Parents Seminar 1 18 Feb 2017 Springdale Primary School 1 A 21 st - PowerPoint PPT Presentation

Parents’ Seminar 1 18 Feb 2017 Springdale Primary School 1

A 21 st Century Necessity “ Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence . ” Ministry of Education, Singapore (2006) Springdale Primary School 2

Mathematics Framework Springdale Primary School 3

Phases of Learning Phase 1 (Readiness)  Prior knowledge  Motivating contexts  Learning environment Phase 2 (Engagement)  Activity-based learning  Teacher-directed inquiry  Direct instruction Phase 3 (Mastery)  Motivated practice  Reflective review  Extended learning Springdale Primary School 4

Approach of Learning Springdale Primary School 5

Approach of Learning Concrete (Enactive) Stage Pupil is introduced to an idea or skill by acting it out with real objects. Springdale Primary School 6

Approach of Learning Pictorial (Iconic) Stage Pupil has sufficiently understood the hands-on experiences and can now relate them to representation, such as a diagram or picture. Springdale Primary School 7

Approach of Learning Abstract (Symbolic) Stage The pupil is capable of representing problems by using mathematical notation. Springdale Primary School 8

What is Addition?  Combining parts to form a whole  Extending a part What is Subtraction?  Taking away from a whole  Comparing parts  Reverse of addition Springdale Primary School 9

Communicating Addition and Subtraction Addition Primary 1 Primary 2 Add, addition equation Add, addition equation 1 more, 2 more, 10 more,… 1 more, 10 more, 100 more,… Total, sum Total, sum How many … altogether? How many…altogether? How many … at first? How many … at first? How many … in all? How many … in all? Springdale Primary School 10

Communicating Addition and Subtraction Subtraction Primary 1 Primary 2 Subtract, take away, Subtract, take away, subtraction equation subtraction equation 1 less/fewer, 2 less/fewer,… 1 less/fewer, 10 less/fewer, 100 less/fewer,… Difference Difference How many … left? How many … left? How many more to …? How many more to …? How many more is … than …? How many more/fewer is … than …? How much cheaper/lighter/heavier/change? Springdale Primary School 11

Addition Strategies Primary 1 • Within 20 Primary 2 o Counting on • Within 1000 o Add ones first, o Counting on then add tens o Add ones first, then o Make 10 add tens, then add ________________ hundreds • Within 100 o Without regrouping o Add ones first, o With regrouping then add tens  without regrouping  with regrouping Springdale Primary School 12

Subtraction Strategies Primary 1 Within 20 • Primary 2 o Count on Within 1000 • o Count backwards o Counting on o Subtract from ones o Count backwards o Subtract to get 10 first o Subtract ones first, o Subtract from 10 first then subtract tens, ________________ then subtract • Within 100 hundreds o Subtract ones first, o Without regrouping then subtract tens o With regrouping  without regrouping  with regrouping Springdale Primary School 13

Common Misconceptions  Confused with the keywords  Mary has 10 apples. She has 2 apples fewer than Tom. How many apples does Tom have?  Confused between different strategies 13 – 7 13 – 3 = 10 3 4 10 + 4 = 14 Springdale Primary School 14

Common Misconceptions  Confused with the place value (subtract 3 ones as 3 tens) • 68 – 3 = 38 (subtract 24 as 4 tens 2 ones) • 57 – 24 = 15  Confused with formal representation (use bigger digit to subtract • 62 – 39 = 37 smaller digit  9 – 2 = 7) • 4 – 9 = 5 (wrong representation of subtracting 4 from 9) Springdale Primary School 15

Common Misconceptions  Confused with formal representation Use bigger digit to subtract smaller digit  6 – 1 = 5  2 – 0 = 2  2 – 1 = 1 Springdale Primary School 16

Common Misconceptions  Confused with formal representation Add instead of subtract  6 + 1 = 7  0 + 2 = 2  2 +1 = 3 Springdale Primary School 17

Common Misconceptions  Confused with formal representation Mixture of addition and subtraction Springdale Primary School 18

What’s next? • Let’s use common terms  regroup • Identifying renaming games Springdale Primary School 19

What’s next? • Practise with smaller values • Estimate  “Will your answer be more than 200 ?” Springdale Primary School 20

