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MIAA 350: Addition and Subtraction

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by

Lori Green

on 19 October 2014

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Transcript of MIAA 350: Addition and Subtraction

Important Prerequisite Understandings & Skills
Addition and Subtraction
Essential Understandings

Comparing
Parts and Wholes
Join
Separate
Regrouping
Zero as a Place holder
Models & Representations
Key Language & Symbols
Helpful Teacher Resources
Meaningful Connections
Addition (+):
To combine, join, extend.
Addend:
Numbers being added.
Sum:
the amount obtained as a result of adding 2 numbers.
Subtraction (-)
To separate, to divide, to shrink.
The
minuend
, C, subtracts the
subtrahend
, B:
C-B=A
Here, A is the difference between terms.
Addition and Subtraction
Equal Sign (=)
Place Value
Digits
Regrouping
Basic Facts
Number sense is the ability to:


1. Take numbers apart and put them together.
2. Move fluently among different representations.
3. Recognize when one representation is more useful than another.
4. Perform mental computation and estimation flexibly.
5. Determine if an answer is reasonable.
Examples
Why?
Models for Addition and Subtraction:
-Fact Families
-Number Bonds
-Part/Part/Whole Models
-Tape Diagrams

Standard Algorithms for Addition & Subtraction
Alternative Algorithms
Algorithms & the Real World
Zero as a place holder
Move from 1-digit to 2-digit to 3-digit
Properties
Online Games
http://pbskids.org/cyberchase/math-games/stop-creature/
http://www.uen.org/3-6interactives/math.shtml#patterns
http://www.coolmath-games.com/0-make15/index.html
http://www.321know.com/add27_x3.htm
http://www.playkidsgames.com/games/shuttleLaunch/shuttleLaunch.htm
Books
Number Sense
Before moving into more complex applications of the addition and subtraction algorithms, students need to have a firm grasp on one-digit and base-ten operations.
Activities
Other useful resources
Books with Addition and
Subtraction
Algorithms
Place value
Decimal
Regrouping
Common Student Errors and Misconceptions
Students can get confused with place value! For Example:
2456
+ 123
24683
2456
+ 123
2579
Wrong
Correct!!!
In this example, the student wants to line up the numbers with place value without matching the decimal's first
Saying "carry" instead of regrouping
http://www.funbrain.com/brain/MathBrain/Games/Instructions.html?GameName=BumbleNumbers1&Brain=math&Gender=F&Grade=4&Language=en_us&GameNumber=1&Color=undefined&OldPassword=EAR4&Password=EAT4&HardCoded=false&Roadblock=undefined
Zero represents 'nothing' so does not need to be included in a number
Example: 103
Child would like think the "0" as nothing therefore the number is actually 13
Example: 103 + 52
38 + 4 = 78
Child incorrectly lined up the numbers
Doesn't understand that 38 means 30 + 8 that is, 3 tens and 8 ones
How they lined it up:
4
+ 38
78
How they should line it up:
38
+4
42
13
+52
65
103
+ 52
155
It's important to always have a variety of models to share with your students. Because all people learn in distinct ways, it will be useful to be able to present similar information in multiple ways. These models involve various thinking strategies, which can be helpful in explaining a concept to a struggling student in a way that is more accessible to them.
70
- 53
23
Common Error in Subtraction:
What they need to do:
7 0
-5 3
1 7
6
Algorithm:
A process or set of rules to be followed in calculations or other problem-solving operations
.
10
Addition & Subtraction as Inverses
6
+23
83
70
- 53
23
2456
+ 123
24683
25
+ 604
854
Algorithms are important to helping students find order and reason in mathematics. When used correctly, the standard algorithms for addition and subtraction will always produce the correct response.
In analyzing the similarities and differences between addition and subtraction, we can capitalize on models to better explain the concept of the two operations as inverses. Using the part-part-whole model and the missing addend model, we can help students develop a clearer understanding of the similarities and differences between addition and subtraction. In formulating their ideas, students will begin to form a more complete picture of the relationship between these two important operations.
Most of these books I found online!
Full transcript