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Sample Lesson Plans

Sample Lesson Plans. Tayo Odusanya. Lesson Sample #1: 2-Step Inequalities. Warm-Up. Name:. Performance Task: Summer Job.

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Sample Lesson Plans

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  1. Sample Lesson Plans TayoOdusanya

  2. Lesson Sample #1: 2-Step Inequalities

  3. Warm-Up Name:

  4. Performance Task: Summer Job Benjamin is considering taking a job at the Farmer’s Market grocery store. Depending on which department he works, his hours vary. The store pays its employees a one-time bonus of $60. In addition, employees make $8.40 an hour. Benjamin is working to save for a class trip. Airfare, hotel and food will cost $1800, so he knows he needs to make more than this amount in order to pay for the trip and have additional spending money during the trip.

  5. If Benjamin would like to make exactly $1800, create an equation and solve to figure out how many hours he should work. So, if Ben would like to make more than $1800, write an inequality statement describing the number of hours he should work. If Ben made less than $1800, write an inequality statement describing the number of hours he may have worked.

  6. When solving inequalities, you must isolate the variable. This means that the variable is on one side of the inequality by itself. Just as with equations, identify the mathematical operation within the equation and perform the inverse operation in reverse. Remember, when multiplying or dividing by a negative number, the inequality sign must be reversed in the final answer.

  7. One-step Inequalities Review

  8. You try… 1) x + 14 ≤ 41 • 4x > 42 • -5x < 205 • ≥ 2

  9. Two-step inequalities Solve for x: 7x + 2 ≤ 23 Step 1: subtract 2 from both sides 7x + 2 ≤23 - 2 -2 7x ≤ 21 Step 2: divide both sides by 7 7x ≤ 21 7 7 x ≤ 3 So x is less than or equal to 3 Check work using any number less than or equal to 3: 7 (2) + 2 ≤ 23 14 + 2 ≤ 23 16 ≤ 23

  10. You try… • 10x + 7 ≤ 37 • 3x – 9 > 6 • -2x + 24 ≥ 14

  11. Word problem application Benjamin is considering taking a job at the Farmer’s Market grocery store. Depending on which department he works, his hours vary. The store pays its employees a one-time bonus of $60. In addition, employees make $8.40 an hour. Benjamin is working to save for a class trip. Airfare, hotel and food will cost $1800, so he knows he needs to make more than this amount in order to pay for the trip and have additional spending money during the trip.

  12. Solution Benjamin makes $60 as a bonus regardless of how many hours he works. In addition, he makes $8.40 an hour. So if x is the number of hours he works, he would have $60 + $8.40x To make exactly $1800, what he needs for the trip, 60 + 8.40x = 1,800 x = 207.1 hours Benjamin could work more than 207.1 hours because then he would make more than he needed for the trip. This introduces the inequality statement 60 + 8.40x > 1800 Because Benjamin could make exactly $1800 OR more than $1800, we will use the “greater than” or equal to” symbol So 60 + 8.40x ≥ 1800

  13. Collaborative 1. Matilda needs at least $112 to buy new jeans. She has already saved $40. She earns $9 an hour babysitting. How many hours will she need to babysit to buy the jeans? 2. Gru wants to spend less than $15 on a carriage ride. The driver tells you there is an initial charge of $5 plus $0.40 per mile. How many miles can Gru ride? 3. The volleyball team is having a carwash fundraiser. The cost of each carwash is $5. They are also selling season ticket packages to their upcoming volleyball season for $40 each. The goal of the team is to make at least $2000 from the combined totals of the two fundraisers. So far, the team has sold 41 season ticket packages. How many cars must they wash in order to meet the team goal of $2000?

  14. Exit PassCreate a 2-step inequality and write in the center of the Frayer Model. Fill out the four corners by 1) translating into a verbal statement 2) solving 3) graphing solution 4) creating a real word scenario that illustrates your inequality

  15. Lesson Sample #2: Percent word problems

  16. Warm-Up Name: Answer: ____ Answer: ____ Answer: ____ Answer: ____ Answer: ____ Answer: ____

  17. Using linking cubes, model the fraction, decimal and percent

  18. Example: Find 20% of $10 I can use three strategies to solve this problem. • Direct translation • Bar models/linking cubes • Proportions

  19. Strategy 1: Direct Translation Find 20% of $10 I know that 20% = 0.2 and of means to multiply. So I can re-write this as 0.2 x $10 = $2

  20. Strategy 2: Bar Models Find 20% of $10 I can model this problem using a bar model. The whole bar represents my total quantity Because 20% is a multiple of 10, I can easily break up my whole into 10 parts, because 2 tenths = 20% So 20% of $10 = $2

  21. You try… Find 30% of $50 Find 10% of $20 Find 12% of $24

  22. Discussion How did you solve 12% of $24? What were the challenges using a bar model? Let’s solve using a third strategy that also uses a bar model.

