PEM 121Helping Children with Primary Mathematicswith a focus on Primary 4 – 6Dr Yeap Ban HarMarshall Cavendish InstituteSingaporebanhar@sg.marshallcavendish.comSlides are available at www.facebook.com/MCISingaporeDa Qiao Primary School, Singapore
Mathematics is “an excellent vehicle for thedevelopment and improvement of a person’sintellectual competence”.Ministry of Education, Singapore (2006)thinkingschoolslearningnation
Ministry of Education, Singapore (1991, 2000, 2006, 2012)
Reflection of the Shifts in the Test QuestionsWhen we compare the tests from the past with the present, we see that:• Questions from previous tests were simpler, one or two steps, or were heavily scaffolded. The newquestions will requires multiple steps involving the interpretation of operations.• Questions from the past were heavy on pure fluency in isolation. The new questions require conceptualunderstanding and fluency in order to complete test questions.• Questions from past tests isolated the math. The new problems are in a real world problem context.• Questions of old relied more on the rote use of a standard algorithm for finding answers to problems.The new questions require students to do things like decompose numbers and/or shapes, applyproperties of numbers, and with the information given in the problem reach an answer. Relying solelyon algorithms will not be sufficient.Department of EducationNew York State (2013)5
What is HappeningAround the World?Bringing Up Children Who Are Ready for the Global, Technological World
Da Qiao Primary School, SingaporePrimary 1 Singapore8Learning by DoingLearning by InteractingLearning by ExploringGardner’s Theory ofIntelligencesBruner’s Theory ofRepresentationsDienes’ Theory of LearningStages
16The sum of the two numbers is 88.The greater number is 6 x (88 11) = 48.The other number is 5 x (88 11) = 40.
High School Attached to Tsukuba University, JapanDraw a polygon with nodots inside it.Investigate.A polygon has 4 dots onthe perimeter. Find anexpression for its area.Grade 9 Japan17
What Do ChildrenLearn in SchoolMathematics?And How You Can Coach Them
Students who have mastered the basic skills which include basicone-step and two-step problems are ready to handle at least theleast demanding of the secondary courses.JaySam34.7 kg34.7 kg x 2 = (68 + 1.4) kg34.7 kg x 2 = 69.4 kgSam’s mass is 69.4 kg.19
4. Find the value of 1000 – 724 . 5. Find the value of 12.2 4 .20999 – 724 = 2751000 – 724 = 27612.20 4 = 3.0512.2 4 =12 2 tenths = 20 hundredths12.24122 02 003.05
What Are theChallengingAspects ofMathematics?And How Children Develop Competencies to Handle Them
Problem 1Mr Lim packed 940 books equally into 8 boxes. What wasthe least number of additional books he would need so thatall the boxes contained the same number of books?Answer:__________22940 8 = 117.54118 × 8 = 944
Problem 1Cup cakes are sold at 40 cents each.What is the greatest number of cup cakes that can be boughtwith $95?Answer:_____________23$95 40 cents = 237.5237
Problem 1Cup cakes are sold at 40 cents each.What is the greatest number of cup cakes that can be boughtwith $95?Answer:_____________24237
Problem 2Mr Tan rented a car for 3 days. He was charged $155 perday and 60 cents for every km that he travelled. He paid$767.40. What was the total distance that he travelled forthe 3 days?25$155 x 3 = $465$767.40 - $465 = $302.40$302.40 60 cents / km = 504 kmHe travelled 504 km.
Problem 2Mr Tan rented a car for 3 days. He was charged $155 perday and 60 cents for every km that he travelled. He paid$767.40. What was the total distance that he travelled forthe 3 days?26(767.40 - 155 x 3) 0.60 = 504He travelled 504 km.
30menwomenThere were 4 x 30 = 120 men and women at first.After
312 fifths of the remainder were 383 fifths of the remainder were 19 x 3 = …There were 19 x 5 pears and peaches.5 twelfths of the fruits = 19 x 5 fruitsSo, there were 19 x 12 fruits altogether.Answer: 228 fruits
• Number Sense• Patterns• Visualization• Communication• MetacognitionFive Core Competencies Try to do as you read the problems. Do not wait till the end of the question to try todo something. Try to draw when you do not get what the question is getting at. Diagrams such asmodels are very useful. Do more mental computation when practising Paper 1.
Problem 735Source: Semestral Assessment 1 River Valley Primary School Primary 4Ravi had 12 more marbles than Jim at first. Then Jim gave Ravi 4 marbles.How many more marbles does Ravi have than Jim in the end?12RaviJim 44
Problem 836Source: Semestral Assessment 1 Keming Primary School Primary 5Daniel had only $2, $5 and $10 notes in his wallet. The ratio of the numberof $2 notes to the number of the other notes was 5 : 3. The number of $5notes was 3 times as many as that of $10 notes. If there were $460 in hiswallet, how many $2 notes did he have?12 parts20 parts9 parts 3 parts20 parts x ($2)9 parts x ($5)3 parts x ($10)115 units = $46040 units = $160He had 80 $2 notes.
(a) 41 is under M(b) 101 is under S(c) 2011 is under T …. Really? How do you know?Problem 10
Problem 11Weiyang started a savings plan by putting 2 coins in a moneybox every day. Each coin was either a 20-cent or 50-cent coin.His mother also puts in a $1 coin in the box every 7 days. Thetotal value of the coins after 182 days was $133.90.(a) How many coins were there altogether?(b) How many of the coins were 50-cent coins?182 7 = …2 x 182 + 26 = …
Suppose each day he put in one 20-cent and one 50-cent coins,the total is $127.40But he only put in $107.90 ..to reduce this by $19.50, exchange 50-cent for 20-cent coins$19.50 $0.30 = 65There were 182 – 65 = 117 fifty-cent coins.