You Mean Three Can Be One?
FRACTIONAL REPRESENTATIONS
PRESENTED BY: SHERILYN STRATTON, CARNEGIE LEARNING
Goals for the Day
• To deepen your own understanding of fraction
and their operations.
• To develop your mathematical reasoning and
problem solving capabilities.
• To provide you with opportunity to reflect on
and develop your own teaching practice.
The Whole: Yellow Hexagon
• Start with the yellow hexagon.
• Cover the hexagon with other pattern
block pieces.
• Record your design.
• Repeat the process to create as many
representations as possible.
The Whole: Yellow Hexagon
1. How many different designs can you create?
How did you know you determined all of the
combinations?
2. Write fraction number sentences to describe
each of your designs.
The Whole: Triple Hexagon
• Create the whole: On a blank sheet of pattern
block paper, put 3 hexagons together to form a
“triple hexagon”. Trace around your triple
hexagon shape(s).
• Determine what fractional part each pattern
block shape represents:
–
–
–
–
Hexagon
Trapezoid
Rhombus
Triangle
The Whole: Large Hexagon
• Cover the large hexagon using one or more
trapezoids, rhombi, triangles, and hexagons.
• Use each shape at least once.
• Draw the result on the
hexagon.
• Label each part with
a fraction.
How is this possible?
7. From her work with pattern blocks in third
grade, Lynn always thought that the
1
trapezoid was called . But when she made
2
her triple hexagon, the trapezoid wasn’t
1
called anymore!
2
What happened? How is this
possible?
How is this possible?
1
3
8. Lynn was trying to figure out which was larger, or
1
.
2
“My third grade teacher said that in fractions,
1
2
larger is smaller and smaller is larger, so is larger
than
1
.”
3
How is this possible?
But then she looked at the three pattern block
1
problems she just did. “The hexagon is and the
trapezoid is
1
3
1
.
2
3
The hexagon is bigger than the trapezoid.
1
.
2
So, IS larger than I knew larger couldn’t be
smaller!” What happened? How is this possible?
Fractional Names of
Pattern Block Pieces
The Whole
Pattern Block
Piece
Hexagon
Trapezoid
Rhombus
Triangle
Hexagon
Triple
Hexagon
Large
Hexagon
The Whole
Pattern Block
Piece
Hexagon
Hexagon
1
Trapezoid
Rhombus
Triangle
1
2
1
3
1
6
Triple
Hexagon
Large
Hexagon
1
3
1
6
1
9
1
18
1
4
1
8
1
12
1
24
With a partner describe any patterns you notice in the
table and explain why you think the patterns exist.
The Whole
Pattern Block
Piece
Hexagon
Hexagon
1
Trapezoid
Rhombus
Triangle
1
2
1
3
1
6
Triple
Hexagon
Large
Hexagon
1
3
1
6
1
9
1
18
1
4
1
8
1
12
1
24
MegaHexa
gon
Determine the fractional part of each piece if the whole
is now a Mega-Hexagon (equivalent to 7 hexagons).
The Whole
Pattern Block
Piece
Trapezoid
1
Hexagon
Trapezoid
Rhombus
Triangle
Hexagon
1
1
2
1
3
1
6
Triple
Hexagon
Large
Hexagon
MegaHexag
on
1
3
1
6
1
9
1
18
1
4
1
8
1
12
1
24
1
7
1
14
1
21
1
42
Determine the fractional part of each pattern
block piece if the whole is now a trapezoid.
The Whole
Pattern Block
Piece
Trapezoid
Hexagon
Hexagon
2
1
Trapezoid
1
Rhombus
Triangle
Rhombus
1
2
3
1
3
1
2
1
3
1
6
Triple
Hexagon
Large
Hexagon
MegaHexag
on
1
3
1
6
1
9
1
18
1
4
1
8
1
12
1
24
1
7
1
14
1
21
1
42
Determine the fractional part of each piece if the
whole is now a rhombus.
The Whole
Pattern Block
Piece
Rhombus
Trapezoid
Hexagon
Hexagon
3
2
1
Trapezoid
3
2
1
Rhombus
1
Triangle
Triangle
1
1
2
2
3
1
3
1
2
1
3
1
6
Triple
Hexagon
Large
Hexagon
MegaHexag
on
1
3
1
6
1
9
1
18
1
4
1
8
1
12
1
24
1
7
1
14
1
21
1
42
Determine the fractional part of each piece if the
whole is now a triangle.
The Whole
Pattern Block
Piece
Triangle
Rhombus
Trapezoid
Hexagon
Hexagon
6
3
2
1
Trapezoid
3
3
2
1
Rhombus
2
1
Triangle
1
1
2
2
3
1
3
1
2
1
3
1
6
Triple
Hexagon
Large
Hexagon
MegaHexag
on
1
3
1
6
1
9
1
18
1
4
1
8
1
12
1
24
1
7
1
14
1
21
1
42
Describe the patterns that you see in the table.
Mathematical Practices
• Describe ways in which you can connect the
mathematical practices to the essential ideas
of these tasks.
Deepening Mathematical Understanding
SOFTWARE CONNECTIONS
REPORTS FOR FURTHER
INTERVENTION
Looking at Reports
• Overview provides you with a summary of the
tools and strategies needed to monitor and
sustain an effective software implementation.