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number and place value - Coggle Diagram
number and place value
difference between a numeral and a number
numeral
the symbol used to represent a number
number
the concept represented by the numeral
numbers can be represented by differentr numerals, such as different languages
what are the cardinal and ordinal aspects of number
cardinal aspect of number
a number being a description of a set of things.
eg. two dogs, eight fishes
by matching different objects of same amount to same number is how learners able to recognise their is something the same about the sets
ordianal aspects
numbers are labelled where they are becuase of the position in which they lay in ordering proccess
numbers tell you what order they come, what is first and what is second.
learners also learn by using numbers as labels to put things in order
birthdays
turn to page 3
landing on a number in a game
norminal aspect
where numeral usedto label or name without any ordering implied
eg. number 5 bus
no expectation for number 6,7,8 bto follow
what are natural numbers and intergers
numbers we use for counting
the set of numbers =
nuatural numbers
can have both
cardinal and ordinals
interpretaions
integers
builds on the ordinal aspect of number extending number line in the other direction
integeral
forming a whole
intgreity
wholeness
negative integers
whole numbers less than zero
positive integers
whole numbers greater than zero
what are rational and real numbers
rational numbers
when we extend our concept of what a number is to include fractions and decimal numbers
term 'rational'
any number that is the ratio of two intergers
includes all fractions even decimal fractions
real numbers
what is meant by 'place value'
There are two sets of materials that provide particularly effective concrete embodiments of the place-value principle and therefore help us to explain the way our number system works. They are (1) base-ten blocks and (2) 1p, 10p and £1 coins.
Use coins (1p, 10p and £1) and base-ten blocks to develop children’s understanding of the place-value system, particularly to reinforce the principle of exchange.
how does number lines support understanding of place value
the number line is an important image that is particularly helpful for appreciating where a number is positioned in relation to other numbers.
Making the connection between numbers and points on the number line provides children with a powerful image to support their understanding of number, emphasizing particularly the position of a number in relation to other numbers
What is meant by saying zero is a place holder
generally thought that the Mayan civilization of South America was the first to develop a numeration system that included both the concept of place value and the consistent use of a symbol for zero.
rounding numbers to the nearest 10 or 100
When rounding to the nearest ten= the units digit less than 5 then round number down to the preceding 10; but if digit is greater than 5 then round up to the next multiple of 10.
The first step in developing this skill is to be able to round a 2-digit number to the nearest ten.
research focus: place value
Thompson(2000)
Thompson has undertaken a critical appraisal of this traditional view (Thompson, 2000).
Thompson concludes that the principle is too sophisticated for many young children to grasp.
mental calculation strategies used by children for two-digit addition and subtraction are based not on a proper understanding of place value but on what he calls quantity value.
Price(2001)
Price (2001), whose research focused on the development of place-value understanding in Year 3 children.
independent-place construct: that children tend to make single-dimensional associations between a place, a set of number words and a digit, rather than taking account of groups of 10.
Thompson and Bramald (2002)
only 19 of the 91 children who had successful strategies for adding two-digit numbers had a good understanding of the place-value principle.