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MEASUREMENT AND GEOMETRY 31_PROBLEM SOLVING
(Year 3) ACMMG064, NSW MA2 16MG
Angles as relative slant of two arms that meet at vertex, and as the amount of turn around a vertex, right angles.
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:
Angles as relative slant of 2 arms
that meet at a vertex.

Annie’s shape had 4 angles.
She labelled the parts of one of the angles.
What part of the angle has she not labelled yet? (vertex)
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Teaching Segment and Video 2:
Angles as the amount of turn
around a vertex.

Billy opened the blades of the scissors to make an angle.
He drew the scissors and labelled the parts of the angle.
What part of the angle has he not labelled yet? (vertex)
Teaching Segment and Video 3:
Right angles.

Kerry turned the blades on her scissors to form a right angle.
Which pair of scissors are Kerry’s?
(a)
(b)
(c)
(
)
More problems

Door
The door was open to this angle.
Do you think the door is open
less than a right angle, larger than a right angle or about a right angle? (less than a right angle)
Shapes

Marjorie used the right angles in a square to check if the angles in this shape are less than a right
angle, larger than a right angle or about a right angle.
She said the angles in this shape are larger than a right angle.
Is she right? (yes)
Clock hands 1

The hands on an analog clock made an angle less than a right angle.
What time could it be?
Draw the time on an analog clock. (any time where the hands make an angle less than a right angle.)
Clock hands 2

The hands on the clock made a right angle.
What time could it be?
Draw the time on an analog clock. (any time where the hands make a right angle.)
Clock hands 3

The hands on the clock made an angle greater than a right angle.
What time could it be?
Draw the time on an analog clock. (any time where the hands make an angle greater than a right angle.)
Clock hands 4

The hands on the clock made an angle less than a right angle.
Which of these times could it not be?
(a) 9 o’clock (b) 10 o’clock (c) 11 o’clock (9 o’clock – the angle would be a right angle. NB: For trickier times, allow children
to use a clock with hands that move in sync – links with Time 12)
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Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
Annie’s shape had 4 angles.
She labelled the parts of one of the angles.
Hint: Change the missing part, and allow children to
solve again!
What part of the angle has she not labelled yet?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
Billy opened the blades of the scissors to make
an angle.
He drew the scissors and labelled the parts of the
angle.
Hint: Change the missing unit, and allow children to
solve again!
What part of the angle has he not labelled yet?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
Kerry turned the blades on her scissors to form a
right angle.
Which pair of scissors are Kerry’s?
Hint: Change the angle, and allow children to
solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
The door was open to this angle.
Is the door is open
(a) less than a right angle,
Hint: Change the angle, and allow children to
(b) larger than a right angle
solve again!
(c) about a right angle?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
Marjorie used the right angles in a square to
check if the angles in this shape are less than a
right angle, larger than a right angle or about a
right angle.
Hint: Change the angle, and allow children to solve again!
She said the angles in this shape are larger than a
right angle.
Is she right?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
The hands on an analog clock made an angle less
than a right angle.
What time could it be?
Draw the time on an analog clock.
Hint: Change the angle, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
The hands on an analog clock made a right angle.
What time could it be?
Draw the time on an analog clock.
Hint: Change the angle, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
The hands on an analog clock made an angle
greater than a right angle.
What time could it be?
Hint: Change the angle, and allow children to solve again!
Draw the time on an analog clock.
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Measurement and Geometry 31 Describe angles as the amount of turn, and as the relative slant of two arms that meet at a vertex,
identifying the vertex and arms. Compare angles as less than, equal to, greater than a right angle.
The hands on an analog clock made an angle less
than a right angle.
Which of these times could it not be?
Hint: Change the angle, and allow children to solve again!
(a) 9 o’clock (b) 10 o’clock (c) 11 o’clock
Make up your own problem!
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