Place Value Workshop Friday, 27 th September. University of Greenwich. Place Value Workshop Objectives. Understand issues & progressions in recording larger numbers Use effectively a range of manipulatives, reflecting place value Know common misconceptions linked with place value
University of Greenwich
Identify a set given the number
Create a set given the number
Correctly name the number of objects in a set
Can do all the above but presented with numbers in a written form rather than spoken, and can record as number symbols sets of 0-9 objects.
Can count from 1 through 10 both with and without objects.
Askew, M. (1998) Teaching Primary Mathematics. London: Hodder & Stoughton
Askew, M. (1998) Teaching Primary Mathematics.
London: Hodder & Stoughton
Work with a partner to fill in the gaps in the Chinese and Bengali number square.
How did you work out the missing numbers?
How does this link to our number system?
1 8 . 7 3 2
This link above looks at other PV written systems. You may want to look at it with children – especially in a cross curricular context.
What about Roman Numerals? …
Year 1: Number and Place Value
Count to and across 100, forwards and backwards beginning with any number
Count, read and write numbers to 100 in numerals
Count in different multiples – 1s, 2s, 5s and 10s
Given a number, give one more and one less
Identify and represent numbers using concrete objects and representations including numberlines
Read and write numbers from 1 to 20
Year 2: Number and Place Value
Count in steps of 2, 3 and 5 from 0, count in 10s from any number, forward and backward
Recognise place value of each digit in a 2 digit number
Identify, represent and estimate numbers using representations including number line
Compare and order numbers from 0 to 100
Read and write numbers to at least 100 and in words
Use place value to solve problems example
Year 3: Number, place value and rounding
Count from 0 in multiples of 4, 8, 50 and 100, give 10 or 100 more or less of a given number
Recognise place value of each digit in a 3 digit number
Compare and order numbers up to 1000
Identify, represent and estimate numbers in different representations
Read and write numbers to 1000 in numerals and words (ie. 768 = seven hundred and sixty eight).
Solve number and practical problems
Count in multiples of 6, 7, 9, 25 and 1000
Find 1000 more an less of a given number
Count backwards through zero to negative numbers
Recognise place value of digits in 4 digit number
Order and compare numbers beyond 1000
Round numbers to nearest 10, 100, 1000
Read and write numbers to 2 decimal places
Round decimal numbers to nearest whole number
Compare two decimal numbers with the same decimal places
Read Roman numerals to 100 and understand how number systems have changed over time and include the concept of zero and place value
Read, write, order and compare numbers to 1,000,000 and determine value of each digit
Count forwards and backwards in powers of 10 up to 1,000,000
Interpret negative numbers in context and count forward and backwards through zero
Round any number up to 1,000,000 to nearest 10, 100, 1000, 100,000
Round decimals to nearest whole number and one decimal place
Read, write, order and compare numbers with 3 decimal places
Read Roman numerals up to 1000, recognise year written in Roman numerals
Read, write, order and compare numbers up to 1,000,000 and determine value of each digit
Round whole numbers
Use negative numbers in context
Identify value of each digit to 3 decimal places and multiple numbers by 10, 100, 1000 answering up to 3 decimal places
They will be able to interpret larger numbers, even though they cannot yet calculate with them
Research suggests that children in Japan develop an understanding of PV younger, this appears to be because number names are explicit (Stigler et al, 1990)
Why isn’t 32 written as 302 … 361 as 300601?
Children who cannot understand groups as units are confined to counting in ones
Children who have learnt traditional calculations by rote can be hindered if they cannot think about the value of digits when calculating
What happens when you multiply / divide by 10?
Children are often taught that when multiplying or dividing by 10, they add or take away the 0…..is this true?
Does the decimal point move?
Can the above cause misconceptions?
To divide by 10, move the digits one place to the right to make 0.74
7.4 ÷ 10 =
To divide by 10, you just take a zero off, so it is 7.4
You move the digits one place to the left so it is 74.0
What do YOU think?
Confusion – consider interpretation – i.e
money on a calculator – when calculator gives monetary answer of 2.5 – children need to know that this is £2.50 (SATs)
As a label
A numerical value in a measure
Can you think of any real life situations where negative numbers are used?
Unifix / multilink
100 beads on string
Base 10 blocks (Dienes)
Gattegno chartLook at some resources to support the understanding of place value
Visualisation helps to bridge the gap between concrete and abstract.
Now try this exercise.