Manipulatives, Adding & Multiplying using Visual Models, Order of Operations, Properties of Operations, Opposites & Reciprocals

Question 1

Attribute Blocks

Answer 1

come in five different geometric shapes with different colors. Can be sued for sorting, patterns, and teaching attributes of geometric figures

Question 2

What shapes do attribute blocks come in?

Answer 2

circle, square, rectangle, triangle, hexagon

Question 3

Base-10 Blocks

Answer 3

Visual models in powers of 10 that represents ones, tens, hundreds, and thousands. These blocks can be used to teach place value, regrouping with addition or subtraction, fractions, decimals, percents, and area and volume

Question 4

Bar Diagrams

Answer 4

used to represent parts and whole and are often used with finding a missing value in a number sentence (e.g., 5+?=12).

Question 5

Counters

Answer 5

come in different shapes and colors (e.g., bears, bugs, chips) and are used for sorting and counting

Question 6

Geoboards

Answer 6

pegboard grids on which students stretch rubber bands to make geometric shapes. They are used to teach basic shapes, symmetry, congruency, perimeter, and area

Question 7

Fraction Strips

Answer 7

Help to show the relationship between the numerator and denominator of a fraction and how parts relate to a whole

Question 8

Numerator

Answer 8

top number of a fraction

Question 9

Denominator

Answer 9

bottom number of a fraction

Question 10

Snap Cubes

Answer 10

cubes that come in various colors that can be snapped together from any face. Snap cubes can be used to teach number sense, basic operations, counting, patterns, and place value

Question 11

Tiles

Answer 11

1 inch squares that come in different colors. Some more common skill tiles can be used to teach including counting, estimating, place value, multiplication, fractions, and probability

Question 12

Polynomials

Answer 12

algebraic expressions that consist of variables and coefficients

Question 13

Operator

Answer 13

+,-,x,÷

Question 14

Variables

Answer 14

a letter that represents an unknown number

Question 15

Coefficient

Answer 15

a number that multiplies a variable

Question 16

Array

Answer 16

puts groups into organized lines, preparing students for additional math topics such as area.

Question 17

Identify the P in PEMDAS

Answer 17

Parenthesis

Question 18

Order of Operations: Parenthesis

Answer 18

includes all grouping symbols, which may include brackets [].

Question 19

Identify the E in PEMDAS

Answer 19

Exponents

Question 20

Order of Operations: Exponents

Answer 20

means anything raised to a power should be simplified after all operations inside of grouping symbols have been simplified

Question 21

Identify the MD in PEMDAS

Answer 21

Multiplication Division

Question 22

Order of Operations: Multiplication Division

Answer 22

essentially the same “type” of operation. Therefore, these operations are performed in order from left to right (whichever comes first), just s you would read a book. ALL multiplication and division should be completed BEFORE any addition or subtraction that is not inside a Parenthesis

Question 23

Identify the AS in PEMDAS

Answer 23

Addition Subtraction

Question 24

Order of Operations Addition Subtraction

Answer 24

essentially the same “type” of operation. these operations are done left to right (whichever comes first). These operations should always come last unless they are inside parenthesis

Question 25

Find the solution: 1+2(28-12)+2x10

Answer 25

1+2(28-12)+2x10 1+2(16)+2x10 1+32+20 33+20 =53

Question 26

7 Examples of common problem solving strategies

Answer 26

- Draw a picture - Find a pattern - Guess and check - Make a chart or table - Work the problem backward - Act it out - Estimating or rounding

Question 27

Commutative Property of Addition Rule

Answer 27

a+b=b+a

Question 28

Commutative Property of Addition Description

Answer 28

Changing the order of two numbers being added does not change their sum

Question 29

Commutative Property of Multiplication Rule

Answer 29

axb=bxa

Question 30

Commutative Property of Multiplication Description

Answer 30

Changing the order of two numbers being multiplied does not change their products

Question 31

Associative Property of Addition Rule

Answer 31

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

Question 32

Associative Property of Addition Description

Answer 32

Changing the groupings of the addends does not change their sum

Question 33

Associative Property of Multiplication Rule

Answer 33

ax(bxc)=(axb)xc

Question 34

Associative Property of Multiplication Description

Answer 34

Changing the grouping of the factors does not change their product

Question 35

Additive Identity Property of 0 Rule

Answer 35

a+0=0+a=a

Question 36

Additive Identity Property of 0 Description

Answer 36

Adding 0 to a number does not change the value of that number.

Question 37

Multiplicative Identity Property of 1 Rule

Answer 37

ax1=1xa=a

Question 38

Multiplicative Identity Property of 1 Description

Answer 38

Multiplying a number by one does not change the value of that number

Question 39

Inverse Property of Addition Rule

Answer 39

For every a, there exists a number -a such that a+(-a)=(-a)+a=0

Question 40

Inverse Property of Addition Description

Answer 40

Adding a number and its opposite results in a sum equal to 0

Question 41

Inverse Property if Multiplication Rule

Answer 41

For every a, there exists a number 1/a such that ax1/a=1/axa=a/a=1

Question 42

Inverse Property if Multiplication Description

Answer 42

Multiplying a number and its multiplicative inverse results in a product equal to 1

Question 43

Distributive Property of Multiplication over Addition Rule

Answer 43

ax(b+c)=axb+axc

Question 44

Distributive Property of Multiplication over Addition Description

Answer 44

Multiplying a sum us the same as multiplying each addend by that number, then adding their products

Question 45

Distributive Property of Multiplication over Subtraction Rule

Answer 45

ax(b-c)=axb-axc

Question 46

Distributive Property of Multiplication over Subtraction Description

Answer 46

Multiplying a difference is the same as multiplying the minuend and subtrahend by that number, then subtracting their products

Question 47

Minuend

Answer 47

a quantity or number from which another is to be subtracted.

Question 48

Subtrahend

Answer 48

a quantity or number to be subtracted from another

Question 49

What is the opposite of a number

Answer 49

the same number with a different sign

Question 50

What is always true about the sum of a number and its opposite?

Answer 50

The sum of a number and its opposite equals 0

Question 51

What is the opposite of 5

Answer 51

-5

Question 52

What is the opposite of -2

Answer 52

2

Question 53

True or False: Zero does not have an opposite

Answer 53

True

Question 54

What is a another word for Reciprocal

Answer 54

Multiplicative Inverse

Question 55

What is a Reciprocal?

Answer 55

What a number is multiplied by to get 1

Question 56

What is the reciprocal of 3

Answer 56

1/3

Question 57

What is always true of the product of a number and its reciprocal?

Answer 57

The product of a number and its reciprocal is 1

Question 58

Does zero have a reciprocal?

Answer 58

No

Question 59

Which of the following is an example of applying the distributive property to the expression 4+14a? A. 2(2+7a) B. 2x2=14a C. 4+(2x7a) D. 18ax1

Answer 59

A

Question 60

Which of the following is an example of the commutative property of addition? A. (2+x)+3=2+(x+3) B. 4+(y+w)=4+(w+y) C. 5a+b+1=5a+b D. 2(3x+8)-1=6x+16-1

Answer 60

B