Cluster 1

Coordinate System: A system using coordinates to determine position.

Coordinate Plane: A 2-dimensional plane with two perpendicular axes, x and y, that intersect at the origin.

Coordinate Grid: A grid used for locating points on a coordinate plane.

Coordinate: A number in an ordered pair. The first number is the horizontal "x-axis." The second number is the vertical "y-axis."

Axis: The horizontal and vertical lines that divide the coordinate plane into quadrants. 5th grade works in Quadrant 1.

x-axis: The horizontal axis on a coordinate grid.

x-coordinate: Location or position of a point on a coordinate grid that is on the x-axis.

y-axis: The vertical axis on a coordinate grid.

y-coordinate: Location or position of a point on a coordinate grid that is on the y-axis.

Ordered Pair: A pair of numbers used to locate a point on a coordinate grid. Example: Ordered pair (1,3) indicates the x-axis is 1 and the y-axis is 3.

Origin: The (0,0) point on a coordinate grid where the x-axis and y-axis cross or intersect.

Line Graph: A graph of data using points connected to form a line.

Numerical Data: Data that is measurable: height, weight, amount, time, how many pages you can read, etc. It can be averaged or ordered least to greatest or greatest to least.

Categorical Data: Sorting data into categories based on their attributes (characteristics). Examples: favorite color, favorite food, favorite juice, favorite place to visit, ages, etc.

Data that Changes Over Time: Data that changes in a given amount of time such as height of a tree over 5 years, total rainfall over 10 years, how many books you read over the summer, etc.

Cluster 2

Multiplication and Division

Multiples: Numbers stated when we skip count by a number.

Ex: Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

Factors: Numbers you multiply together to get a product.

Factor X Factor = Product

Ex: 5 x 5 = 25 5 is a factor of 25

Multiplication: An operation where a number is added to itself a specific number of times.

Product: Answer to a multiplication problem.

Ex: 5 x 5 = 25 25 is the product of 5 x 5

Division: Splitting into equal parts or groups.

Ex: 25 ÷ 5 = 5 There are 5 groups of 5 in 25.

Divisor: Number used to divide the dividend.

Dividend: Number to be divided.

Quotient: Answer to a division problem.

Remainder: The amount left over that is less than the divisor.

Ex: 25 ÷ 2 = 12 remainder 1

25 is the dividend. 2 is the divisor.

Array: A strategy used to arrange numbers in a row or column.

Decompose: Breaking down numbers by place value

Distributive Property: Multiply a sum by multiplying each addend separately and then add the products

Ex: 25 x 35 (20 + 5) x (30 + 5) Multiply the tens place value in the first number by the tens in the second number (20 x 30); multiply tens in first number by ones in second number (20 x 5); multiply ones in first number by tens in second number (5 x 30); multiply ones place values together in each number (5 x 5).

Composite Numbers: Numbers that have more than 2 factors.

Prime Numbers: Numbers that have only 2 factors: 1 and itself.

Square Numbers: A number multiplied by itself that results in a product that is a square number. The product can be represented in the shape of a square.

Order of Operations: Rules for doing calculations in expressions that have more than one operation. Complete the operations in parentheses first, then multiply and divide in order from left to right, and then add and subtract in order from left to right.

Expression: Number sentence that includes two or more numbers and one or more operation (addition, subtraction, multiplication, division).

Equation: Number sentence that includes two or more numbers and one or more operation (addition, subtraction, multiplication, division) with an equal sign and solved.

Volume:

3-Dimensional: Having three (3) dimensions of length, width and height. A cube is 3 dimensional.

Solid: A 3-dimensional object with length, width and height.

Rectangular Prism: A solid 3-dimensional object with six rectangular faces.

Dimensions: The measure of length, width, depth or height of an object or container.

• Length x Width x Height = _____ units cubed or Units³
• Units represents the unit of measure such as inches, feet, yards, centimeters, meters, etc.

Cluster 3

Fractions: A number that names part of a whole.

Equivalents: Equal in value; numbers that are written differently but have the same value.

Common Denominator: The denominators of fractions are the same digit.

Mixed Numbers: A whole number and a fraction.

Numerator: The number above the fraction bar in a fraction; parts out of the whole that are identified.

Denominator: The number below the fraction bar in a fraction; names parts in the whole.

Multiplication: An operation where a number is added to itself a specific number of times.

Product: Answer to a multiplication problem.

