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Fifth Grade
Categorical Data: Data with no established
arrangement or numerical order. Data that can
be put into categories.
Compose/Decompose: To put shapes together
(compose) or to take shapes apart (decompose).
Convex Polygon: A polygon in which all
vertices are “pushed outward.” If you connect
two non-consecutive vertices, the segment
would lie entirely inside the polygon.
Example: For M&Ms, each M&M is either red,
green, blue, yellow, orange or brown. Thus, we
can classify each M&M by putting it in one of
each of these categories.
The hexagon is composed of six
triangles.
The trapezoid
can be decomposed
into a triangle and a rectangle, making it easier
to find its area.
Convex
Not convex
Divisibility Rules: Rules that determine whether
a number is divisible by a certain number.
*All even numbers are evenly divisible by two.
*If the sum of the digits of a number is
divisible by 3, the number is divisible by 3.
*Numbers ending in 5 or 0 are divisible by 5.
Edges/Faces: A line segment where two faces of
a polyhedron meet is an edge. A flat surface on a
3-dimensional shape is a face.
edge
face
Equation (Modeling): A mathematical
sentence that shows that two quantities are equal
To solve an equation, find a value for the
variable that makes the sentence true.
x+3
=
7
x=4
Exponential Notation: A way to show repeated
multiplication by the same factor. A number
written with a base and an exponent.
2 × 2 × 2 × 2 = 2 4 = 16
Exponent
Base
Greatest Common Factor/Least Common
Multiple: The largest number that can be
divided evenly into each number in a set is
called the greatest common factor.
The smallest number that each number in a set
divides into evenly (the smallest multiple of
every number in a set) is called the least
common multiple.
Inverse Operation: An “operation” that
reverses another operation. It undoes the effect
of another operation such as addition,
subtraction, multiplication or division.
112
=
12
2
18
2
3
3
64
Use a Venn Diagram
to find the LCM and
GCF:
12 = 2 ⋅ 2 ⋅ 3
18 = 2 ⋅ 3 ⋅ 3
Their intersection:
2 ⋅ 3 = 6 is the GCF
Their union: 2 ⋅ 2 ⋅ 3 ⋅ 3 = 36 is the LCM
Addition and subtraction are inverse operations
(undo adding 3 by subtracting 3)
Multiplication and division are inverse operations
(undo multiplying by 2 by dividing by 2)
Linear Equations/Inequalities (Solve): An
x + 8 < 12 is a linear inequality
equation or inequality containing variables of
degree one or constants; (no squares, cubes, etc.)
such as x + 8 = 12. To solve an equation, find a
x<4
value for the variable that makes the sentence
true.
Mean: The average value of a set of data. The
In the data set 95, 85, 92, 84, the mean is 89.
sum of a set of numbers divided by the number
89
of numbers in the set. It is one of the measures
4 )(95 + 85 + 92 + 84)
of central tendency.
Millions/Millionths: The seventh place value
position is the millions. The sixth place value
position after the decimal point is the
millionths.
One million is written 1,000,000.
One millionth is written
0.000001
One million pennies
Mixed number: A number that is written using
both a whole number and a fraction.
25
9
9
9
is a mixed number. 25
is 25 +
10
10
10
Net: Two-dimensional representation for
constructing 3-dimensional shapes.
A net for a cylinder. The length of the side of
the rectangle is equal to the circumference of
the circle.
Order of Operations: Rules that tell in what
order to perform operations in arithmetic and
algebra: Parentheses, exponents, multiplication
and/or division from left to right, addition and/or
subtraction from left to right.
Orthogonal/Projective View:
Orthogonal views of an object are from the top,
front and sides.
Projective views are picture views.
PEMDAS:
Parentheses, Exponents, Multiply or Divide
from left to right, Add or Subtract from left to
right. (The mnemonic to remember this is
“Please excuse my dear Aunt Sally”).
Orthogonal views of a rectangular prism:
Top:
Projective view:
Side:
Front:
Outliers: A number which is far removed from
the other numbers in a data set. Technically,
they are values that lie more than one and a half
times the length of the box in a box-andwhiskers plot from either end of the box.
Upper quartile = 93,
lower quartile = 64.
The length of the box or interquartile range
(IQR) is 93 – 64 = 28
So, an outlier is any point that is more than
(1.5) (28) = 42 away from the upper or lower
quartiles.
This means any point greater than 93 + 42=135
or less than 64 − 42 = 22 .
Since there is a data point at 10, (a number less
than 22), it is an outlier.
Polygon (Regular/Irregular): A closed 2dimensional figure that is made up of line
segments joined end to end. A regular polygon
is one whose sides are all the same length and
whose angles are all equal.
Regular polygons
pentagon
octagon
Not regular polygons
Polyhedral (Regular/Platonic) Solids: A
geometric solid with polygons as faces. The
faces intersect at edges and the edges come
together at the vertices.
The five special solids having faces which are
all congruent regular polygons and the same
number of polygons at each vertex are called
Platonic solids.
The five Platonic Solids
Tetrahedron
4 faces
Dodecahedron
12 faces
Cube
6 faces
Octahedron
8 faces
Icosahedron
20 faces
Precision of Measurement: The level of detail
of a measurement, determined by the unit of
measure. Precision depends on the smallest unit
of measurement being used. The number of
significant digits in a measurement is an
indication of the precision with which the
measurement was taken.
Prism: A solid with two congruent, parallel
faces; its other faces are all parallelograms
formed by joining the vertices of the two bases.
1
" markings would have greater
16
1
precision than a ruler with only " markings.
4
A ruler with
Triangular
Prism
Rectangular Prism
Proper/Improper Fraction: A fraction whose
numerator is less than the denominator is
proper. A fraction whose numerator is greater
than or equal to its denominator is improper.
Significant Digits: Digits that express a
quantity to a specified degree of accuracy. Nonzero digits are always significant. Zeros at the
end of a decimal and zeros between two nonzero digits are significant. Zeros at the end of a
whole number and zeros immediately following
a decimal point in front non-zero digits are not
significant.
Substitution Property: A mathematical rule
that states that if two quantities are equal one of
the quantities can be substituted for the other in
any expression.
Surface Area: The sums of the areas of the
faces of a solid figure.
Terminating/Repeating Decimals: A decimal
number that contains a finite number of digits is
called terminating. A decimal number in which
one or more of its digits repeat infinitely is
called repeating.
7
proper
9
9
improper
7
7.957 has 4 significant digits.
0.07957 has 4 significant digits.
0.79570 has 5 significant digits.
7,957 has 4 significant digits.
79,570 has 4 significant digits.
79,057 has 5 significant digits.
70,905,007 has 8 significant digits.
If x = 51, what is the value of the expression:
x + 99 ?
x + 99 = 51 + 99 = 150
The surface area of 3 cm
this solid
(rectangular prism) 2 cm
is the sum of the
5 cm
areas of the six faces:
SA = 2(10) + 2(15) + 2(6) = 62 cubic cm
0.25 is a terminating decimal
Repeating decimals:
1
2
= 0.1111111... = 0. 1
= 0.2
9
9
3
4
5
= 0.3
= 0.4
= 0.5
9
9
9
Variable: A letter or other symbol that is used to
In the equation x + 15 = 60, x is the variable,
represent a number. Numbers are called
15 and 60 are constants.
constants since their values do not change.