Welcome! UPPER PRIMARY MATHS. TRAINER: MR. MOHAMAD IDRIS ASMURI WELLINGTON PRIMARY SCHOOL ACTING HEAD of DEPARTMENT (MATHEMATICS) 1

Welcome! UPPER PRIMARY MATHS TRAINER: MR. MOHAMAD IDRIS ASMURI WELLINGTON PRIMARY SCHOOL ACTING HEAD of DEPARTMENT (MATHEMATICS) 1

1. Introduction What can parents do? P5 Topical Distributions P6 Topical Distributions Cognitive Levels & Supporting Your Child 2. Whole Numbers Model Drawing Number Pattern 3. Fractions Model Drawing Branching 4. Quantity vs Value ( per set concept) 5. Percentage 2

How parents can help their child prepare for the PSLE Mathematics/Foundation Mathematics Paper? 3

Help your child to: 1. See the importance and relevance of Mathematics in everyday life. 2. Know the formula, the multiplication and division tables and common systems of units. 3. Analyse the word problems by asking the following questions so that you can check for understanding. What the word problem is about? What is the quantity/value the problem asking for? What are the keywords? What are/could be the steps involved? 4

How can we present the interpreted information? o Graphs o Diagrams o Tabular forms (E.g. tables or diagrams/models to be drawn) What are the steps they can take to solve the question? o Use of the 4 operations (+,,, ) and any appropriate heuristics to solve the problem. o Use of formulae or rule involved. o Use the 4 steps of Polya method. 5

4. Show all workings neatly. 5. Make it a habit to: Check the reasonableness of results (final answers) Use calculator for Paper 2 questions Perform estimation for short-answer questions in Paper 1. 6. Have sufficient daily practice in Mathematics. 7. Set a reasonable time limit for your child to complete work at home. 8. Allow the use of calculator to solve word problems (Paper 2 questions) Use the time to analyse the word problems instead of performing long computations 6

Remember! Every child is unique! Some children may need more practice than others. Know your child s strengths and weaknesses in Mathematics. (Obtain information from Math teachers.) Give a reasonable amount of practice accordingly. 7

Standard Mathematics Paper Booklet Item Type Number of Questions Number of Marks per Question Weighting Duration 1 A B Multiplechoice Shortanswer 10 1 10% 5 2 10% 10 1 10% 5 2 10% 50 min 2 Structured/L ong-answer 5 2 10% 13 3/4/5 50% 1 h 40 min Total 48 -- 100% 2 h 30 min The examination consists of two written papers comprising three booklets. For more information on PSLE matters, go the website: http://www.seab.gov.sg 8

Foundation Mathematics Paper Booklet Item Type Number of Questions Number of Marks per Question Weighting Duration 1 A Multiplechoice 10 2 20% 10 1 10% 1 h B Shortanswer 10 2 20% 2 Structured /Longanswer 10 2 20% 1 h 15 min Structured 8 3/4/5 30% Total 48 -- 100% 2 h 15 min The examination consists of two written papers comprising three booklets. For more information on PSLE matters, go the website: http://www.seab.gov.sg 9

Standard Mathematics (SA2) Topics Proposed Weightings (%) Whole Numbers, Fractions, Decimals 45 Ratio 8 Percentage 8 Measurement (Area and Perimeter, and Volume) Geometry (4-sided Figures, Angles and Triangles) Data Analysis (Average and Graphs) Total 100 18 16 5 10 17

Foundation Mathematics (SA2) Topics Proposed Weightings (%) Whole Numbers, Fractions, Decimals 55 Measurement (Time, Area and Perimeter, and Volume) Geometry 15 Data Analysis (Average, Tables and Graphs) Total 100 22 8 11 17

Standard Mathematics (PSLE) Topics Proposed Weightings (%) Whole Numbers, Fractions, Decimals 30 Measurement 25 Geometry 15 Data Analysis 10 Ratio and Percentage 12 Algebra 4 Speed 4 Total 100 12 17

Foundation Mathematics (PSLE) Topics Proposed Weightings (%) Whole Numbers, Fractions, Decimals 36 Measurement 28 Data Analysis 14 Geometry 12 Percentage 10 Total 100 13 17