Ex: 5 x 5 = 25 25 is the product of 5 x 5

Division: Splitting into equal parts or groups.

Ex: 25 ÷ 5 = 5 There are 5 groups of 5 in 25.

Divisor: Number used to divide the dividend.

Dividend: Number to be divided.

Quotient: Answer to a division problem.

Remainder: The amount left over that is less than the divisor.

Ex: 25 ÷ 2 = 12 remainder 1

25 is the dividend. 2 is the divisor.

Cluster 4

Decimal: Fractional part of a whole number represented by using a decimal point; number is less than one whole.

Equivalent: Equal in value; numbers that are written differently but have the same value.

Tenths: First digit to the right of the decimal point.

Hundredths: Second digit to the right of the decimal point (to the right of the tenths place value).

Thousandths: Third digit to the right of the decimal point (to the right of the hundredths place value).

Ten Thousandths: Fourth digit to the right of the decimal point (to the right of the thousandths place value).

Place Value: The value of a digit in a number.

Representations: Diagrams, number lines, area models

Cluster 5

Decimals

Decimal: Fractional part of a whole number represented by using a decimal point; number is less than one whole.

Equivalent: Equal in value; numbers that are written differently but have the same value.

Tenths: First digit to the right of the decimal point.

Hundredths: Second digit to the right of the decimal point (to the right of the tenths place value).

Thousandths: Third digit to the right of the decimal point (to the right of the hundredths place value).

Ten Thousandths: Fourth digit to the right of the decimal point (to the right of the thousandths place value).

Place Value: The value of a digit in a number.

Representations: Diagrams, number lines, area models

Fractions

Fractions: A number that names part of a whole.

Equivalents: Equal in value; numbers that are written differently but have the same value.

Common Denominator: The denominators of fractions are the same digit.

Mixed Numbers: A whole number and a fraction.

Numerator: The number above the fraction bar in a fraction; parts out of the whole that are identified.

Denominator: The number below the fraction bar in a fraction; names parts in the whole.

Sum: Answer to an addition problem.

Difference: Answer to a subtraction problem.

Cluster 6

Multiplication: An operation where a number is added to itself a specific number of times.

Product: Answer to a multiplication problem.

Ex: 5 x 5 = 25 25 is the product of 5 x 5

Factors: Numbers multiplied together to get a product. 5 is a factor of 25; 3 is a factor of 12.

Division: Splitting into equal parts or groups.

Ex: 25 ÷ 5 = 5 There are 5 groups of 5 in 25.

Divisor: Number used to divide the dividend.

Dividend: Number to be divided.

Quotient: Answer to a division problem.

Remainder: The amount left over that is less than the divisor.

Ex: 25 ÷ 2 = 12 remainder 1

25 is the dividend. 2 is the divisor.

Algorithm: A procedure or set of steps to solve a mathematical problem.

Fractions: A number that names part of a whole.

Numerator: The number above the fraction bar in a fraction; parts out of the whole that are identified.

Denominator: The number below the fraction bar in a fraction; names parts in the whole.

Equivalents: Equal in value; numbers that are written differently but have the same value.

Improper Fractions: A fraction where the numerator is greater than or equal to the denominator.

Mixed Numbers: A whole number and a fraction.

Cluster 7

Attributes: Characteristics; descriptions

Property: Attributes (characteristics) of a polygon

Polygon: A closed plane figure with line segments as sides.

Parallel: Lines are an equal distance apart and never intersect.

Triangle: A plane figure with three line segments and three angles.

• Acute triangle: Each angle measures less than 90 degrees.
• Equilateral triangle: All sides are equal length and all angles are equal.
• Obtuse triangle: One angle is greater than 90 degrees.
• Right triangle: One angle is 90 degrees.
• Isosceles triangle: Two sides are the same length and two angles are equal measurements.
• Scalene triangle: All sides have different lengths.

Quadrilateral: A polygon with four sides.

• Trapezoid: A quadrilateral with exactly one pair of parallel sides.
• Parallelogram: A quadrilateral with opposite sides parallel and congruent.
• Rectangle: A parallelogram with four right angles.
• Rhombus: A parallelogram with all sides congruent and opposite angles are congruent.
• Square: A square is a parallelogram, rectangle, and rhombus with all sides congruent and foru right angles.

Note:

• All rectangles are parallelograms
• Some rectangles are squares.
• Some parallelograms are rectangles.
• All squares are rectangles.
• Some rhombuses are squares.

Hierarchy of Polygons