math quiz 2

Additive Identity

0 n + 0 = n and 0 + n = n

Multiplicative Identity

1 n x 1 = n and 1 x n = n

Interpretations of multiplication

1. Additive - given a number of sets, each with the same number of objects, find the total number of objects Ex: Gary has 4 packs of gum; each pack has 5 pieces. How many pieces of gum does Gary have? 4 (packs) x 5 (pieces) = 20 (total) xxxxx xxxxx xxxxx xxxxx 2. Array (row by column) - given a number of rows, each with the same number of objects, find the total number of objects. Ex: three children can sit in each row of the bus. The bus has four rows. How many children can go on the bus? 4 x 3 = 12 xxx xxx xxx xxx 3. Comparative - comparing two quantities for which one is described as a multiple of the other. Ex: Tacito has four dogs. His brother has twice as many dogs. How many dogs does his brother have? 2 x 4 = 8 4. Combination - given two (or more) sets, choose one item from each set, find the total number of possible combinations. Ex: a lunch menu has 3 entrees and 2 sides. How many different meals are possible? 3 x 2 = 6 (make web)

Interpretations of addition

1. Combination - elements or objects are combined Ex: amy has 2 apples. Bill has 3 apples. How many apples all together? 2. Incremental - no objects or elements, but something gets larger Ex: my cat was 2 years old when I got him 3 years ago. How old is he now

Interpretations of division

1. Subtractive - the total number of objects and how many in each set are known. You need to find the number of sets. Ex: there are 20 cookies. You will put 5 on each plate. How many plates are needed? 20 / 5 = 4 2. Distributive - the total number of objects and how many sets are known. You need to find the number in each set. Ex: there are 20 cookies and 5 plates. To share the cookies equally, how many cookies should go on each plate? 20 / 5 = 4 3. Comparative - (a) given a total number of objects that is a multiple of another given number, find how many times the total number is of the other given number, or (b) given a total number and that this is a given multiple of another number, find the other number. Ex: Troy collects hats. He has 40 hats. His little brother has also decided to collect hats. Troy's little brother has 10 hats. Troy has how many times as many hats as his brother? 4x as many.

Interpretations of subtraction

1. Take away Ex: five birds are sitting on a fence. Two birds fly away. How many birds are still on the fence? 2. Additive Ex: there are 7 children on the playground. You need 9 to play a game. How many more children are needed? 7 + ? = 9 : 9 - 7 = 2 3. Comparative Ex: jerry has 5 apples. Latisha has 2 apples. Who has more apples? How many more? (Draw out apples & line them up against one another to compare) 5 - 2 = 3 4. Partitioning Ex: there are 7 children on the playground. Four of the children are boys. How many of the children are girls? 7 - 4 = 3 (make drawing representing the boys and girls) 5. incremental/decremental ex: the temperature is 56 degrees. It will be 74 degrees later today. How much will the temperature rise? 75 - 56 = 18

Doubles

5 + 6 = 5 + 5 is 10, so 11

Counting back

8 + 5 = 15, 14, 13...

Counting on

8 + 5 = 9, 10, 11, 12, 13

Remainder

Amount left over after dividing a number

Missing factor

The missing number in a multiplication problem/number sentence that makes the number sentence true. Ex: 5 x ? = 20

Missing addend

The missing number in an addition number sentence that makes the number sentence true. Ex: 5 + ? = 20

If n is prime

There are only 2 facts in the family

Associative Property of Addition

a + (b + c) = (a + b) + c

Commutative Property of Addition

a + b = b + a

number sentence

a mathematical statement that has numbers, at least one operation sign, and an equal or inequality sign. Ex: 2 + 3 = 5

Associative Property of Multiplication

a x (b x c) = (a x b) x c

Distributive Property of multiplication over addition

a x (b+c) = a x b + a x c

Commutative Property of Multiplication

axb=bxa

Pythagorean Theorem

a²+b²=c²

Zero element

n x 0 = 0 and 0 x n = 0

Quotient

the answer to a division problem

Product

the answer to a multiplication problem

Difference

the answer to a subtraction problem

Sum

the answer to an addition problem

Dividend

the number that is being divided (inside of the box)

Divisor

the number you divide by (outside of the box)

Addend

the numbers being added in an addition problem

Factor

the numbers being multiplied in a multiplication problem