Grade 6 - Math
Terms
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- additive inverse
- A number that when added to a given number results in a sum of zero.
- opposites
- Numbers that are the same distance from zero in opposite directions on the number line.
- integers
-
The set of whole numbers and their additive inverses.
{...-3,-2,-1,0,1,2,3...} - rounding
-
To approximate the value of a number to a given decimal place.
Examples:
2.56 rounded to the nearest tenth is 2.6;
2.54 rounded to the nearest tenth is 2.5;
365 rounded to the nearest hundred is 400 - place value
- The value given to a place a digit may occupy in a numeral.
- benchmark
- A point of reference from which measurements can be made.
- ratio
-
A comparison of two numbers.
Example:
the ratio of consonants to vowels in the alphabet is 21:5 - proportion
- A statement that two ratios are equal.
- fraction
- A number representing some part of a whole. A quotient in the form a/b.
- decimals
- Decimals, like whole numbers, are based on the number ten. The digits and the position of each digit determine the value of a decimal. The decimal point separates the whole number part of the decimal from the part that is less than one.
- percents
-
A number expressed in relation to 100, represented by the symbol %.
Example:
76 out of 100 students use computers
76 percent of students use computers - least common multiple
-
The smallest nonzero whole number that is a multiple of two or more whole numbers.
Example:
the least common multiple of 3,9, and 12 is 36 - multiple
-
The product of a given number and an integer.
Examples:
8 is a multiple of 4
3.6 is a multiple of 1.2 - factor
-
A number or expression that is multiplied by another to yield a product.
Example:
3 and 11 are factors of 33 - numerator
- The top number in a fraction, In the fraction a/b, a is the numerator.
- denominator
- The bottom number in a fraction.
- number line
- A line showing numbers at regular intervals in which any real number can be indicated.
- cross product
-
A method used to solve proportions and test whether ratios are equal:
a/b=c/d if ad=bc -
circle graph
(pie chart) - A way of displaying statistical data by dividing a circle into proportionally-sized "slices".
- common denominator
-
A whole number that is the denominator for all members of a group of fractions.
Example:
the fractions 5/8 and 7/8 have a common denominator of 8 - least common denominator
-
The least common multiple of the denominators of two or more whole numbers.
Example:
12 is the least common denominator of 1/3, 2/4, and 3/6 - improper fraction
-
A fraction in which the numerator is greater than the denominator.
Example:
21/4, 4/3,2/1 - mixed number
-
A number composed of a whole number and a fraction.
Example:
5 1/4 - simplify fraction
- Taking a fraction to the simplest form; when the GCF of the numerator and denominator is 1.
- products
- The result obtained by multiplying two numbers or variables.
-
greatest common factor
(GCF) -
The greatest number that is a factor of two or more multiples.
Example:
30, 60, 75
the greatest common factor is 15 - sum
-
The result of adding two numbers or quantities.
Example:
6+4=10
10 is the sum of the two addends, 6 and 4 - difference
- The result obtained when one number is subtracted from another.
- product
- The result obtained by multiplying two numbers or variables.
- quotient
- The result obtained from dividing one number or variable (the divisor) into another number or variable (the dividend).
- inverse operations
- Operations that undo each other.
- multiplicative inverse
- The number for any given number that will yield 1 when the two are multiplied; same as reciprocal.
- exponent
- A numeral that indicates how many times a number or expression is to be multiplied by itself.
- base
-
(1)The side or face on which a three-dimensional shape stands.
(2)The number of characters a number system contains. - power
- Represented by the exponent n, to which a number is raised by multiplying itself n times.
- perfect square
- A number that is the square of an integer.
- square root
-
A number that when multiplied by itself produces a given number.
For example, 3 is the square root of 9. - square
- A rectangle with congruent sides.
- cube
- (v.)To multiply a number by itself again.
- cube root
- The number that must be multiplied by itself and then by itself again to produce a given number.
- rule
- A statement that describes a relationship between numbers or objects.
- prime number
- A whole number greater than 1 whose only factors are 1 and itself.
- composite number
- A number exactly divisible by at least one whole number other than itself and 1.
- order of operations
-
To find the answer to an equation, follow this 4 step process:
1)do all operations with parentheses first;
2)simplify all numbers with exponents;
3)multiply and divide in order from left to right;
4) add and subtract in order from left to right. - pattern
- A regular, repeating design or sequence of shapes or numbers.
- degree
-
[1](algebraic) the exponent of a single variable in a simple algebraic term;
[2](algebraic) the sum of the exponents of all the variables in a more complex algebraic term;
[3](algebraic) the highest degree of any term in an equation;
[4](geometric) a unit of measurement of an angle or arc, represented by symbol - vertex
- The common point of two rays of an angle, two sudes if a polygon, or three or more faces of a polyhedron.
- acute angle
- Any angle that measures less than 90°.
- obtuse angle
- Any angle that measures more than 90° but less than 180°.
- right angle
- An angle that measures 90°.
- complementary angles
- Two angles whose sum is 90°.
- supplementary angles
- Two angles whose sum is 180°.
- metric system
- A decimal system of weights and measurements based on the meter as its units of length, the kilogram as its unit of mass and the liter as its unit of capacity.
- meter
- Basic unit of length in the metric system; width of a doorway; 1m approximate to 1.1 yard.
