A Brief Comparison of Two Math Curricula and the Impact

Each May have on Your Child’s Learning.

Investigations (TERC) Mathvs.

Singapore Math

Differentiation means varying learning activities or teaching strategies to provide multiple methods for students to explore concepts. Students are given (permitted) alternative paths to manipulate the ideas embedded within the concept. Translation: Some students speed ahead, others get mired in inefficient math strategies. Tracking???

Mathematical Flexibility: a student’s ability to approach a mathematical problem using multiple strategies. Translation: Let your child discover their own comfort zone in math (even if it is inefficient).

Mathematical Efficiency: a student’s ability to solve a problem through the most direct route possible. The highest level of efficiency is direct recall of facts. Just below that is generally the use of standard algorithms to problem solve. Translation: The algorithm generally allows learners more opportunities to explore higher difficulty problems because they do not get bogged down in process.

BUT FIRST SOME DEFINITIONS

Question: A square and a rectangle have the same area. If the rectangle has a length of 36 cm and a perimeter of 104 cm, find the length of the sides of the square.

Perimeter (P) = 104 cm

104 cm = 36 cm + 36 cm + n + n

104 cm – 72 cm = n + n

32 cm = n + n

16 cm = n

36 cm

36 cm

nn

From Singapore Math – Grade 5

Perimeter (P) = 104 cm

104 cm = 36 cm + 36 cm + n + n

104 cm – 72 cm = n + n

32 cm = n + n

16 cm = n

36 cm

36 cm

nn

104 cm- 72 cm 32 cm

Standard Algorithm

100 – 70 = 30 30 – 2 = 28 28 + 4 = 32

Answer = 32

Flexible ThinkingModerate EfficiencySINGAPORE TERC

16 cm x 36 cm = Area of Rectangle

36 cm

36 cm

16 cm16 cm

16x 36 96 480 576 cm2

Standard Algorithm

10 cm x 36 cm = 360 cm2

+ 2 cm x 36 cm = 72 cm2

+ 2 cm x 36 cm = 72 cm2

+ 2 cm x 36 cm = 72 cm2

16 cm x 36 cm = 576 cm2

Flexible Thinking – Cluster ProblemModerate Efficiency

576 cm2

TERCSingapore

576 cm2 x cmx cm

x cm

x cm

To determine the length of the sides of this square (w/o a calculator) the student must factor 576 until they identify two factors that are the same. The student should know that 576 is a “square number.” Trial and error is suggested since square root functions are not generally an elementary math activity. Division or multiplication may be used.

576 cm2

Trial and Error - Cluster-type Division - Moderate Efficiency – Investigations

x cmx cm

x cm

x cm

576 cm2 57620-200376

-200176

20 x 10 = 200

20 x 10 = 200

-160 20 x 8 = 160

20 x 28 = 560r16

28 r16First Try

Second Try57625-100476-100376

25 x 4 = 100

25 x 4 = 100

-100 25 x 4 = 100

25 x 4 = 100

23 r1

276-100 176

25 x 7 = 175-17525 x 23 = 175r1

24 x 2 = 48

57624-480

96-4848

24 x 20 = 480

24 x 2 = 48

-4824 x 24 = 5760

24 Third Try

x cmx cm

x cm

x cm

576 cm2

Knowledge of Square Numbers Simplifies this Process.

10 X 10 = 100

12 X 12 = 144

20 X 20 = 400

25 X 25 = 625

These facts would be rote memorized.

This would likely be solved by mental math.

Too high…so student backs down to 24 X 24 which is 576.

24x 24 576

Singapore Process

Now let’s compare the two solutions side-by-side!

104 cm- 72 cm 32 cm

Singapore

16x 36 96 480 576 cm2

25 X 25 = 625

24x 24 576

2.

4.

Answer: 24 cm

1.

3.

Investigations100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32

10 cm x 36 cm = 360 cm2

+ 2 cm x 36 cm = 72 cm2

+ 2 cm x 36 cm = 72 cm2

+ 2 cm x 36 cm = 72 cm2

16 cm x 36 cm = 576 cm2

20 x 10 = 200

20 x 10 = 200

20 x 8 = 16020 x 28 = 560

57620-200376

-200176-160

r16

28 r16

57625-100476

-100376

25 x 4 = 100

25 x 4 = 100

-100 25 x 4 = 100

25 x 4 = 100

23 r1

276-100 176

25 x 7 = 175-17525 x 23 = 175r1

57624-480

96-4848

24 x 20 = 480

24 x 2 = 48

-48 24 x 2 = 4824 x 24 = 5760

24

1.

3.

2.

4.

5.

Answer: 24 cm

What are the ramifications for your children when they go out into the real world? Let’s rephrase the original question to find out.

Question: A contractor wants to pour a 36’ x 16’ concrete pad to place a chiller. At the last minute the foreman says” “Hey Ben, we gotta pour that square foundation for the the plaza fountain first. How much concrete can we pour with the load we got coming?”

100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32

10 ft x 36 ft = 360 ft2

+ 2 ft x 36 ft = 72 ft2

+ 2 ft x 36 ft = 72 ft2

+ 2 ft x 36 ft= 72 ft2

16 ft x 36 ft = 576 ft2

20 x 10 = 200

20 x 10 = 200

20 x 8 = 16020 x 28 = 560

57620-200376

-200176-160

r16

28 r16

57625-100476

-100376

25 x 4 = 100

25 x 4 = 100

-100 25 x 4 = 100

25 x 4 = 100

23 r1

276-100 176

25 x 7 = 175-17525 x 23 = 175r1

57624-480

96-4848

24 x 20 = 480

24 x 2 = 48

-48 24 x 2 = 4824 x 24 = 5760

24

1.

3.

2.

4.

5.

Answer: 24 x 24 ft. sq.

Singapore Ben

104 ft- 72 ft 32 ft

16x 36 96 480 576 ft2

25 X 25 = 625

24x 24 576

2.

4.

Answer: 24 x 24 ft2

1.

3.

Investigations Ben