TC1, TC2, TC3, TC4, TC5

Angle

Area

Associative Property

of Multiplication

Base

Benchmark

Cardinal Number

Chord

Circle

Circumference

Combination

Common Factor

Commutative Property

of Multiplication

Composite Number

Congruent

Decimal Division

Degree

Denominator

Distributive Property

Division Terms

Divisibility Rules

Division Steps

Equivalent

Equivalent Fraction

Equivalent Fraction

(Method of Finding)

Equilateral Triangles

TC2, TC3, TC4, TC5

Equally Likely

Factor

Factors, Prime

Fraction

Fraction (Simplest

Form)

Fraction, Improper

Face

Geometry

Gram

Greatest Common Factor

Hexagon

Hundredth

Inequality

Impossible

Interval

Intersecting Lines

Isosceles Triangle

Inverse Operation

Kilo

Line

Line Segment

Leaf

Likely

Like Fractions

Mean

Median

Minuend

TC1, TC3, TC4, TC5

Mixed Number

Mode

Multiple

Multiplication Properties

Net

Number, Nominal Number

Number, Mixed

Number, Mixed Decimal

Obtuse Angle

Octagon

Ordered Pair

Ordinal Numbers

Outcomes

Parallel Lines

Parallelogram

Pattern1, Pattern2, Pattern3

Pentagon

Period

Perimeter

Perpendicular

Place Value

Plane

Point

Polygon

Precise

Prime Number

Prism

Probability

TC1, TC2, TC4, TC5

Product

Pyramid

Quadrilateral

Quotient

Radius

Range

Ray

Rectangle

Reflection

Rhombus

Rotation

Rounding Rules

Scale

Similar Figures

Simplest Form

Stem-Leaf Plot

Strategies

Subtrahend

Symbols

Time

Transformation

Translation

Triangle

Unlike Fractions

Vertex

Venn Diagram

Volume

Zero Property of Multiplication

TC1, TC2, TC3, TC5

TC1, TC2, TC3, TC4

Conversion

Decimal Place Value

Formula

Subtrahend

Symbols

Time

Transformation

Translation

Triangle

Unlike Fractions

Vertex

Vinn Diagram

Volume

Zero Property of Multiplication

Angle – what is formed when two rays have the same endpoint. An angle can be named by the vertex and one point on each ray or just by the vertex. Example:

Area – the number of square units needed to cover a surface. (Note - area is measured in square units.)

Rectangular Area = L x W (length times width)

W

L

Note – the middle letter of the angle namemust be the name of the vertex end point.

Angle ABC, Angle CBA, Angle B ABC, CBA, BB

C

A

-- Acute Angle – an angle that measures less than 90 degrees. Example: ABC is acute

-- Obtuse Angle – an angle that measures more than 90 degrees. Example: ABC is obtuse

B

C

A

CB

A

-- Perpendicular Angle (Right Angle) – an angle that measures 90 degrees (90°). Example: ABC is a right angle/ perpendicular angle

Associative Property of Multiplication – see section M, under “Multiplication.”

A

B C

Benchmark – a point of reference.

Base – a face of a solid figure by which the figure is measured or is named. Example:

Base

Note – the base is a square, so the figureis a square pyramid

Cardinal Number – a number that “counts” or tells how many are in a group or set of something. Example: 9 players are on a baseball team. “9” is a cardinal number.

Composite Number – a number that has more than two factors. Example: 4 is a composite; factors – 1, 2, 4 12 is composite; factors – 1, 2, 3, 4, 6, 12

Common Factor – a number that is a factor of two or more numbers at the same time. Example: Factors of 24 – 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36 – 1, 2, 3, 4, 6, 9, 12, 18, 36 Common Factors of 24 & 36 – 1, 2, 3, 4, 6, 12

Combination – any of the subsets into which a set of units or elements may be arranged, paying no attention to order. Example: Set 1 – Bread: Wheat (Wh), White (Wt), Italian (It) Set 2 – Meat: Bologna (B), Ham (H), Salami (S)Note – You may have 1 bread and any 2 different meats

Meat Combination Sandwich CombinationsB , HB , SH , SH , BS , BS , H

21

3

B, HWh H, S S, B B, HWt H, S S, B B, HIt H, S S, B

Computation:Bread Elements times Meat Elements 3 x 3 Set 1 x Set 2 = 9 possible combinations of sandwiches

●r

rr

Circle – a closed figure with all points on the figure the same distance from the center point. Example:

-- Circumference – the perimeter of a circle. Example:

-- Radius – a line segment with one endpoint at the center of the circle and the other endpoint on the circumference of the circle. Example:

Note – all r’s are the same length.

