Bloggers.AnswerKey (r1.1 vs. r1.17)
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 <<O>>  Difference Topic AnswerKey (r1.17 - 10 Apr 2006 - CatherineJohnson)

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Line: 101 to 101

 the craft of math
subtraction as the difference between 2 numbers
study sheet: subtracting integers & absolute value
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<		 notes on integer, subtraction, & absolute value study sheet

 answers
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>		 notes on integer, subtraction, & absolute value study sheet

 Carolyn on introducing absolute value
keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud
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>

answers
study sheet for class quiz on pages 2 - 16, Prentice Hall Mathematics: Explorations & Applications & Prentice Hall Pre -Algebra

outloud sheets: integers & absolute value
answer key
notes on outloud sheets for integers & absolute values
Carolyn on introducing absolute value
keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud







 <<O>>  Difference Topic AnswerKey (r1.16 - 10 Apr 2006 - CatherineJohnson)

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Line: 8 to 8
go back to:
integers & absolute value outloud worksheet
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What is subtraction?

 <<O>>  Difference Topic AnswerKey (r1.15 - 10 Apr 2006 - CatherineJohnson)

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Line: 6 to 6



Added:
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>		 go back to:
integers & absolute value outloud worksheet

 What is subtraction?

 <<O>>  Difference Topic AnswerKey (r1.14 - 10 Apr 2006 - CatherineJohnson)

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Line: 98 to 98

 subtraction as the difference between 2 numbers
study sheet: subtracting integers & absolute value
notes on integer, subtraction, & absolute value study sheet
Added:
>
>		 answers
Carolyn on introducing absolute value
keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud

study sheet for class quiz on pages 2 - 16, Prentice Hall Mathematics: Explorations & Applications & Prentice Hall Pre -Algebra


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<


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>






 <<O>>  Difference Topic AnswerKey (r1.13 - 16 Sep 2005 - CatherineJohnson)

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Line: 40 to 40

Changed:
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<		 -1 - ( - 2 )
>
>		 -1 - ( - 2 ) = ____



Line: 48 to 48

 He pencils in a vertical line across both of the minus signs in the middle, turning them into plus signs:

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<		 - 1 + ( + 2 ) =
>
>		 - 1 + ( + 2 ) = ___



Line: 56 to 56

 That works for him every time, no matter what the numbers, and he isn't thrown off by the same problem written with an absolute value:

Changed:
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<		 -1 - | - 2 | =
>
>		 -1 - | - 2 | = ___



Line: 68 to 68

 For some reason a problem like:

Changed:
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<		 -1 - 2
>
>		 -1 - 2 = ___

makes sense to him. He 'sees' that he's adding two negative numbers.

Line: 76 to 76

 Here, too, however, he does a swoop and swoop thing: he squeezes in a plus sign between the 1 and the second minus sign, like this:

Changed:
<
<		 -1+-2 =
>
>		 -1+-2 = ___

Ed's explanation to Christopher that you can think of -1 - 2 as adding two debts -- first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3 -- seems to have been the ticket.


 <<O>>  Difference Topic AnswerKey (r1.12 - 16 Sep 2005 - CatherineJohnson)

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Line: 36 to 36

notes

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<		 Here is how Christopher does this problem:
>
>		 Here is how Christopher does this problem:




 <<O>>  Difference Topic AnswerKey (r1.11 - 16 Sep 2005 - CatherineJohnson)

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Line: 36 to 36

notes

Changed:
<
<		 Christopher does the -1 - ( - 2 ) problem by penciling a vertical line across both the minus signs, turning both of the center minus signs into plus signs:
>
>		 Here is how Christopher does this problem:

-1 - ( - 2 )


He pencils in a vertical line across both of the minus signs in the middle, turning them into plus signs:

Added:
>
>

- 1 + ( + 2 ) =
Added:
>
>


That works for him every time, no matter what the numbers, and he isn't thrown off by the same problem written with an absolute value:

-1 - | - 2 | =


This reminds me of Carolyn's belief that you need to get math into a child's hand.


For some reason a problem like:

-1 - 2


Changed:
<
<		 That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value). This reminds me of Carolyn's belief that you need to get math into a child's hand.
>
>		 makes sense to him. He 'sees' that he's adding two negative numbers.

Changed:
<
<		 For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers. Here, too, however, he does a swoop and swoop thing: he squeezes in a plus & minus sign, like this:
>
>		 Here, too, however, he does a swoop and swoop thing: he squeezes in a plus sign between the 1 and the second minus sign, like this:

Added:
>
>

-1+ -2 =
Added:
>
>

Changed:
<
<		 Ed's explanation that you can think of this as adding two debts (first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3) seems to have been the ticket there.
>
>		 Ed's explanation to Christopher that you can think of -1 - 2 as adding two debts -- first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3 -- seems to have been the ticket.

Changed:
<
<		 I tried that on a friend of mine who is severely math phobic, and she instantly got it, too. Adding debt to debt is something everyone can grasp! It's EVERYDAY MATH FOR THE MASSES!!!
>
>		 I tried that explanation on a friend of mine who is severely math phobic, and she instantly got it, too. Adding debt to debt is something everyone can grasp! It's EVERYDAY MATH FOR THE MASSES!





 <<O>>  Difference Topic AnswerKey (r1.10 - 16 Sep 2005 - CatherineJohnson)

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Line: 60 to 60

Changed:
<
<		 posts
>
>		 swoop and swoop

 the craft of math
Added:
>
>		 subtraction as the difference between 2 numbers
study sheet: subtracting integers & absolute value
notes on integer, subtraction, & absolute value study sheet


 <<O>>  Difference Topic AnswerKey (r1.9 - 16 Sep 2005 - CatherineJohnson)

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Line: 40 to 40

- 1 + ( + 2 ) =

Changed:
<
<		 That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value). This reminds me of Carolyn's belief that you need to get math into a child's hand.
>
>		 That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value). This reminds me of Carolyn's belief that you need to get math into a child's hand.

