10.5. Pedagogical Explorations 1. Child's invented algorithms: A student explained her strategy for adding 56 +39. Marta: Ms. L.: Marta: Her explanation implies the following steps: a) 56+39=(5x10+6)+(3×10+9) TUUERLee. Well, 5 and 3 is 8. [Interrupting] Where are the 5 and the 3? Okay, it's 50 and 30. That's like 5 tens and 3 tens. So it's 8 tens; that's 80. And 80 and 6 is 86, and 4 more is 90, and 5 more onto that is 95. k) =(5x10+3x10)+(6+9) = (5+3)x10+(6+9) =8x10+(6+9) = 80+(6+9) =(80+6) +9 = 86+9 = 86+(4+5) = (86+4)+5 90+5 = <-95 For each step, identify the property of the base-10 system or the property of operations that justifies the step. Some steps may require more than one property. (Adapted from Carpenter, Franke, & Levi, 2003)
10.5. Pedagogical Explorations 1. Child's invented algorithms: A student explained her strategy for adding 56 +39. Marta: Ms. L.: Marta: Her explanation implies the following steps: a) 56+39=(5x10+6)+(3×10+9) TUUERLee. Well, 5 and 3 is 8. [Interrupting] Where are the 5 and the 3? Okay, it's 50 and 30. That's like 5 tens and 3 tens. So it's 8 tens; that's 80. And 80 and 6 is 86, and 4 more is 90, and 5 more onto that is 95. k) =(5x10+3x10)+(6+9) = (5+3)x10+(6+9) =8x10+(6+9) = 80+(6+9) =(80+6) +9 = 86+9 = 86+(4+5) = (86+4)+5 90+5 = <-95 For each step, identify the property of the base-10 system or the property of operations that justifies the step. Some steps may require more than one property. (Adapted from Carpenter, Franke, & Levi, 2003)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please include justifications for each step.
![10.5. Pedagogical Explorations
th
1. Child's invented algorithms: A student explained her strategy for adding 56 +39.
Marta:
Ms. L.:
Marta:
Well, 5 and 3 is 8.
[Interrupting] Where are the 5 and the 3?
Okay, it's 50 and 30. That's like 5 tens and 3 tens. So it's 8 tens; that's 80. And
80 and 6 is 86, and 4 more is 90, and 5 more onto that is 95.
Her explanation implies the following steps:
a) 56+39=(5x10+6)+(3×10+9)
= (5x10+3×10) +(6+9)
= (5+3)x10+(6+9)
= 8x10+(6+9)
= 80+(6+9)
i)
=(80+6) +9
= 86+9
= 86+(4+5)
= (86+4)+5
= 90+5
<-95
k)
For each step, identify the property of the base-10 system or the property of operations that
justifies the step. Some steps may require more than one property. (Adapted from Carpenter,
Franke, & Levi, 2003)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c60e9dc-9541-469d-8098-00c54f69ea68%2Ffe98dca8-e537-4a92-8d8b-cdaf8408a43e%2Fm6ccgj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10.5. Pedagogical Explorations
th
1. Child's invented algorithms: A student explained her strategy for adding 56 +39.
Marta:
Ms. L.:
Marta:
Well, 5 and 3 is 8.
[Interrupting] Where are the 5 and the 3?
Okay, it's 50 and 30. That's like 5 tens and 3 tens. So it's 8 tens; that's 80. And
80 and 6 is 86, and 4 more is 90, and 5 more onto that is 95.
Her explanation implies the following steps:
a) 56+39=(5x10+6)+(3×10+9)
= (5x10+3×10) +(6+9)
= (5+3)x10+(6+9)
= 8x10+(6+9)
= 80+(6+9)
i)
=(80+6) +9
= 86+9
= 86+(4+5)
= (86+4)+5
= 90+5
<-95
k)
For each step, identify the property of the base-10 system or the property of operations that
justifies the step. Some steps may require more than one property. (Adapted from Carpenter,
Franke, & Levi, 2003)
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