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
an additive numerical system that uses slashes to count
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
A place value system with numbers 1,2,3,4
A system in which symbols are not added but the position of numbers is important
Instead of learning one problem such as 1+2=3 students learn four facts (I can subtract 3-2=1)
We go to the tens, no tens we must go to the hundreds to subtract
This property of any order addition means that the places are interchangeable for example, 6+2=2+6
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)
This property of addition means that you add zero to any number you will get the same number
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
A reverse operation to addition
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
A subtraction problem in which I have X number of something I remove Y how many do I have left?
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.
A way of representing multiplication and using pictures to show how many groups of something we have.
A way of representing multiplication by showing the problem as a series of "jumps" on a number line.
A way of representing multiplication by showing the problem in rows and columns.
A property of multiplication that means we can multiply numbers in any order and get the same answer for example 3x5=5x3
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)
A property of multiplication that means we can multiply any number by one and get that number, for example, 4x1=4
A property of multiplication with addition that is important for algebra meaning that if we have 2(3+4) we must multiply 2x3+2x4
A way of using mental math by breaking the numbers into easier parts for example 7850/2=78/2+50/2
A reverse of multiplication
A way of representing division by drawing pictures into a variety of groups
A way of representing division by drawing bars or using a number line
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?
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?
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
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
A mental math strategy in which you take, for example 6x108=6(100+8)=648
These problems should be short, clear, interesting, realistic, self-contained and be of great variety (measurement/set)
A way to solve a problem that is precise, step-by-step, correct in all cases.
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
This Egyptian numeral is called heel and is shaped like a U upside down
This Egyptian numeral is called scroll and looks like a squiggle
This Egyptian numeral is called lotus and looks like a flower
This Roman Numeral looks like I
This Roman Numeral looks like X
This Roman Numeral looks like C
This Roman Numeral looks like M
This Roman Numeral looks like V
This Roman Numeral looks like L
This Roman Numeral looks like D