English in Math

1. English in Math - Solving equations from word problems MacDonald Math 9

2. Expressions • Expressions can be translated directly to an English sentence • 14 + n  fourteen increased by a number • 11 – n  eleven reduced by a number • Words are nothing more than a longer version of what you are already looking at!

3. Synonyms are different words with almost identical or similar meanings • Let’s review some of the words we use in association with our normal math operators: + - x ÷

4. Synonyms are different words with almost identical or similar meanings • Let’s review some of the words we use in association with our normal math operators: + - x ÷ - plus - minus - times - divided by - sum - difference - product - quotient - increased by - decreased by - double - halve - reduced by

5. Solving Word Problems • How do we do it? • Why are they so hard? • I just don’t get it! • Forget it …. I’m done.

6. Word Problems • What is the most difficult part about these: • The first side of a triangle is seven cm shorter than twice the second side. The third side is four cm longer than the first side. The perimeter is eighty cm. Find the length of each side. • Matt is 3 times as old as Jenny. In 15 years, their ages will total 58. How old is each person now? • Find three even numbers in a row whose sum is 156.

7. Word Problems • What is the most difficult part about these: • The first side of a triangle is seven cm shorter than twice the second side. The third side is four cm longer than the first side. The perimeter is eighty cm. Find the length of each side. • Matt is 3 times as old as Jenny. In 15 years, their ages will total 58. How old is each person now? • Find three even numbers in a row whose sum is 156. There’s no numbers! A tongue twister with #s Trial & Error takes so long

8. Successful Method • 1. Draw any necessary diagrams to provide a visual. Read sentences one at a time to slow down your racing thoughts. • 2. Define any variables. This is sometimes referred to as a “Let statement”. You assign a variable to anything you do not know. (What are you looking for?) • 3. Create an equation using the variable(s) • 4. Solve for any unknown values

9. Example 1 • The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side.

10. Example 1 • The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side. • Let b represent Side B A = 2B B = B C = 2B + 1

11. Example 1 • The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side. A = 2B B = B C = 2B + 1

12. Example 1 • The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side. Sum means add! a + b + c =76 (2B)+B+(2B+1)=76

13. Example 1 • The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side. a + b + c =76 (2B)+B+(2B+1)=76 5B+1=76 5B=75 b= 15 cm

14. Example 1 • The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side. a + b + c =76 (2B)+B+(2B+1)=76 5B+1=76 5B=75 b=15 cm a= 2(15) = 30 cm c=2(15)+1=31 cm

15. Example 2 • Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now?

16. Example 2 • Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now? • Let k represent Kate’s age Kates age = K Andys age = 2K  twice

17. Example 2 • Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now? Kates age = K Andys age = 2K 6 years from now Kates age = K + 6 Andys age = 2K + 6

18. Example 2 • Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now? Kates age = K Andys age = 2K 6 years from now Kates age = K + 6 Andys age = 2K + 6 In 6 years their ages total 60 K+6+2K+6 = 60  total

19. Example 2 • Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now? Kates age = K Andys age = 2K 6 years from now Kates age = K + 6 Andys age = 2K + 6 In 6 years their ages total 60 K+6+2K+6 = 60 3K+12=60 3K=48 K=16 Kate = 16 & therefore Andy=2(16)=32

20. Example 3 • Find three consecutive numbers whose sum is forty-five.

21. Example 3 • Find three consecutive numbers whose sum is forty-five. • Let n represent the first number What’s a number?? First number = N

22. Example 3 • Find three consecutive numbers whose sum is forty-five. What’s a number?? First number = N Therefore Second number = N + 1 Third number = N + 2 Consecutive (in a row)

23. Example 3 • Find three consecutive numbers whose sum is forty-five. What’s a number?? First number = N Therefore Second number = N + 1 Third number = N + 2  Sum #1+#2+#3 = 45 N+(N+1)+(N+2) =4 5

24. Example 3 • Find three consecutive numbers whose sum is forty-five. What’s a number?? First number = N Therefore Second number = N + 1 Third number = N + 2 #1+#2+#3 = 45 N+(N+1)+(N+2) =4 5 Finally 3N+3=45 3N=42 N=14 #1=14, #2=15 & #3=16

25. Successful Method • This carries over to other courses as well as real life scenarios. • We have already seen it at use in science, but what about problems we face in our lives

26. Successful Method • Lets say you need to buy a NEW XBox 360. You have $800 to spend on everything. You know a new system costs $400 and extra controller $40. Assuming a game costs $60 how many games could you get? • Let x= the number of Games$800 = $400 + $40 +$60x800=460+60x360=60xx = 6 Games

27. So now… try the original three • 1. The first side of a triangle is seven cm shorter than twice the second side. The third side is four cm longer than the first side. The perimeter is eighty cm. Find the length of each side. • 2. Matt is 3 times as old as Jenny. In 15 years, their ages will total 58. How old is each person now? • 3. Find three consecutive even numbers whose sum is 156.

28. Don’t forget your practice sheet!

29. So learn to think… • What are four things that a car and a tree have in common?

30. They have trunks • The could be used for shelter • They give off gasses • They take in gasses

31. They have trunks • The could be used for shelter • They give off gasses • They take in gasses • …. Both hard to eat • You can sit in both • They could both be green