# Teaching Math

## 51 terms · Saint Mary's Math 118 Test1

### Counting Set Model

Putting things together with objects X X X to count for the number 3

### Counting Measurement Model

Using a number line to count

### Tally System

an additive numerical system that uses slashes to count

### Egyptian System

an additive numerical system that uses I, II, III and heel

### Roman Numeral System

An additive system using I, II, III, IV, V, X and L

### Decimal System

A place value system with numbers 1,2,3,4

### Place Value

A system in which symbols are not added but the position of numbers is important

### Four Facts

Instead of learning one problem such as 1+2=3 students learn four facts (I can subtract 3-2=1)

### Complex Regrouping

We go to the tens, no tens we must go to the hundreds to subtract

### Commutativity

This property of any order addition means that the places are interchangeable for example, 6+2=2+6

### Associativity

This property of any order addition means that you can group numbers together in whichever way is easiest for example (2+3)+5=2+(3+5)

### Identity

This property of addition means that you add zero to any number you will get the same number

### Compensation

When looking at an addition problem you can subtract from one number and add an equal amount to the other number to make it easier for example, 9+6=(9+1)+(6-1)=10+5=15

### Part-Whole Interpretation

A subtraction problem in which I have X number of something in a certain situation, if so many are one particular thing of X and the rest are Y how many of X are there? I have a whole I tell how much I have of one part

### Take-Away Interpretation

A subtraction problem in which I have X number of something I remove Y how many do I have left?

### Comparison

A subtraction problem in which I have X number of something but someone else has Y more how many more does the other person have than me?

### Count Down Method

A way of doing a subtraction problem that involves taking a larger number and moving backwards on the number line

### Count Up Method

A way of doing a subtraction problem that involves taking the smaller number and going up on the number line to a larger number and using the difference as your answer.

### Set Model

A way of representing multiplication and using pictures to show how many groups of something we have.

### Measurement Model

A way of representing multiplication by showing the problem as a series of "jumps" on a number line.

### Rectangular Array

A way of representing multiplication by showing the problem in rows and columns.

### Commutativity

A property of multiplication that means we can multiply numbers in any order and get the same answer for example 3x5=5x3

### Associativity

A property of multiplication that means we can group multiplication together in any order and get the same answer for example (2x3)x5=2x(3x5)

### Identity

A property of multiplication that means we can multiply any number by one and get that number, for example, 4x1=4

### Distributivity

A property of multiplication with addition that is important for algebra meaning that if we have 2(3+4) we must multiply 2x3+2x4

### Distributivity

A way of using mental math by breaking the numbers into easier parts for example 7850/2=78/2+50/2

### Division

A reverse of multiplication

### Set Model

A way of representing division by drawing pictures into a variety of groups

### Measurement Model

A way of representing division by drawing bars or using a number line

### Partitive Division

An interpretation of division that says I have a group of X I need to make Y number of groups; how many will be in each group?

### Measurement Division

An interpretation of division that says I have a group of X I need to Y number in each group; how many groups can I make?

### Compensation

This strategy can be used in division if we multiply both numbers by a common number to make the problem easier for example 75/5=150/10

### Division by Zero

does not work because you can check with four facts
1/0=? we cannot figure out the ? by going ?x0=1 is not possible because every number x0 is equal to 0 also does not work because you can come up with a situation in which every number would work by checking for example 0/0=? but ?x0=0 every number would work because every number x0 is equal to 0

### Quotient-Remainder Theorem

This theorem states that you can't divide every number evenly, sometimes there will be a remainder HOWEVER the remainder must be less than what you are dividing by

### Place Value Strategy

A mental math strategy that involves multiplying each place value by itself such as 20x40=
2x4=8 then 10x10=100 adding the two together =800

### Distributivity

A mental math strategy in which you take, for example 6x108=6(100+8)=648

### Word Problems

These problems should be short, clear, interesting, realistic, self-contained and be of great variety (measurement/set)

### Algorithm

A way to solve a problem that is precise, step-by-step, correct in all cases.

### Base 5

multiply 1, 5, 25, 125 into the number to get to base 5 then for getting it from base 10 to 5 multiply first digit by corresponding number in sequence

### 10

This Egyptian numeral is called heel and is shaped like a U upside down

### 100

This Egyptian numeral is called scroll and looks like a squiggle

### 1000

This Egyptian numeral is called lotus and looks like a flower

### 1

This Roman Numeral looks like I

### 10

This Roman Numeral looks like X

### 100

This Roman Numeral looks like C

### 1000

This Roman Numeral looks like M

### 5

This Roman Numeral looks like V

### 50

This Roman Numeral looks like L

### 500

This Roman Numeral looks like D