  23. Strategy 3: Bar Model using Proportions Find 12% of $24 I can set up a proportion using the bar as a guide. Cross-multiply

  24. We try… Find 15% of $34 Find 32% of $30

  25. Markups and Markdowns Taxes and gratuities are examples of MARKUPS because you are adding to a given amount Discounts are examples of MARKDOWNS because your are subtracting from a given amount

  26. Real World Applications Sara would like to leave a 20% tip on a $42 restaurant bill. Calculate her total bill after the tip. Total bill = original bill + tip Solve using Direct Translation Tip is 20% of the total bill  20% of $42 .20 x 42 = $8.40 Total bill = $42 + $8.40 = $50.40 Solve using proportions/bar model

  27. Solve using proportions/bar model You can use the bar model two ways: • Find 20% of $42 Set up a proportion solve by cross-multiplying

  28. b)

  29. Maggie purchased a shirt for $24.50 after a 15% discount. What was the original price of the shirt? Since the shirt was marked down, she paid LESS for it than the original price. x = original price

  30. Exit Pass • Calculate 12% tip on $42 restaurant bill. • How much would a refrigerator with an original price of $899 be with a 30% off discount? • Fabio and Peter went out to eat. Their total restaurant bill was $32.50. They would like to leave 18% gratuity. If tax rate is 4%, calculate the total bill. How much would each pay if they shared the total bill equally?

  31. Lesson Sample #3: Circumference of a Circle

  32. Vocabulary Notes

  33. Script Today we are going to do an activity to explore circles using circular objects. On your desks are circular objects of varying sizes labeled A-F, a ruler, a piece of string and your calculator. We are going to take some measurements using our tools, but first we will review some vocabulary terms. The circumference of a circle is its perimeter, or the distance going around the circle. The diameter of a circle is the distance from one point on its circumference that passes through the center, to another point on the circumference. In your groups of three, you have a recording sheet with four columns. The first columns is labeled A-F, the objects that you will be measuring. In the second column, you will record the circumference of your object. In the 3rd column, you will record the diameter of your object. Finally, I’d like you to find the ratio of the circumference to the diameter of your object by dividing circumference by diameter. I will model what you are to do using circular object A. I’m trying to use a straight ruler to measure the circumference but because a circle does not have a straight edge, that is impossible. What I will do is wrap my piece of string around the circular base of my object and mark off a point using my pencil or a marker. I will cut the length of string that represents my circumference. Using a ruler, I will measure the length of my string and record it in column 2 for the circumference. Now, I am going to measure my diameter using a ruler. notice that I made sure to place my ruler so that it passes through the center to get my most accurate measure. I will record my measurement in column 3. Now in your groups, I would like you to determine the circumference and the diameter of each object of varying sizes. When you are done collecting data on C and d, divide C by d and record in column 4. round your quotient to the nearest tenths. Discussion What you will notice is that each of your ratio is close to 3. the difference in the ratios may be due to errors in measurements or in tools. But all around the classroom, regardless of the size of our circle, the ratio of C to D is ABOUT 3 for each circle. This is actually a rule in math that applies to ALL circles. The circumference of a circle is about three times its diameter and it is a constant value. This works for circles as small as a dot, to circular objects as large as the earth. I’ll show you by using my string for object A that represented its circumference. I will measure the diameter using the same string and cut off each length. I notice that I am also able to cut off about 3 pieces of string, each representing diameter, from my longer circumference string. Mathematicians have used precise tools and measurements to figure out the exact value of the constant ratio of C to d. That number is represented using a Greek symbol known as pi, which is an irrational number. To recap our lesson objective, today we explored the relationship between the circumference of a circle and its diameter. Can you tell me what the circumference of a circle is? tell me what the diameter of a circle is. the circumference is about how many times the diameter of the circle? Precisely what is this constant value called?

  34. Recording Sheet

  35. Notes

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