Curriculum - Upper Elementary Mathematics

Numeration

1.00 Counts sequentially to any value, given any pattern or sequence
2.00 Knows place value concepts through billions2.10 Writes number in expanded notation
2.20 Writes number through billions using commas correctly
2.30 Writes number in words
2.40 Identifies place value in various numbers
2.50 Understands >, <, =, =3.00 Classification3.10 Identifies ordinal numbers (first – “n”thieth)
3.20 Identifies Roman numerals to 10004.00 Order and sequencing4.10 Understands positive and negative numbers and relationship to number line
4.20 Sequences from least to greatest, numbers to one billion
4.30 Sequences decimals from least to greatest
4.40 Sequences fractions from least to greatest
4.50 Finds missing numbers using multiples or with knowledge of number relationships
4.60 Recognizes and identifies patterns and sequences within groups of numbers 4.60.1 Can fill in an unidentified number when given a sequence5.00 Understands and applies operations (+, - ) on a numberline
6.00 Rounds numbers to any identified place value

Addition

1.00 Memorizes addition facts through 18
2.00 Adds numbers in columns2.10 With and without regrouping (static and dynamic)
2.20 Understands concept of regrouping in addition
2.30 Maintains correct place value for money and decimals3.00 Adds numbers in order presented horizontally3.10 Converts to a vertical orientation, maintaining place value4.00 Adds fractions4.10 Equivalent
4.20 Proper and Improper
4.30 Converted to decimals
4.40 Converted to percentages 5.00 Adds positive and negative numbers

Subtraction

1.00 Memorizes subtraction facts through 18
2.00 Subtracts numbers in columns2.10 With and without regrouping (static and dynamic)
2.20 Understands concept of regrouping in subtraction
2.30 Maintains correct place value for money and decimals3.00 Subtracts fractions3.10 Equivalent
3.20 Proper and Improper
3.30 Converted to decimals
3.40 Converted to percentages 4.00 Subtracts positive and negative numbers

Multiplication

1.00 Memorizes multiplication facts through 12
2.00 Multiplies with one-“n” multipliers
3.00 Moves decimal point appropriately to maintain correct place value
4.00 Multiplies fractions4.10 Equivalent
4.20 Proper and Improper
4.30 Converted to decimals or percentages5.00 Multiples positive and negative numbers
6.00 Factors numbers6.10 Understands prime numbers
6.20 Understands prime factorization
6.30 Understands composite numbers

Division

1.00 Memorizes division facts through 12
2.00 Performs long division without materials
3.00 Identifies remainders as integer and in decimal notation
4.00 Divides fractions4.10 Equivalent
4.20 Proper and Improper
4.30 Converted to decimal

Elements Across Operations

1.00 Understands properties of zero for +, -, x, and
2.00 Understands properties of one for +, -, x, and
4.00 Conserves numbers
5.00 Averages numbers
6.00 Solves > and < equations with numbers to one billion
7.00 Solves > and < equations with fractions and percentages
8.00 Understands and illustrates concepts of commutative, associative, and distributive properties
9.00 Follows orders of operations with parentheses

Measurements

1.00 Understands and applies English and metric measurements
2.00 Finds the perimeter of rectangles and other figures
3.00 Finds the area of rectangles and other figures
4.00 Finds the volume of a rectangle with a formula
5.00 Measures in capacity: teaspoon, tablespoon, cup, pint, quart, gallon
6.00 Solves simple conversion problems with weight, capacity, and length
7.00 Estimates7.10 Length, width, height, and weight
7.20 Quantity and amounts

Word Problems

1.00 Solves multi-step word problems
2.00 Solves word problems with all four operations, fractions, time, and money
3.00 Makes up word problems with all four operations

Squaring

1.00 Squares a number
2.00 Cubes a number
3.00 Finds the square root of a simple number with and without materials

Fractions and Decimals

1.00 Reads, writes, and compares fractions and decimals
2.00 Coverts between fractions, decimals, and percentages for all operations

Ratios

1.00 Defines and identifies ratios
2.00 Introduction to analogies through ratio

Exponents

1.00 Defines exponents
2.00 Begins operations with “n” and the powers of 10

Charts and Graphs

1.00 Reads and understands a chart, bar or circle graph
2.00 Creates charts and graphs from nominal data
3.00 Works with “x” and “y” coordinate graphs
4.00 Reads and interprets tables

Geometry

1.00 Fundamental concepts: Defines and identifies point, surface, solid, line
2.00 Plane geometry2.10 Lines: Define, identify, and construct2.10.1 Straight, curved, horizontal, vertical, oblique, perpendicular
2.10.2 Line, ray, and line segment
2.10.3 Parallel, convergent, and divergent2.20 Angles: Define, identify, and construct2.20.1 Right, straight, acute, obtuse, reflex, whole
2.20.2 Adjacent, vertical, complementary and supplementary
2.20.3 Vertical angles that are equal
2.20.4 Sizes of angles
2.20.5 Convex and reflex angles 2.30 Exploration of three straight lines2.30.1 Alternate exterior, alternate interior, interior angles on the same transversal and corresponding angles
2.30.2 Parallel lines cut by a transversal2.30.2a Alternate lines are equal
2.30.2b Corresponding angles are equal
2.30.2c Exterior or interior angles on the same side as the transversal are supplementary 2.40 Correctly measures using ruler, protractor
3.00 Geometric Solids: 3.10 Defines and identifies: Ellipsoid, ovoid, sphere, cylinder, pyramid, rectangular prism, triangular prism
3.20 Measures volume of simple solids 4.00 Defines and identifies equal, similar, and equivalent figures
5.00 Properties of circles5.10 Defines and identifies: center, radius, diameter, circumference
5.20 Defines and identifies: are, chord, segment, sector, annulus
5.30 Understands relationship to a straight line: exterior/tangent/secant
5.40 Understands intersecting circles, sets, etc.6.00 Study of area and properties of additional shapes6.10 Triangles: equilateral, right, isosceles
6.20 Squares, rectangles, parallelograms, rhombus, trapezoid
6.30 Regular polygon
6.40 Recognizes symmetry, mirror, flip, rotation, etc.7.00 Defines and understands Pythagorean Theory7.10 Euclid on Pythagorean

Higher Level Skills

1.00 Determines probability through dice or spinner games
2.00 Pre-Algebra skills2.10 Understands order of operations
2.20 Solves problems with parentheses3.00 Algebra skills3.10 Solves for “x”