1. Middle Maths Focus Group
Number Sense
and Place Value
9 March 2011

2. Number Sense
Having a good intuition about numbers and their relationships.
Develops gradually as a result of exploring numbers, visualising numbers in a range of contexts, and relating them in ways that are not limited by traditional algorithms.
Grows more complex as children learn more, eventually being able to think flexibly about fractions, decimals, percent and integers.

3. Big ideas
Numbers are related to each other through a variety of number relationships - more than, less than, composed of
“Really big” numbers possess the same place-value structure as smaller numbers. Best understood in terms of real- world contexts
Whole numbers can be described by different characteristics, even and odd, prime and composite, square, understanding characteristics increases flexibility when working with numbers

4. Key Mathematical Ideas
Developing Meanings for the operations
Addition and subtraction are related. Addition names the whole in terms of the parts, subtraction names a missing part
Multiplication is related to addition
Multiplication involves counting groups of like size and determining how many there are in all. Multiplicative thinking
Multiplication and Division are related. Division names a missing factor in terms of the known factor and the product.
Models can be used to solve contextual problems for all operations, regardless of the size of the numbers. They can be used to give meaning to number sentences.
Van de Walle & Louvin
Teaching Student Centred Mathematics,

5. Fifty and some more
Say a number between 50 and 100. Children respond with “50 and ____.
For 63, the response is “50 and 13”
Use other numbers that end in fifty such as 350, 650

6. Read, say, do - Peter Hughes
Say the numeral one
way, e.g. 63 is sixty three
Say the numeral in the
other way, e.g. 63 is 6 tens
and three ones
Read 63 as “sixty three” and
Sixty three as “sixty three”
Model the PV form of the
numeral e.g. 63
is 6 tens and 3 ones
Model the numeral
as ones
e.g. as 63 ones

7. Extend - read, say, do
If we have 243 lollies, how many packets of ten would we have?
How many loose ones?
If we pack ten packets into a box, how many boxes will we have, how many packets and how many loose ones?
Continue the model – crates, pallets, container and so on
Peter Hughes

8. Canon of Place Value one for ten or ten for one
the canon of place value means…
Ten ones must be exchanged for ten
Ten tens must be exchanged for one hundred
Ten hundreds must be exchanged for one thousand...

9. Modeling with Place value money
Children need to be able to verbalise the ten for one exchange in problems such as
I have $1003 and I owe my friend $7 – must follow ten for one rule.
Try the same with problems like $
Aim for children to be able to verbalise the ten for one exchange fluently.
Peter Hughes

10. Equipment for developing place value concepts
Stage
Equipment
Stage 2- 4
Concrete representation of ones
Bundling sticks, beans and containers
Counters and plastic bags,
Slavonic Abacus
Stage 5
Non representational
Place value money, place value blocks, arrow cards, place value houses
Stage 6
Number Lines
Stage 7
Decimal Fraction Mats

11. Important activities for developing place value
Early
Reading numbers as words
Move flexibly from sixty to six tens to 60
Making sense of 20 + seventy = ___ tens
Explaining where the tens are in 67, 17, 127.
Then
Reading, writing and saying numbers up to a million and beyond
Develop the concept of really big numbers – what does a thousand look like?
Familiar real world contexts for big numbers

12. Listening/Watching to learn
Ask children to write numbers such as twenty three thousand and four –
What might children write if they don’t understand?
Place Value Play Money and Place value Houses
How many tens in 124? How do you know?
How many ways can you show 243?

13. Bundling To Ten Bundles of ten board, Ice block sticks, Dice
Pipe cleaners
Roll the dice - put the number of ice block sticks in ones column - in tens frame pattern.
Roll again add ice block sticks - what happens when we get to ten? Bundle the 10 put into tens column - Part whole thinking
Record the story
Introduce to group
Play in pairs - first to 100.
Remember to unbundle too!

14. Hundred or Bust You need - a dice
Tens
Ones
Total
You need - a dice
Aim is to make 100 in seven throws or be the nearest to 100.
Children draw a table with 8 rows, 3 columns write tens, ones and total.
Roll the dice, children choose to put the number in the tens or ones column. Keep a running total.

15. Activities that reinforce place value knowledge
100 or bust
Rocket - change numbers to suit the level.
Traffic Light - book 4 page 25
Thousands book
Digit Cards - playing cards deal out three card , make the largest, smallest number you can - order them in your group. Who has the highest? Lowest? How do you know?
Staircase/Grid and a dice - strategy game. Make the highest lowest number