Problem solvingstrategies pp
- 1. Ms. Collins 7 th Grade Math Class
- 2. 1. Understand the problem Step 1: Read the problem. Ask yourself A. What information am I given? B. What is missing? C. What am I being asked to find or do?
- 3. 2. Make a Plan to Solve the Problem A. Choose a Strategy. B. The more you try using different strategies, the better you will pick a good strategy to solve a problem. PRACTICE!
- 4. 3. Carry Out the Plan A. Solve the problem using your plan. B. Show all your work. C. Give yourself enough space to organize your work!
- 5. 4. Check your answer to be sure it is REASONABLE!!! A. Look back at your work and compare your answer to what information and/or questions in the problem. B. Ask yourself “Is there a way I can check my answer? TRY SUBSTITUTION! C. Did you check your work for errors?
- 6. 1. Draw a Picture 2. Look for a Pattern 3. Systematic Guess and Check 4. Act it out 5. Make a Table 6. Work A Simpler Problem 7. Work Backwards 8. Write an Equation
- 7. A worm is trying to escape from a well 10 feet deep. The worm climbs up 2 feet per day, but each night it slides back 1 foot. How many days will it take for the worm to climb out of the well? Use THE FOUR STEP PLAN. 1. Understand 2. Plan 3. Carry Out 4. Check
- 8. 1. UNDERSTAND READ!! What am I given? 10 foot deep well 2 feet per day up 1 foot down per night What do you need to solve for? I need to know the number of days needed to get out of the well
- 9. Strategy 1: Draw a picture given the information! 10 foot well 2 feet up per day 1 foot down per night Show me your picture! What is your answer!!! Does your picture show that the worm progresses 1 foot per day, except the last day when it can crawl 2 feet and get out of the well, not have to spend another night in the well? The answer is 9 days!!!
- 10. 9 8 7 Number of 6 Feet 5 Climbed 4 3 2 1 1 2 3 4 5 6 7 8 9 Days
- 11. Day Night Progress Total 1 2 -1 1 2 2 -1 1 2 3 2 -1 1 3 4 2 -1 1 4 5 2 -1 1 5 6 2 -1 1 6 7 2 -1 1 7 8 2 -1 1 8 9 2 0 2 10
- 12. Suppose the worm in the example climbs up 3 feet per day and slides back 2 feet per night. How many days will it take for the worm to climb out of the 10 feet well?
- 13. Suppose the worm in the example climbs up 3 feet per day and slides back 2 feet per night. How many days will it take for the worm to climb out of the 10 feet well? HERE IS MY TABLE: 9 DAYS AGAIN! Day Night Progress Total 1 3 -2 1 2 3 -2 1 2 3 3 -2 1 3 4 3 -2 1 4 5 3 -2 1 5 6 3 -2 1 6 7 3 -2 1 7 8 3 -2 1 8 9 3 3 11
- 14. How about if the worm needed to climb out of a 12 foot well and went up 3 feet during the day and slid back 2 foot per night? How long would it take for the worm to get out of the well? DRAW THE PICTURE ANY WAY YOU WANT!
- 15. How about if the worm needed to climb out of a 12 foot well and went up 3 feet during the day and slid back 2 foot per night? How long would it take for the worm to get out of the well? ANSWER 8 DAYS!
- 16. days!!! Day Night Progress Total 1 3 -1 2 2 2 3 -1 2 4 3 3 -1 2 6 4 3 -1 2 8 5 3 -1 2 10 6 3 0 3 13
- 17. A Pizza party is having pizzas with pepperoni, pineapple chunks, and green pepper slices. How many different pizzas can you make with these toppings? What are the questions you ask? Read What Am I Given? What Am I Solving For?
- 18. A Pizza party is having pizzas with pepperoni, pineapple chunks, and green pepper slices. How many different pizzas can you make with these toppings? 7 Pizza Combinations p P,GP P,PC P,GP,P C GP GP,P C PC
- 19. You can look for a pattern by looking at similar cases. For Example: What is the sum of the measures of the angles of a 12 sided polygon? Well—you don’t have this memorized so can you look at a easier shape and figure out the pattern?
- 20. 3 sides 4 sides 5 sides 6 sides The number of triangles formed is TWO LESS than the number of sides of a polygon. This means the sum of the measures of the angles of each polygon is the number of triangles TIMES 1800. For a 12 sided polygon, the number of triangles is 12-2=10. The sum of the measures of the angles is 10 x 1800=1,8000.
- 21. Step 1: Understand The goal is to find the sum of the measures of the angles. So can we start from a triangle and work up? Step 2: Plan Draw a 3 sides polygon, 4 sided polygon, etc. to look for a pattern. Step 3: Carry out We know a triangle has three angles that total 1800.
