Progression of Early Number and Counting

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Progression of Early Number and Counting

Modelling

Modelling is very important for students to learn these big ideas and strategies

Is there a way to model this problem that might help me start working on this problem?

Big Ideas:

Representation

Decomposition and Composition of Numbers

Abstraction- the idea that a quantity can be represented by different things

Relationships

Anchors of 5 and 10- students develop the understanding that numbers such as 2 can be thought of in relation to 5

Unitizing- the idea that in the base ten system, objects are grouped into tens once the count exceeds 9

Part-Part Whole- the ideas that quantities represented by such numbers are made up of different parts

Quantity

Proportions

Conservation of Number - the idea that the count for a set group of objects stays the same no matter whether the objects are spread out or are close together

Cardinality- the idea that the last count of a group of objects represents the total number of objects in the group

Order Irrelevance- the idea that the counting of objects can begin with any object in a set and the total will still be the same

Operational Sense

Rational Numbers

Subitizing- recognize small quantities without having to count each of the objects

Counting

Movement is Magnitude- the idea that as one moves up the counting sequence, the quantity increases or vice versa

Hierarchical Inclusion

One-to-One Correspondence- the idea that each object being counted must be given one count and only one count

Rote Counting

Stable Order - the idea that the counting sequence stays consistent

Cognitive reorganizing when looking at big ideas

Brain needs to develop new synapses- similar to when mathematicians figure these big ideas out

Like Piaget's development of structures

Strategies

Used to figure out problems

Students will be surprised that the strategy works so they ask- will it work all the time?

Big ideas can help students create new strategies

Start with strategies that are less efficient gets refined and then are more efficient

Examples

For part-part-whole relationships, use things like counters, blocks, number lines, rekenreks (grade 1)

Use number lines and hundreds charts along with concrete materials to help with addition and subtraction (grade 1)

Concrete materials (i.e. beans) can be helpful for rote counting, one-to-one correspondence and cardinality (Kinder and grade 1)

Supporting students in identifying, developing, and describing useful strategies for solving addition and subtraction problems – for example, using known facts, using doubles (which are often readily remembered), making tens, using compensation, counting up, counting down, using a number line or hundreds chart, using the commutative property of addition (grade 1)

For number conservation, use things like linking cubes, games, dot strips, and other concrete materials to start learning about composing and decomposing numbers and addition and subtraction (Kinder)

Dot cards, dominos, number of fingers, and dice for subitizing (Kinder)

Subitizing is a good way to start learning estimation skills (Kinder)

Composing and Decomposing numbers is a strategy for subitizing (Kinder)

Using everyday situations as contexts for problems (calculating milk money, taking attendance) and/or using real-life contexts for problems (grade 1)

Encourage group work and drawing representations of math problems to help find the solution (grade 1 and Kinder)

Use number lines or hundreds carpet for rote counting (Kinder)