Math
Concepts in Montessori Math are always presented in concrete, manipulative form. Later, when the child has understood the meaning and the use of symbols by manipulating the concrete objects, are more abstract forms introduced. The materials are designed to help the child to understand the concepts of associating quantity and number symbols, beginning with numbers from 1-10 and extending to the concepts of the decimal system and place value. As the child progresses, materials are available for working with the processes of addition, multiplication, subtraction and division.

Pre-Math Concepts

Temporal Relations Related Activities  
Beginning and ending
Ordering of events
Time periods
Performing sequence of steps in materials and activities
Learning daily schedule
Keeping track of days, weeks, months (calendar activities)
Conversations (discussions of progression of events)
Stories (beginning, middle, end)
Sequence puzzles
Performing sequence of steps in materials and activities
Learning daily schedule
Keeping track of days, weeks, months (calendar activities)
Conversations (discussions of progression of events)
Stories (beginning, middle, end)
Sequence puzzles
Spatial Relations Related Activities
Position (on, under, over, beside, etc.)
Direction (toward, away from)
Distance (near, far)
Using prepositions in various listening games
Movement activities: positional challenges (crawl under the table, climb on the chair, stand in front of the door, etc.)
Verbal locating games (ˇ°hot and coldˇ±)
One-to-One Correspondence Related Activities
Awareness of a pairing of two groups of things such that each item in one group is paired with one item in the other group.
Ability to make such a pairing
Individual coat hooks or cubbies, one per child Serving food, one serving per child
Nuts and Bolts
Locks and Keys
Name cards
Matching activities
Combination Related Activities
Understanding that various items can be combined, forming a new item Color mixing with food coloring or paints
Making home-made clay
Food preparation activities (jello)
Science experiments involving mixing (salt/water, sugar/water, etc.)
Difference Related Activities
Sharpening and refining perceptions of differences Sorting activities
Puzzles
Similarities Related Activities
Sharpening and refining perceptions of similarities Sorting activities, matching activities
Gradation Related Activities
Understanding of gradation
Ability to grade a series of objects (long to short, heavy to light, etc)
Items to grade
Color shades
Number Theory and Numeration
  • Ordering to 10
  • Association of quantity with symbol
  • Concept of 0
Linear Counting
  • 11-19
  • Counting of groups of tens
  • 1-100
Decimal System
  • Introduction of units, tens, hundreds, thousands
  • Decimal layout
  • Number composition
  • Exchange tray
  • Exchange game
Operations (Concrete)
  • Knowledge of the meanings of addition, multiplication, subtraction, division
  • Experience with the processes
  • Recording the process
  • Word problems
Parallel Activities
Time Money Measurement Geometry Fractions Probability and Statistics
- Familiarity with calendar (days, weeks, months)
- Familiarity with clock (hours, minutes, telling time)
- Recognition of coins (pennies, nickels, dimes, quarters)
- Estimating costs (too much/too little)
- Longer/shorter
- Heavier/lighter
- Units of measure
- Practical applications
- Circles
- Triangles( sides/angles)
- Rectangles
- Regular polygons
- Irregular plane closed figures
- Geometric solids
- Equal parts of a whole (concrete)
- Half, quarters, thirds
- Prediction outcomes
- Conducting experiments
- Recording data (tallying)
- Bar graphs
- Tables/charts

   
 

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