** Do NOT forget... line up the decimals when adding or subtracting!!!
Algorithm - a step by step procedure to complete a math problem
ADDITION ALGORITHMS Addend + Addend = Sum
Partial-Sums Method - add from left to right, one place value at a time, then add the partial sums.
Ex: 348 + 177 = (300 + 100) + (40 + 70) + (8 +7)
400 + 110 + 15
525
Ex: 43.62 + 7.54 = (40 + 0) + (3 +7) + (0.6 + 0.5) + (0.02 + 0.04)
40 + 10 + 1.1 + 0.06
51.16
Column Addition Method - using lines to seperate place values, add each column, then trade all 2-digit sums to the left.
Ex: 3| 5 | 9 Ex: 4| 9| .| 6| 2| 5
+ 2| 9 | 8 + 4| .| 1| 7| 8
5| 14| 17 4| 13|.| 7| 9| 13
5| 15| 7 4| 13|.| 7|10| 3
6 5 7 5 3 . 8 0 3
Short Method (Carry Method) - add right to left, carrying the tens value.
1 1 1 1 1
Ex: 4 6. 25 Ex: 7. 0 0 4
+ 3. 98 + 9. 8 8 9
5 0. 23 1 6. 8 9 3
Opposite-Change Rule - Use subtraction on one addend to increase the value of the other addend.
Ex: 57 + 23 Ex: 59 + 26 Ex: 47.9 + 3.1
60 + 20 60 + 25 48 + 3
80 85 51
SUBTRACTION ALGORITHMS Minuend - subtrahend = difference
Trade First Method - subtract from right to left, borrowing ten if necessary.
Ex: 3 15 13 Ex: 4 16 11
4 6 3 8 5 . 7 1
- 2 7 5 - 1 4 . 9 9
1 8 8 7 0 . 7 2
Counting Up Method - increase the smaller number until it reaches the larger number, then add the increases.
Ex: 425 - 48 48 + 2 + 50 + 300 + 25 = 377
+ 2
50
+50
100
+300
400
+ 25
425
Ex: 13.5 - 4.2 4.2 + 0.3 + 9.0 = 9.3
+0.3
4.5
+9.0
13.5
Left to Right Method - subtract place values from left to right.
Ex: 932 - 356 = 932 Ex: 10.82 - 4.93 = 10.82
- 300 - 4.00
632 6.82
- 50 - 0.90
582 5.92
- 6 - 0.03
576 5.89
Partial-Differences Method - subtract from left to right one place value at a time, then add the differences.
Ex: 846 - 363 = (800 - 300) + (40 - 60) + (6 - 3) =
500 + (-20) + 3
483
Same Change Rule - add or subtract the same amount to/from both numbers
Ex: 83 - 27 = add three Ex: 83 - 27 = subtract 7
86 - 30 = 56 76 - 20 = 56
Ex: 40.8 - 17.5 = add 2.5 Ex: 40.8 - 17.5 = subtract 2.5
43.3 - 20 = 23.3 38.3 - 15 = 23.3
NUMBER STORIES
When reading number stories, be sure to ask yourself some important questions.
1. What numbers do I need to solve the problem?
2. What do I want to find?
3. What is my plan? or "open number sentence"?
4. What is the solution?
5. Does my answer have a label or unit?
Ex: Ms. Morgan has 24 students, Mrs. Ochoa has 23 students and Mrs. Gauss has 28 students. How many students are in all three rooms?
1. 24, 23, 28
2. How many students are in all three rooms
3. 24 + 23 + 28 = s
4. s = 75
5. 75 students
Relation symbols
> greater than < less than > greater than or equal < less than or equal
= equal to
STATISTICAL LANDMARKS
Minimum - smallest number in a set of data
Maximum - largest number in a set of data
Range - difference between the maximum and minimum
Mode - the number that appears most in a set of data
Median - middle value (**ONLY when the numbers are in order)
Mean (average) - add numbers in a set together and then divide by how many numbers in the set
EX: (96, 94, 88, 97, 56, 79, 85, 88, 94) put in order (56, 79, 85, 88, 88, 94, 94, 96, 97)
Minimum - 56 Maximum - 97 Range - 97 - 56 = 41
Mode - 88 and 94 Median - 88 Mean - 777 / 9 = 86.33
No comments:
Post a Comment