Addition and Subtraction 11 Patterns Algebra 6_Guided and Independent Investigations
(Year 1) ACMNA015, NSW MA1 5NA, MA1 8NA
Add 3 or more numbers using associativity.
GUIDED INVESTIGATION
Children learn
how to investigate the concept by following teacher’s instructions until they
are ready to investigate the concept independently.
INDEPENDENT INVESTIGATION
Children investigate and explain independently over many lessons at their
current level of understanding informing both themselves and the teacher of their current
level of understanding
Resources: Playing cards, pencil, paper
What could we do?
Children:
1. sit in pairs
2. select 3 cards that include 2 that
are friends of 10, to add using the
associative property, as guided by
the teacher
3. record their number sentence
4. record their solution strategy
What language could we use to ask
questions and explain?
 What number did you select?
 What does your number
sentence say?
 How did you record your
strategy?
 How did you work it out?
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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Email: [email protected]
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What language could we use to
explain?
What could we do?
Children:
1. sit in pairs
2. select 3 cards that include 2 that are
friends of 10, to add using the
associative property, that are neither
too challenging, nor too easy
3. record their number sentence
4. record their solution strategy
5. explain their solution strategy to
their friend
6. repeat
 My number is ...
 My number sentence
says ...
 I worked it out by ...
 I recorded my strategy as ...
What is addition?
Do we have to add numbers in the order they are recorded?
How can we use friends of 10 to add 3 numbers?
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CONGRUENT INVESTIGATIONS
If you can’t explain it
simply, you don’t
understand it well enough.
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.
Anyone who has
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
never made a
at their current level of understanding.
mistake has never
tried anything new.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding,

Children place 6 cards in a row. They select 3 cards to add, making sure that 2 of them are friends of 10. They add them
together, recording their addition on a number line. They explain how they added the numbers to a friend.

In pairs, children select 3 cards to add. Each child adds the numbers, then compares their strategies with their friend.

Children place cards in a three-by-three array. They select 3 cards to add, making sure 2 of them are friends of 10 or a known
sum. They add them and explain their strategy to a friend.

In pairs, children select 3 cards. Each child adds them in a different order. They compare their recordings, identifying that they
both ended with the same number. They discuss which order they thought was most efficient.

In pairs, children place 36 cards in a 3 x 3 array with 4 cards in each pile. Children take turns to pick up 2 cards that are friends
of 10, plus one more card, and state the total. For example, a child mat pick up 2 and 8 as their friends of 10, and the 6 to
make 16.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
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Investigating Adding using the Associative Property
ADDITION AND SUBTRACTION 11 PATTERNS AND ALGEBRA 6 Adding 3 or more numbers using the associative
property
Place 6 number cards in a row.
Select 3 cards to add, making sure that 2 of them are friends of 10.
Add them together, recording your addition on a number line.
Explain how you added the numbers to a friend.
http://www.alearningplace.com.au
Investigating Adding using the Associative Property
ADDITION AND SUBTRACTION 11 PATTERNS AND ALGEBRA 6 Adding 3 or more numbers using the associative
property
Sit with a friend.
Select 3 cards to add.
Each of you add the numbers.
Compare your strategy with your friend.
http://www.alearningplace.com.au
Investigating Adding using the Associative Property
ADDITION AND SUBTRACTION 11 PATTERNS AND ALGEBRA 6 Adding 3 or more numbers using the associative
property
Place cards in a three-by-three array.
Select 3 cards to add, making sure 2 of them are friends of 10 or a known sum.
Add the numbers.
Explain your strategy to a friend.
http://www.alearningplace.com.au
Investigating Adding using the Associative Property
ADDITION AND SUBTRACTION 11 PATTERNS AND ALGEBRA 6 Adding 3 or more numbers using the associative
property
Select 3 cards.
Each of you add them in a different order.
Compare your recordings, identifying that you both had with the same total.
Discuss which order you think is the most efficient.
http://www.alearningplace.com.au
Investigating Adding using the Associative Property
ADDITION AND SUBTRACTION 11 PATTERNS AND ALGEBRA 6 Adding 3 or more numbers using the associative
property
Sit with a friend.
Place 36 cards in a 3 x 3 array with 4 cards in each pile.
Take turns to pick up 2 cards that are friends of 10, plus one more card.
State the total.
http://www.alearningplace.com.au