Week 3 - Pre And Early Number

Question 1

What are early concepts of pre number?

Answer 1

1. Ditermining attributes
2. Matching by attributes
3. Sorting by attributes
4. Comparing attributes
5. Ordering attributes and
6. Patterning

Question 2

What are attributes

Answer 2

A quality or a feature of something

Question 3

What are key features of determining attributes?

Answer 3

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

Question 4

What are key features for matching by attributes

Answer 4

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

Question 5

Key features to sorting by attributes

Answer 5

Involves 3 or more objects

Attribute blocks are great and have the four attributes of colour, shape, size or thickness

Question 6

Key features of comparing

Answer 6

Initially compare two objects

Look for more or less of a mathematically significant attribute

Question 7

Ordering by attributes

Answer 7

Order more than two objects at a time

Based on an increase or decrease of attribute

Order 3 things first before ordering other 3

Question 8

Key features of patterning

Answer 8

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

Question 9

What are patterning skills?

Answer 9

Build or create patterns

Copy a pattern

Extend/grow a pattern

Insert the missing element into a pattern

Translate a pattern

Question 10

What can be used for establishing the relationship between elements?

Answer 10

Use the function machine

Something goes in and something comes out - processing and identifying relationships. Identifying a rule and understanding the pattern

Question 11

Why is patterning important?

Answer 11

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

Question 12

What are numbers?

Answer 12

Ideas and concepts

Question 13

What are the types of numbers?

Answer 13

Natural

Whole

Integers

Rational numbers

Irrational

Complex and imaginary

Question 14

Uses for numbers?

Answer 14

Cardinal numbers

Ordinal numbers

Nominal numbers

Question 15

What are cardinal numbers?

Answer 15

cardinality of numbers

Counting - how many?

Quantity - how much?

Relates to integers - can be negative numbers

Question 16

What are ordinal numbers

Answer 16

Position - 1st, 2nd and 3rd etc

Question 17

Nominal numbers

Answer 17

No cardinality or position

Numbers as a label only such as street number id number etc

Question 18

What are the 5 counting principles?

Answer 18

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)

Question 19

Subtilising - number understanding

What is it?

Answer 19

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

Question 20

What is the basic structure to teaching any algorithms?

What do you need to remember when the initial algorithm is being developed?

Answer 20

1. Use materials (mab’s, bundling sticks, place value mats) language and recording
2. 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

4. Demonstrate and practice non-traditional algorithms
5. Link back to the concept and also the language for mental computation
6. Avoid the need to do trading or regrouping
7. Continually check for understanding of the process