Children
ADDITION AND SUBTRACTION 22, PATTERNS AND ALGEBRA 19_PROBLEM SOLVING
(Year 3) ACMNA054, ACMNA055, NSW MA2-5NA
Solve missing and equivalent number sentences, explaining equality and the relationship between addition and subtraction.
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:
Equivalent Number Sentence
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.

Gerry said that this number sentence is true: 85 + 27 = 141 – 29. Is he right? Why? (yes, both sides equal 112)
Missing number sentence 1

What number makes this number sentence true? 153 – 87 = 38 + ____ (202, both sides equal 140)
Missing number sentence 2

79 + 43 has the same value as 43 + ____ (79)
Addition and subtraction
relationship

What number is missing from all of these number sentences? 56 + ___ = 64, 64 - ___ = 56, 64 – 56 = ___ (8)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
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.
Toys

Alan had 37 toy cars and 58 marbles. Betty had 29 toy cars and 66 marbles. Do they have the same number of
toys, or does one of the children have more toys? Record a number sentence to show this. (same number, 37 + 58
= 29 + 66, both sides of the equals sign equal 95)
Goals

The Sharks scored 37 points in game 1 and 58 points in game 2. The Goats scored 29 points in game 1 and 66
points in game 2. Did they score the same number of goals? Record a number sentence to show this. (same
number of goals, 37 + 58 = 29 + 66, both sides of the equals sign equal 95)
Addition and Subtraction

April wrote this correct number sentence. 87 + 34 = 121. How could you complete these missing number
sentences? 34 + ____ = 121 121 - ____ = 34 121 - ____ = 87 (34 + 87 = 121, 121 - 87 = 34, 121 - 34 = 87)
http://www.alearningplace.com.au
Problem Solving
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
Gerry said that this number sentence is true:
85 + 27 = 141 – 29.
Is he right?
Why?
Hint: Change the numbers sentence, and allow children
to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
What number makes this number
sentence true?
153 – 87 = 38 + ____
Hint: Change the number sentence, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
79 + 43 has the same value as 43 + ____
Hint: Change the numbers sentence, and allow children
to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
What number is missing from all of these
number sentences?
56 + ___ = 64,
64 - ___ = 56,
Hint: Change the numbers of cans, and allow children to
solve again!
64 – 56 = ___
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
Alan had 37 toy cars and 58 marbles.
Betty had 29 toy cars and 66 marbles.
Do they have the same number of toys, or does
one of the children have more toys?
Record a number sentence to show this.
Hint: Change the numbers of toy cars and marbles, and allow
children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
The Sharks scored 37 points in game 1 and 58 points in game 2.
The Goats scored 29 points in game 1 and 66 points in game 2.
Did they score the same number of goals?
Record a number sentence to show this.
Hint: Change the numbers of goals, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
April wrote this correct number sentence.
87 + 34 = 121.
What number makes these number sentences true?
34 + ____ = 121
121 - ____ = 34
121 - ____ = 87
Hint: Change the numbers, and allow children to solve
again!
Make up your own problem
http://www.alearningplace.com.au
Problem Solving Steps (back to Problems)
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
alk
http://www.alearningplace.com.au