Problem Solving made easy

Transcription

1 P5 & P6 MATHEMATICS WORKSHOP Problem Solving made easy 4 MARCH 2017

2 Objectives of the workshop a. parents role in helping their child overcome learning difficulties in mathematics b. application of appropriate strategies to help my child grasp mathematical concepts better. c. experiential learning approach 2

3 Strategies for Parents In Coaching 1. Be involved 4. Allow mistakes 1+1 =3 2. Be positive about math 5. Teach concepts 3. Make Math relevant in real life 6. Reinforcements 3

4 Mathematical Problem Solving application of mathematical concepts, skills and processes entails designing and carrying out a set of steps to reach the desired goal in a given solution problem to be solved is one where pupils experience difficulty in achieving solutions to it. 4

5 Problem Solving Strategies Thinking Skills Heuristics 5

6 Heuristics Act it out Restate the problem in another way Use a diagram/model Use tabulation Make a systematic list Look for pattern(s) Work backwards Use before-after concept Use open sentence Make a supposition Simplify the problem Solve part of a problem Thinking Skills Classifying Comparing Sequencing Analysing parts and whole Identifying patterns and relationship Induction Deduction Spatial Visualisation 6

7 A Model for Problem Solving Understanding the problem Think of a plan (choose a heuristic) Carry out the plan Needs modification/a new plan? No Checking Yes Look Back (Reflection) - Improving on the method used. - Seeking alternative solutions. - Extending the method to other problems Is the answer reasonable? No Yes Look Back (Reflection) 7

8 MODEL DRAWING 8

9 MODEL DRAWING (MORE THAN/LESS THAN) EXAMPLE 1 There were 80 more boys than girls at a carnival. When 90 boys left the carnival, there were twice as many girls as boys who remained in the carnival. How many boys were there at the carnival at first? 9

10 MODEL DRAWING (MORE THAN/LESS THAN) EXAMPLE 1 At first B: G: 80 End B: G: 1u 1u 2u 1u u = 10 Boys =

11 MODEL DRAWING (MORE THAN/LESS THAN) EXERCISE 1 Ben had $20 more than Ron at first. Ben spent $52. As a result, Ron had three times as much money as Ben. How much did Ben have at first? 11

12 MODEL DRAWING (MORE THAN/LESS THAN) EXERCISE 1 At first B: R: 20 End 32 B: R: 1u 1u 2u 1 u = 32 2 = 16 Ben =

13 MODEL DRAWING (INTERNAL TRANSFER) EXAMPLE 2 Mary had $80 more than Ken at first. Mary gave $150 to Ken. As a result, he had three times as much money as Mary. How much did Ken have at first? 13

14 MODEL DRAWING (INTERNAL TRANSFER) EXAMPLE 2 At first: M : K : M : K : 1u 1u u 2u = = 220 1u = Ken = 110 =

15 MODEL DRAWING (INTERNAL TRANSFER) EXERCISE 2 Ali had 23 more stamps than Bala. Bala gave 146 stamps to Ali. As a result, Ali had 4 times as many stamps as Bala. How many stamps did Ali have at first? 15

16 MODEL DRAWING (INTERNAL TRANSFER) EXERCISE 2 At first: A: B: End: A: B: 1u 1u u u = 146 x u = =315 = 105 Ali x =

17 FRACTIONS (MODEL DRAWING/BRANCHING) EXAMPLE 3 Alice spent 1 3 of her money on food and 1 5 of the remainder on a dress. As a result, she had $72 left. How much did Alice have at first? 17

18 FRACTIONS (MODEL DRAWING/BRANCHING) EXAMPLE 3? METHOD 1 food dress 4 small units = 72 1 small unit = 72 4 = 18 5 small units = 18 x 5 = 90 $72 Alice had $135 at first 2 big units = 90 1 big unit = 90 2 = 45 3 big units = 45 x 3 =

19 FRACTIONS (MODEL DRAWING/BRANCHING) EXAMPLE 3 METHOD 2 Total amount of money ( 3 3 ) food 1 3 dress 1 5 remainder 2 3 left ($72) = x 5 = = 45 Total x 3 =135 19