Addition and Subtraction  Primary 3 • Addition and Subtraction within 10 000 • Problem Solving  Primary 4 • Addition and Subtraction within 100 000 • Problem Solving Springdale Primary School 21

Time to play!! Springdale Primary School 22

Please download this multiplication game Springdale Primary School 23

Multiplication and Division It is really not as easy as we think Video – 3 Times 5 http://www.youtube.com/watch?v=E4nLyV7YAb4 Springdale Primary School 24

And it is probably not as intuitive as we think Video - 25 Divided by 5 http://www.youtube.com/watch?v=omyUncKI7oU Springdale Primary School 25

What is Multiplication?  Repeated Addition (applicable for whole numbers only) 3 x 2  3 groups of 2  2 + 2 + 2 • Equal Groups  2 sets of 5 petals 3 sets of 2 gloves Springdale Primary School 26

What is Multiplication?  Scaling (applicable for fractions and decimals) To make the whole according to a given scale [ how many] OF [this unit] = [the whole amount] [ how much] OF [this unit] = [the whole amount ] How much of them? Springdale Primary School 27

What is Division?  Equal Grouping (Repeated Subtraction – for whole numbers only) Alan Bryan Carl Springdale Primary School 28

What is Division?  Equal Sharing Alan Bryan Carl  Reverse of multiplication Springdale Primary School 29

Communicating Multiplication and Division Multiplication Division Multiply Divide, divided by, divided into 1 group of, 2 groups of, Each group of … 10 groups of ,… Pairs, twos, threes, sevens,… … groups of … Times Share, share equally Total How many … equal groups ? product Quotient, remainder How many … altogether? How many …in each group? Springdale Primary School 30

What Pupils Need to Learn For Primary 1 Concepts of multiplication & division  Use of the multiplication sign “x”  Multiplying within 40  Dividing within 20  Solving 1-step word problems involving multiplication  & division with pictorial representation Springdale Primary School 31

What Pupils Need to Learn For Primary 2 Multiplication tables of 2, 3, 4, 5 & 10  Use of the division sign “ ÷ ”  Relationship between multiplication & division  Multiplying & dividing within the multiplication tables  Solving 1-step word problems involving multiplication  & division within the multiplication tables Mental calculation involving multiplication & division  within the multiplication tables of 2, 3, 4, 5 and 10 Springdale Primary School 32

What Pupils Need to Learn For Primary 3 Multiplication tables of 6, 7, 8 & 9  Multiplying & dividing within the multiplication tables  Division with remainder  Multiplication & division algorithms  (up to 3 digits by 1 digit) Solving up to 2-step word problems involving the 4  operations Mental calculation involving multiplication & division  within the multiplication tables Springdale Primary School 33

Multiplication & Division Examples of Word Problems There are 6 rows of chairs in a classroom. Each row has 4 chairs. How many chairs are there altogether? Mrs Lim gave 20 stickers to some children. Each child received 4 stickers. How many children did she give the stickers to? Mrs Chan paid $16 for 8 similar boxes of tarts. How much did each box of tarts cost? Springdale Primary School 34

Strategies to Learn Multiplication & Division Always start with concrete objects, i.e. sweets, beans, cookies.  Have children show equal grouping  I have 10 M&Ms. I am giving each child 5 M&Ms.  How many children will receive the M&Ms? Have children show equal sharing  Share 10 M&Ms between 2 children.  How many M&Ms does each child get? Progress with pictures when children are more familiar  with the concept of grouping & sharing. Link multiplication and division to real-life context.  Springdale Primary School 35

Strategies to Learn Multiplication & Division There are 100 multiplication facts, from 1 x 1 to 10 x 10. Springdale Primary School 36

Strategies to Learn Multiplication & Division Strategy #1 You Times Me is the Same as Me Times You That leaves us with 55 facts . Springdale Primary School 37

Strategies to Learn Multiplication & Division Strategy #2 Any Number Times One is that Number Itself That leaves us with 45 facts . Springdale Primary School 38

Strategies to Learn Multiplication & Division Strategy #3 To Multiply by Ten, Add a Zero That leaves us with 36 facts . Springdale Primary School 39

Strategies to Learn Multiplication & Division Strategy #4 To Multiply by Two, Double the Number That leaves us with 28 facts . Springdale Primary School 40