1. Multiple-choice Question For each question, four options are provided of which only one is the correct answer. A candidate has to choose one of the options as his correct answer. 2. Short-answer Question For each question, a candidate has to write his answer in the space provided. Any unit required in an answer is provided and a candidate has to give his answer in that unit. 3. Structured / Long-answer Question For each question, a candidate has to show his method of solution (working steps) clearly and write his answer(s) in the space(s) provided. 14

Supporting your child in their learning journey! 15

Standard and Foundation Levels Knowledge Comprehension Application and Analysis Cognitive Level Knowledge items require students to recall specific mathematical facts, concepts, rules and formulae, and perform straightforward computations. Comprehension items require students to interpret data and use mathematical concepts, rules and formulae to solve routine or familiar mathematical problems. Application and Analysis items require students to analyse data and/or apply mathematical concepts, rules and formulae in a complex situation, and solve unfamiliar* problems. * In the school context, students may be exposed to problems that are deemed unfamiliar as part of the regular practice. These questions should remain as Application and Analysis so long as the problem involves a complex situation, even though the nature of the problems may have become familiar to the students. 16

Be involved in your child s learning in school and at home. Ask Praise Encourage Ensure that your child attends all his/her classes punctually. Ensure your child revises his/her work Ensure that your child completes his/her work. Ensure that your child attempts his/her Koobits portal @problemsums.koobits.com 17

Whole Numbers 18

Example 1: Model Drawing Harry had $475 more than Anna. He gave $150 to Anna How much more money than Anna had Harry in the end? Common mistake: $475 - $150 = $325 Harry $475 $150 Anna $325 Solution: $475 - $150 = $325 $325 - $150 = $175 Harry Anna $475 $175 $150 Why do we subtract $150 twice? 19

Example 2: Number Pattern Type 1 Figure 1 Figure 2 Figure 3 Study the pattern carefully. a) How many squares are there in Figure 4? Figure 1 3 + 2 Figure 2 5 + 2 Figure 3 7 Figure 4 7 + 2 = 9 Method: Counting on 20

Example 2: Number Pattern Type 1 Figure 0 Figure 1 Figure 2 Figure 3 Study the pattern carefully. b) How many squares are there in Figure 78? Figure 0 3 2 = 1 Figure 1 1 + (1 2) = 3 Figure 2 1 + (2 2) = 5 Figure 3 1 + (3 2) = 7 Figure 78 1 + (78 2) = 157 21

Example 2: Number Pattern Type 1 Figure 1 Figure 2 Figure 3 Study the pattern carefully. c) Which figure contains 199 squares? Number of squares 1 + (Figure Number 2) 199 1 = 198 198 2 = 99 22 Method: Working backwards

Let s practise! (1) Figure 1 Figure 2 Figure 3 Study the pattern carefully. a) How many squares are there in Figure 4? Figure 1 3 + 3 Figure 2 6 + 4 Figure 3 10 Figure 4 10 + 5 = 15 23 Method: Counting on

Let s practise! (1) Figure 1 Figure 2 Figure 3 (1 + 2) (1 + 2 + 3) (1 + 2 + 3 + 4) Study the pattern carefully. b) How many squares are there in Figure 18? Figure 18 1 + 2 + (3 + 4 + + 17 + 18 + 19) = What is the relationship between the last number to add and the figure number? 24

Example 3: Number Pattern Type 2 Find the sum of 1 + 2 + 3 + + 16 +17 +18 +19 +20 +21. Step 1: Find the number of terms. No. of terms last no. first no. common difference + 1 21 1 1 + 1 = 21 25

Example 3: Number Pattern Type 2 Find the sum of 1 + 2 + 3 + +19 + 20 + 21. 22 22 22 Step 2: Find the average of each term. Average^ of each pair of numbers ^Average is a concept taught only in P5 (Term 3). last no. +first no. 21+1 2 = 11 2 26

Example 3: Number Pattern Type 2 Find the sum of 1 + 2 + 3 + + 16 +17 +18 +19 +20 +21. Step 3: Find the sum of all the terms. Multiply the no. of terms (step 1) and the average (step 2) 21 11 = 231 27

Let s practise! (2) Find the sum of 3 + 6 + 9 +... + 21 + 24 + 27. Step 1: Find the number of terms. last no. first no. No. of terms + 1 = common difference Step 2: Find the average of each term. Average of each pair of numbers last no. +first no. 2 = Step 3: Find the sum of all the terms. Multiply the no. of terms (Step 1) and the average (Step 2) = 28

