Measurement and Geometry 60_Problem Solving
(YEAR 6) ACMMG142, NSW MA3 15MG
Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
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. 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.
The formulation of a problem is far
more essential than its solution,
which may be merely a matter of
mathematical or experimental skills.
It’s not that I’m
so smart
– I just stay with
problems longer.
The problem solving steps may be followed to solve problems.

Marjorie drew a shape, then translated it to the right, reflected it downwards, and rotated it 90 degrees clockwise. Which drawing is Marjorie’s?
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1

Kanye makes each of these designs by using the triangle four times. In which of Kanye’s designs did he only
translate the tiles?

Donald made this design. He then reflected the design to the right, then rotated it 90 degrees anticlockwise. What will the design look like?

This shape turns around the black dot.

Marcus has these tiles. They are white on one side and black on the other.
Marcus makes a pattern with the white side facing up. Which of these patterns could Marcus not have made?

Which of these designs looks identical after a quarter turn?

What does it look like after a three-quarter turn clockwise?
During a single leap, a dancer made 2 full rotations of his body. By how many degrees did the dancer rotate his body in this leap?
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Problem Solving
MEASUREMENT AND GEOMETRY 60 Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
Marjorie drew a shape, then translated it to the right,
reflected it downwards, and rotated it 90 degrees
clockwise.
Which drawing is Marjorie’s?
Make up your own problem!
Website: http://www.alearningplace.com.au
Problem Solving
MEASUREMENT AND GEOMETRY 60 Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
Kanye makes each of these designs by using the
triangle four times.
In which of Kanye’s designs did he only translate
the tiles?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MEASUREMENT AND GEOMETRY 60 Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
Donald made this design. He then reflected the
design to the right, then rotated it 90 degrees anticlockwise.
What will the design look like?
Make up your own problem!
Website: http://www.alearningplace.com.au
Problem Solving
MEASUREMENT AND GEOMETRY 60 Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
This shape turns around the black dot.
What does it look like after a three-quarter turn clockwise?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MEASUREMENT AND GEOMETRY 60 Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
Marcus has these tiles.
They are white on one side and black on the other.
Marcus makes a pattern with the white side facing up.
Which of these patterns could Marcus not have made?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MEASUREMENT AND GEOMETRY 60 Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
Which of these designs looks identical after a
quarter turn?
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
MEASUREMENT AND GEOMETRY 60 Transforming effects and patterns of combinations of translation, reflection and degree of rotation.
During a single leap, a dancer made 2 full rotations
of his body.
By how many degrees did the dancer rotate his
body in this leap?
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
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place