Multiplication and Division 18, Patterns and Algebra 23_Guided and Independent Investigations
(Year 4) ACMNA074, NSW MA1-4NA
Patterns skip counting, identifying rule and terms through multiplication, describing rule and creating the number pattern.
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: pencil, paper
What could we do?
What language could we use to ask
questions and explain?
1. create a number pattern by
starting at a multiple of the
number, and repeatedly
adding or subtracting as
guided by the teacher
2. identify how the pattern
repeats
3. identifying a rule and terms
through multiplication
 Is this a number pattern? How do
you know?
 How does the pattern repeat?
 How could we record the pattern
on a number line?
 How could we describe the
number pattern in a rule that uses
multiplication?
 How could we use the rule to find
terms in the number pattern?
4. describe a rule using
multiplication
5. create a number pattern using
the rule
 How could we describe a rule
using multiplication?
 How could we create a number
pattern using the rule?
Children:
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
What could we do?
1.
2.
3.
4.
5.
6.
Children:
sit in pairs
create a number pattern by starting at
a multiple of the number, and
repeatedly adding or subtracting as
guided by the teacher
identify how the pattern repeats
identifying a rule and terms through
multiplication
describe a rule using multiplication
create a number pattern using the rule
What language could we use to explain?
 This is a number pattern because we are
repeatedly adding / subtracting ...
 The part that repeats is adding /
subtracting ...
 The terms increase / decrease by ...
 I recorded the pattern on a number line.
 A rule using multiplication that describes
this number pattern is …
 I could use the rule to find terms in the
number pattern by …
 My rule using multiplication to describe
a number pattern is …
 The number pattern I created following
the rule is …
What is a number pattern?
How can we identify a rule using multiplication to describe a number pattern?
How can we describe rules using multiplication to create number patterns?
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Email: [email protected]
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1
If you can’t explain it
simply, you don’t
understand it well enough.
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.
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,
 In pairs, children record a number pattern skip counting forwards by 2, 3, 4, 5, 6, 7, 8, 9 or 10. Children identify whether the
terms are multiples, or multiples plus or minus a number. They use this to describe a rule using multiplication. They use the rule
to find terms in the number pattern.
For example, 3, 6, 9, 12, … is a number pattern with multiples of 3 so the rule could be ‘multiply the term by 3’.
For example, 4, 7, 10, 13, … is a number pattern with non-multiples of 3 so the rule could be ‘multiply the term by 3, then add 1’
 In pairs, children record a number pattern skip counting backwards by 2, 3, 4, 5, 6, 7, 8, 9 or 10. Children identify whether the
terms are multiples, or multiples plus or minus a number. They use this to describe a rule using multiplication. They use the rule
to find terms in the number pattern.
For example, 21, 18, 15, 12, … is a number pattern with multiples of 3 so the rule could be ‘multiply the term by 3 and subtract
from 24’.
For example, 22, 19, 16, 13, … is a number pattern with non-multiples of 3 so the rule could be ‘multiply the term by 3, then
subtract from 25’
 In pairs, children record a rule using multiplication. They create a number pattern that follows the rule.
For example, the rule could be ‘multiply the term by 6’ and the pattern would be 6, 12, 18, 24, …
For example, the rule could be ‘multiply the term by 6, then add 2’ and the pattern would be 8, 14, 20, 26, …
For example, the rule could be ‘multiply the term by 6 then subtract from 48’ and the pattern would be 42, 36, 30, 24, …
For example, the rule could be ‘multiply the term by 6, then subtract from 52’ and the pattern would be 46, 40, 34, 28, …
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Investigating Number Pattern Rules using Multiplication
MULTIPLICATION AND DIVISION 18 PATTERNS AND ALGEBRA 22 Identifying the rule and terms through multiplication,
and from any point on the number line, identifying the rule, describing a rule using multiplication or division and
creating the number pattern
Record a number pattern skip counting forwards by 2, 3, 4, 5, 6, 7, 8, 9 or 10.
Identify whether the terms are multiples, or multiples plus or minus a number.
Use this to describe a rule using multiplication.
Use the rule to find terms in the number pattern.
For example, 3, 6, 9, 12, … is a number pattern with multiples of 3 so the rule could be ‘multiply
the term by 3’.
For example, 4, 7, 10, 13, … is a number pattern with non-multiples of 3 so the rule could be
‘multiply the term by 3, then add 1’
http://www.alearningplace.com.au
Investigating Number Pattern Rules using Multiplication
MULTIPLICATION AND DIVISION 18 PATTERNS AND ALGEBRA 22 Identifying the rule and terms through multiplication,
and from any point on the number line, identifying the rule, describing a rule using multiplication or division and
creating the number pattern
Record a number pattern skip counting backwards by 2, 3, 4, 5, 6, 7, 8, 9 or 10.
Identify whether the terms are multiples, or multiples plus or minus a number.
Use this to describe a rule using multiplication.
Use the rule to find terms in the number pattern.
For example, 21, 18, 15, 12, … is a number pattern with multiples of 3 so the rule could be
‘multiply the term by 3 and subtract from 24’.
For example, 22, 19, 16, 13, … is a number pattern with non-multiples of 3 so the rule could be
‘multiply the term by 3, then subtract from 25’
http://www.alearningplace.com.au
Investigating Number Pattern Rules using Multiplication
MULTIPLICATION AND DIVISION 18 PATTERNS AND ALGEBRA 22 Identifying the rule and terms through multiplication,
and from any point on the number line, identifying the rule, describing a rule using multiplication or division and
creating the number pattern
Record a rule using multiplication.
Create a number pattern that follows the rule.
For example, the rule could be ‘multiply the term by 6’ and the pattern would be 6, 12, 18, 24, …
For example, the rule could be ‘multiply the term by 6, then add 2’ and the pattern would be 8, 14,
20, 26, …
For example, the rule could be ‘multiply the term by 6 then subtract from 48’ and the pattern
would be 42, 36, 30, 24, …
For example, the rule could be ‘multiply the term by 6, then subtract from 52’ and the pattern
would be 46, 40, 34, 28, …
http://www.alearningplace.com.au