Manipulatives, Adding & Multiplying using Visual Models, Order of Operations, Properties of Operations, Opposites & Reciprocals Flashcards
Attribute Blocks
come in five different geometric shapes with different colors. Can be sued for sorting, patterns, and teaching attributes of geometric figures
What shapes do attribute blocks come in?
circle, square, rectangle, triangle, hexagon
Base-10 Blocks
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
Bar Diagrams
used to represent parts and whole and are often used with finding a missing value in a number sentence (e.g., 5+?=12).
Counters
come in different shapes and colors (e.g., bears, bugs, chips) and are used for sorting and counting
Geoboards
pegboard grids on which students stretch rubber bands to make geometric shapes. They are used to teach basic shapes, symmetry, congruency, perimeter, and area
Fraction Strips
Help to show the relationship between the numerator and denominator of a fraction and how parts relate to a whole
Numerator
top number of a fraction
Denominator
bottom number of a fraction
Snap Cubes
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
Tiles
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
Polynomials
algebraic expressions that consist of variables and coefficients
Operator
+,-,x,÷
Variables
a letter that represents an unknown number
Coefficient
a number that multiplies a variable
Array
puts groups into organized lines, preparing students for additional math topics such as area.
Identify the P in PEMDAS
Parenthesis
Order of Operations: Parenthesis
includes all grouping symbols, which may include brackets [].
Identify the E in PEMDAS
Exponents
Order of Operations: Exponents
means anything raised to a power should be simplified after all operations inside of grouping symbols have been simplified
Identify the MD in PEMDAS
Multiplication Division
Order of Operations: Multiplication Division
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
Identify the AS in PEMDAS
Addition Subtraction
Order of Operations Addition Subtraction
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
Find the solution: 1+2(28-12)+2x10
1+2(28-12)+2x10
1+2(16)+2x10
1+32+20
33+20
=53
7 Examples of common problem solving strategies
- Draw a picture
- Find a pattern
- Guess and check
- Make a chart or table
- Work the problem backward
- Act it out
- Estimating or rounding
Commutative Property of Addition Rule
a+b=b+a
Commutative Property of Addition Description
Changing the order of two numbers being added does not change their sum
Commutative Property of Multiplication Rule
axb=bxa
Commutative Property of Multiplication Description
Changing the order of two numbers being multiplied does not change their products
Associative Property of Addition Rule
(a+b)+c=a+(b+c)
Associative Property of Addition Description
Changing the groupings of the addends does not change their sum
Associative Property of Multiplication Rule
ax(bxc)=(axb)xc
Associative Property of Multiplication Description
Changing the grouping of the factors does not change their product
Additive Identity Property of 0 Rule
a+0=0+a=a
Additive Identity Property of 0 Description
Adding 0 to a number does not change the value of that number.
Multiplicative Identity Property of 1 Rule
ax1=1xa=a
Multiplicative Identity Property of 1 Description
Multiplying a number by one does not change the value of that number
Inverse Property of Addition Rule
For every a, there exists a number -a such that a+(-a)=(-a)+a=0
Inverse Property of Addition Description
Adding a number and its opposite results in a sum equal to 0
Inverse Property if Multiplication Rule
For every a, there exists a number 1/a such that ax1/a=1/axa=a/a=1
Inverse Property if Multiplication Description
Multiplying a number and its multiplicative inverse results in a product equal to 1
Distributive Property of Multiplication over Addition Rule
ax(b+c)=axb+axc
Distributive Property of Multiplication over Addition Description
Multiplying a sum us the same as multiplying each addend by that number, then adding their products
Distributive Property of Multiplication over Subtraction Rule
ax(b-c)=axb-axc
Distributive Property of Multiplication over Subtraction Description
Multiplying a difference is the same as multiplying the minuend and subtrahend by that number, then subtracting their products
Minuend
a quantity or number from which another is to be subtracted.
Subtrahend
a quantity or number to be subtracted from another
What is the opposite of a number
the same number with a different sign
What is always true about the sum of a number and its opposite?
The sum of a number and its opposite equals 0
What is the opposite of 5
-5
What is the opposite of -2
2
True or False: Zero does not have an opposite
True
What is a another word for Reciprocal
Multiplicative Inverse
What is a Reciprocal?
What a number is multiplied by to get 1
What is the reciprocal of 3
1/3
What is always true of the product of a number and its reciprocal?
The product of a number and its reciprocal is 1
Does zero have a reciprocal?
No
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
A
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
B
