not to scale) ? 20, 5 O

29. SIC_32 How Close? How close is the line passing through points ? and ? to point ?? ? 20,24 ? 22, 16 (not to scale) ? 20, 5 P