exam 2

Question 1

Sufficient Justification: Generalizable Example

Answer 1

A concrete exmaple that is more than just an example. dmeonstarted with a specfiic case but the numbers chosen are not important to the argument; it is clear that the argument would hold true no matter what numbers are chosen.

Question 2

Sufficient Justification: Explanation of a general principle

Answer 2

A general principle is given that explains why a conjecture is always true. The explanantion is not tied to a specific example.

Question 3

Insufficient Justification: Consensus

Answer 3

A conjecture is accepted as true by general agreement, or the outcome of a formal or informal vote.

Question 4

Insufficient Justification: Appeal to Authority

Answer 4

A recognized authority (ex a teacher, parent textbook) states that the conjecture is true

Question 5

Insufficient Justification: Restating the conjecture

Answer 5

A child argues that the conjecture is true by restating the conjecture using different wording.

Question 6

Insufficient Justification: By Example

Answer 6

One specific example, or a set of specific examples, is given as evidence that the conjecture works, and is therefore true

Question 7

Insufficient Justification: Incomplete Generalization

Answer 7

A general principle or generalizable example is given that only explains the property for a limited set of cases (ex only for odd numbers or somehting similar to it)

Question 8

A number is divisble by: 2

Answer 8

the last digit is divisible by by 2

Question 9

A number is divisble by: 3

Answer 9

the sum of the digits is divisble by 3

Question 10

A number is divisble by: 4

Answer 10

the last two digits together are divisble by 4

Question 11

A number is divisble by: 5

Answer 11

the last digit is 0 or 5

Question 12

A number is divisble by: 6

Answer 12

the number is divisble by both 2 and 3; the number is divisble by 3 and is even

Question 13

A number is divisble by: 8

Answer 13

the last 3 digits together are divisible by 8

Question 14

A number is divisble by: 9

Answer 14

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Question 15

A number is divisble by: 10

Answer 15

the last digit is 0

Question 16

direct modeling

Answer 16

count large numbers and diretc model the problem

Question 17

incrementing

Answer 17

students add or subtract incrementally by building up or down by tens or ones

Question 18

Operating sperately on tens and ones

Answer 18

children operate by place value and then recombine accordingly

Question 19

Compensating

Answer 19

changing one or more numbers to “easier” numbers (tens or twenty fives for ex) and then compensate somehow–
WITHIN THE PROBLEM: itself 29 + 34 to 30 +33 or 76-38 to 78-40.
WITHIN THE ANSWER: 29 +34, add 30 and 34 then add back the extra 2 that were subtracted to get 38.

Question 20

Teaching Concepts: Method 1

Answer 20

Memorization: students memorize the fact

ex: “an even times an odd is always even”
problem: fact overload

Question 21

Teaching Concepts: Method 2

Answer 21

Pattern Recognition: Students do many examples and look for a pattern
problem: conceptual connection is missing, the pattern essentially just becomes another fact

Question 22

Teaching Concepts: Method 3

Answer 22

Explanation First: teacher explains the rule and gives students the reason for the rule
Problem: many students do not internalize the reason for the rule

Question 23

Teaching Concepts: Method 4

Answer 23

Concept Development: through engaging in a series of accessible tasks, students progress from a familiar process to anabstract concept