MULTIPLICATION AND DIVISION 5_INVESTIGATION AND REFLECTION
(Year 2) ACMNA026, ACMNA031, NSW MA1-6NA MA1-8NA
Divide into equal rows (arrays), describe using division and multiplication, finding total using skip counting and repeated addition.
GUIDED AND INDEPENDENT INVESTIGATIONS and REFLECTION
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.
Children investigate and explain independently over many lessons at just beyond their current level of understanding, informing
both themselves and the teacher of their current level of understanding. It is during independent investigation that deep understanding and
metalanguage develops.
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 wouldn’t be called learning!
GUIDE children through the INVESTIGATION process until they are ready to investigate INDEPENDENTly.
Children DISCUSS then RECORD their response to the REFLECTION question.
Teaching Segment and Video 1:
2 division number sentences.
These investigations and reflections are directly linked to Explicit Teaching, and also appear on the Explicit Teaching Plan. Instructions for students
appear on this PDF, on the corresponding Video and on the Explicit Teaching PowerPoint.

In pairs, children divide counters into an array, describing how they divided in 2 division number sentences.
Reflection: How can we divide counters into an array?

In pairs, children divide counters into an array, describing how they divided in 2 division number sentences. They
describe the array in 2 multiplication number sentences. Reflection: How can we divide counters into an array,
then describe the array using multiplication?
Teaching Segment and Video 2:
2 multiplication number
sentences.
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Teaching Segment and Video 3:
Skip count.

In pairs, children collect some counters and divide them into an array. They use skip counting to find the total
number of counters. They describe how you created their array in 2 division number sentences. They describe
their array in 2 multiplication number sentences. Reflection: How can we divide counters into an array to help us
to count them using skip counting?
More investigations.
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.
Multiple carpark arrays.

In pairs, children are told there are 12 cars in a car park parked in an array. Children make arrays using 12
counters to represent the 12 cars. They record skip or rhythmic counting, and 2 division and 2 multiplication
number sentences to describe the array. Reflection: How can we divide into an array?
Carpark array.

In pairs, children are told that cars are parked in 4 rows of 5. They make the array using counters to represent
the cars and use skip counting or multiplication of the number of rows by the number in each row to work out
the number of cars. Reflection: How can we divide into an array?
Multiple concert array.

In pairs, children are told that 15 children want to sit on chairs to watch a show. Children make arrays using 15
counters to represent the 15 chairs. They record 2 division and 2 multiplication number sentences to describe
the array. They explain which array would be best to watch a show. Reflection: How can we divide into an array?

In pairs, children are told that some people sit in 5 rows of 6 to watch a show. Children use skip counting or
multiplication of the number of rows by the number in each row to work out the number of people. Reflection:
How can we divide into an array?
Rows of an array.

In pairs, children each make the top row and side row of an array. They use the array structure
and skip counting to work out the total number of counters in the array. They show their array
to their friend who also uses the array structure and skip or rhythmic counting to work out the
number of counters needed altogether to complete the array. They share their strategy for
working it out. Reflection: How can we divide into an array?
Division number sentence array.

In pairs, children are given a division number sentence which they represent in an array. They record their array
and number sentence. They then record another division number sentence and 2 multiplication number
sentences to describe the array. Reflection: How can we divide into an array?
Concert array.
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2
Multiplication number sentence
array.

In pairs, children are given a multiplication number sentence which they represent in an array. They record their
array and number sentence. They then record another multiplication number sentence and 2 division number
sentences to describe the array.
PROBLEM SOLVING directly linked to explicit teaching, investigations and reflections
Problems allow children to investigate concepts in new and varied situations. Any problem worth solving takes time and effort
– that’s why they’re called problems!
Problems are designed to develop and use higher order thinking. Allowing children to grapple with problems, providing minimal
support by asking strategic questions, is key. Differentiating problems allows children to solve simpler problems, before solving
more complex problems on a concept.
Problems may not always be solved the first time they are presented – or at all. The focus of problem solving is the development
of problem solving understanding and capacity – not mastery! Returning to a problem after further learning, develops both
resilience and increased confidence as children take the necessary time and input the necessary effort.
After solving problems, children also create their own problems.
Create 3 levels of a problem. GUIDE children through the first level using the problem solving steps. Allow children to investigate the second level
with friends, with minimal guidance. Allow children to investigate the third level INDEPENDENTly. Children create their own problem.
Teaching Segment and Video 1:
Chocolates 1
Teaching Segment and Video 2:
Chocolates 2
Teaching Segment and Video 3:
Stickers
These problems are directly linked to Explicit Teaching, are embedded in the Explicit Teaching Plan, and appear on the Explicit Teaching PowerPoint.
These, and more problems, appear as blackline masters on the Problem Solving PDF and are differentiated on the Problem Solving PowerPoint.

