Sample Lesson Plans Tayo Odusanya Lesson Sample 1

Sample Lesson Plans Tayo Odusanya

Lesson Sample #1: 2 -Step Inequalities Domain: Expressions and Equations Common Core Standard: 7. EE. B. 4. B Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Learning Target: Students will be able to solve 2 -step inequalities Students will be able to write an inequality for a word problem Vocabulary Words: equation, inverse operations, inequality, solution set, open circle, closed circle, at most, at least, greater than, less than (≤, ≥, <, >) Background Knowledge/Connections: Students should be able to solve one-step equations and inequalities. Students should be able to graph inequalities such as x > 3 or x < -5 on a number line. Students should be able to use the order of operations to solve multi-step problems. Students should be able to add, subtract, multiply and divide positive fractions and decimals Students should be able to solve 2 -step equations Common Misconceptions: Students may not distinguish between the less than and less than or equal to signs with an open or closed circle when graphing When solving an inequality, students may find a decimal or fractional answer for items that cannot be partial values. Students must round up or down to the closest reasonable answer. Students may attempt to change the direction of the inequality sign when adding or subtracting a negative number. Remind students that this reversal is done only when the inverse operation includes multiplying or dividing by a negative number. Materials: algebra tiles, Frayer model Other Resources: Graphing inequalities on a number line Graphing Inequalities Review- School Yourself Adding and Subtracting with Inequalities (One Step)- Khan Academy Multiplying and Dividing Inequalities by a negative number- School Yourself Inequalities Dominoes (pdf file) Partner Problems (pdf file) Closure/Assessment: Exit Pass- Frayer Model

Warm-Up 1. Solve for x 2 x + 4 = 42 3. Write the inequality. Define your variable. Name: 2. Jeremy has $25 in his savings. He spent $7 at the movies. If he spends $3 everyday for bus fare, how many days will Jeremy be able to pay the fare? Write a 2 step equation and solve. 4. Solve for the variable Mr. Smith has at least 73 books. The price of a new pair of Toms is more than $30. 5. Write the solution of the graph 6. Julie wants to average earning $100 per week babysitting. If Julie earned $95 the first week and $115 the second week, how much must she earn in the third week to meet her goal? Total Correct: ___/6

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. Summer Job Summer Hours Cashier 250 Stock Person 210 Deli 195 Bakery 180 Workspace Does he have enough money?

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.

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.

One-step Inequalities Review 1. X + 4 > 12 -4 -4 x>8 subtract 4 on both sides x is greater than 8. So possible solutions include all values greater than 8. Because x cannot be 8, it is an open circle x>8

You try… •

Two-step inequalities Solve for x: 7 x + 2 ≤ 23 Step 1: subtract 2 from both sides 7 x + 2 ≤ 23 - 2 -2 7 x ≤ 21 Step 2: divide both sides by 7 7 x ≤ 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

You try… 1) 10 x + 7 ≤ 37 1) 3 x – 9 > 6 1) -2 x + 24 ≥ 14

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 onetime 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.

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. 40 x To make exactly $1800, what he needs for the trip, 60 + 8. 40 x = 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. 40 x > 1800 Because Benjamin could make exactly $1800 OR more than $1800, we will use the “greater than” or equal to” symbol So 60 + 8. 40 x ≥ 1800

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?

