FRACTIONAL REPRESENTATIONS

PRESENTED BY: SHERILYN STRATTON, CARNEGIE LEARNING

You Mean Three Can Be One?

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 trapezoid was called . But when she made her triple hexagon, the trapezoid wasn’t called anymore! What happened? How is this possible?

How is this possible?

8. Lynn was trying to figure out which was larger, or . “My third grade teacher said that in fractions, larger is smaller and smaller is larger, so is larger than .”

How is this possible?

But then she looked at the three pattern block problems she just did. “The hexagon is and the trapezoid is . The hexagon is bigger than the trapezoid. So, IS larger than . I knew larger couldn’t be smaller!” What happened? How is this possible?

The Whole

Pattern Block Piece Hexagon Triple

HexagonLarge

Hexagon

Hexagon

Trapezoid

Rhombus

Triangle

Fractional Names of Pattern Block Pieces

The Whole

Pattern Block Piece Hexagon Triple

HexagonLarge

Hexagon

Hexagon

Trapezoid

Rhombus

Triangle

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 Triple

HexagonLarge

HexagonMega-Hexagon

Hexagon

Trapezoid

Rhombus

Triangle

Determine the fractional part of each piece if the whole is now a Mega-Hexagon (equivalent to 7 hexagons).

The Whole

Pattern Block Piece

Trape-zoid Hexagon Triple

HexagonLarge

HexagonMega-Hexag

onHexagon

Trapezoid

Rhombus

Triangle

Determine the fractional part of each pattern block piece if the whole is now a trapezoid.

The Whole

Pattern Block Piece

Rhom-bus

Trape-zoid Hexagon Triple

HexagonLarge

HexagonMega-Hexag

onHexagon

Trapezoid

Rhombus

Triangle

Determine the fractional part of each piece if the whole is now a rhombus.

The Whole

Pattern Block Piece

Tri-angle

Rhom-bus

Trape-zoid Hexagon Triple

HexagonLarge

HexagonMega-Hexag

onHexagon

Trapezoid

Rhombus

Triangle

Determine the fractional part of each piece if the whole is now a triangle.

The Whole

Pattern Block Piece

Tri-angle

Rhom-bus

Trape-zoid Hexagon Triple

HexagonLarge

HexagonMega-Hexag

onHexagon

Trapezoid

Rhombus

Triangle

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.

SOFTWARE CONNECTIONS

Deepening Mathematical Understanding

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.