20 FRACTIONS (MODEL DRAWING/BRANCHING) EXERCISE 3 Mary used 2 of her eggs to bake a chocolate 7 cake and 1 5 of it to bake a banana cake. She then threw away 1 3 of the remaining eggs. As a result, she had 36 eggs left. How many eggs did Mary have at first? 20

21 FRACTIONS (MODEL DRAWING/BRANCHING) EXERCISE 3 chocolate cake = METHOD 1 banana cake = units total 17 units chocolate+banana 18 units left 18 big units = 54 1 big unit = = 3 35 big units = 3 x 35 =105 threw 36 eggs left 2 small units = 36 1 small unit = 36 2 =18 3 small units = 18 x 3 = 54 21

22 FRACTIONS (MODEL DRAWING/BRANCHING) EXERCISE 3 METHOD 2 Total amount of money cc ( bc 7 35 ) threw 1 3 remainder left (36) = x 3 = = 3 Total x 3 =105 22

23 FRACTIONS (WORKING BACKWARDS) EXAMPLE 4 Jane had some stickers. She gave 18 more than 1 3 of her stickers to her sister. She gave 12 more than 1 2 to of the remaining stickers to her brother. As a result, she had 68 stickers left. How many stickers did Jane have at first? 23

24 EXAMPLE 4 FRACTIONS (WORKING BACKWARDS) sister 18 remainder of the remainder =80 of the remainder x 2 =160 of total =178 of total =89 Total x 3 = 267 brother left 24

25 EXERCISE 4 FRACTIONS (WORKING BACKWARDS) Maisy spent $6 more than 1 6 of her money on a dress. She then spent $8 more than 1 8 of her remaining money on a blouse. As a result, she had $13 left. How much money did she have at first? 25

26 EXERCISE 4 FRACTIONS (WORKING BACKWARDS) 6 dress 8 remainder blouse of the remainder =21 of the remainder x 8 =24 of total =30 of total =6 Total x 6 = 36 $13 left 26

27 RATIO (MODEL DRAWING, UNITS / PARTS) EXAMPLE 5 The ratio of Sumin s money to Meili s money was 4:1. After Sumin had spent $26, Sumin had $2 less than Meili. How much money did Sumin have at first? 27

28 Sumin: 4 units Method 1 Meili : 2 1 unit 3 units = 26-2 =24 1 unit = 24 3 = 8 4 units = 8 x 4 = 32 Sumin had $32 at first. 3 units 28

29 Method 2 Sumin Meili Before 4u 1u - $26 After 1u - 2 1u Amount of money Meili had remained the same. 4u 26 = 1u - 2-1u -1u 3u - 26 = u = 24 1u = 8 4u = 8 x 4 = 32 29

30 RATIO (MODEL DRAWING, UNITS / PARTS) EXERCISE 5 The ratio of Peter s money to John s money was 3:5 at first. After Peter s money was increased by $250 and John s money was decreased by $350, they each had an equal amount of money. How much money did Peter have at first? 30

31 3 units 2 units Method 1 Peter: John: units 2 units = = unit = = units = 300 x 3 =

32 Peter John Before 3u 5u After 1p 1p Method 2 1p = 3u p = 5u u = 3u u -3u 5u 3u = u = 600 1u = 300 Peter at first x 3 =

33 PERCENTAGE (MORE/LESS THAN) EXAMPLE 6 At a concert, the number of girls is 35% fewer than the number of adults. The number of boys is 35 fewer than the number of girls. If there are 224 more adults than boys, how many people attended the concert? 33

34 PERCENTAGE (MORE/LESS THAN) EXAMPLE 6 Girls is 35% fewer than adults ---- Girls is 7 20 is fewer than adults Ratio of A: G : 13 ( difference is 7units) A: 13 u 7 u G: 13 u B: ? 7 u = =189 1 u = = u = 27 x 46 = 1242 Total =

35 PERCENTAGE (MORE/LESS THAN) EXAMPLE 7 At a concert, the number of girls is 35% fewer than the number of adults. There were 50% as many boys as girls. If there are 324 more adults than boys, how many people attended the concert? 35

36 PERCENTAGE (MORE/LESS THAN) EXAMPLE 7 A : G 20 : : 26 B : G 13 : u = u = = 12 Total = 40 u + 26 u + 13 u = 79 u Total x 12 =

37 37