Working with tens, ones
and hundreds in Stage 1
Peter Gould, 2016
From counting to place value
Students develop the connection
between number words and quantities,
and then connect both the spoken
number words and quantities to the
written symbols.
one
two
three
3
Peter Gould, 2016
From counting to place value
Children’s initial understanding of
numbers is as the things produced
by a count.
Twelve is initially just the twelfth
word said when counting.
Peter Gould, 2016
From last term
What was Key message 1?
Students need to move from thinking
of numbers as part of a sequenced
count to recognising tens and
hundreds within numbers.
16 is 1 ten and 6, not just the
number after 15.
Peter Gould, 2016
From counting to place value
Counting:
How many of your Kindergarten students
(what percentage) cannot correctly count to at
least 13?
Numerals:
How many of your Year 1 students (what
percentage) cannot identify all numerals to 20?
Does it matter?
Peter Gould, 2016
Introducing numerals
87% of children can count to 10 when they
start school but only 57% can identify the
corresponding symbols.
Approximately one-and-a-half times as many
children can count to 10 as can identify the
corresponding symbols.
Oral counting develops before facility with
the written symbols.
Peter Gould, 2016
Words and symbols
Do we respond to numerals by reading
them or interpreting them?
Try this with Year 2
What are these numbers?
1001
101
Many students
identified 1001 as
101 (59% for year 2).
1010
110
Recognise, model, represent and order numbers to at least
1000 (ACMNA027).
Peter Gould, 2016
Encourage interpreting
Do we respond to numerals by reading
them or interpreting them?
Try this with Year 2
Tell me a number that is larger than…
1001
101
1010
110
Peter Gould, 2016
The numeral pathway
In Flash Anzan, a
Japanese competition,
15 numbers are
flashed consecutively
on a giant screen.
Each number is
between 100 and 999.
The challenge is to
add them up.
Peter Gould, 2016
The numeral pathway
796
290 The video shows
15 numbers in
856 1.85 seconds.
473
318
650
254
680
359
How many did
295 you see?
132
146
789
502
317
What is the total?
6857
Peter Gould, 2016
The numeral pathway
Two Japanese nineyear-olds play the
word game
shiritori, while
SIMULTANEOUSLY
adding 30 numbers
flashed in 20
seconds.
They are using a
technique called
"anzan", which is to
imagine an abacus
in your head.
http://youtu.be/_vGMsVirYKs)
Peter Gould, 2016
What does it mean?
Chinese based counting
systems are more
transparent to place
value, use shorter words
and have an advantage
in the acquisition and
elaboration of the
counting system…
but this doesn’t explain
what you just witnessed!
Peter Gould, 2016
What does it mean?
Although students connect both the spoken
number words and quantities to the written
symbols…
number words and symbols are different.
“I don't see how you can represent whatever
that number was on a mental abacus faster
than you can say it.” (Brian Butterworth).
The symbol system plays an increasingly
important role as students develop.
Peter Gould, 2016
Using number to quantify
Two processes are involved with learning
number - acquisition and elaboration.
1. Acquisition - Refers to learning the
ordered sequence of number words and
learning the names of numerals.
2. Elaboration - Refers to being able to
continue the counting sequence from
any point (e.g. Number word after) and
using the structure in numerals.
Peter Gould, 2016
Interpreting symbols 53 – 27
Year 3
Peter Gould, 2016
From last term
What was Key message 2?
We need to teach place value
through adding and subtracting
two-digit and three-digit numbers.
Neither before or after…with.
Peter Gould, 2016
Questioning multiples
of ten
Peter Gould, 2016
Prompting
Promoting place value
37
+ 25
Question
Before you work out the
question above, will the answer
be more than 60 or less than
60?
Why do you think that?
I decided to change the heading
Peter Gould, 2016
Using a comparison
This a multiple of ten comparison.
Just as addition is usually easier than
subtraction, subtraction comparisons
may require a little more thought than
those used in addition.
Peter Gould, 2016
Promoting place value
54 – 38
Question
Before you work out the
question above, is the answer
more than 20 or less than 20?
Why do you think that?
Peter Gould, 2016
Promoting place value
75 – 57
Question
Before you work out the
question above, is the answer
more than 20 or less than 20?
Why do you think that?
Peter Gould, 2016
What is your question?
Look at this question.
54 – 28
Before you work it out…
Is the answer more than 30
q
or less than 30
q?
Why do you think that?
Peter Gould, 2016
Revisiting One is a Snail…
http://www.earlyactionforsuccess.com.au/mathsblock/interactive.html
Sayre, A. & Sayre, J.
Peter Gould, 2016
Units of 10 and 1
1 is a snail
10 is a crab
Building
composite
units of 10.
What would 3 crabs be?
How many crabs is 50?
Reversible
What would 3 crabs and a snail be?
Peter Gould, 2016
20 feet, what could I see?
Units of 10 and 1
Peter Gould, 2016
Units in the teens
The numbers from 11 to 19 (and often
beyond) are learnt initially as number
words and not composite units.
We need to provide learning
experiences that require students to
see the ten in these numbers.
Peter Gould, 2016
Making fourteen
Peter Gould, 2016
Units in the teens
I see 12 feet, someone walked away, 2 feet left.
Who walked away?
Peter Gould, 2016
12 feet, 2 remain - who left?
Select A Year 1 mathematics lesson
on the interactive version of the guidelines
Video 3: Who walked away?
Peter Gould, 2016
I can see 12 feet. Who can I see?
Using
images
A Kindergarten response
Peter Gould, 2016
12 feet. Who can I see?
Year 1
Peter Gould, 2016
Stage 1 syllabus
•use the equals sign to record
equivalent number sentences involving
addition, and to mean ‘is the same as’,
rather than as an indication to perform
an operation, e.g. 5 + 2 = 3 + 4
check given number sentences to
determine if they are true or false and
explain why, e.g. ‘Is 7 + 5 = 8 + 4 true?
Why or why not?’
Addition and Subtraction 1
Peter Gould, 2016
Mark it off
2
3
4
5
6
7
8
9
10
11
12
Roll a pair of dice.
Cross off the total you roll.
Continue until all the numbers are crossed off.
What if…
Peter Gould, 2016
Put it down
2=
7=
3=
8=
4=
9=
5=
10 =
6=
11 =
Roll a pair of
numeral dice.
Record the sum
next to the total
you roll.
What if you roll a
different
combination?
12 =
Peter Gould, 2016
Make 20
Is 13 a
better
target?
manipulates, sorts, represents,
describes and explores twodimensional shapes, including…
pentagons, hexagons and
octagons MA1-15MG
Roll three
dodecahedral dice.
First to roll 20 wins.
Peter Gould, 2016
23 feet, some walked away
Challenges of
symbolising
Peter Gould, 2016