Montessori Upper Elementary Curriculum

Our Upper Elementary class curriculum includes Language Arts, Math, Science, and History objectives. Extra-curricular offerings including P.E., Spanish, art, computer technology, and music are also incorporated for all students.

Specific Objectives for Upper Elementary Mathematics

Numeration

1.00 Counts sequentially to any value, given any pattern or sequence
2.00 Knows place value concepts through billions
     2.10 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 Compares numbers using >, <, =
3.00 Classification
    3.10 Identifies ordinal numbers (first – “n”thieth)
    3.20 Identifies Roman numerals to 1000
4.00 Order and sequencing
     4.10 Understands positive and negative numbers and 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 knowledge of number
            relationships
     4.60 Recognizes and identifies patterns and sequences
          4.60.1 Can fill in an unidentified number when given a sequence
5.00 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 columns
     2.10 With and without regrouping (static and dynamic)
     2.20 Understands concept of regrouping in addition
     2.30 Maintains correct place value for money and decimals
3.00 Adds numbers in order presented horizontally
     3.10 Converts to a vertical orientation, maintaining place value
4.00 Adds fractions
     4.10 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 columns
     2.10 With and without regrouping (static and dynamic)
     2.20 Understands concept of regrouping in subtraction
     2.30 Maintains correct place value for money and decimals
3.00 Subtracts fractions
     3.10 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 two and three digit multipliers
3.00 Moves decimal point appropriately to maintain correct place value
4.00 Multiplies fractions
     4.10 Calculates least common multiple
     4.10 Equivalent fractions
     4.20 Converts proper and improper fractions
     4.30 Converts fractions to decimals and percentages
5.00 Multiplies positive and negative numbers
6.00 Factors numbers
     6.10 Understands prime numbers
     6.20 Understands prime factorization
     6.30 Understands composite numbers
     6.40 Calculates greatest common factor

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
3.00 Conserves numbers
4.00 Averages numbers
5.00 Solves > and < equations with numbers to one billion
6.00 Solves > and < equations with fractions and percentages
7.00 Understands and illustrates concepts of commutative, associative,
       and distributive properties
8.00 Follows orders of operations with parentheses

Measurement

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 Estimates
     7.10 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 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

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”