Mathematics Foundation: 2 - Computation and Algebraic Thinking

Topic: M2.1 - Exhibit understanding of mathematical structure

Mathematical structure is the application of previously developed skills, such as language, to make sense of new mathematical ideas. Provided the opportunity to experience mathematics in a variety of forms, children will develop an understanding of new mathematical concepts.

The development of understanding mathematical structure skills leads to:
*Applying known structures to new structures.
*Counting by ones (1,2,3), then counting by tens (10,20,30) etc.
*Development of strategies that children show in performing simple arithmetic
*The ability to reason and explain their mathematical activities

Looking Ahead to Kindergarten Family Engagement Special Populations
In kindergarten, students will use objects, drawings, etc. to decompose numbers less than or equal to 10 into pairs in more than one way, and record each decomposition with a drawing or an equation (K.CA.3). Encourage families to:

*Have their child distribute cookies or toys to family members, with each person getting an equal number.
*Help their child think about the permanence of a set. (e.g. Put a specific number of objects in a row, and then change the arrangement. Then families can ask, “Are there more or less?”).
*At the grocery store, encourage families to ask questions about what there is more of in the cart (e.g. ”Did we buy more apples or tomatoes?”).

Educators can:

*Pre-teach new terms and language and post visuals around the room.
*For DLL, use interventions focused on matching quantity and comparison terms in the child’s home language to English.

Powerful Practices
Across all developmental stages, educators can:

*Play games where small quantities are combined or taken away, and point child’s attention to the new quantity (e.g. a numeric card game or a simple educator created game using a dice or spinner.)
*Provide loose parts that can be grouped and ungrouped.
*Share simple math boards in zip-lock bags for families to use at home.

Infant
Younger Toddler
Provide materials and encourage children to fill and dump

Play simple games that encourage the child to take away or add to a larger group (e.g. “Can you take all the dogs out of the pile of animals?”)

Older Toddler
Play games where child guesses what items are added or taken away from a larger group of items

Provide opportunities during play for child to play with numbers and make predictions (e.g. “How much playdough would you like?” or “How many blocks tall do you think you are?”)

Younger Preschool
Provide a variety of materials (e.g. loose parts) that can be grouped and ungrouped, drawing attention to the concept that combining groups creates a larger group and taking away creates a smaller group

Older Preschool
Play games where small quantities are combined or taken away drawing attention to the new quantity

Provide materials that can be used for adding and subtracting