MTE 280

Wk 1: Problem Solving

Wk 2: Numeration Systems

Wk 3: Bases

Wk 4: understanding Algorithms

Addition meaning & properties: Putting together; Joining
Identity-- a + 0 = a *when I add zero to a number the identity doesn't change*
Commutative-- (order property) a+b= b+a *the order of numbers doesn't matter*
Associative--(grouping) (a+b)+c= a+(b+c) *the grouping of numbers doesn't matter*

Subtraction
1. takes away --> 4-3=1
2. comparison --> compare the 2 groups
3. Missing addend--> 3 + =7 * A 7th grader will add until 7. It's an addition problem so us telling them to take away doesn't make sense

Multiplication
3 x 4 --> 3 groups of 4
* simply is a repeated addition

Cartesian Product- combining items from one group to another

Properties of Multiplication:
Identity-- a x 1 = a --> when multiply by 1. Identity doesn't change
Commutative: (order) The order you multiply doesn't matter. a x b = b x a
Associative: (grouping) (2x5)x5 = 2x (5x5)
Zero: a x 0 = 0 Multiply number by zero is always zero.

Division
Practice: John has 15 cookies. He puts 3 cookies in each bag. How many bags can he fill?
15 divided by 3 = 5. First grader would make 15 cookies and make 3 piles. Then count the piles at the end.

Wk 5: Addition/subtraction/multiplication Algorithms

Multiplication Algorithms:

American Standard-
23
x 14
192
+ 230
322
Place Value-
23 --> 4x3= 12
x 14 4x20=80 *add all products
10x3=30
10x20=200
322
Expanded Notation-
23 Take 23, 14 times or 14 groups of 23
x 14 10
20+3
x 10+4
100 90+ 2 --> comes from taking 23, 4 times
200+ 30+0
300+ 20+2 = 322

Lattice method-
shown in video

Subtraction Algorithms:

American Standard-
576 R to L w/ no reference to place value
- 289
287
Reverse Indian-
17 16
576 L to R
- 289
3
2
9
8 7
287

Left to Right- (added place value)
170 16
576
- 289
300
200
90
80
7
287

Expanded Notation:
400 160 16
576 = 500+70+6
- 289= 200+80+9
287= 200+80+7

Integer Sub. Algor. -
576
- 289
-3
-10
+300
287

Addition Algorithms:

American Standard- (last step)
576 R to L
+279
855

Partial Sum-
576 R to L
+279
15
+ 1 4
7
855

With Place Value-
576
+ 279
15
+ 140
700
855
Left to Right-
576
+ 279
700
+ 140
15
855
Expanded Notation-
100 10
576 = 500 + 70 + 6
+279 = 200 + 70 + 9
855 = 800 + 50 + 5 *start with this algorithm then when understood-- American standard. *

Lattice Methods-

shown in video