algebrain singapore

m a t h

Dr Yeap Ban HarMarshall Cavendish Institute

Singaporeyeapbanhar@gmail.com

Slides are available at

www.banhar.blogspot.comHawa

i’iwww.facebook.com/MCISingapore

Marshall Cavendish Institute www.mcinstitute.com.sg

M A P 2 1 3

si.mcinstitute.com.sg

More information at

www.si.mcinstitute.com.sg

Some Questions from Participants

www.eaieducation.com

http://moe.edu.sg/education/education-statistics-digest/average class size

Algebraic Thinking Model Method

Peter

Natalia

x

x 12

58 – 12 = 4646 2 = 23

Peter’s bag weighs 23 kg.Natalia’s bag weighs 23 kg + 12 kg = 35 kg.

23

462

12582

58122

58)12(

x

x

x

x

xx

Page 7 MAP111

• Managing information through word problems

• Visualization through drawing bar models

• Number sense through mental calculation

• Evaluating solutions through discussing solutions to anchor task

1st Day

2nd Day 4

3rd Day 4 4

4th Day 4 4 4

5th Day 4 4 4 4

6th Day 4 4 4 4 4

7th Day 4 4 4 4 4 4

8th Day 4 4 4 4 4 4 4

250

Page 8 MAP111

1st Day

2nd Day 4

3rd Day 4 4

4th Day 4 4 4

5th Day 4 4 4 4

6th Day 4 4 4 4 4

7th Day 4 4 4 4 4 4

8th Day 4 4 4 4 4 4 4

250

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = ?

There are 45 fours.45 x 4 = 180

10 units = 250 – 180 = 7001 units = 70 10 = 7

She made (7 + 9 x 4) = 43 paper cranes on the last day.

1st Day

2nd Day 4

3rd Day 4 4

4th Day 4 4 4

250

5

5th Day 4 4 4 4

250 – 40 = 210

210 5 = ?

42 + 16 = ?

Rosa made 58 paper cranes on the last day.

x

x

x

x

x

Struggling Average Advanced

Draw the model for all 10 days. Or reduce the problems to 4 days. Or act the situation out using counters.

Draw the model for about 7 or 8 days.

Draw the model for 3 or 4 days. Using algebra.

1st Day x

2nd Day x 4

3rd Day x 4 4

4th Day x 4 4 4

5th Day x 4 4 4 4

6th Day x 4 4 4 4 4

7th Day x 4 4 4 4 4 4

8th Day x 4 4 4 4 4 4 4

x + (x + 4) + (x + 8) + (x + 12) + … = 250

x + (x + 4) + (x + 8) + (x + 12) + … (x + 36) = 250

10x + (4 + 8 + 12 + … + 32 + 36) = 250

10x + (40 4 + 20) = 250

10x + 180 = 250

10x = 70

x = 7 x + 36 = 43

Differentiation for Struggling Learners

Sam

Terry

Vanessa

72

y y

y

Sam

Terry

Vanessa y y y

72

6y = 72

y = 72 6 = 12

Sam

Terry

Vanessa

72

36 years old

36

Vanessa

Terry72

Differentiation for Advanced Learners

Sam

Terry

Vanessa

72

Sam

Pablo

Wynn

Zena

100

?

210

38

15

38

−15=

740

740

→210

140

→210 7=30

3040

→30 × 30=900

Courtesy of one of our colleagues

Algebraic Expressions

2

1

5

43

numberstotal

middle number

1, 2, 3, 4, 5

2, 3, 4, 5, 6

3, 4, 5, 6, 7

89

10

135

111213

246

141516

357

m, …

m

m

m

Try it!

Factoring

Modeling with Algebra

Grade Five

Grade Six