Low Impact Development and Bioretention Maintenance

1. Low Impact Development and Bioretention Maintenance Module 2: Math

2. Contributors The Low Impact Development Center, Inc. John Shorb Landscaping, Inc. Logo Groundwork Anacostia River, D.C. Logo

3. Overview • Some basic math skills are needed to perform bioretention maintenance activities • Calculate quantities, lengths, and volumes of materials needed • Estimate material and labor costs

4. Overview • Basic math skills • Conversions • Geometry • Calculating the area of landscaped features • Calculating volumes for soil modification and topdressing • Estimating water use

5. 2 hours • Reading: Mathematics for the Green Industry • Chapters 1-4, pp.174-190, 191-194, 211-221

6. Expected Outcomes • Be able to estimate installation, maintenance, and repair costs • Be able to calculate area and volume of landscape features

7. Basic math operations • Purpose: to be able to set up and perform calculations correctly • Estimates are no good if you get the wrong answer!

8. Order of Operations PEMDAS • Parentheses • Exponents • Multiplication and Division (left to right) • Addition and Subtraction (left to right)

9. 1. Parentheses

10. 2. Exponents • Powers and square roots

11. 3. Multiplication and Division • Proceed from Left to Right CORRECT

12. 4. Addition and Subtraction • Proceed left to right CORRECT INCORRECT

13. Put it all together 1. Parenthesis 2. Exponents 3. Multiplication and Division L -> R 4. Addition and Subtraction L->R

14. Solving for x • An unknown value in an equation is represented by a letter, usually x • Determining which value x represents is done by isolating x on one side of the equation • This is done by manipulating the equation to isolate x on one side of the equals sign • X is isolated by making the same change to both sides of the equation

15. Solving for x Subtract 2 from both sides

16. Solving for x Divide both sides by 4

17. Solving for x Multiply both sides by 4 Add 5 to both sides

18. Ratios and proportions Ratio – the relative size of two quantities expressed as one divided by the other Written as or

19. Proportion • A proportion is a statement that two ratios are equal • Examples

20. Cross multiplication If , then For example,

21. Solving problems Use cross-multiplication to solve for x: Divide both sides by 2

22. Calculating quantities A recommended soil amendment ratio is 1 part compost to 2 parts topsoil. How much compost do you need to add to 4 cubic yards of topsoil? You’ll need 2 cubic yards of compost

23. Conversions Proportions can be used to convert values from one number system to another Example: convert 0.25 acres to sqft

24. Convert ratio to percentage

25. Geometry • How to calculate the area of different shapes • Used to calculate the size of an area to be maintained • Estimate plant quantities • Estimate water needs • Estimate materials (e.g. mulch)

26. Area of a rectangle Width (w) Length (l)

27. Area of a parallelogram Height (h) Base (b)

28. Area of a trapezoid Base2 (b2) Height (h) Base1 (b1)

29. Area of a triangle Height (h) Base (b)

30. Area of a circle Where d = diameter d

31. Area of an ellipse rminor rmajor

32. Area of irregular shapes • Geometric method • Offset method • Modified offset method

33. Geometric method • Used to calculate the area of spaces that are composed of simple geometric shapes

34. Composite geometric forms 1 2

35. Offset method • Step 1: establish a line along the longest axis

36. Offset method • Step 2: establish equally spaced offset lines perpendicular to the first line

37. Offset method • Step 3: measure each line from end to end 24 ft 24 ft 24 ft 22 ft 20 ft 23 ft 21 ft 20 ft 20 ft 10 ft 100 ft

38. Offset method • Step 4: Sum the lengths of all the offset lines 24 ft 24 ft 24 ft 22 ft 20 ft 23 ft 21 ft 20 ft 20 ft 10 ft 100 ft

39. Offset method • Step 5: Multiply the sum by the distance between the offset lines 24 ft 24 ft 24 ft 22 ft 20 ft 23 ft 21 ft 20 ft 20 ft 10 ft 100 ft

40. Offset method • Formula: • Where • , and

41. Modified offset method • Used when areas cannot easily be traversed to measure the offset lines

42. Modified offset method • Step 1: create a rectangle around the area to be measured l B A w C D

43. Modified offset method • Step 2: establish equally spaced offset lines perpendicular to lines AB and CD J1 F1 E1 G1 H1 I1 B A 10 ft C D J2 F2 E2 G2 H2 I2

44. Modified offset method • Step 3a: measure the lengths of each of the offset line segments J1 F1 E1 G1 H1 I1 B A C D J2 F2 E2 G2 H2 I2

45. Modified offset method • Step 3b: Add up each pair of offset measurements

46. Modified offset method • Step 4: For each of the line segments, subtract each of the sums from the width of the rectangle. Each of the results = the actual width of the figure at the offset location

47. Modified offset method • Step 5: Sum the widths of the figure calculated in Step 4

48. Modified offset method • Step 6: Multiply the summed value from Step 5 by the distance between offsets

49. How would you estimate this area?

50. Calculating volume • Used to estimate volumes of media, gravel, soil amendments, and topdressing