Math’s Buddy name: Patrick
Grade: One
Domain
G.P.(#)
Growth Point (description)
Counting
1
Place Value
Addition &
Subtraction
Multiplication
& Division
1
Rote counts the number sequence to at least 20, but is not yet able
to reliably count a collection of that size.
Can read, write, interpret and order single digit numbers.
1
Counts all to find the total of two collections
1
To find the total in a multiple group situation, refers to individual
items only.
Insights
The mathematics assessment interview completed on the 21st of March 2011 shows that Patricks’
“zone of proximal development” is currently placed in growth point one for counting, growth
point one for place value, growth point one for addition and subtraction growth point one moving
into growth point two for multiplication and division. Patrick enjoys mathematics and recalls that
the majority of his mathematical learning is through work books and sheets. Including hands on
activities using visual aids, small group work and peer discussions could be highly beneficial to
further Patricks’ mathematical knowledge.
Patrick stated in question 1.d that twenty-nine was one less then twenty three, however in
question 3.b he was successful in stating that 55 was one less then 56 without the access to
counters. It seems that Patrick does not understand the concept of visual quantities, therefore he
was unable to take one away from the group of objects in front of him. It appears that Patrick
may have gone back to his original estimate then removed one. Using subitising activities and
building quantities may build up Patricks understanding towards constructing the ability to
recognise visual quantities.
Patrick showed confidence in place value relating to one digit numbers however his
understanding of two digit numbers was limited. Misconceptions that Patrick had relating to two
digit numbers including question 9.a, where he had difficulty matching the correct digit and
name writing fifteen as fifty-one. Patrick ordered the two digit numbers in question 10 in the
correct sequence however pointed to the opposite ends when asked the smallest and largest
number. Introducing number lines or bead strings to Patrick using one and two digit numbers
could introduce the skills required to understand the value of units.
Patrick seemed to guess many of his answers related to addition and subtraction; he found it
difficult to give answers to questions without counting on his fingers. When asked if he could
use a different strategy other then estimation Patrick responded “no, I always just guess”.
Patricks’ limited understanding relating to concepts of qualities impact on his ability to combine
two quantities.
Patrick is close to moving into growth point two for multiplication and division, however he used
a non preferred strategy in question 27.b and counted all by ones, when asked if he could do this
another way he skip counted, with additional practice he may begin to automatically recognise
strategies that are more effective.
Teaching Implications
Patrick would benefit from visual and hands on learning experiences in counting, place value,
addition and subtraction, multiplication and division. Activities that could be adapted to some of
these domains include:
Subitising
Counting- Recognising single digit numbers by looking at it quickly and connecting the position
of the object to the correct number.
Addition and subtraction- Once Patrick can recognise the numbers 1-10 addition and
subtraction can be introduced by showing two subitised numbers.
Multiplication and division- Subitising can be implemented to multiplication and division with
small one and two digit numbers for Patrick.
Number line/ bead string
Counting- bead string counting by either 1,2,4,5 or 10 to a given number.
Addition and subtraction- Adding and subtracting from the number line by more then one
number at a time using the strategy of count on not count all.
Place value- Practicing putting numbers in the correct order using one and two unit numbers
then moving onto three digit numbers and identifying the smallest and largest on the number line
and where they would be placed.
Two minute dice games
Counting- The student roles the dice and collects that amount of counters they have rolled, they
continue this until the time is up, and then count the whole quantity at the end.
Addition and subtraction- The two minute dice game can incorporate addition as well as
counting, however the game could be used for subtraction where the child starts with a certain
amount of counters and subtracts from that amount every time they role the dice.
Multiplication and division- The two minute dice game could incorporate both multiplication
and division, however this would not be a preferred implementation with Patrick as the numbers
may become too high.
Place value- After the total has been counted Patrick could use paddle pop sticks to show how
many one digit numbers and bundles of ten he has.
Memory game:
Counting- using the concept of the number triad to match the number word, collection and
symbol.
Addition and subtraction- play the game in pairs, each child picks up two cards and adds or
subtracts the number depending on the focus in that lesson. The student with the highest card for
addition or the lowest number for subtraction at the end of the game wins.
Multiplication and division- The same game as addition and subtraction could be implemented
for multiplication and division.
Ten facts
Counting- Game of snap with numbers that add up to ten.
Addition and subtraction- Once Patrick learns the concept of ten facts he may be able to adapt
the same game using addition and subtraction.
Multiplication and division- Once Patrick learns the concept of ten facts he may be able to
adapt the same game using multiplication and division.