Exit Pass Create 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

Lesson Sample #2: Percent word problems Domain: Ratios and Proportional Relationships Common Core Standard: 7. RP. A. 3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Learning Target: Student will calculate discounts and taxes using strategies to include direct translation; bar models; and ratios and proportions Vocabulary Words: proportion, ratio, proportional relationships, percent, rate, discounts, taxes Background Knowledge/Connections: In 6 th grade, students solved problems involving unit rate. They also learned to find a percent of a quantity as a rate per 100. Students also solved problems involving finding the whole given a part and the percent. In prior unit, students learned to solve ratio and proportion problems using cross multiplication. Students should also know how to convert between fractions, decimals and percents. Common Misconceptions: Students struggle with placement of numbers in a proportion. Emphasize the multiple relationships within a proportion and show students a variety of ways that a proportion for a problem could and could not be set up. When setting up proportions, model using units so students keep numerator and denominator consistent. When discussing percent, emphasize that there are percentages larger than 100% when illustrating percent increases (taxes, gratuities, markups, etc) Materials: linking cubes, Other Resources: www. thinkingblocks. com Discounts Spinner Game (attached) Word Problems number cube Game (attached) Activities 1. Warm up- formative assessment to identify skills deficits for standard. Used to form remediation groups 2. Show pictures that represent parts of a whole and represent the model as fraction, then as a decimal using a tenths grid. Using the same grid, break parts further into hundredths to model equivalent relationships between decimals. e. g. 0. 3 = 0. 30 3. Remind students that percent means out of 100. Relate hundredths grids to percent 4. Using direct translation, show to find 20% of $10. 5. Using a bar model, solve 20% of $10. Be sure to explain to students that because 20% is a multiple of 10, it is convenient to break up the whole bar into 10 tenths, because 20% is the same as 2 tenths. 6. In collaborative groups, have students solve using both strategies a) 30% of $50 b) 10% of $20 c) 12% of $24 7. After sufficient practice time, discuss challenges students may have faced with solving the problems. In solving 12% of $24, students should notice that using the bar model would be difficult as it would be impossible to break up the whole bar into equal parts since 12 is not a multiple of 100. 8. Discuss how you can use a bar to model the problem. This time, the bar is oriented vertically. The entire bar still represents 100%, which is the total amount we have ($24). Then mark off 12% on the bar. 9. Model real word scenarios involving markups and markdowns. Closure/Assessment: Exit Pass

Warm-Up Name: 1. Shade 80% of the bar below: 2. What is 3/10 as a percent? Answer: ____ 4. What is 30% of $800? Answer: ____ 5. Mark is buying a jacket that costs $55. He pays $5 in taxes. What is his total? Answer: ____ 6. Mark is buying a jacket that costs $55. He pays 5% in taxes. What is his total? Answer: ____ Total Correct: ___/6

Using linking cubes, model the fraction, decimal and percent

Example: Find 20% of $10 I can use three strategies to solve this problem. 1) Direct translation 2) Bar models/linking cubes 3) Proportions

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

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

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

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.

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

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

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

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

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

b)

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

Exit Pass 1. Calculate 12% tip on $42 restaurant bill. 2. How much would a refrigerator with an original price of $899 be with a 30% off discount? 3. 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?

Lesson Sample #3: Circumference of a Circle Domain: Geometry Common Core Standard: 7. G. B. 4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Learning Targets: Students will determine the relationship between the circumference of a circle and its diameter and determine that the circle’s circumference is about three times it diameter Students will identify pi (π) as the ratio of a circle’s circumference to its diameter Vocabulary Words: radius, diameter, pi, circumference Background Knowledge/Connections: Students have worked with perimeter in prior grades. Linking perimeter to circumference of a circle will help link the new material to students’ background knowledge Common Misconceptions: Students often confuse the definitions of the words “diameter” and ‘radius”. Students incorrectly divide diameter by circumference when finding the ratio. Students have difficulty measuring accurately or reading measurements on a ruler Materials: yarn/string; circular objects of varying sizes; ruler, scissors recording sheet, calculator Other Resources: N/A Closure/Assessment: Notes Sheet

Vocabulary Notes

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 3 rd 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?

Recording Sheet Object A B C D E F Circumference Diameter Ratio of circumference to diameter

Notes Record your observations Using an equation, write the relationship between the circumference of a circle, pi and diameter The diameter of Earth is 7, 917. 5 mi. Using the value 3. 14 for pi, calculate the circumference of the Earth. Extension The International Space Station travels in orbit around Earth at a speed of roughly 17, 150 miles per hour (that's about 5 miles per second!). How long would it take to orbit Earth?