MTE280 Exam 1

1. Tally Marks

1.1. always in groups of 5

1.2. correct example: IIII/ (slash across the first 4)

1.3. incorrect example: IIIIII

2. Base Systems

2.1. Base 2- uses digits 0-1 before regrouping into the next place value

2.2. Base 5- uses digits 0-4 before regrouping into the next place value

3. Modeling Addition

3.1. have lots of different methods in order to cater to all students' learning styles

3.2. using manipulatives- Have students build two different towers, one of 5 and one of 3. Then have them count them all together to find that the sum is 8.

3.3. using pictures- Draw a set of 5 pictures on the board, followed by a set of 3 of the same picture. Have students count them all together to find that the sum is 8.

3.4. using touch math- find the points on each number and have the students count the 5, then continue onto those on the 3. They will end up on the sum- 8.

3.5. using a number line- Have students draw humps on their number line all the way to 5. Then have them draw 3 more. They will find that they land on the sum-8.

4. Subtraction

4.1. minuend-subtrahend=difference

4.2. Models: manipulatives, trading off, using friendlier numbers

5. Division

5.1. Vocab- dividend/divisor=quotient

5.2. Models- Standard algorithm, array, repeated subtraction

5.3. Identity property= 1. 4/1=4

5.4. Division of a number by 0 is meaningless

6. Order of Operations

6.1. Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

7. Base 10 (place values and expanded form)

7.1. uses digits 0-9 before regrouping into next place value

7.2. read from right to left, place values are considered ones, tens, hundreds, thousands, and so on

7.3. expanded form example= Write 4,938 in expanded form: (4*1,000)+(9*100)+(3*10)+(8*1)=4,938

8. Roman Numerals

8.1. I=1, V=5, X=10, L=50, C=100, D=500, M=1000

8.2. putting a roman numeral that is less than the one after it means subtraction (example: CD=400 or IX=9)

9. Properties of Addition

9.1. Closure Property- If a and b are whole numbers, than a+b will equal a whole number.

9.2. Commutative Property- a+b=b+a; numbers can be rearranged without affecting the sum

9.3. Associative Property- (a+b)+c=a+(b+c); groupings can be moved because it doesn't matter what gets added first, the sum will be the same

9.4. Identity Property- a+0=a=0+a; adding 0 to a number means the sum will come out to be the same number as the other addend (ex: 4+0=4)

10. Multiplication

10.1. vocab- factor x factor = product

10.2. models- memorizing facts, trading off, using 10's

10.3. commutative property- a x b=b x a

10.4. identity property= 1 x 4=4

10.5. associative property= grouping numbers in any combinations

10.6. Property of 0- 7 x 0=0, 394 x 0 = 0

10.7. distributive property- 4(8+9)= 4(8)+4(9)

11. All Operations

11.1. Inverse Operations- addition undoes subtraction and vice versa, 8-3=5, 5+3=8

11.2. Inverse Operations- multiplication undoes division and vice versa. 8 x 4=32, 32/4=8

11.3. Fact Families- use inverse operations to create fact families ex: 4+3=7, 3+4=7, 7-3=4, 7-4=3