{"id":315,"date":"2023-01-19T00:15:43","date_gmt":"2023-01-19T00:15:43","guid":{"rendered":"http:\/\/newsite.seriouslyaddictivemaths.com.sg\/?p=315"},"modified":"2025-01-22T06:33:45","modified_gmt":"2025-01-22T06:33:45","slug":"math-heuristics-method","status":"publish","type":"post","link":"https:\/\/seriouslyaddictivemaths.com.sg\/math-heuristics-method\/","title":{"rendered":"Singapore Math Heuristics: Act It Out, Draw A Diagram, Look For Patterns"},"content":{"rendered":"
In\u00a0part one of our Singapore Math Heuristics series<\/a>, we gave an overview of the 12 heuristics in Singapore Primary Math syllabus, with tips from the curriculum team at Seriously Addictive Mathematics (S.A.M) on how to solve various math word problems using them.<\/p>\n To recap, heuristics are methods or strategies students can use to solve complex math word problems. They are general guidelines of what students can do to tackle a word problem when the solution is not obvious.<\/p>\n<\/div>\n<\/div>\n Besides using heuristics to solve a word problem, Singapore Math also adopts Polya\u2019s 4-step problem-solving process:<\/p>\n 1.\u00a0Understand the problem<\/b>: What to find? What is known and unknown? To solve word problems efficiently, students must be familiar with both the problem solving methods (heuristics) and the problem solving process (Polya\u2019s 4-step).<\/p>\n In this article, we will focus on 3 heuristics \u2013\u00a0Act it out<\/b>,\u00a0Draw a diagram\/model<\/b>, and\u00a0Look for pattern(s)<\/b>.<\/p>\n Sample word problems are solved using these 3 heuristics and Poly\u2019s 4-step process in the step-by-step worked solutions provided by the curriculum team at S.A.M.<\/p>\n<\/div>\n<\/div>\n<\/div>\n _______________________________________________________________________________________________________<\/p>\n Heuristic: Act it out<\/strong><\/p>\n Word Problem (Grade 2)<\/b>:<\/p>\n Ben cuts a cake into 5 equal pieces. He wants to eat some of the pieces of cake so that the fraction of cake he eats is smaller than the fraction of the cake left. What is the greatest possible fraction of the cake that Ben can eat?<\/p>\n<\/div>\n<\/div>\n Solution<\/b>:<\/span><\/p>\n 1. Understand: 2. Choose: Act it out<\/p>\n 3. Solve:<\/p>\n<\/div>\n<\/div>\n<\/div>\n If Ben eats 3 pieces, 2 pieces are left. 3\/5 is greater than 2\/5. This does not match the word problem.<\/p>\n The greatest possible fraction of the cake that Ben can eat is 2\/5.<\/p>\n 4. Check: Try solving the following word problem using Polya\u2019s 4-step process.<\/p>\n Word Problem (Grade 1)<\/b>:<\/p>\n Alan, Ben and Carol are in the school\u2019s Art Club. Their teacher, Mr Tan, wants two of them to join a contest. How many ways can Mr Tan choose two pupils?<\/p>\n<\/div>\n<\/div>\n _______________________________________________________________________________________________________<\/p>\n Heuristic: Draw a diagram\/model<\/strong><\/p>\n Word Problem (Grade 2)<\/b>:<\/p>\n There were 158 children in a movie theatre. There were 267 more adults than children in the theatre. 236 of the adults were men. How many women were there in the theatre?<\/p>\n<\/div>\n<\/div>\n Solution<\/b>:<\/span><\/p>\n 1. Understand: 2. Choose: Draw a diagram\/model<\/p>\n 3. Solve:<\/p>\n There were 158 children.<\/p>\n<\/div>\n<\/div>\n<\/div>\n Try solving the following word problem using Polya\u2019s 4-step process.<\/p>\n Word Problem (Grade 3)<\/b>:<\/p>\n The smaller of two numbers is 1217. The greater number is 859 more than the smaller number. Word Problem (Grade 5)<\/b>:<\/p>\n Tammy has 3 boxes of apples. Box A is 550 grams heavier than Box B and 770 grams heavier than Box C. The average mass of the 3 boxes is 2150 grams. Find the average mass of Box B and Box C. Give your answer in kilograms and grams.<\/p>\n<\/div>\n<\/div>\n Solution<\/b>:<\/span><\/p>\n 1. Understand: 2. Choose: Draw a diagram\/model<\/p>\n 3. Solve:<\/p>\n Box A is 550 grams heavier than Box B.<\/p>\n<\/div>\n<\/div>\n<\/div>\n _______________________________________________________________________________________________________<\/p>\n Heuristic: Look for pattern(s)<\/strong><\/p>\n Word Problem (Grade 4)<\/b>:<\/p>\n Carmen uses the letters in her name to form the pattern below. Solution<\/b>:<\/span><\/p>\n 1. Understand: 2. Choose: Look for patterns<\/p>\n 3. Solve:<\/p>\n CARMEN is the repeating block of letters. 4. Check: Try solving the following word problem using Polya\u2019s 4-step process.<\/p>\n Word Problem (Grade 1)<\/b>:<\/p>\n Draw the shape that comes next.<\/p>\n<\/div>\n<\/div>\n
\n2.\u00a0Devise a plan<\/b>: Choose the most suitable heuristic
\n3.\u00a0Carry out the plan<\/b>: Solve the problem
\n4.\u00a0Look back<\/b>: Check the answer<\/p>\n
\nWhat to find: The greatest possible fraction of the cake that Ben can eat.
