AchieveMath Instructional Intervention
High School Success SAMPLE LESSONS
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HS Math Success — Lesson 6
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©2013 This information is confidential and proprietary to Catapult Learning™. For internal distribution only.
High School Success – Lesson 6
AchieveMath
Lesson Objective and Standards Interpret units, use units to evaluate the appropriateness of a solution, and choose appropriate units for a given context (N.Q.1, PS.1, PS.2, PS.6)
Word Problem Objective Use expressions to solve area and volume problems
Materials/Manipulatives dry-erase boards, markers, erasers
Welcome (3 min.) Brief Review and Practice (10 min.)
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Skill: Converting customary units (inches, feet, yards and miles)
Say: “We are going to review converting units. Recall the following conversion factors: 12 inches = 1 foot; 3 feet = 1 yard; 1,760 yards = 1 mile; 5,280 feet = 1 mile. I will write 6 problems on the board. Use the conversion factors to figure out the answer. Do your work on your dry-erase boards.”
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Teacher: Write the following problems on the board: • 36 in. = _____ yd. • 8 ft. = _____ in.
• 7920 ft. = _____ mi.
(1)
(96)
(1.5)
•
2 mi.= _____ yd.
(3,520)
•
9 ft. = _____ yd.
(3)
•
10 yd. = _____ ft.
(30)
Teacher: Once the students have completed the problems discuss them.
Word Problem Teacher: Write the problem on a board. Have students read the problem silently to themselves. Then choose a student to read it out loud. Students will solve this problem on their dry-erase boards. Remind the students to make sure that they are answering the question. Cameron has a new rectangular patio connected to his house that measures 2 meters by 5 meters. He wants to plant a garden around the patio that is 1.5 meters wide. How much soil does he need if the soil in his garden is 0.5 meters deep?
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High School Success – Lesson 6
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Drawing a picture helps. The shaded areas represent Cameron’s garden. Find the area of the shaded region. (8 • 1.5) + 2 (2 • 1.5) = 12 + 2 (3) = 12 + 6 = 18 square meters The volume of soil needed is the area of the garden multiplied by the depth: 18 • 0.5 = 9 cubic meters The amount of soil needed for Cameron’s garden is 9 cubic meters. 8m 5m
1.5 m
2m
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Corresponding Vocabulary
Patio
2m
House
Teacher: Write the following vocabulary word on a board. Discuss this word and its meaning throughout the lesson. units
Concept Development (10 min.) Say: “We all deal with different types of units in real life. Units indicate the magnitude of the measurement. If you need new furniture for your bedroom and you want to make sure it fits, taking a measurement of the space would help when you go out to buy furniture. Or if you want to travel by car from one state to another, it would help to know how many miles you will be traveling to estimate how much gas will be needed along the way. It’s also very important to understand what type of unit should be used for different situations. For example, if you want to buy new furniture, it won’t make sense to measure the space in terms of miles. You’d measure in inches or feet. Today we will be learning about choosing appropriate units and interpreting units for different situations. Can you think of a scenario in which you may need to choose appropriate units?” Teacher: As a class, discuss different scenarios
Say: “Let’s consider the following scenario: A chef is buying meat for his restaurant for the next week. What would be the most appropriate unit of measurement for meat?” (pound)
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High School Success – Lesson 6
AchieveMath
Say: “In this case, it makes sense to measure meat in terms of pounds rather than ounces or tons. Ounces will work if it is for an individual person or family. A ton, which equals about 2,000 pounds, will be way too much meat. Let’s consider another scenario.” Teacher: Write on a board: We want to calculate the speed at which a ball rolls down a hill. It takes 2.3 minutes for the 1-pound ball to roll down a hill sloped at a 53 degree angle. If the distance from the top of the hill to the bottom is 72 feet, our answer will be in which units?
Say: “What do we want to calculate in this problem?” (speed)
Say: “What information is given that involves units?” (2.3 minutes, 1 pound, and 72 feet)
Say: “What will be the unit when calculating the speed?” (feet per minute)
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Say: “Since we know from our previous knowledge that Distance is equal to Speed times Time, we can say Speed is equal to Distance divided by Time. The unit for Distance in our problem is in terms of feet and the unit for Time is in terms of minutes; therefore, speed will be measured in feet per minute.”
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Teacher: Write on a board:
In last week’s cross country meet, Taylor’s time in the 5k race was 24 minutes. What would her mile pace be? How many minutes would it take her to run a mile?