●

●r●

-- Diameter – a line segment that passes through the center of the circle and has its endpoints on the circumference of the circle. Example:

-- Chord – a line segment with its endpoints on the circumference of the circle, but it does not pass through the center. Example:

●

●

●

●●

chord

●d

diameter

Commutative Property of Multiplication – see section M, under Multiplication.

Congruent (Figures) – figures that have the same shape and size

A

B

C

D

D

C

B

A

Divisibility Rules:Divisible by:2 - If the last digit is even, the number is divisible by 2.

3 - If the sum of the digits is divisible by 3, the number is also.

4 - If the last two digits form a number divisible by 4, the number is also.

5 - If the last digit is a 5 or a 0, the number is divisible by 5.

6 - If the number is divisible by both 3 and 2, the number is also divisible by 6.

7 - Take the last digit, double it, and subtract it from the rest of the number; ifthe answer is divisible by 7 (including 0), then the number is also.

8 - If the last three digits form a number divisible by 8, then so is the wholenumber.

9 - If the sum of the digits is divisible by 9, the number is also.

10 - If the number ends in 0, it is divisible by 10.

Division Terms:

Divisor Dividend

Quotient Definitions:

Divisor – the quantity by which another number (the Dividend) is divided.

Dividend – a quantity to be divided.

Quotient – the quantity resulting from the division of one quantity by another.

Division – the operation of determining how many times one quantity is contained in another quantity.

Division Steps: Decide where to place the first digit.

2 3 6 5 3 6 25 5 5 0 25 1 5 0

Operations: Divide Multiply Subtract Check Bring Down (if none) ----------------------------- Write Remainder

DMSCB ---R

If none

Decimal Division: Example:

1, 6 6 0 . 0 01 5 4 1 2 0 1 1 0 1 0 0 8 8 1 2 0 1 1 0 1 0

7 5 . 4 522

Denominator – the number that is below the bar in a fraction and tells the total number of equal parts. Example: ¼, the 4 is the denominator and it is showing there are four equal parts in the total.

Degree – a unit for measuring angles and for measuring temperature. Example:

A

B C

Angle ABC is 90 degrees or 90°.

Equivalent Fraction – fractions that name the same number or amount; fractions that name the same part of the whole or a set.

Example: 1/2 = 2/4 0 11/2

¼ ¼ ¼ ¼

¼

¼

¼

¼ 1/2 The diagrams show that ½ of the figure is equal to

2/4 ( 2 x ¼ ) of the figure.

-- Mathematical Solution - 1 2 2 2 2 4

Method for Finding Equivalent Fractions:-- Multiply the numerator and the denominator by any number, provided you use the same number in the numerator and the denominator. Example: Change ½ into fourths Change ½ into sixths

1 2 2 1 3 3 2 2 4 2 3 6

-- Divide the numerator and the denominator by the greatest common factor (GCF) of the numerator and denominator. Example: Change 2/4 into an equivalent fraction Factors of 2 are 1, 2; Factors of 4 are 1, 2, 4; GCF is 2

2 2 1 4 2 = 2●

●

Equivalent – means having the same value.

Equally Likely – see section P, under Probability.

Equilateral Triangles – see section T, under Triangles.

Factor – a number multiplied by another number to find a product. Example: 2 x 4 = 8; factors are 2, 4.

Fraction – a fraction is a number that names a part of a wholeor a part of a group. Example: using pizza

1

4

2

3

1 = each person’s part4 = total number of equal parts

Test for Simplest Form of a Fraction: find the Greatest Common Factor (GCF) of the numerator and the denominator.If the GCF is 1, then the fraction is in simplest form.

Factors, Prime (Prime Factors) – all the prime numbers thatwhen multiplied together give the desired product. Example: The product is 24; the prime factors of 24 are 2 X 2 X 2 X 3.

