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MTH 320 Exam 1 Review
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Flashcards
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Terms in this set (27)
Four types of subtraction situations
1. Take Away
2. Missing-Addend
3. Comparison
4. Missing Subraction
Take Away
ex. Sophia has 7 toy cars and she gives three of them to Joey. How many does she have left?
Missing-Addend
ex. I have 8 dollars. I need 11 dollars to buy a CD. How many dollars do I need to earn?
Comparison
ex. Kristen has 4 marbles. Rebecca has 9 marbles. How many more marbles does Rebecca have than Kristen?
Missing Subtraction
ex. When Cindy left for school this morning, she had 8 quarters in her pocket. When she got off the bus, she only had 5 quarters left. How many did she lose?
Four models of multiplication
1. Repeated Addition
2. Array
3. Area
4. Cross Product (Cartesian)
Repeated Addition
ex. 5x3 = 3+3+3+3+3
Array
ex. 5x3
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
Area
ex. 5x3
Cross Product
ex. 5x3
If you have 3 shirts and 5 pairs of pants, how many different outfits can you make?
pants 1
pants 2
shirt 1 pants 3
pants 4
pants 5
pants 1
pants 2
shirt 2 pants 3
pants 4
pants 5
pants 1
pants 2
shirt 3 pants 3
pants 4
pants 5
Which models of multiplication are best for showing commutative strategies? Why?
Array and Area. All you have to do is rotate it (change perspective) so the 5x3 becomes 3x5.
Two concepts of division
1. Measurement
2. Sharing
Measurement
ex. I have 15 cookies and I need to stack them in 3 stacks each. How many stacks of 3 can I make?
Sharing
ex. I have 24 pennies and I want to share them (equally) with 4 people? How many does each person get?
Partial sum alogarithm
ex.
3679
768
6834
+ 8671
----------------
22
230
2700
17000
----------------
=19,952
Scratch alogrithm
ex.
3 6 7 9
7-6-8-
6-8-3 4-
+ 8 6 7-1
----------------
=19,952
Constant difference alogarithm
watch video!!!
Divide by zero: sharing
I have 24 cookies, and I want to share them with 0 people. How many will each person get?
Note the division question! Must actually ask it for the problem to arise.
This question doesn't make sense. If there are no people, how can you ask someone to figure out how many the non-existent people each get.
Divide by zero: measurement
I have 15 cookies, and I need to stack them in stacks of 0 each. How many stacks of 0 can I make?
Note the division question! Must actually ask it for the problem to arise.
This question makes sense, but it is unanswerable (can make stacks of zero forever).
Russian Peasant
A B add
27 58 58
13 116 116
6 232
3 464 464
1 928 928
Answer:
1566
(We're just moving a factor of two around, but multiplication is commutative and associative, so that doesn't change anything.) We are dropping fractional parts, we lose part of the product whenever we halve an odd number. And the amount we lose from that product is precisely the amount that was in column B next to the odd number before we halved it.
Lattice Method
watch video!
Gaussian Method
watch video!
Partial Quotients
...
Area Model and Partial Products
...
Write Numbers 1-100 in base 12
1, 2, 3, 4, 5, 6, 7, 8, 9, T, E, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 1T, 1E, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 2T, 2E, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 3T, 3E, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 4T, 4E, 50,
51, 52, 53, 54, 55, 56, 57, 58, 59, 5T, 5E, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 6T, 6E, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 7T, 7E, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 8T, 8E, 90,
91, 92, 93, 94, 95, 96, 97, 98, 99, 9T, 9E, T0,
T1, T2, T3, T4, T5, T6, T7, T8, T9, TT, TE, E0,
E1, E2, E3, E4, E5, E6, E7, E8, E9, ET, EE, 100
Partial Products in base 12
...
2 reasons pre-service teachers might use base 12
Develops empathy and a deeper understanding of base 10 for teachers.
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