Week 3 - Pre And Early Number Flashcards
What are early concepts of pre number?
- Ditermining attributes
- Matching by attributes
- Sorting by attributes
- Comparing attributes
- Ordering attributes and
- Patterning
What are attributes
A quality or a feature of something
What are key features of determining attributes?
Observant to five senses
Recognise and name attributes such as colour, shape, size, mass or weight, texture, type of material or function
List likeness or differences - are they the same and how
What are key features for matching by attributes
Initially use two objects as it makes it more simplistic
Describe the sameness
Match Object to object Object to outline Picture to picture Picture to outline
Key features to sorting by attributes
Involves 3 or more objects
Attribute blocks are great and have the four attributes of colour, shape, size or thickness
Key features of comparing
Initially compare two objects
Look for more or less of a mathematically significant attribute
Ordering by attributes
Order more than two objects at a time
Based on an increase or decrease of attribute
Order 3 things first before ordering other 3
Key features of patterning
Weaves all pre number concepts together - required matching, sorting, comparing and ordering skills
Creating visual, auditory and movement patterns
Practicing copying a pattern, building or creating a pattern, filling in the missing elements
What are patterning skills?
Build or create patterns
Copy a pattern
Extend/grow a pattern
Insert the missing element into a pattern
Translate a pattern
What can be used for establishing the relationship between elements?
Use the function machine
Something goes in and something comes out - processing and identifying relationships. Identifying a rule and understanding the pattern
Why is patterning important?
Children use their senses to learn by exploring
Requires children to organise and remember mathematics ideas and relationships
Facilitated creativity
It’s engaging- hands on
Encourages risk taking which is a necessary ingredient of problem solving
Essential prerequisite to later mathematics such as algebra
Key in the language model when working with materials
What are numbers?
Ideas and concepts
What are the types of numbers?
Natural
Whole
Integers
Rational numbers
Irrational
Complex and imaginary
Uses for numbers?
Cardinal numbers
Ordinal numbers
Nominal numbers
What are cardinal numbers?
cardinality of numbers
Counting - how many?
Quantity - how much?
Relates to integers - can be negative numbers
What are ordinal numbers
Position - 1st, 2nd and 3rd etc
Nominal numbers
No cardinality or position
Numbers as a label only such as street number id number etc
What are the 5 counting principles?
One to one correspondence
Stable order (1-9)
Cardinal principle (last number counted tells us how many are in the set)
Abstraction (what it is possible to count - non homogeneous objects) 1 glass of water and one ice cube aren’t counted together
Order irrelevance (left to right or right to left)
Subtilising - number understanding
What is it?
Counting without physically counting.
Picking up a dice and knowing there are 5 on it.
The picture children see in their head when seeing a number without counting
The use of a pattern makes it easy - Caldwell pattern is very good - squares around counters makes it easier to count and make sense of numbers
- can be used with odd/even number patterns
- used with domino patterns
10 frames helps with subsidising
What is the basic structure to teaching any algorithms?
What do you need to remember when the initial algorithm is being developed?
- Use materials (mab’s, bundling sticks, place value mats) language and recording
- Once students are familiar with modelling the algorithm using materials, they can be discarded and students can just use language and recording
3 eventually students will be able to complete it by solely recording
- Demonstrate and practice non-traditional algorithms
- Link back to the concept and also the language for mental computation
- Avoid the need to do trading or regrouping
- Continually check for understanding of the process