The Prime Factor Tree for product 24: 24 2 X 12 3 X 4 2 X 2

Note – Only prime numbers makeup the prime factors.

Fraction, Improper (Improper Fraction) – a fraction in which the Numerator is larger than the denominator. Example: 5/4; 5 > 4 or 5 (the numerator) is greater than 4 (the denominator).

Face – a flat surface of a solid figure. Example:

Note – a cube has six faces.Face

Face

Geometry – a branch of mathematics that deals with points,lines, angles, shapes, and solids.

Greatest Common Factor (GCF) – the largest factor that twoOr more numbers have in common (i.e., share). Example: For products 18 and 30, what is the GCF? Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 The Greatest Common Factor (GCF) is 6.

Gram – the unit for measuring mass in the Metric System.

Hexagon – a polygon with six sides and six internal angles. Example: 1

23

45

6

Hundredth – the decimal or fraction that names one part of one hundred equal parts. Example: 1 or 0.01 100

Intersecting Lines – lines that cross at one point. Example: ●●

●●●A

B

Y

zCrossing Point

Impossible – see section P, Probability.

Isosceles Triangle – see section T, Triangles.

Inverse Operation – opposite operations that undo each other. Example: Addition and subtraction are inverse operations. Multiplication and division are inverse operations.

D

Interval – the distance between the numbers on a scale of a graph. Example:

Note – The interval of the Y axis is 1. The interval of the X axis is 5.

12345

5 10 15 20 25

Y

X

Interval

Inequlaity – a mathematical sentence that shows two expressions do not represent the same quantity. Example: 3 + 2 > 4 - 1

Kilo – a prefix used in the Metric System that means “times 1,000.”Note - see the Measurement Conversion Aid

Line – a straight path in a plane. It has no end. It can be named by any two points on that line. Example:

Line Segment – a part of a line between two endpoints. Example:

●●A B Line AB or A B

Line BA or B A

A B●● Line Segment AB or A BLine Segment BA or B A

Leaf – see section S, under Stem and Leaf Plot.

Likely – see section P, Probability.

Like Fractions – are fractions that have the same denominator. Example: 1/ 8 and 5/8 are like fractions.

Multiplication Properties:1. Commutative Property of Multiplication - you can multiply numbers in any order. The product is always the same. Example: 8 X 5 = 40 or 5 X 8 = 40

2. Associative Property of Multiplication – you can group factors differently. The product is always the same. Example: (5 X 4) X 2 = (5 X ( 4 X 2)) 20 X 2 = 5 X 8 = 40

3. Property of One – when one of the factors is 1, the productequals the other number. Example: 8 X 1 = 8; 1 X 8 = 8

4. Zero property for Multiplication – when one factor is zero,the product is zero. Example: 6 X 0 = 0; 0 X 6 = 0

5. Distributive Property of Multiplication – multiplying a sumby a number is the same as multiplying each addend by the number and then adding the products. Example: 3 X (4 + 2) = (3 X 4) + (3 X 2) 3 X 6 = 12 + 6 = 18

Minuend – the number from which another number is to be subtracted. Example: 14 - 9 = 5; 14 is the minuend.

Median – the middle number in an ordered set of data or seriesof numbers. Example: Data Set – 5, 6, 8, 7, 4; Ordered data – 4, 5, 6, 7, 8 The median is 6

Mode – the number that occurs most often in an ordered set of data or series of numbers. Example: Data Set – 3, 5, 7, 6, 8, 7, 4; Ordered data – 3, 4, 5, 6, 7, 7, 8 The mode is 7.

Mean – the number that represents all the numbers in a set ofData, often called the “average.” Example: Date Set – 3, 6, 11, 8 Add the elements – 3 + 6 + 11 + 8 = 28; Divide the sum by the number of elements in the data set –

4 2 87 7 is the mean.

Multiple – a number that is the product of a given number andAnother whole number. Example: 3 X 2 = 6; 6 is a multiple of 3 X 2 3 X 3 = 9; 9 is a multiple of 3 X 3

Mixed Number – a number that is made of a whole number anda fraction. Example: 2 ½ is a mixed number; 2 is the whole number and ½ is the fraction.

Nominal Number – a number that names things. Example: 909 Courtney Lane; “909” is a nominal number.