Say: “Let’s look at this problem. What does 5k mean?” (5 kilometers)
Say: “Since we are looking for the answer in terms of miles, we need to know that 1 kilometer is 0.621 miles. So, what would 5 kilometers equal in terms of miles?” (3.105 miles)
Say: “Since Taylor ran 3.105 miles in 24 minutes, how can we find out how many minutes it took her to run 1 mile?” (24 divided by 3.105)
Say: “So, once you divide 24 minutes by 3.105 miles, what do you get?” (7.73 minutes per mile)
Say: “As you can see, it is very important to understand which unit is appropriate for different scenarios and to use the correct unit to answer problems.”
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High School Success – Lesson 6
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Guided Practice (15 min.) Teacher: Write the problems, one at a time, on a board. Students will work with a partner on the problems. Check student work before proceeding to the next problem.
Say: “For each scenario, write down which unit of measure would be appropriate to answer the problem and why. Then, solve the problem.” • Area of a circle with a radius of 3 feet Square feet because area of a circle formula is area = π • r2, when multiplying 3 feet by 3 feet you will get 9 square feet. Area = 3 feet • 3 feet • π = 9 square feet • π = 9π square feet • Radius of a circle with a diameter of 4 inches
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Inches. If the diameter is 4 inches, radius is half of the diameter, so it will be still in inches. 4 inches = 2 inches 2
• How long it will take to travel 330 miles with a speed of 60 miles per hour (mph). Distance . Miles divided by miles per hour will cancel Hours. Distance = Speed • Time, which means Time = Speed the miles out and leave with hour only.
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Time =
330 miles = 5.5 hours 60 mph
• Volume of a rectangular prism with dimensions 8 meters, 2 meters, and 3 meters
Cubic meters. Volume = length • width • height, so meters • meters • meters = cubic meters. Volume = 3 meters • 2 meters • 3 meters = 18 cubic meters
Independent Practice/Application (7 min.) Teacher: Write the problems on a board. Students work independently to solve the problems, using most appropriate units.
Say: “Read each problem carefully and answer the question using the appropriate unit.” • Nicole drives her car a distance of 129 miles. If she drives at an average speed of 45 miles an hour (mph), about how long will it take her to reach her destination? (Distance = Speed • Time; Time =
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Distance 129 miles ; Time = ; About 3 hours) Speed 45 mph
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High School Success – Lesson 6
AchieveMath
• Joseph has determined that he can read about 150 words per minute. This weekend, he needs to read a 310 page book. If a typical paperback has about 350 words per page, how many hours should Joseph set aside for reading? To get the total number of words, we can multiply 310 pages by 350 words = 108,500 words total. 108,500 words = 723 minutes 150 words per minute 723 minutes To determine how many hours, ; about 12 hours. 60 minutes • It takes Casper the Ghost 62 minutes to from his haunted house to another one that is 47 miles away from his haunted house. If he at the same speed, how long would it take him to to Wendy’s house, which is 71 miles away from his? First, find out how many miles per minute Casper can fly. 62 minutes =1.32 minutes per mile 47 miles
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1.32 minutes per mile • 71 miles = 94 minutes About 94 minutes.
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Closure (15 min.)
• Lesson Summary – (7 min.)
What did we do today?
Provide a real-life application of this skill.
• Administer Daily Lesson Assessment – (8 min.)
Check all work. Score and record results on the Math Group Skills Sheet. 1.
16π square inches; area = radius2 • π; area = 4 inches • 4 inches • π; 16π square inches
2.
84 cubic feet; volume = length • width • height; volume = 4 feet • 3 feet • 7 feet = 84 cubic feet 111,000 words = 505 minutes ; 8 hours; 300 pages • 370 words per page = 111,000 words; 220 words per minute
3.
505 minutes = about 8 hours 60 minutes 4.
4.5 hours; Distance = Speed • Time; Time =
250 miles Distance = about 4.5 hours ; Time = Speed 55 mph
• Tokens/Token Tracker/Awards Center – (6 min.)
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High School Success – Lesson 6
Daily Lesson Assessment
Name: _____________________________________________________________________________________
Date ____________________________
SKILL: Determining the correct unit for the given problem Directions: Read each problem carefully and answer the question by using the correct unit. 1.
Find the area of a circle with a diameter of 8 inches.
2.
Find the volume of a rectangular prism with dimensions 4 ft., 3 ft., and 7 ft.
3.
Brittany says she can read about 220 words per minute. She has a book that is 300 pages long and each page has about 370 words per page. How many hours will it take Brittany to finish the book?
4.
Carl drives his car a distance of 250 miles. If he drives at an average speed of 55 miles an hour, about how long will it take him to reach his destination?
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