Putting Your Translation Skills To Work Solving Word Problems Putting Your Translation Skills To Work

Let’s Make A Plan Verbal Model Labels Algebraic Model Solve Ask yourself what you need to know to solve the problem. Labels This means define the variable Algebraic Model Write a math equation or inequality using your labels and verbal model Solve Check to make sure your solution makes sense

Let’s Try Together You and some friends are at a Chinese restaurant. You order several $2.00 plates of wontons, egg rolls, and dumplings. Your bill is $25.20, which includes tax of $1.20. Use modeling to find out how many plates you ordered. Start with a verbal model. What do you know about buying food in the restaurant and how you find your bill.

Verbal Model Final verbal model Cost of food + tax = amount paid How do you determine cost of food? Each plate costs $2.00 so # of plates  $2.00 = cost of food Final verbal model $2.00  # of plates + tax = amount paid

Labels X = number of plates you purchased 2 = amount paid per plate 1.20 = tax paid on food 25.20 = amount paid for food and tax

Algebraic Model Substitute the labels for the words in the verbal model $2.00  # of plates + tax = amount paid 2x + 1.20 = 25.20

Solve it and Check your answer 2x + 1.20 = 25.20 1.20 - 1.20 2x = 24.00 2 2 x = 12.00 There were 12 plates of food ordered 2(12) + 1.20 = 25.20 ? 24 + 1.20 = 25.20 √

Choose a Strategy to Solve the Problem: Write an Equation or Inequality Make a Table Drawings and illustrations Working Backwards (try given answers) Guess and Check

WRITE AN EQUATION John and 2 friends are going out for a pizza for lunch. They split one pizza and 3 large drinks. The pizza costs $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. What is the cost of one large drink.

Solution 3 drinks (John + 2 friends = 3) = 3d 1 pizza = 14:00 Discount = -7.00 Total = 12.10 3d + 14.00 – 7.00 = 12.10

MAKE A TABLE Andy and his parents decided that for his allowance would go up one dollar and 50 cents every week for 3 consecutive weeks. If he starts out at getting 6 dollars how much would he make week 5? Week $ allowance 1 $6.00 2 $7.50 3 $9.00 4 $10.50 5 $12.00 $12.00

DRAWINGS AND ILLUSTRATIONS Drawing a picture is a great way to solve word problems. Makes it is easy to see WHY you get the answer. EXAMPLE: The length of a rectangle is 3 more than twice the width. If the Perimeter is 36 feet, how wide id the rectangle? 2w + 3 2w+3+w+2w+3+w = 36 6w +6 =36 w w 2w + 3

WORKING BACKWARDS This works well for Multiple Choice Questions A Camera manufacturer spends $2,100 a day plus $9 per camera. The cameras sell for $14 each. How many cameras must they sell top break even? a) 420 b) 480 c) 380 d) 150 2100 + 9( number of cameras) = 14(number of cameras) 2100 + 9(420) = 14(420) ? (hint start with the middle value) 2100 + 9(480) = 14(480) ? 2100 + 9(380) = 14(380) ? 2100 + 9(150) = 14(150) ?

GUESS AND CHECK Plan: Select random numbers that add up to 22 If two sisters ages add up to 22 years and one is 4 years older than the other what are there two ages? Plan: Select random numbers that add up to 22 until you find two that are 4 apart. 10 and 12: 10+12=22 but 12-10=2 not 4; 8 and 14: 8+14= 22 but 14-8=6; 9 and 13: 9+13=22 and 13-9=4 so their ages are 9 and 13!

Example Pete and Bryan are cousins. Bryan is three times older than Pete. If the sum of the age of the cousins is 36, how old are Pete and Bryan?

Step #1 Bryan is three times as old as Pete, but Pete’s age is unknown. Since it’s an unknown, let’s use x to represent Pete’s age. If Pete is x, and Bryan is three times as old as Pete, picture represents their ages? 3x + x = 36 Bryan Pete = x

Writing Algebraic Expressions to Solve Word Problems. How many minutes in 1 hour, 14 hours, in "n" hours?

Algebra is used every day to solve everyday problems. For example: You have a job and you get paid $8.25 an hour. You want to figure out how much pay you will receive if you worked 16 hours.

You can write in words, I get paid $8.25 for every hour I work. Algebraically, you would write: $8.25h which means 8.25 TIMES the number of hours you worked.

You should always write the formula FIRST for every question SO, you would write $8.25h = pay Then, substitute the number of hours into the formula. $8.25(16) = p (pay) Calculate the result Your pay would be $132.00 Write your answer as p = $132.00

Now it’s your turn. Using the formula, calculate your pay if you worked: 20 hours? 32 hours? 18.5 hours? 22 hours? 110 hours? Every question must start with the formula $8.25h = p Then substitute into the formula the hours that you worked. Remember the answer is MONEY and should be in that form!

Now the same question with a twist! If you got paid $189.75, how many hours did you work? You get paid $8.25 an hour. You can divide the pay by your rate of pay, ($8.25) to get the number of hours you worked. Algebraically, it would look like this. Calculate and you find: You worked, 23 hours!

New Problems Some problems require that you know basic facts. How many seconds in a minute? How many minutes in an hour? How many hours in a day? How many days in a week? How many days in a year? How many weeks in a year? How many months in a year? How many centimeters in a meter? How many meters in a kilometer?

How Many Days in Three Weeks? Since you know that there are 7 days in a week, you can write: 7 days X the number of weeks = the number of days in a week. Or Algebraically: 7(w) = d Substitute into the formula what you know. 7(3)= d Calculate d = 21 There are 21 days in three weeks!

How many hours in four days? There are 24 hours in one day. So 24d = hours in day 24 (4) = h h = 96 There are 96 hours in 4 days.

Using the facts, write a formula for each and solve. How many days in 3 weeks? How many hours in 4 days? How many cm in 1500 metres? How many months in 13 years? How many weeks in 7 years? How many years in 3250 weeks? (careful) How many years in 250 months? (careful) How many minutes in 4 hours? How many hours in 17 days? How many kilometres in 4509 metres? (careful)

Video Link https://www.youtube.com/watch?v=DfbQjiSooOohttps://www.youtube.com/watch?v=DfbQjiSooOo https://www.youtube.com/watch?v=7x7Hl9ztYbk