20 chocolates were arranged in an array in a box. What might the array have looked like? How could you
describe the array using division? (20 ÷ 2 = 10, 20 ÷ 10 = 2, 20 ÷ 4 = 5, 20 ÷ 5 = 4)

20 chocolates were arranged in an array in a box. What might the array have looked like? How could you
describe the array using multiplication and division?
(2 x 10 = 20, 10 x 2 = 20, 20 ÷ 2 = 10, 20 ÷ 10 = 2, 4 x 5 = 20, 5 x 4 = 20, 20 ÷ 4 = 5, 20 ÷ 5 = 4)

Jillian placed some stickers in a book. How many stickers did she put in her book?
(3, 6, 9, 12, 15 or 3 x 5 = 15 or 5 x 3 = 15 or 5, 10, 15)
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Email: [email protected]
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YouTube: A Learning Place A Teaching Place
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3
Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Select some counters.
Divide the counters into an array of equal rows, for example,
Record your array.
Describe how you created your array in a division sentence, for example, 12 ÷ 2 = 6
Reflection: How can we divide counters into an array?
Problem Solving
20 chocolates were arranged in an array in a box.
What might the array have looked like?
How could you describe the array using division?
Hint: Change the number of chocolates, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Select some counters.
Divide the counters into an array of equal rows, for example,
Record your array.
Describe how you created your array in a division sentence, for example, 12 ÷ 2 = 6
Describe your array in a multiplication sentence, for example, 2 x 6 = 12
Turn the array, for example,
Describe how you created your array in a different division sentence, for example,
12 ÷ 6 = 2.
Describe your array in a multiplication sentence, for example, 6 x 2 = 12
Reflection: How can we divide counters into an array, then describe the array using
multiplication?
Problem Solving
20 chocolates were arranged in an array in a box.
What might the array have looked like?
How could you describe the array using
multiplication and division?
Hint: Change the number of chocolates, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Select some counters.
Divide the counters into an array of equal rows, for example,
Record your array.
Use skip counting to find the total number of counters, for example, 2 4 6 8 10 12
Describe how you created your array in 2 division number sentences, for example,
12 ÷ 2 = 6 and 12 ÷ 6 = 2
Describe your array in 2 multiplication number sentences, for example, 2 x 6 = 12
and 6 x 2 = 12
Reflection: How can we divide counters into an array to help us to count them using
skip counting?
Problem Solving
Jillian placed some stickers in a book.
How many stickers did she put in her book?
Hint: Change the number of stickers, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
There are 12 cars in a car park parked in an array.
Use counters to make all possible arrays
Record multiplication number sentences for each array you make.
Record division number sentences for each array you make.
Reflection: How can we divide into an array?
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Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Cars are parked in 4 rows of 5.
Make the array using counters to represent the cars.
Use skip counting or multiplication of the number of rows by the number in each
row to work out the number of cars.
Reflection: How can we divide into an array?
http://www.alearningplace.com.au
Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
15 children want to sit on chairs to watch a show in equal rows.
Use counters to make all possible arrays
Record multiplication number sentences for each array you make.
Record division number sentences for each array you make.
Explain which array you think will be the best to arrange chairs to watch a show.
Reflection: How can we divide into an array?
http://www.alearningplace.com.au
Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Some people sit in 5 rows of 6 to watch a show.
Make the array using counters to represent the people.
Use skip counting or multiplication of the number of rows by the number in each
row to work out the number of people.
Reflection: How can we divide into an array?
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Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Sit with a friend.
Each of you make the top row and side row of an array, for example,
Show your array to your friend who also uses the array structure and skip or
rhythmic counting to work out the number of counters needed altogether to
complete the array.
Share your strategy for working it out.
Reflection: How can we divide into an array?
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Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Select cards to make a division number sentence, for example, select 1, 5 and 3,
make the division number sentence, 15 ÷ 3.
Make an array that the division number sentence is describing.
Record the array.
Record another division number sentence and 2 multiplication number sentences to
describe the array.
Reflection: How can we divide into an array?
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Investigating Arrays
MULTIPLICATION AND DIVISION 5 Divide into equal rows (arrays), describe using multiplication, skip count, repeated addition and
subtraction, even numbers.
Select cards to make a multiplication number sentence, for example, select 3 and 4,
make the multiplication number sentence, 3 x 4 or 4 x 3.
Make an array that the multiplication number sentence is describing.
Record the array.
Record another multiplication number sentence and 2 division number sentences to
describe the array.
Reflection: How can we divide into an array?
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