- liter
- A basic metric unit of capacity.
- gram
- A metric unit used to measure mass.
- customary system
- Units of measurement used in the United States to measure length in inches, feet, yards, and miles; capacity in cups, pints, quarts and gallons; weight in ounces, pounds, and tons; and temperature in degrees Fahrenheit.
- height
- The distance from the base to the top of the figure.
- altitude
- The perpendicular distance from the base of a shape to the vertex; altitude indicates the height of a shape.
- pi
- The ratio of a circle's circumference to its diameter. It approximately equal to 3.14.
- radius
- A line segment from the center of a circle to any point on its circumference.
- diameter
- A line segment that passes through the center of a circle and divides it in half.
- circle
- A perfectly round shape with all points equidistant form a fixed point, or center.
- polygon
- A simple, closed plane figure, having three or more line segments as sides.
- triangle
- A polygon that has three sides.
- quadrilateral
- A polygon that has four sides.
- pentagon
- A polygon that has five sides.
- hexagon
- A polygon that has six sides.
- heptagon
- A polygon that has seven sides.
- octagon
- A polygon that has eight sides.
- nonagon
- A polygon that has nine sides.
- decagon
- A plane polygon with ten angles and ten sides.
- parallel
- Straight lines or planes that remain a constant distance from each other and never intersect.
- perpendicular
- Two lines or planes that intersect to form a right angle.
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reflection
(flip) - To "turn over" a shape.
-
translation
(slide) - A transformation in which a geometric figure is slid to another position without rotation or reflection.
-
rotation
(turn) - A transformation in which a figure is turned a certain number of degrees around a fixed point or line.
- x-axis
- The horizontal reference line in the coordinate graph.
- y-axis
- The vertical reference line in the coordinate graph.
- quandrant
-
[1]One quarter of the circumference of a circle;
[2]On a coordinate graph, one of the four regions created by the intersection of the x-axis and the y-axis. - area
- The size of a surface, usually expressed in square units.
- perimeter
- The distance around the outside of a closed figure.
- outcome
- A possible result in a probablilty experiment.
- probability
- The study of likelihood or chance that describes the chances of an event occurring.
- tree diagrams
- A connected, branching graph used to diagram probablilties or factors.
- theoretical probability
- The ratio of the number of favorable outcomes to the total number of possible outcomes.
- random sampling
- A population sample chosen so that each member has the same probability of being selected.
- like terms
- Terms that include the same variables raised to the same powers; like terms can be combined.
- parentheses
- The enclosing symbols (), which indicate that the terms within are a unit.
- variable
- A letter or other symbol that represents a number or set of numbers in an expression or an equation.
- equivalent expressions
- Expressions that always result in the same number, or have the same mathematical meaning for all replacement values of their variables.
- equivalent ratios
- Ratios that are equal.
- protractor
- Used to measure angles.
- distributive property
- This property states that multiplying a sum b a number is the same as multiplying each addend by that number and then adding the two products.
- negation
- Something considered the opposite of something positive.
- equal
- Of the same measure, quantity,amount, or number as another; identical in value.
- factor tree
- Used to find the prime factorization of a number.
- divisibility rules
-
A whole number is divisible by:
2 if the ones digit is divisible by 2
3 if the sum of the digits is divisible is divisible by 3
5 if the ones digit is 0 or 5
10 if the ones digit is 0 - standard form
- Numbers written without exponents.
- centimeter
-
2.5cm approximate to 1 inch;
half the width of a penny - kilometer
- 6.2km approximate to 1 mile; 6 city blocks
- inch
- width of a quarter
- foot
- equal to 12 inches; length of a large adult foot
- yard
- equal to 3 feet; length from nose to fingertip
- mile
- equal to 1,760 yards; 10 city blocks
- fluid ounce
- 2 tablespoons of water
- cup
-
8 fluid ounces;
coffee cup - pint
-
2 cups
small ice cream container - quart
-
2 pints;
large measuring sup - gallon
-
4 quarts;
large plastic jug of milk - transversal
- The line that intersects a pair of parallel lines.
- favorable outcomes
- The specific outcome the player is looking for is an event or favorable outcome.
- sample space
- Set of all possible outcomes.
- biased sample
- Group whose inclination is marked with strong prejudice.
- term
- When a plus sign or minus sign separates an algebraic expression into parts, each part is called a term.
- multiplicative identity
-
The product of any number and 1 is the number.
Example:
7x1=7
1xn=n - additive identity
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The sum of any number and 0 is the number.
Examples:
5+0=5
a+0=a - kilogram
-
1 kg is approximate to 2 lb;
six medium apples - square units
- Number of squares that would cover a surface.
- pre-image
- An figure before it is transformed.
- image
- A figure in a coordinate plane that is produced from a transformation.
- 1st Quadrant
-
positive, positive
(+,+) - 2nd Quadrant
-
negative, positive
(-,+) - 3rd Quadrant
-
negative, negative
(-,-) - 4th Quadrant
-
positive, negative
(+,-) - like denominators
- Fractions having the denominator as the same number.
- unlike denominators
- Fractions that have different denominators.
- Fundamental Counting Principle
- Rule to determine possible outcomes when you multiply the number of possibilities in each group together.