1. 1 Lesson 1.2.7 Understanding Problems

2. 2 Lesson 1.2.7 Understanding Problems California Standards: Algebra and Functions 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Mathematical Reasoning 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. What it means for you: Key Words: You’ll learn how to spot which pieces of information are important in answering a question, and how to check that your answer has the correct units. relevant irrelevant unit

3. 3 Lesson 1.2.7 Understanding Problems Math problems are full of all kinds of details. To be able to do this you need to understand exactly what the question is asking. The challenge is to work out which bits of information you need and which bits you don’t need.

4. 4 You Can’t Solve a Problem with Information Missing Lesson 1.2.7 Understanding Problems Sometimes a piece of information needed to solve a real-life problem will be missing. You need to be able to read the question through and identify exactly what vital piece of information is missing.

5. 5 Example 1 Solution follows… Lesson 1.2.7 Understanding Problems Brian’s mechanic charged $320 to fix his car. The bill for labor was $157.50. How many hours did the mechanic work on the car? Solution The question tells you that Brian’s total bill for labor was $157.50. But to use this piece of information to work out how many hours the mechanic worked on the car you would also need to know what the mechanic’s hourly rate was, as hours worked = bill for labor ÷ hourly rate. You can’t solve the problem as the mechanic’s hourly rate is missing.

6. 6 Guided Practice Solution follows… Lesson 1.2.7 Understanding Problems In Exercises 1–4 say what piece of information is missing that you need to solve the problem. 1. Samantha is 20 inches taller than half Adam’s height. How tall is Samantha? 2. A coffee bar charges $2 for a smoothie. Sol buys a smoothie and a juice. How much is his check? 3. Erin has $36 and is going to save a further $12 a week. How many weeks will it take her to save enough for a camera? 4. A box contains 11 large tins and 17 small tins. A large tin weighs 22 ounces. What is the weight of the box? Adam’s height is missing. You need to know the cost of a juice. The camera’s price is missing. You need to know the weight of a small tin.

7. 7 Some Information in a Question May Not Be Relevant Lesson 1.2.7 Understanding Problems You will often come across real-life problems that contain more information than you need to find a solution. You need to be able to sort out the information you do need from the information you don’t. Information that you don’t need to solve a problem is called irrelevant information. A good example of this is a question where you have to pick out the information that you need from a table.

8. 8 Example 2 Solution follows… Lesson 1.2.7 Understanding Problems At the hardware store Aura spent $140 on paint. She bought four cans of blue paint and spent the rest of the money on green paint. Use the table below to calculate how many liters of green paint she bought. Aura only bought blue paint and green paint. So you only need the circled data in these two rows to answer the question. Color of paintVolume of can (l)Price of can ($) Blue120 Yellow235 Red120 Green1.530 To answer the question you need the price of a can of blue paint, and the volume and price of a can of green paint. Solution The volume of cans of blue paint is irrelevant, as is the information about red and yellow paint. Color of paintVolume of can (l)Price of can ($) Blue–20 Green1.530 First work out how much Aura spent on blue paint. You know that she bought four cans of blue paint that cost $20 each. So she spent $80 on blue paint. That means she spent $140 – $80 = $60 on green paint. Each can of green paint is $30. So she bought $60 ÷ $30 = 2 cans. A can of green paint is 1.5 liters. So she bought 1.5 2 = 3 liters. The data about yellow and red paint is irrelevant. This is all the information you need.

9. 9 Guided Practice Solution follows… Lesson 1.2.7 Understanding Problems Use the table from Example 2 in Exercises 5–7. Color of paintVolume of can (l)Price of can ($) Blue120 Yellow235 Red120 Green1.530 5. Eduardo bought one can of yellow paint and three liters of blue paint. How much did he spend? 6. Lamarr bought 2 cans of green paint and some yellow paint. He spent $165. How many liters of yellow paint did he buy? 7. Amber spent $120. She bought twice as much red paint as blue paint. How many cans of red paint did she buy? $95 6 liters 4 cans

10. 10 Answers Should Always Have the Correct Units Lesson 1.2.7 Understanding Problems When you work out the answer to a problem, you need to think about the right units to use. If you apply the same operations to the units as you do to the numbers, you’ll find out what units your answer should have. You can do this with any calculation to find the correct units for the answer.

11. 11 Example 3 Solution follows… Lesson 1.2.7 Understanding Problems Laura drives her car 150 km in 2 hours. Use the formula speed = distance ÷ time to calculate her average speed. Solution Speed = distance ÷ time speed = 150 ÷ 2 = 75 Now do the same operations to the units of the numbers: speed = distance ÷ time speed = km ÷ hours = km/hour. So the average speed of the car is 75 km/hour.

12. 12 Example 4 Solution follows… Lesson 1.2.7 Understanding Problems The power consumption of a computer is 0.5 kilowatts. If the computer is running for 4 hours, how much energy will it use? Use the equation: Power Consumption Time Used = Energy Used. Solution First do the numerical calculation. Power Consumption Time Used = Energy Used 0.5 4 = 2 Then work out the units. kilowatts hours = kilowatt-hours The computer will use 2 kilowatt-hours of energy.

13. 13 Guided Practice Solution follows… Lesson 1.2.7 Understanding Problems Say what units the answers will have in Exercises 8–11. 8. 40 miles ÷ 2 hours = 20 ? 9. 5 newtons 3 meters = 15 ? 10. 6 persons 4 days = 24 ? 11. $25 ÷ 5 hours = 5 ? miles/hour newton-meters person-days $/hour

14. 14 Independent Practice Solution follows… Lesson 1.2.7 Understanding Problems 1. The sale bin at a music store has CDs for $4 each. Eric buys four CDs and some posters, and uses a coupon for $2 off his purchase. He pays $26. How many posters did he buy? Say what information is missing from the question that you would need to solve the problem. You need to know the price of a poster.

15. 15 Independent Practice Solution follows… Lesson 1.2.7 Understanding Problems 2. Liz meets Ana to go ice-skating at 7 p.m. Admission is $8 and coffee costs $1.50. Liz has $14 and wants to buy some $2 bottles of water for her and Ana to drink afterwards. Calculate how many bottles of water Liz can buy. What information are you given that isn’t relevant? You don’t need to know who Liz meets, when they meet, or the price of a cup of coffee. 3 bottles

16. 16 Independent Practice Solution follows… Lesson 1.2.7 Understanding Problems 3. Sean has $60 to buy books for math club. A book costs $9.95. He orders them on a Monday. Shipping costs $10 an order. How many books could he buy? What information are you given that isn’t relevant? Say what units the answers will have in Exercises 4–7. 4. 4 persons 4 hours = 16 ? 5. 100 trees ÷ 10 acres = 10 ? 6. 6 meters 7 meters = 42 ? 7. 21 meters/second ÷ 7 seconds = 3 ? You don’t need to know what he gets them for or when he orders them. He could buy 5 books. person-hours trees/acre meters meters, or meter 2 meters/second/second, or meters/second 2

17. 17 Round Up Lesson 1.2.7 Understanding Problems When you’re solving a math problem, you need to be able to pick out the important information. Always remember to check what units your answer needs to be written in too. Then you can use the relevant bits to write an equation and find the solution.