Number, Mixed Decimal (Mixed Decimal Number) – a number that is made of a whole number and a decimal number. Example: 1. 2 – 1 is the whole number; .2 is the decimal number.

Numerator – the number above the bar in a fraction that tellsHow many parts are being considered. Example: 3/5; 3 is the numerator and tells that we are considering 3 parts out of the total of 5 equal parts.

Net – a two dimensional pattern for a three dimensional solid. Example:

Net forThe cube

Ordinal Number – a number that tells the position or order. Example: 1st , second, 15th , 3rd

Outcomes (Total Possible Outcomes Different Ways) Note – order or arrangement does matter.Definition – all the possible different ways objects or numberscan be put together in a specified manner. Example: If you flip two coins, how many possible outcomes can you have? Two Coins - C1, C2 H1, T1 H2, T2

There are 16 possible outcomes.

●●

H2H1 T2

H2T1 T2

T2T1 H2

T2H1 H2

H1H2 T1

H1T2 T1

T1T2 H1

T1H2 H1

Octagon – a polygon with eight sides and eight internal angles. Example: 8

7

65

4

3

21

Obtuse Angle – an angle that measures more than 90 degrees;see section A, Angle.

Ordered Pair – a pair of numbers used to locate a point on aGrid. Example: (5, 3) is an ordered pair of numbers. Note – with an ordered pair of numbers, the first number is on the X axis and the second number is on the Y axis.

Y

12345

1 2 3 4 5X

● (5, 3)

Product – the answer to a multiplication problem; the number(answer) gotten when two factors are multiplied. Example: 2 X 4 = 8; the factors are 2 & 4; the product is 8.

Perimeter – the measure of the distance around the outside ofa closed figure. Example: for a rectangle

W

W

LL

Perimeter = W + L + W + LUsing the Mathematical Properties:W + L + W + L = PW + W + L + L = P (Associative Property of Addition) 2 W + 2L = P 2 X ( W + L) = P (Distributive Property of Multiplication)

Prime Number – a number that has only two factors, 1 and thenumber itself. Example: 2, 3, 5, 7, 11, 13, 17, 19 are prime numbers. For the number 3, the only way to get the number as a product is using the factors 1 and 3 (1 X 3 = 3).

Pattern – a set of characteristics that are displayed repeatedly. Example: Continue the sequence 35, 40, 45, 50, ___, ___, … First, find the difference for 3 sequential pairs of numbers – 40 – 35 = 5, 45 – 40 = 5, 50 – 45 = 5. the difference is 5; therefore, you can continue the sequence by “adding” 5 to the last number in the sequence – 50, 55 (50 + 5), 60 (55 +5).

Precise – finding a unit that measures nearest to the actuallength of an object.

Point – identifies a location on an object or in space. It isnamed by a letter. Example: Point B● B

Plane – a flat surface with no end. Planes are named by any three points in the plane. Example: Plane ABC

A B

D C

Probability – the chance that an event will happen.

-- Event – something that happens in a probability experiment that results in an outcome.

-- Certain – an event will always happen (the probability is equal to 1).

-- Impossible – an event will never happen (the probability is equal to 0).

-- More Likely – an event that has more chances to happen than another event (its probability is greater than the probability of another event).

Probability (continued).

-- Less Likely – an event that has fewer chances to happen than another event (its probability is less than the probability of another event).

-- Equally Likely - an event that has the same number of chances to happen as another event (its probability is equal to the probability of another event).

The number of Probability = ways an event occurs = Possible Outcomes The number of ways Total Possible Outcomes all events can occur

Perpendicular – lines that intersect and form four right angles atthe point of intersection. Example:

Parallel Lines – lines that never intersect and are the samedistance apart at opposite points along the lines. Example:

1 2

34●

●

ZY●●

A

B

Y

● ●

● ●

A B

Z

Polygon – a closed plane figure with straight sides that is named by the number of its sides and angles. Example:

65

4

32

1

Pentagon – a polygon with five sides and five internal angles. Example:

5

4

3

21

Period – a three digit grouping on a Place Value chart or in a Number. Example: 6, 000, 000

Period

Prism – a solid figure whose ends are congruent, parallel polygons and whose sides are rectangles. Example:

EndEnd

Side

Pyramid – a solid figure with a base that is a polygon and three or more other faces that are triangles with a commonvertex. Example:

Vertex

TriangleFace

Base

Note – the base is a square, so the figureis a square pyramid

Quotient – the answer in a division problem. Example:

2 3 61 8

21 61 6

0

Quotient

Quadrilateral – a polygon that has four sides and four internalangles.

