Montessori Lower Elementary Curriculum

Hilltop's Lower Elementary (first through third grade) curriculum focuses on Language Arts, Math, Science, History, and Geography. Extra-curricular studies including P.E., Spanish, art, computer technology, and music are also incorporated for all students.

Lower Elementary math studies include numeration, addition, subtraction, multiplication, division, elements across operations, measurement, money, time, squaring, fractions, charts and graphs, geometry, and higher level skills.

Specific Objectives for Lower Elementary Math

Numeration

1.00 Counts sequentially to any value
2.00 Knows place value concepts to one million
     2.10 Writes number in expanded notation
     2.20 Writes number to one million using commas correctly
     2.30 Writes number in words
     2.40 Identifies place value in various numbers
3.00 Classification
     3.10 Identifies ordinal numbers (first, second, third)
     3.20 Identifies odd and even numbers
     3.30 Identifies Roman numerals to 20
4.00 Order and sequencing
     4.10 Lists numbers before and after any given number, to one million
     4.20 Understands that there are number less than zero
     4.30 Sequences from least to greatest, numbers to one million
     4.40 Sequences decimals from least to greatest
     4.50 Sequences fractions from least to greatest
     4.60 Finds missing numbers using multiples or knowledge of number          
            relationships
5.00 Understands and applies strategies
6 .00 Rounds numbers to the nearest 10, 100, and 1,000
7.00 Understands >, <, =

Addition

1.00 Memorizes addition facts through 18
2.00 Understands concept of addition with and without materials (beads/rods)
3.00 Adds numbers in columns
     3.10 With and without regrouping (static and dynamic)
     3.20 Understands concept of regrouping in addition
     3.30 Maintains correct place value for money and decimals
4.00 Adds numbers in order presented horizontally
     4.10 Converts to a vertical orientation, maintaining place value
          4.10.1 Numbers above zero
          4.10.2 Money
          4.10.3 Decimals

Subtraction

1.00 Memorizes subtraction facts through 18
2.00 Understands concepts of subtraction with and without materials
3.00 Subtracts numbers in columns
     3.10 With and without regrouping (static and dynamic)
     3.20 Understands concept of regrouping in subtraction
     3.30 Maintains correct place value for money and decimals

Multiplication

1.00 Memorizes multiplication facts through 12
2.00 Understands the concept of multiplication
3.00 Multiplies with one and two multipliers with regrouping (dynamic)
4.00 Lists multiples of numbers
5.00 Begins to find lowest common multiples of numbers
6.00 Can make a factor tree for a given number
7.00 Begins to find greatest common factors of numbers

Division

1.00 Memorizes division facts through 12
2.00 Understands the concepts of division
3.00 Performs long division with and without materials

Elements Across Operations

1.00 Understands properties of zero for +, -, x, and
2.00 Understands properties of one for +, -, x, and
3.00 Adds or subtracts numbers above zero with a numberline
4.00 Conserves numbers
5.00 Averages numbers
6.00 Solves > and < equations with numbers to one million
7.00 Solves > and < equations with fractions
8.00 Understands and illustrates concepts of commutative, associative, and
       distributive properties (with materials)

Measurements

1.00 Measures in centimeters and inches with a ruler
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

Money

1.00 Identifies correct value to U.S. currency
2.00 Manipulates money maintaining decimal points and dollar sign:
       Adds, subtracts, multiplies, divides
3.00 Makes change to $100.00

Analogue and Digital Time

1.00 Tells time to the minute
2.00 Solves elapsed time word problems without aid of clock

Word Problems

1.00 Solves two and three 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
4.00 Figures the square of a binomial with the aid of materials
5.00 Figures the square of a trinomial with the aid of materials

Fractions

1.00 Identifies fractions with materials, in relationship to cooking and
       geometric shapes
2.00 Sequences fractions from smallest to largest
3.00 Finds fraction equivalencies with >, <, and equal to, without materials
4.00 Adds and subtracts fractions with the same denominator without materials
5.00 Multiplies and divides fractions without materials

Decimals

1.00 Identifies decimals concepts to ten thousandths
2.00 Sees relationship of decimals to fractions

Charts and Graphs

1.00 Reads and understands a simple chart, bar or circle graph, grid
2.00 Creates charts and graphs from nominal data
3.00 Understands 100%, 50%, 25%

Geometry

1.00 Defines and identifies point, surface, solid, line, surface, side, edge, vertex
2.00 Plane geometry
     2.10 Lines: Define, identify, and construct
          2.10.1 Straight, curved, horizontal, vertical, oblique, perpendicular
          2.10.2 Line, ray, and line segment
          2.10.3 Parallel, convergent, and divergent
     2.20 Angles: Define, identify, and construct parts of an angle
          2.20.1 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: protractor
          2.20.5 Convex and reflex angles
     2.30 Exploration of three straight lines
          2.30.1 Alternate exterior, alternate interior, interior angles on
                    the same transversal and corresponding angles
          2.30.2 Parallel lines cut by a transversal
               2.30.2a 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
3.00 Geometric Solids- defines and identifies: Ellipsoid, ovoid, sphere, cylinder,
        pyramid, rectangular prism, triangular prism
4.00 Triangles
     4.10 Classification by side: Scalene, isosceles, equilateral
     4.20 Classification by angle: Acute, obtuse, right
     4.30 Classification by side and angle
     4.40 Equilateral triangles
     4.50 Cases of scalene and isosceles triangles
     4.60 Base and height exploration
     4.70 Study of Orthocenter
     4.80 Catheti
     4.90 Interior and exterior angles of a triangle
5.00 Quadrilaterals: Define, identify, and construct
     5.10 Square, rectangle, rhombus, parallelogram, trapezoid, quadrilaterals    
          5.10.1 Types of trapezoids
     5.20 Sum of the interior angles
6.00 Regular and Irregular Polygons
     6.10 Types of polygons
     6.20 Intuition of regular polygon
     6.30 Regular to irregular polygons
     6.40 Angles of a polygon
          6.40.1 Sum of interior angles
          6.40.2 Sum of exterior angles with more than four sides
     6.50 Constructing polygons
7.00 Circle
     7.10 Identifies parts of a circle
     7.20 Mutual position of a line and circle
     7.30 ? with and without radius
     7.40 Relationship of two circles
          7.40.1 Without a radius
          7.40.2 With radii
          7.40.3 Understands intersecting circles, sets
8.00 Determines if objects are symmetrical and congruent
     8.10 Symmetry: mirror, flip, reverse, rotate
     8.20 Congruency: includes image matching

Higher Level Skills

1.00 Determines probability through dice or spinner games
2.00 Pre-Algebra skills
     2.10 Understands order of operations
     2.20 Solves problems with parentheses
3.00 Algebra skills
     3.10 Uses hands-on material to solve for “x”
4.00 Predictions and estimates