Elementary School Mathematics

Goals

1. Intuitive understanding of the counting numbers
2. Facility with basic arithmetic computations
3. Working ability in identifying pattern existence and relevance
4. Working knowledge of non-negative rational numbers
5. Working knowledge of equivalence among representations of values
6. Working ability to share quantitative knowledge with others

Next: intermediate.

Objectives

• Concepts of sequence
  • Count from 1 to 100 without error
  • Recite the next 5 numbers after any counting number between 1 and 100
  • Identify the bigger and smaller number of any pair of counting numbers
  • Arrange a set of counting numbers into ascending order
  • Identify the place values (1, 10, 100, etc.) for integers in decimal notation
• Concepts of shape
  • Name simple shape categories including circle, square, rectangle, triangle, and so on
  • Classify regular and irregular polygons by shape category
  • Draw recognizable approximations of regular polygons with 3 to 8 vertices
  • Arrange convex polygons in order by number of vertices
  • Use patterns of dots to represent numbers
• Concepts of addition
  • Add 1 to any counting number
  • Illustrate a simple addition problem using objects
  • Express the combination of 2 groups of objects as addition
  • Solve a simple addition problem using counting
  • Use the addition table to solve a simple addition problem
  • Identify patterns and symmetries in the addition table
  • Demonstrate how to recreate the addition table with counting
  • Illustrate commutativity of addition using the addition table
  • Illustrate commutativity of addition using counting
• Concepts of subtraction
  • Count backwards from any given counting number
  • Subtract 1 from any counting number greater than 1
  • Subtract 1 from any counting number
  • Use zero as a representation of "nothing"
  • Illustrate subtraction using a group of objects
  • Solve a simple subtraction problem by counting backwards
  • Use the addition table to answer a simple subtraction problem
  • Explain how addition and subtraction are inverse operations
• Concepts of multiplication
  • Explain multiplication in terms of repeated addition
  • Use the multiplication table to answer a simple multiplication problem
  • Demonstrate how to recreate the multiplication table with addition
  • Demonstrate how to recreate the multiplication table with counting
  • Illustrate commutativity of multiplication using symmetry in the multiplication table
  • Explain identity of multiplication using the multiplication table
  • Illustrate a simple multiplication problem using groups of objects
  • Illustrate a simple multiplication problem using rectangular arrays of objects
  • Explain how a rectangular array illustration is also an illustration using groups
  • Illustrate commutativity of multiplication using objects
• Concepts of division
  • Illustrate division using rectangular arrays of objects
  • Illustrate division by cutting a whole object into parts (e.g., the classic pie)
  • Illustrate division by distributing objects among receivers (e.g., dealing cards)
  • Illustrate division with a remainder by distributing objects among receivers
  • Use the multiplication table to answer a simple division problem
  • Explain how multiplication and division are inverse operations
  • Explain identity of division using an illustration
• Fractions and ratios
  • Express partitioning a group of objects into equal subsets using fractions
  • Arrange a set of fractions (with common denominators) into ascending order
  • Express cutting a single object into equal parts using fractions
  • Use fractions to handle remainders of a division problem
  • Express relationships of quantity using ratios [discrete metrics]
  • Express relationships of volume and mass using ratios [continuous metrics]
  • Illustrate the equivalence of ratios and fractions using groups of objects
  • Illustrate the equivalence of ratios and fractions for volume and mass
  • Identify simple equivalent fractions
  • Convert simple fractions to equivalent expressions with various denominators
  • Express pairs of fractions in common terms
  • Convert a fraction to lowest terms
  • Arrange a set of fractions (not given in common terms) into ascending order
• Decimal fractions and percents
  • Identify the special fractions 1/10, 1/100, etc.
  • Identify the symmetry of these special fractions with integer place values
  • Express sums of integers and decimal fractions using decimal notation
  • Convert simple fractions to decimal notation by changing denominators
  • Convert simple fractions to decimal notation by using extended division
  • Use '%' in place of '/100' for writing fractions with a denominator of 100
  • Convert simple fractions to percent notation by changing the denominator
  • Convert decimal fraction notation to percent notation
  • Convert percent notation to decimal fraction notation
  • Convert simple fractions to percent notation using extended division

May, 2014