A Brief Comparison of Two Math Curricula and the Impact Each May have on Your Child’s Learning. Investigations (TERC) Math vs. Singapore Math
BUT FIRST SOME DEFINITIONS 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.
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. 36 cm n Perimeter (P) = 104 cm n 36 cm 104 cm = 36 cm + n + n 104 cm – 72 cm = n + n 32 cm = n + n 16 cm = n From Singapore Math – Grade 5
36 cm n n 36 cm Perimeter (P) = 104 cm = 36 cm + n + n 104 cm – 72 cm = n + n 104 cm - 72 cm 32 cm Standard Algorithm 32 cm = n + n 16 cm = n 100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32 SINGAPORE TERC Flexible Thinking Moderate Efficiency
36 cm 16 cm 576 cm 2 36 cm 16 cm x 36 cm = Area of Rectangle Singapore 16 x 36 96 480 576 cm 2 Standard Algorithm TERC 10 cm x 36 cm = 360 cm 2 + 2 cm x 36 cm = 72 cm 2 16 cm x 36 cm = 576 cm 2 Flexible Thinking – Cluster Problem Moderate Efficiency
x cm 576 cm 2 2 576 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.
Trial and Error - Cluster-type Division - Moderate Efficiency – Investigations x cm 576 cm 2 x cm 23 r 1 25 576 -100 476 -100 376 -100 276 -100 176 -175 r 1 Second Try 25 x 4 = 100 25 x 7 = 175 25 x 23 = 175 28 r 16 First Try 20 576 -200 20 x 10 = 200 376 -200 20 x 10 = 200 176 20 x 8 = 160 -160 r 16 20 x 28 = 560 24 24 576 -480 96 -48 48 -48 0 Third Try 24 x 20 = 480 24 x 2 = 48 24 x 24 = 576
x cm Singapore Process x cm 576 cm 2 x cm Knowledge of Square Numbers Simplifies this Process. 10 X 10 = 100 12 X 12 = 144 These facts would be rote memorized. 20 X 20 = 400 25 X 25 = 625 This would likely be solved by mental math. Too high…so student backs down to 24 X 24 which is 576. 24 x 24 576
Now let’s compare the two solutions side-by-side! Singapore 1. 2. 3. 4. 104 cm - 72 cm 32 cm Investigations 100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32 4. 16 x 36 96 480 576 cm 2 2. 3. 28 r 16 20 576 -200 20 x 10 = 200 376 -200 20 x 10 = 200 176 -160 20 x 8 = 160 r 16 20 x 28 = 560 5. 24 24 576 -480 24 x 20 = 480 96 -48 24 x 2 = 48 48 -48 24 x 2 = 48 0 24 x 24 = 576 10 cm x 36 cm = 360 cm 2 + 2 cm x 36 cm = 72 cm 2 16 cm x 36 cm = 576 cm 2 25 X 25 = 625 23 r 1 25 576 -100 25 x 4 = 100 476 -100 25 x 4 = 100 376 -100 25 x 4 = 100 276 -100 25 x 4 = 100 176 -175 25 x 7 = 175 r 1 25 x 23 = 175 24 x 24 576 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 plaza fountain first. How much concrete can we pour with the load we got coming? ”
Singapore Ben Investigations Ben 1. 2. 3. 4. 104 ft - 72 ft 32 ft 16 x 36 96 480 576 ft 2 25 X 25 = 625 24 x 24 576 Answer: 24 x 24 ft 2 100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32 4. 28 r 16 20 576 -200 20 x 10 = 200 376 -200 20 x 10 = 200 176 -160 20 x 8 = 160 r 16 20 x 28 = 560 5. 24 24 576 -480 24 x 20 = 480 96 -48 24 x 2 = 48 48 -48 24 x 2 = 48 0 24 x 24 = 576 10 ft x 36 ft = 360 ft 2 + 2 ft x 36 ft = 72 ft 2 + 2 ft x 36 ft= 72 ft 2 16 ft x 36 ft = 576 ft 2 3. 23 r 1 25 576 -100 25 x 4 = 100 476 -100 25 x 4 = 100 376 -100 25 x 4 = 100 276 -100 25 x 4 = 100 176 -175 25 x 7 = 175 r 1 25 x 23 = 175 Answer: 24 x 24 ft. sq.
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