-- General Quadrilateral – has four sides of any length and four internal angles of any size. Example:

-- Trapezoid – has one pair of parallel sides. Example:

2

3

4

1

1

2

3

4

Note – sides 2 & 4 are parallel.

Quadrilateral (Continued)

-- Parallelogram – has two pairs of congruent sides, two pairs of congruent angles, and two pairs of parallel sides. Example:

-- Rhombus – has four congruent sides and two pairs of congruent angles. Example:

1

2

3

4

Note – sides 2 & 4 are parallel and sides 1 & 3 are parallel

1 2

34

Note – sides 1, 2, 3, & 4 are congruent and opposite angles are congruent

Quadrilateral (Continued)

-- Square – has four congruent sides and four right (90°) angles. Example:

-- Rectangle – has two pairs of congruent sides, four right (90°) angles, and two pairs of parallel sides. Example:

1

2

3

4

Note – sides 1, 2, 3, & 4 are congruent and all angles are right (90°) angles.

1

2

3

4

Note – sides 2 & 4 are parallel, sides 1 & 3 are parallel, and all angles are right (90°) angles.

Rounding Rules –

1. Decide which digit is to be rounded (use place value position names).

2. If the digit to its right is less than 5, the digit being roundedstays the same and all digits to the right change to 0’s.

3. If the digit to its right is 5 or more, the digit being rounded is increased by 1 and all the digits to the right change to 0’s.

Example: 423 rounded to the nearest “ten” is 420. 289 rounded to the nearest “ten” is 290.

Ray – a part of a line that has one end point and goes on forever in one direction. A ray is named by its endpoint and one other point on the ray. Example: ● ●

A B Ray A B or A B

Range – the difference between the greatest and the least numbers in an ordered set of data. Example: Data Set – 5, 9, 15, 26, 4, 1;

Ordered data – 1, 4, 5, 9, 15, 26The range is 25 ( 26 – 1 = 25).

Radius – see section C, under Circle.

Reflection – when a figure is flipped across a line (or an axis). Example:

Note – points that are near the line or axison one side are near the line or axis on the other side. Points that are far on one side are far on the other side.

A A’

B B’

Rotation – when a figure is turned around a point or a vertex. Example:

●

A

A’

B’B

Symbols – signs that have meaning.

= is the symbol for “equals.” (Example: 4 = 4 x 1 )> is the symbol for “greater than.” (Example: 5 > 4)< is the symbol for “less than.” (Example: 4 < 5)≠ is the symbol for “does not equal.” (Example: 4 ≠ 5)≈ is the symbol for “approximately equals.”

(Example: 99 ≈ 100)

Subtrahend – a number that is to be subtracted from anothernumber (minuend). Example: 14 – 9 9 is the subtrahend

5

Strategy – a plan or way for solving a problem Examples: 1. Act out the problem. 2. Make a picture or diagram. 3. Make a table. 4. Make an organized list. 5. Guess and check. 6. Look for a pattern. 7. Work backwards. 8. Use logical reasoning 9. Solve a simpler problem.

Similar (Figures) – figures that have the same shape, but may not have the same size. Example:

A A’

Note – Figure A is similar to figure A’.

Simplest Form – a fraction that has “1” as the Greatest Common Factor (GCF) of the numer-ator and the denominator is in simplest form. Example: 3 1 1 9 3 3

= is in simplest form because the GCF of “1” and “3” is “1.”

Scale – a series of numbers placed at fixed distances on a graph. Example:

12345

5 10 15 20 25

Y

X

Scale

Stem – Leaf Plot – a table tha shows data organized by placevalue. Example: Data Set (Student grades) – 71, 84, 95, 73, 76, 87, 95, 96, 97. Stem Leaf

789

1, 3, 64, 75, 5, 6, 7

Time Measurement: 1 Year = 365 days or 52 weeks or 12 months. 1 Week = 7 days. 1 Day = 24 hours. 1 Hour = 60 minutes. 1 Minute = 60 seconds.

