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How To Add and Subtract- And How We Got This Far by Mind Map: How To Add and Subtract- And
How We Got This Far
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How To Add and Subtract- And How We Got This Far

The goal of this map is for teachers to find resources and information regarding the most important math, adding and subtracting. This map comes equipped with links to videos, teaching games, and the definitions that teachers need.

Numeration Systems

A collection of properties and symbols agreed upon to represent numbers systematically.

Tally

Uses single strokes, or tally marks, to represent each object that was counted. We see that in tally system a diagonal line is placed across four to group them as five.

Roman Numeration

Hindu-Arabic

The numeration system that we use today was developed by the Hindus and was transported to Europe by the Arabs. System relies upon 2 properties, Digits and place value.

History

Place Value

Face Value

Digits

Other Base Systems

Bianary

Quinary

Patterns

Patterns are everywhere! Mathematics has been described as the study of patterns.

Inductive Reasoning

Is the method of making generalizations based on observations and patterns.

Conjecture

Counterexample

Arithmetic Sequence

Is one in which each successive term from the second term on is obtained from the previous term by the addition or subtraction of a fixed number. For example: 0,5,10,15,20,.... Each sucessive number is obtained by adding 5 to the previous number.

Geometric Sequence

In geometric sequences each successive term is obtained from its predecessor by multiplying by a fixed nonzero number, the ratio. For example: 2,4,8,16,32,...

Figurate Numbers

Provide examples of sequences that are neither arithmetic nor geometric. Such numbers can be represented by dots arranged in the shape of certain geometric figures.

Triangular Numbers

Square Numbers

Addition of Whole Numbers

To define addition, let A and B be two disjoint finite sets. If n(A)= a and n(B)= b, then a+b= n(A U B). The numbers a and b in a +b are the addends and a + b is the sum.

Set Model

Can be referred to as uniting sets. This is the combination of two groups. The importance is that the two groups must not have any elements in common.

Number Line Model

Can also be referred to as counting on. In this method, one set gets bigger. For example: A little boy had two chicken nuggets on his plate. Then his mother put three more chicken nuggets on the plate. How many chicken nuggets does this little boy have on his plate? This example uses a story problem to show that his first set (2 chicken nuggets), got bigger by addind 3 more chicken nuggets to it. This is a visual way that children can see the set getting bigger.

Subtraction of Whole Numbers

The definition of subtracting whole numbers is for any whole numbers a and b such that a is greater than or equal to b, a-b is the unique whole number c such that b+c=a.

Comparison Model

For comparison model of subtraction you need two sets. One of the ets is larger than the other set. But by how much? For example, Juan has 8 blocks and Susan has 3 blocks. How many more blocks does Juan have than Susan. The chiildren can see by lining up the blocks that Juan has 5 more blocks than Susan does.

Take away Model

In the take away model of subtraction you have one set and that set gets smaller. For example, you have eight blocks, and three blocks are taken away. How many blocks do you now have? (5 blocks)

Missing-Addend Model

Missing-addend model gives elementary school students an opportunity to begin algebraic thinking. For example: Al has read 4 chapters of a 9 chapter book. How many more chapters does Al have to read?  In this model, the children need to find the missing number, or the missing-addend.

Number Line Model

Addition Properties

Identity

In identity property od addition of any whole numbers, there is a unique whole number, 0. That additive identity is such that for any whole number a, a+0=a=0+a. So any number plus 0 is going to be the number.

Associative

Associative property of addition states that if a, b, and c are whole numbers, then (a+b)+c=a+(b+c).

Commutative

If a and bare any whole numbers, then a+b= b+a

Closure

Any time two whole numbers are added, we are guaranteed that a unique whole number will be obtained. We say that "the set of whole number is closed under addition." If a and b are whole numbers, than a + b is a whole number.

Algorithms

Equal-Additions Algorthm

Addition Algorithms

Left to Right

Lattice

Scratch