Math 2130 Unit 2 Exam Study Guide
Associative Property of Addition
(a+b)+c=a+(b+c)
Doubling and Adding One
18 x 3 = 18 x (2+1) = 18 x 2 + 18 36 + 18 = 40 + 14 The final result is 54. We applied two useful techniques here: expansion and making tens.
Partial products algorithm
24 x13 ------ 12 60 40 +200 ----- 312
Partial Sums Algorithm
428 +295 ------ 13 110 600 ------ 723
Meaning of Multiplication
A ×B means the total in A groups of B.
Addition and subtraction problem types and subtypes
Add To -Result Unknown, Change Unknown, Start Unknown Take From -Result Unknown, Change Unknown, Start Unknown Put Together/Take Apart -Total Unknown, Addend Unknown, Both Addends Unknown Compare -Difference Unknown -How many more? -How many less? -Bigger Unknown -How many more? -How many less? -Smaller Unknown -How many more? -How many less?
Properties of Multiplication
Commutative, Associative, Distributive
Addition Fact Strategies
Counting All, Counting On, Decomposing
Mental strategies for multiplication
Doubling and Adding One, Expanding
Put Together/ Take Apart: Addend Unknown
Five apples are on the table. Three are red and the rest are green. How many apples are green? 3+?=5 or 5-3=?
Take From: Change Unknown
Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat? 5-?=3
Take From: Result Unknown
Five apples were on the table. I ate two apples. How many are on the table now? 5-2=?
Put Together/ Take Apart: Both Addends Unknown
Grandma had five flowers. How many can she put in her red vase and how many in her blue vase? 5= 0+5 5= 1+4 5= 2+3 5=4+1 5=3+2
Interpretations of Division
How many groups? And How many in each group?
Compare: Smaller Unknown (How many more)
Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have? ?+3=5
Compare: Bigger Unknown (How many more)
Julie has three more apples than Lucy. Lucy has two apples. How many apples does Julie have? 2+3=?
Compare: Smaller Unknown (How many less)
Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have? 5-3=?
Compare: Bigger Unknown (How many less)
Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have? ?-3=2
Compare: Difference Unknown (How many less)
Lucy has two apples. Julia has five apples. How many fewer apples does Lucy have than Julia? 5-?=2
Compare: Difference Unknown (How many more)
Lucy has two apples. Julia has five apples. How many more apples does Julia have than Lucy? 2+?=5
Standard Algorithms for Addition and Subtraction
Normals ways you figure out the problem
Expanding
Numbers can be expanded to make multiplication easier 18 x 7 = (8 + 10) x 7 = 7 x 8 + 7 x 10 = 56 + 70 = 126
Scaffold Method
Partial Quotients Method
Take From: Start Unknown
Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before? ?-2=3
Add to: Start Unknown
Some bunnies were sitting on the grass. Three more bunnies hopped there. Then, there was five bunnies. How many bunnies were on the grass before? ?+3=5
Standard Deviations Algorithms
Standards Long Division Algorithms
Put Together/ Take Apart: Total Unknown
Three red apples and two green apples are on the table. How many apples are on the table? 3+2=?
Add To: Result Unknown
Two bunnies sat on the grass. three more bunnies hopped there. How many bunnies are on the grass now? 2+3=?
Add To: Change Unknown
Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there was five bunnies. How many bunnies hopped over to the first two? 2+?=5
Decomposing
Understanding how a number can be added together. For example, 5. 5= 0+5, 1+4,2+3,3+2,4+1,5+0
Counting All
When children add by beginning with number 1 to count
Distributive Property of Addition
a(b+c)=ab+ac
Commutative Property of Addition
a+b=b+a
Mental strategies for addition and subtraction
counting on, making ten, using known facts to derive unknown facts
Counting On
when students add by beginning at a variable and adding the rest. For example if the question was 6+4 they would know they have six so they'd count by six, seven, eight, nine, ten.
