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A Brief Comparison of Two Math Curricula and the Impact Each May have on Your Child’s Learning.

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.

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A Brief Comparison of Two Math Curricula and the Impact Each May have on Your Child’s Learning.

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  1. A Brief Comparison of Two Math Curricula and the Impact Each May have on Your Child’s Learning. Investigations (TERC) Mathvs.Singapore Math

  2. 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.

  3. 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 n 36 cm 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 From Singapore Math – Grade 5

  4. 36 cm n n 36 cm 100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32 104 cm- 72 cm 32 cm Standard Algorithm Flexible ThinkingModerate Efficiency 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 TERC SINGAPORE

  5. 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 16x 36 96 480 576 cm2 Standard Algorithm Flexible Thinking – Cluster ProblemModerate Efficiency 36 cm 16 cm 16 cm 576 cm2 36 cm 16 cm x 36 cm = Area of Rectangle TERC Singapore

  6. x cm x 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 576 cm2

  7. x cm Trial and Error - Cluster-type Division - Moderate Efficiency – Investigations 576 cm2 x cm x cm First Try x cm Second Try 23 r1 28 r16 25 576 20 576 -100 25 x 4 = 100 20 x 10 = 200 -200 476 376 25 x 4 = 100 -100 20 x 10 = 200 -200 24 376 Third Try 176 25 x 4 = 100 -100 24 576 20 x 8 = 160 -160 24 x 20 = 480 276 -480 25 x 4 = 100 96 -100 r16 20 x 28 = 560 24 x 2 = 48 -48 176 48 25 x 7 = 175 -175 24 x 2 = 48 -48 r1 25 x 23 = 175 0 24 x 24 = 576

  8. x cm 576 cm2 x cm x cm x cm 24x 24 576 Singapore Process Knowledge of Square Numbers Simplifies this Process. These facts would be rote memorized. 10 X 10 = 100 12 X 12 = 144 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.

  9. Singapore Investigations 100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32 1. 104 cm- 72 cm 32 cm 24 4. 24 576 23 r1 1. -480 24 x 20 = 480 96 25 576 24 x 2 = 48 -100 25 x 4 = 100 -48 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 48 476 2. -48 24 x 2 = 48 -100 25 x 4 = 100 16x 36 96 480 576 cm2 2. 0 24 x 24 = 576 376 -100 25 x 4 = 100 276 -100 25 x 4 = 100 176 -175 25 x 7 = 175 25 x 23 = 175 r1 3. 28 r16 5. 3. 25 X 25 = 625 20 576 -200 20 x 10 = 200 376 -200 20 x 10 = 200 24x 24 576 4. 176 -160 20 x 8 = 160 20 x 28 = 560 r16 Answer: 24 cm Answer: 24 cm Now let’s compare the two solutions side-by-side!

  10. 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?”

  11. 100 – 70 = 30 30 – 2 = 28 28 + 4 = 32 Answer = 32 1. 104 ft- 72 ft 32 ft 24 4. 24 576 23 r1 1. -480 24 x 20 = 480 96 25 576 24 x 2 = 48 -100 25 x 4 = 100 -48 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 48 476 2. -48 24 x 2 = 48 -100 25 x 4 = 100 16x 36 96 480 576 ft2 2. 0 24 x 24 = 576 376 -100 25 x 4 = 100 276 -100 25 x 4 = 100 176 -175 25 x 7 = 175 25 x 23 = 175 r1 3. 28 r16 5. 3. 25 X 25 = 625 20 576 -200 20 x 10 = 200 376 -200 20 x 10 = 200 24x 24 576 4. 176 -160 20 x 8 = 160 20 x 28 = 560 r16 Answer: 24 x 24 ft2 Answer: 24 x 24 ft. sq. Singapore Ben Investigations Ben

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