For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers. Here, too, however, he does a swoop and swoop thing: he squeezes in a plus & minus sign, like this:

Line: 59 to 59


Added:
>
>		 posts
the craft of math

-- CatherineJohnson - 16 Sep 2005


 <<O>>  Difference Topic AnswerKey (r1.8 - 16 Sep 2005 - CatherineJohnson)

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Line: 42 to 42

That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value). This reminds me of Carolyn's belief that you need to get math into a child's hand.

Changed:
<
<		 For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers. Here, too, however, he does a Swoop and swoop thing: he squeezes in a plus & minus sign, like this:
>
>		 For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers. Here, too, however, he does a swoop and swoop thing: he squeezes in a plus & minus sign, like this:

-1+ -2 =

Line: 52 to 52


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<
>
>		 From one of Carolyn's first posts:

Added:
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>		 That's what the standard algorithms are: they are moves that you learn how to make. Those moves get into your fingers, just like learning the piano or the violin or typing, and eventually you can do them completely mindlessly.



-- CatherineJohnson - 16 Sep 2005


 <<O>>  Difference Topic AnswerKey (r1.7 - 16 Sep 2005 - CatherineJohnson)

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Line: 42 to 42

That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value). This reminds me of Carolyn's belief that you need to get math into a child's hand.

Changed:
<
<		 For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers. Here, too, however, he does a Swoop and swoop thing: he 'edits' the problem like this:
>
>		 For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers. Here, too, however, he does a Swoop and swoop thing: he squeezes in a plus & minus sign, like this:

-1 + -2 =


 <<O>>  Difference Topic AnswerKey (r1.6 - 16 Sep 2005 - CatherineJohnson)

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Line: 40 to 40

- 1 + ( + 2 ) =

Changed:
<
<		 That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value).
>
>		 That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value). This reminds me of Carolyn's belief that you need to get math into a child's hand.

Changed:
<
<		 For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers.
>
>		 For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers. Here, too, however, he does a Swoop and swoop thing: he 'edits' the problem like this:

-1 + -2 =


Ed's explanation that you can think of this as adding two debts (first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3) seems to have been the ticket there.


 <<O>>  Difference Topic AnswerKey (r1.5 - 16 Sep 2005 - CatherineJohnson)

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Line: 35 to 35


Changed:
<
<		 Christopher does the -1 - ( - 2 ) problem by turning both of the center minus signs into plus signs:
>
>

notes

Christopher does the -1 - ( - 2 ) problem by penciling a vertical line across both the minus signs, turning both of the center minus signs into plus signs:

- 1 + ( + 2 ) =


 <<O>>  Difference Topic AnswerKey (r1.4 - 16 Sep 2005 - CatherineJohnson)

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Line: 9 to 9

 What is subtraction?
Changed:
<
<		 Subtraction is the _INVERSE_ of addition.
>
>		 Subtraction is the INVERSE of addition.




Changed:
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<		 When you subtract, you _ADD_ __THE__ _OPPOSITE_ of the number you are subtracting.
>
>		 When you subtract, you ADD THE OPPOSITE of the number you are subtracting.




Changed:
<
<		 An absolute value is always _POSITIVE_.
>
>		 An absolute value is always POSITIVE.





 <<O>>  Difference Topic AnswerKey (r1.3 - 16 Sep 2005 - CatherineJohnson)

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 <<O>>  Difference Topic AnswerKey (r1.2 - 16 Sep 2005 - CatherineJohnson)

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Line: 9 to 9

 What is subtraction?
Changed:
<
<		 Subtraction is the INVERSE of addition.
>
>		 Subtraction is the _INVERSE_ of addition.




Changed:
<
<		 When you subtract, you ADD _THE_ OPPOSITE of the number you are subtracting.
>
>		 When you subtract, you _ADD_ __THE__ _OPPOSITE_ of the number you are subtracting.




Changed:
<
<		 An absolute value is always POSITIVE.
>
>		 An absolute value is always _POSITIVE_.





 <<O>>  Difference Topic AnswerKey (r1.1 - 16 Sep 2005 - CatherineJohnson)
Line: 1 to 1
Added:
>
>
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What is subtraction?

Subtraction is the INVERSE of addition.


When you subtract, you ADD _THE_ OPPOSITE of the number you are subtracting.


An absolute value is always POSITIVE.


1 - 2 = -1

1 - ( - 2 ) = 3

-1 + -2 = -3

1 - | 2 | = -1

-1 - | 2 | = -3

-1 - | -2 | = -3


Christopher does the -1 - ( - 2 ) problem by turning both of the center minus signs into plus signs:

- 1 + ( + 2 ) =

That works for him every time, no matter what the numbers (and he isn't thrown off by the same problem written with an absolute value).

For some reason a problem like -1 - 2 makes sense to him; he 'sees' that he's adding two negative numbers.

Ed's explanation that you can think of this as adding two debts (first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3) seems to have been the ticket there.

I tried that on a friend of mine who is severely math phobic, and she instantly got it, too. Adding debt to debt is something everyone can grasp! It's EVERYDAY MATH FOR THE MASSES!!!


-- CatherineJohnson - 16 Sep 2005

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Topic: AnswerKey . { View | Diffs | r1.17 | > | r1.16 | > | r1.15 | More }

Revision r1.1 - 16 Sep 2005 - 13:11 - CatherineJohnson
Revision r1.17 - 10 Apr 2006 - 16:04 - CatherineJohnson