Let s practise! (3) 1. Add all the numbers from 32 to 60. 2. Add all the even numbers from 368 to 400. 3. Find 250 + 255 + 260 + + 345 + 350 + 355. 4. *Find 300 290 + 280 270 + 230 + 220 210. 29

Prepared by Mr Idris Asmuri 2015 Fractions 30

Example 4: Model Drawing String A is 21 cm shorter than String B. 2 3 of String A and 4 5 of String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first. Misconception: String A (left) 1-2 3 = 1 3 String B (left) 1-4 5 = 1 5 1 3 is a bigger fraction than 1 5. Why is the remaining String B more than String A? 31

Example 4: Model Drawing String A is 21 cm shorter than String B. 2 3 of String A and 4 5 of String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first. Q: How to help my child make meaning of the fractions? A: Provide scaffolding for your child. Allow your child some time to think before answering. Are we talking about 2 3 of String A or B? (String A) So, 2 3 of String A represents a VALUE. Are we talking about 4 of String A or B? (String B) 5 So, 4 of String B represents another VALUE. 5 We re not comparing fractions here, but the values. 32

Tips! If your child doesn t understand, you can use the following example: 1 4 of 8 is 2. 1 Both fractions are 1 of each set. 4 However, the values are different. 4 of 16 is 4. 33

Step 1: Understand the problem. Step 2: Devise a plan. Step 3: Carry out the plan. Step 4: Look back. (Are the results reasonable?) 34

Example 4: Model Drawing String A is 21 cm shorter than String B. 2 3 of String A and 4 5 of String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first. Step 1: Understand the question. String A (at first) 21 cm shorter than String B String A (used) String B (used) 2 3 4 5 String A (left) 2 units String B (left) 1 units String B (at first)? 35

Example 4: Model Drawing String A is 21 cm shorter than String B. 2 3 of String A and 4 5 of String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first. Step 3: Carry out the plan. (Solve it.) A B used 21 cm shorter 7 units 21 cm 1 unit 3 cm 10 units 10 3 cm = 30 cm used Step 4: Look back. (Are the results reasonable?) 37

Example 5: Model Drawing Sally had some money. She spent 1 of her money on a blouse and 3 3 of the remaining money on a scarf. What fraction of her money 4 was left? Step 1: Understand the question. (Key words) Blouse 3 Remainder? Remainder 1 1 3 = 2 3 1 Scarf 3 4 3 of the remainder 4 2 3 = 1 2 38

Example 5: Model Drawing Sally had some money. She spent 1 of her money on a blouse and 3 3 of the remaining money on a scarf. What fraction of her money 4 was left? Step 2: Devise a plan. blouse scarf? 39

Example 5: Model Drawing Sally had some money. She spent 1 of her money on a blouse and 3 3 of the remaining money on a scarf. What fraction of her money 4 was left? Step 3: Carry out the plan. (Solve it.) blouse scarf? 1 1 3 = 2 3 1 4 2 3 = 1 6 Step 4: Look back. (Are the results reasonable?) 40

Example 5: Branch Method Sally had some money. She spent 1 of her money on a blouse and 3 3 of the remaining money on a scarf. What fraction of her money 4 was left? Step 2: Devise a plan. Fraction of the whole 1 3 Blouse Money 3 4 R scarf 1 1 3 = 2 3 Remaining 1 4 R Money left 1 3 4 = 1 4 41

Example 5: Branch Method Sally had some money. She spent 1 of her money on a blouse and 3 3 of the remaining money on a scarf. What fraction of her money 4 was left? Step 3: Carry out the plan. (Solve it.) Money 1 3 Blouse 3 4 R scarf Fraction of the whole 1 3 = 2 6 3 4 2 3 = 1 2 = 3 6 1 1 3 = 2 3 Remaining R Money left Step 4: Look back. (Are the results reasonable?) 1 4 1 4 2 3 = 1 6 Checking: 2 6 + 3 6 + 1 6 = 1 42

Quantity versus Value ( per set concept) 43

There are 4 times as many 10-cent coins as 50-cent coins. The total value of the 10-cent coins and 50-cent coins is $9. How many coins are there in all? Example 6: Model Drawing Step 1: Understand the question. (Keywords) 44