Time (meaning of the digits): 7 : 5 5 A. M. - School starts

Hours Minutes

Time (Subtracting): 2 m 4 sec 1 m 64 sec-1m 25 sec - 1 m 25 sec 39 sec

514

Triangle – a polygon with three sides and three internal angles. -- Scalene Triangle – a triangle with three sides of different length and three angles of different measure. Example:

-- Isosceles Triangle – a triangle with two congruent sides and two congruent angles. Example:

1 2

3

Note – sides 1, 2, & 3 are all differentin length.

1 2

3

Note – sides 1 & 2 are the samein length.

Triangle – a polygon with three sides and three internal angles. -- Equilateral Triangle – a triangle with three congruent sides and three congruent angles. Example:

-- Right Triangle – a triangle with one right (90°) angle. Example:

1 2

3

Note – sides 1, 2, & 3 are all congruent.

Right Angle

Triangle – a polygon with three sides and three internal angles. -- Acute Triangle – a triangle with three acute angles. Example:

-- Obtuse Triangle – a triangle with one obtuse angle. Example:

1 2

3

Note – all angles are acute angles

Obtuse Angle

Translation – when a figure slides in any direction (vertically, horizontally, diagonally). Example:

Start Stop

Transformation – the movement of a figure; either a Translation, Rotation, or Reflection.

Unlike Fractions – fractions that have different denominators. Example: 3 2 4 3

and are unlike because their denominators are different (4 & 3).

Vertex – the point where two rays of an angle, two sides of a Polygon, or three or more edges of a solid figure meet. Example: Vertex

Venn Diagram – a diagram that uses geometric shapes (usuallycircles) to show relationships. Example:

4810

16

39

1521

618

2412

Divisible by 2 Divisible by 3

Divisible by 2 & 3

Volume – the measure of the space a solid figure occupies. Example:

W

HD

Computing volume - W x H x D;volume is expressed in cubic units.

Zero Property of Multiplication – see section M, under Multiplication.

Numbers – there are three ways to write a number. -- Standard Form – a number that is written using thenumeral symbols. Example: 1, 456, 729

-- Written Form – a number that is written using the wordsthat show how many (quantity) and place value. Example: One million, four hundred fifty-six thousand, seven hundred twenty-nine.

-- Expanded Form – a number that is written by separatingit into parts by place value and by using multiplication to show the value of the digit. Example: 1 x 1, 000,000 + 4 x 100,000 + 5 x 10,000 + 6 x 1, 000 + 7 x 100 + 2 x 10 + 9 x 1.

Place Value – the system used to give meaning to numbers written in a series. Example: 9 0 1, 2 3 4, 5 6 7, 8 9 0 Billions Millions Thousands Units 9 0 1, 2 3 4, 5 6 7, 8 9 0 Hundreds Tens Ones

9 x 100, 000, 000, 000 + 0 x 10, 000, 000, 000 + 1 x 1, 000, 000, 000 + 2 x 100, 000, 000 + 3 x 10, 000, 000 + 4 x 1, 000, 000 + 5 x 100, 000 + 6 x 10, 000 + 7 x 1, 000 + 8 x 100 + 9 x 10 + 0 x 1

PatternsWhen finding the missing number in a list of numbers, you need to figure out what pattern exists in the list. First, figure out whether the numbers are increasing or decreasing. Then, figure out how much more or how much less each number is than the previous number.

Example: 10, 11, 12, ? , 1413 is the missing number.

Example: 40, 39, 38, ? , 3637 is the missing number.

Example: 4, 8, 12, 16, ? 20 is the missing number.

PatternsWhen finding the missing picture in a list of pictures, you need to figure out what pattern exists in the list. First, look at the increasing or decreasing in the number of objects in each picture in the list. Then, figure out how much bigger or how much smaller each picture is than the previous picture.

Example: Complete the geometric patterns.

Answer:

Answer:

ConversionTo change from one unit of measure to another unit of measure E.x., 12 inches = 1 foot 12 inches / 12 inches per foot = 1 foot

Formula A set of symbols that expresses a mathematical rule.

E.x., Area = Length times Width (A = L x W)

Decimal Place Value – the system used to give meaning to decimal numbers written in a series. Example: 0 . 2 3 4

0 . 2 3 4 Tenths Hundredths Thousandths

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