MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18_PROBLEM SOLVING
(Year 3) ACMNA056, ACMNA057, ACMNA051, NSW MA2-6NA, MA2-8NA
Multiply and divide by 3 using the distributive property and the relationship between division and fractions.
PROBLEM SOLVING
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:
Multiply by 3 (i)
These problems are directly linked to Explicit Teaching and appear on this PDF, are embedded in the Explicit Teaching Plan, appear on the Investigation
PDF and the Explicit Teaching PowerPoint, and are differentiated into 3 levels on the Problem Solving PowerPoint.

The teacher made 3 teams of 8 children. How many children altogether? (32)
Multiply by 3 (ii)
Teaching Segment and Video 2:
Divide by 3 (i)

The school had 3 classes of 28 children. How many children altogether? (112)

27 children are divided into 3 teams. How many in each team? (8)
Divide by 3 (ii)

The school divided 87 children into 3 classes. How many children in each class? (24)
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More problems
These problems are not directly linked to Explicit Teaching and appear here and are differentiated into 3 levels on the Problem Solving PowerPoint.
Show

A group of children paid $3 each to see a show. Altogether the group paid $24. How many children were in the
group? (8)
Cupcakes

Cupcakes are sold in boxes of 3. Jemima wants to give one cupcake to each of her 27 classmates. What is the
least number of boxes that Jemima needs? (9)
Tomato plants

In a garden, there are 3 tomato plants for every 1 lettuce plant. There are 4 lettuce plants. How many tomato
plants are in the garden? (12)
Lawns

Roland is paid the same amount for each lawn he mows. He gets paid $18 for mowing 3 lawns. How many lawns
does he need to mow to get paid $24? (4)
Pizzas

Jenna makes 12 pizzas. She puts them on 3 trays. What number sentence shows how Jenna could work out the
number of pizzas on each tray? (12 ÷ 3 = 4 or 3 x 4 = 12 or 4 x 3 = 12)
Apples 1

Toni bought 3 apples. Apples cost 30 cents each. How much did Toni have to pay? (90c)
Classes

3 classes each have 24 children and 1 class has 25 children. How many children altogether? (72 + 25 = 97)
Number cards 1

There are 2 number cards.
x 3 = 39 (13)
Number cards 2

Jenna has 2 cards.
Jenna make?
2
3
3
1
Use the number cards to make this number sentence true:
She makes a two-digit number and multiplies it by 3. What products could
(69 and 96)
Budgie and parrot

A budgie is about 13 cm long. A parrot is about 3 times as long as a budgie. About how long is a parrot? (39 cm)
Pencils

A child has 6 packets of pencils. There are 4 pencils in each small packet. There are 10 pencils in each large
packet. The child has 3 small packets. How many pencils does he have altogether? (3 x 4 = 12, 3 x 10 = 30, 12 + 30 =
42)
Number sentences

Sophie recorded this true number sentence. 6 x 3 = 18. What other number sentence is also true? 18 x 6 = 3, 3 x
6 = 18, 6 x 18 = 3 (3 x 6 = 18)
Beads

Mary had 27 beads. Tom had a third as many. How many beads did Tom have? (9)
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Forks

A fork is 9 centimetres long. 4 forks are the same length as 2 chop
sticks. How many centimetres long is 1 chop stick? (20)
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Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
The teacher made 3 teams of 8 children.
How many children altogether?
Hint: Change the number of children, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
The school had 3 classes of 28 children.
How many children altogether?
Hint: Change the number of children, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
27 children are divided into 3 teams.
How many in each team?
Hint: Change the number of children, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
The school divided 87 children into 3 classes.
How many children in each class?
Hint: Change the number of children, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
A group of children paid $3 each to see a show.
Altogether the group paid $24
How many children were in the group?
Hint: Change the amount of money, and allow children
to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
Cupcakes are sold in boxes of 3.
Jemima wants to give one cupcake to each of
her 27 classmates.
What is the least number of boxes that Jemima
needs?
Hint: Change the number of classmates, and allow
children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
In a garden, there are 3 tomato plants for every 1 lettuce plant.
There are 4 lettuce plants.
How many tomato plants are in the garden?
Hint: Change the number of lettuce plants, and allow
children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
Roland is paid the same amount for each lawn he mows.
He gets paid $18 for mowing 3 lawns.
How many lawns does he need to mow to get
paid $24?
Hint: Change the money amounts, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
Jenna makes 12 pizzas.
She puts them on 3 trays.
What number sentence shows how Jenna could
work out the number of pizzas on each tray?
Hint: Change the number of pizzas, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
Toni bought 3 apples.
Apples cost 30 cents each.
How much did Toni have to pay?
Hint: Change the cost of an apple, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
3 classes each have 24 children and 1 class has 25
children.
How many children altogether?
Hint: Change the number of children, and allow children
to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
There are 2 number cards.
3
1
Use the number cards to make this number
sentence true:
x 3 = 13
Hint: Change the numbers and number sentence, and
allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
Jenna has 2 cards.
2
3
She makes a two-digit number and multiplies it
by 3.
What products could Jenna make?
Hint: Change the numbers, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
A budgie is about 13 cm long.
A parrot is about 3 times as long as a budgie.
About how long is a parrot?
Hint: Change the length of the animal, and allow children
to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
A child has 6 packets of pencils.
There are 4 pencils in each small packet.
There are 10 pencils in each large packet.
The child has 3 small packets.
How many pencils does he have altogether?
Hint: Change the numbers of packets and the numbers
of pencils, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
Sophie recorded this true number sentence.
6 x 3 = 18.
What other number sentence is also true?
18 x 6 = 3
3 x 6 = 18
6 x 18 = 3
Hint: Change the number sentence, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
Mary had 27 beads.
Tom had a third as many.
How many beads did Tom have?
Hint: Change the number of beads, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MULTIPLICATION AND DIVISION 12, PATTERNS AND ALGEBRA 18 Multiply and divide by 3 using the distributive property and the
relationship between division and fractions.
A fork is 9 centimetres long.
4 forks are the same length as 2 chop sticks.
How many centimetres long is 1 chop stick?
Hint: Change the length of the fork, and allow children
to solve again!
Make up your own problem!
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http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
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