\nWhat is known: The cake is cut into 5 equal pieces. The fraction of cake he eats is smaller than the fraction of the cake left.<\/p>\n
\nDid I give the answer as a fraction? Yes
\nIs the fraction he ate smaller than the fraction left? Yes
\nIs it the greatest possible fraction of cake he can eat? Yes<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\nSee the solution in\u00a0part one of our Singapore Math Heuristics series<\/a>.<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\nWhat to find: The number of women in the theatre.
\nWhat is known: There were 158 children. There were 267 more adults than children. There were 236 men.<\/p>\n
\nThere were 425 adults in the theatre.<\/div>\n<\/div>\n<\/div>\n
\nThere were 189 women in the theatre.4. Check:
\nHow many adults were there? 236 + 189 = 425
\nWere there 267 more adults than children? 425 \u2013 158 = 267. Yes<\/div>\n<\/div>\n<\/div>\n
\n(a) What is the greater number?
\n(b) What is the sum of the numbers?<\/p>\n<\/div>\n<\/div>\n
\n(a) The greater number is 1217 + 859 = 2076.
\n(b) The sum of the numbers is 2076 + 1217 = 3293.
\nSee the solution in\u00a0part one of our Singapore Math Heuristics series<\/a>.<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\nWhat to find: The average mass of Box B and Box C.
\nWhat is known: Box A is 550 grams heavier than Box B. Box A is 770 grams heavier than Box C. The average mass of Box A, Box B and Box C is 2150 grams.<\/p>\n
\nThe total mass of the 3 boxes is 6450 grams.<\/div>\n<\/div>\n<\/div>\n
\nBox B is 220 grams heavier than Box C.<\/div>\n<\/div>\n<\/div>\n
\n1 unit = 5460 \u00f7 3 = 1820
\nThe mass of Box C is 1820 grams.1820 + 220 = 2040
\nThe mass of Box B is 2040 grams.2040 + 1820 = 3860
\nThe total mass of Box B and Box C is 3860 grams.3860 \u00f7 2 = 1930 grams
\nThe average mass of Box B and Box C is 1 kilogram 930 grams.4. Check:
\nWhat is the mass of Box A? 1820 + 770 = 2590 grams.
\nWhat is the total mass of the 3 boxes? 1820 + 2040 + 2590 = 6450.
\nIs the average mass of the 3 boxes 2150 grams? 6450 \u00f7 3 = 2150 grams. Yes
\nDid I give the answer in kilograms and grams? Yes<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\nC A R M E N C A R M E N C A . . .
\nWhat will be the 405th<\/sup>\u00a0letter in the pattern?<\/p>\n<\/div>\n<\/div>\n
\nWhat to find: The 405th<\/sup>\u00a0letter in the pattern.
\nWhat is known: The pattern is formed by the letters CARMEN. The pattern starts repeating itself from the 7th<\/sup>\u00a0letter.<\/p>\n
\nThere are 6 letters in each block.
\n405 \u00f7 6 = 67 remainder 3
\nThere are 67 such blocks.
\nThe remainder of 3 means we have to count 3 more letters to get to the 405th<\/sup>\u00a0letter.
\nC A R M E N
\n1 2 3
\nThe 405th<\/sup>\u00a0letter in the pattern is the letter R.<\/p>\n
\nHow many letters are there in 67 blocks of CARMEN? 67 x 6 = 402
\nDid I count to the 405th<\/sup>\u00a0letter? 402 + 3 = 405. Yes<\/p>\n<\/div>\n<\/div>\n<\/div>\n