Example 6: Model Drawing There are 4 times as many 10-cent coins as 50-cent coins. The total value of the 10-cent coins and 50-cent coins is $9. How many coins are there in all? Step 2: Devise a plan. Draw a model. Number of coins 10 Value of coins 10 10 10 10 10 50 50 45

Example 6: Model Drawing There are 4 times as many 10-cent coins as 50-cent coins. The total value of the 10-cent coins and 50-cent coins is $9. How many coins are there in all? Step 3: Carry out the plan. (Solve it.) Number of coins 10 Value of coins 10 10 10 10 10 50 50 In 1 set: No. of coins four 10 coins and one 50 coin 5 coins Value of coins 4 10 + 50 = 90 No. of sets Total value value = $9 $0.90 = 10 No. of coins 9 sets of 5 coins 10 5 = 50 Step 4: Look back. (Are the results reasonable?) 46

There are 4 times as many 10-cent coins as 50-cent coins. The difference in value between the 10-cent coins and 50-cent coins is $1. How many coins are there in all? Example 7: Model Drawing Step 1: Understand the question. (Keywords) 47

Example 7: Model Drawing There are 4 times as many 10-cent coins as 50-cent coins. The difference in value between the 10-cent coins and 50-cent coins is $1. How many coins are there in all? Step 3: Carry out the plan. (Solve it.) Number of coins 10 Value of coins 10 10 10 10 10 50 50 In 1 set: No. of coins 4 10- coins and 1 50- coin 5 coins Difference in value 50 - (4 10 ) = 10 No. of sets Total difference difference per set = $1 $0.10 = 10 No. of coins 10 sets of 5 coins 10 5 = 50 Step 4: Look back. (Are the results reasonable?) 49

Let s practise! (4) The ratio of the number of 10-cent coins to the number of 50-cent coins is 4:1. The difference in value between the 10-cent coins and the 50- cent coins is $1. How many coins are there in all? Step 3: Carry out the plan. (Solve it.) Number of coins 10 Value of coins 10 10 10 10 10 50 50 In 1 set: No. of coins four 10 coins and one 50 coin 5 coins Value of coins 4 10 + 50 = 90 No. of sets Total value value = $9 $0.90 = 10 No. of coins 9 sets of 5 coins 10 5 = 50 Step 4: Look back. (Are the results reasonable?) 52

Let s practise! (5) There are 8 more $2 notes than $5 notes in my wallet. The difference between the $2 notes and $5 notes is $14. How many $5 notes are there in my wallet? Step 1: Understand the question. (Keywords) 53

Let s practise! (5) There are 8 more $2 notes than $5 notes in my wallet. The difference between the $2 notes and $5 notes is $14. How many $5 notes are there in my wallet? Step 2: Devise a plan. Draw a model. $5 $5 $5 $5 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $14 54

Let s practise! (5) There are 8 more $2 notes than $5 notes in my wallet. The difference between the $2 notes and $5 notes is $14. How many $5 notes are there in my wallet? Step 3: Carry out the plan. (Solve it.) Draw a model. $5 $5 $5 $5 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $14 In unknown sets: No. of notes one $2 note and one $5 note 2 notes Difference $14 + $16 = $30 Difference per set $5 $2 = $3 No. of sets Difference difference per set = $30 $3 = 10 Step 4: Look back. (Are the results reasonable?) 55

Percentage 56

What does percent mean? % Out of 100 i.e. 70% 70 out of 100 Q: How to help your child make meaning of percentage? A: Help them relate to everyday context. 1. If a television is selling at a discount of 20%, what is the amount I have to pay for it? 2. A movie ticket was sold at 10% discount. If I bought 3 such tickets, do I get 30% off the total price? 3. A dinner meal cost $120 before GST and service charge. How did I pay in all, after GST and service charge? 57 ALWAYS RELATE PERCENTAGE TO A VALUE.

Let s practise! (3) Answer Key 1) 368 2) 12672 3) 6655 4) Find 300 290 + 280 270 + 230 + 220 210. How many tens do we have to add? 5 5 10 = 50 Let s practise! (5) Answer Key 10 10 10 10 $5notes 58