The six major foundations of Math are listed below

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Number Sense

Number Relationships

Number sense means more than just counting. It also includes the ability to think and work with numbers easily and to understand their uses and relationships. Children learn about numbers through experience and discovery, and from hands-on activities. Adults can support children's efforts to understand numbers by providing daily opportunities for counting, measuring and discussing the ways in which we use numbers. Young children can begin to understand concepts such as volume, capacity, length, area, shape, space, time and size.





Computation

Counting, Sorting, Classifying, and Comparing Objects

The ability to use addition and subtraction to solve problems is based on counting, sorting and comparing objects. To build the foundation for computation, children need a variety of materials that can be used for addition and subtraction.

These materials might include shells, keys, cereal, pebbles, bottle caps, or nuts and bolts. Provide plates or egg cartons for children to use for sorting and grouping. Ask children why they sorted, classified or ordered objects in a certain way.





Algebra and Functions

Finding Patterns and Relationships

Algebra is a language that is used to create mathematical models of real-world situations. Algebra includes the four basic operations of arithmetic, but instead of using words, symbols are used to make statements about things. In algebra, letters are often used to represent numbers.

To build the foundation for algebra, young children need opportunities to explore a variety of shapes, sizes, colors, patterns, textures, sounds and symbols. They should also have opportunities to duplicate and describe patterns and relationships.





Geometry

Spatial Awareness and Reasoning

The first steps towards understanding geometry are taken when children begin exploring sizes, shapes and spatial arrangements. Spatial reasoning begins when children explore their environment and become aware of their bodies and personal space. Spatial reasoning is one of the abstract reasoning skills that the brain uses to perform both common, everyday activities such as walking and running, and complex functions such as solving problems in mathematics and engineering.





Measurement

Time and Measurement Relationships

Children need a variety of opportunities to explore and discover measurement and apply the results to real-life situations. Quantity, weight, distance and length are all attributes that can be measured.

Are things hot or cold? Heavy or light? Long or short? Adults can talk to children about words that are used to measure temperature or weight, and ask them to think of other measurement words. Measurement concepts can be discussed as a part of everyday activities, by making comments such as "Your cup is almost full," or "It's hot in here today." As children's understanding increases, they will begin to use words such as inch, mile, hour, degrees, cup and gallon. Adults can support their understanding by asking questions that require prediction.





Problem Solving

Ability to Reason, Predict, and Problem Solve through Exploration

The ability to solve problems is needed in all aspects of young children's lives. As they explore relationships, manipulate objects, and interact with people, children are able to formulate ideas, try them out, and accept or reject what they learn. Constructing knowledge by making mistakes is part of problem solving. Through exploring, experimenting, testing hypotheses, and solving problems, children build knowledge.

The process of problem solving -- making choices and learning from them -- is supported by adults who observe, listen, and ask open-ended questions that further the process.

These questions might include, "What will happen if...?" and "What other ways can you think of to do that?" Problem solving becomes part of learning when mistakes are made and different solutions have to be tried. This discovery process allows children to realize that most problems have more than one solution and some problems cannot be solved.