- 22. Step 4 Check Your Answer Draw a 12 sides polygon and CHECK that there are exactly 10 triangles formed when you draw diagonals from one vertex of a 12 sides polygon.
- 23. Can you draw a pattern and calculate the number of black tiles needed to have nine rows of tiles. See Page 35
- 24. Page 35, Practice problem 2: A triangle has four rows of small triangles. How many small triangles will you need for eight rows?
- 25. 64 small triangles
- 26. In a 3 x 3 grid, there are 14 squares of different sizes. There are 9 1 x 1 squares, four 2 x 2 squares, and one 3 x 3 square. How many squares of different sizes are in a 5 x 5 grid?
- 27. 55 squares
- 28. This strategy works when you can make a reasonable estimate of the answer. A group of students is building a sailboat. The students have 48 ft2 of material to make a sail. They design the sail in the shape of a right angle. Find the length of the base and height. 1.5 x x
- 29. Understand The height is 1 and ½ times more than the base. Plan Test possible dimensions where the height is 1 and ½ times more than the base. Carry Out The formula for area of triangle is : ½ bh So guess a few height/base 6 base 9 height 10 base 15 height What else could you try?
- 30. Did you try 8 base and 12 height? ½( 8) (12) = 48
- 31. The width of a rectangle is 4 cm less than its length. The area of the rectangle is 96 cm2. Find the length and width of the rectangle. x x-4 Area = 96 cm2
- 32. Answer: 12 cm and 8 cm 12 cm 8 cm Area = l w = 12(8) = 96 cm2
- 33. Exit Ticket: A dance floor is a square with an area of 1,444 square feet. What are the dimensions of the dance floor? Try systematic guess. Answer: 38 x 38
- 34. You have $10 saved and plan to save an additional $2 each week. How much will you have after 7 weeks? Make a table Answer: $24 When you simplify 10347, what is the digit in the ones place? Answer: 0 (use work a simpler problem)
- 35. You can use this strategy to simulate a problem. Use a coin, spinner, or number cube. We use this in probability quite often! A cat is expecting a litter of four kittens. The probability of male and female kittens are equal. What is the probability that the litter contains three females and one male? We can use a head and tail simulation since that is close to simulating male and female (only two options available).
- 36. Understand Your goal is to find the EXPERIMENTAL PROBABILITY that a litter of four kittens contains 3 females and 1 male. Plan Act out the problem (if you act it out, it is experimental) Carry Out When you flipped the coin 100 times, each T was a female and a H was a male kitten. So of 25 “litters” (4 x 100) the trials showed that 6 of 25 trials had 3 female and 1 male . 6/25=24% Check The THEORETICAL PROABILITY IS : (TTTH), (TTHT), (THTT) and (TTHT) OR 4/16 =25%
- 37. A sports jersey number has two digits. Even and odd digits are equally likely. Use a simulation to find the probability that both digits are even.
- 38. Answer What are the possible digits in the first number? 0-9 What are the possible digits in the second number? 0-9
- 39. If you are given a set of data and asked to draw a conclusion. Example: A wildlife preserve surveyed its wolf population in 1996 and counted 56 wolves. In 2000 there were 40 wolves. In 2002 there were 32 wolves. If the wolf population changes at a constant rate, in what year will there be fewer than 15 wolves?
- 40. Understand Given the data, predict when the wolves will number less than 15. Plan Find a rate of change. Make a table to check for the rate of change. Carry Out Make a Table
- 41. Year Wolves 2000 40 2002 40-8=32 2004 32-8=24 2006 24-8=16 At the beginning 0f 2006 there are 16 wolves so we can assume there will be less than 15 by the end of the year.
- 42. Check Set up an equation. 56 wolves-15 wolves=41 wolves The population of wolves decreases 4 wolves/yr. Let X represent the number of years until there is 15 wolves. Solve 4x=41 X is about 10 years. From 1996 -2006 is 10 years. So the correct answer is 2o06.
- 43. You are starting a business selling lemonade. You know that it cost $6 to make 20 cups of lemonade and $7 to make 30 cups of lemonade. Who much will it cost to make 50 cups of lemonade? Set up a table.
- 44. Cost Cups Cost/Cup $6 20 $7 30 $8 40 $9 50
- 45. Exit Ticket: A dance floor is a square with an area of 1,444 square feet. What are the dimensions of the dance floor? Try systematic guess.
- 46. You have $10 saved and plan to save an additional $2 each week. How much will you have after 7 weeks? Make a table Answer: $24
- 47. Answer: $24
- 48. Some problems seem to have a lot of steps, or a lot of numbers and mysterious operations. Try using smaller numbers. This strategy works finding numerical or geometrical patterns.