Place Value, Friends of 10, Partitioning 8 _Guided and Independent Investigation
(Year 1) ACMNA014, NSW MA1-4NA
Partition single-digit numbers and teen numbers in place value and non-place value.
GUIDED INVESTIGATION
Children learn
INDEPENDENT INVESTIGATION
Children investigate and explain independently over many lessons at their
how to investigate the concept by following teacher’s instructions until they
are ready to investigate the concept independently.
current level of understanding informing both themselves and the teacher of their current
level of understanding.
Resources: numeral cards, pack of playing cards, connecting blocks, pencil, paper
What language could we use to ask
questions and explain?
What could we do?
Children:
1. select a single-digit numeral card as guided
by the teacher
1. make a tower of the corresponding number
of blocks
2. repeatedly partition the tower into 2 parts,
recording the partitions
3. identify any partitions that have commuted
1. make a teen number using playing cards as
guided by the teacher
2. make a tower of the corresponding number
of blocks
3. repeatedly partition the tower into 2 parts,
recording the partitions
4. identify any partitions that use place value
 What number did we select?
 How could we partition this
number?
 How could we record the partitions?
 Have any of the partitions swapped
places?
 What teen number did we make?
 How could we partition this
number?
 How could we record the partitions?
 Do any of the partitions use place
value?
REFLECTION
Before, during and after lessons, children discuss then record responses to reflection
questions to inform themselves and the teacher of their current level of understanding
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What language could we use to
explain?
What could we do?
Children:
1. sit in pairs
2. select a single-digit numeral card that is neither too
easy nor too challenging
3. make a tower of the corresponding number of blocks
4. repeatedly partition the tower into 2 parts, recording
the partitions
5. identify any partitions that have commuted
1.
2.
3.
4.
make a teen number using playing cards as guided
by the teacher
make a tower of the corresponding number of blocks
repeatedly partition the tower into 2 parts,
recording the partitions
identify any partitions that use place value
 My number is…
 I partitioned my number
into …
 I recorded my partition
as …
 These partitions have
swapped places.
 My teen number is …
 I partitioned my number
into …
 This partition uses place
value because …
What is partitioning? How can we partition a number? Can all numbers be partitioned?
How can we partition a teen number using place value?
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CONGRUENT INVESTIGATIONS
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative
assessment data for both the child and the teacher.
‘Doing’ mathematics is not enough and is not a good indicator of understanding.
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts at
their current level of understanding.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop resilience
and deep understanding, If children knew what it was they were doing, it would be called learning!
Create single digit tower,
repeatedly partition into 2 parts,
commute and explain.
 In pairs, each child selects a single-digit number and makes a tower out of the corresponding number of connecting
blocks. Each child repeatedly partitions the tower into 2 parts, recording and explaining each partition. Children who are
ready also explain commutativity by identifying that partitions whose parts have swapped places are the same partitions.
Children who have not demonstrated understanding of levels 1 to 20 in Early Counting and Grouping Concepts, will
investigate these concepts, while other children are investigating this Friends of 10 concept.
Create teen digit tower,
repeatedly partition into 2 parts,
commute and explain.
 In pairs, each child makes a teen number and makes a tower out of the corresponding number of connecting blocks.
Each child repeatedly partitions the tower into 2 parts, recording and explaining each partition. Children who are ready
also explain place value of teen numbers by identifying which partitions have been created using place value. Children
who have not demonstrated understanding of levels 1 to 20 in Early Counting and Grouping Concepts, will investigate
these concepts, while other children are investigating this Friends of 10 concept.
Partition towers into various
parts, identifying if parts are
equal or unequal.
Partition counters into various
parts, identifying if parts are
equal or unequal.
 In pairs, each child has a tower of connecting blocks. Each child partitions the towers into 2 parts, 3 parts, 4 parts, …,
recording each partition. Children identify whether the parts are equal or unequal.
 In pairs, each child has a group of counters. Each child partitions the counters into 2 parts, 3 parts, 4 parts, …, recording
each partition. Children identify whether the parts are equal or unequal.
 In small groups, children have a tower of connecting blocks. They take turns to partition the tower, describing their
partition as equal or unequal parts, place value or not place value parts.
 As children develop their understanding of partitioning single-digit and teen numbers, they use partitioning to add and
subtract in Addition and Subtraction 6, 7, 8 and 9.
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Email: [email protected]
Twitter: @learn4teach
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Facebook: A Learning Place
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Investigating Partitioning Single-digit Numbers and Teen Numbers
PLACE VALUE FRIENDS OF 10 PARTITIONING 8 Partition single-digit numbers and teen numbers in place value and non-place value.
Select a card to make a single-digit number that is neither too easy nor too
challenging to partition.
Select the corresponding number of connecting blocks and make a tower.
Partition the tower into 2 parts.
Record the parts.
Swap the places of the parts.
Record the parts.
Explain that the parts can change places.
Put the tower back together.
Repeat.
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Investigating Partitioning Single-digit Numbers and Teen Numbers
PLACE VALUE FRIENDS OF 10 PARTITIONING 8 Partition single-digit numbers and teen numbers in place value and non-place value.
Select an Ace and another card to make a teen number that is neither too easy nor
too challenging to partition.
Select the corresponding number of connecting blocks and make a tower.
Partition the tower into 2 parts.
Record the parts.
Put the tower back together.
Repeat.
Identify which partitions use place value and which partitions do not use place
value.
http://www.alearningplace.com.au
Investigating Partitioning Single-digit Numbers and Teen Numbers
PLACE VALUE FRIENDS OF 10 PARTITIONING 8 Partition single-digit numbers and teen numbers in place value and non-place value.
Select a card to make a single-digit number that is neither too easy nor too
challenging to partition.
Select the corresponding number of connecting blocks and make a tower.
Partition the tower into 2 parts or 3 parts or 4 parts ...
Record the parts.
Identify which parts are equal or unequal.
Put the tower back together.
Repeat.
http://www.alearningplace.com.au
Investigating Partitioning Single-digit Numbers and Teen Numbers
PLACE VALUE FRIENDS OF 10 PARTITIONING 8 Partition single-digit numbers and teen numbers in place value and non-place value.
Select a card to make a single-digit number that is neither too easy nor too
challenging to partition.
Select the corresponding number of counters and make a pile.
Partition the pile into 2 parts or 3 parts or 4 parts ...
Record the parts.
Identify which parts are equal or unequal.
Put the pile back together.
Repeat.
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