Shapely understandings - PowerPoint Presentation

Slide1

Shapely understandings

Resources to help teach geometry By Nathan Cook

EDCU11022

Numeracy

in Action

S0241762Slide2

Geometry – Why is it important?

Geometrical understanding has many real world contexts to which it can be applied. All people face a variety of geometric problems daily. How much shopping can I fit in this bag? What shape do I want my swimming pool? How big do I want my shed? Why is there never enough room in this house?

“There

is an opportunity to apply understanding to

design.” (Australian Curriculum, Assessment and Reporting Authority (ACARA), 2010)

“Geometric reasoning and mathematical visualization are fundamental to spatial sense” (

Siemon

et al., 2011, p. 211)Slide3

Geometry and measurement

Geometry and measurement are closely linked and should not be taught as individual concepts. All shapes are defined by measurement. A square is only a square if all of its angles are 90 degrees and the length of each of its sides are the same.

“Measurement

and Geometry are presented together to

emphasise

their relationship to each other, enhancing their practical

relevance.” (ACARA, 2010).

Geometry and measurement link to many other areas of mathematics (

Seimon

et al., 2011).Slide4

Common Learning Problems

Students may not have sound knowledge on what a defines a certain shape. (

eg

: a triangle will always have three sides)

Students may become confused at the specifics of each shape. A quadrilateral is any shape that has four sides, but the other properties of the shape helps to identify it, (

eg

: A parallelogram has two pairs of parallel sides, where as a trapezium has only one pair of parallel sides.)

Students may only identify the name of a shape with the “regular” version of that shape. (

eg

: a regular hexagon is a hexagon that has all sides the same length and all interior angles equal., but the word “hexagon” is used to describe any shape with six sides.)

Some children have difficulties “seeing” a 2D representation of a 3D shape as being three dimensional.

These learning difficulties often arise from learners not comprehending the nomenclature behind the naming of shapes.

All learning difficulties

sourced from

Booker

, Bond, Sparrow &

Swan (2010).Slide5

A focus on the Australian curriculum

Shapely Understandings is designed to assist in the teaching of the following content descriptors, taken from the Measurement and Geometry strand of Australian Curriculum: Mathematics (ACARA, 2010). Please be aware that these are not a replacement for good quality teaching practices.

Year 3: Using units of measurement

- Measure, order and compare objects using familiar metric units of length, mass and

capacity

(ACMMG061

)

Year 4: Using units

of measurement - Use scaled instruments to measure and compare lengths, masses, capacities and temperatures

(ACMMG084)

Year 4: Using units of measurement

- Compare objects using familiar metric units of area and

volume

(ACMMG290)

Year 5: Using units of measurement

- Calculate the

perimeter

and area of rectangles using familiar metric units

(ACMMG109

)

Year 6: Using units of measurement

- Solve problems involving the comparison of lengths and areas using appropriate units

(ACMMG137

)

Year 6: Using units

of measurement - Connect

volume

and

capacity

and their units of measurement

(ACMMG138)

All descriptors in the “Shape”

substrand

from Years 1-5Slide6

What is Shapely understandings?

Shapely Understandings is a

resource package

with a heavy theoretical underpinning that is aimed to assist educators in the teaching of geometry in the classroom.

The variety of resources included are designed to be useful for both learners who are struggling and learners who need extension.

Shapely Understandings is designed to be useful for all learners, and therefore includes resources to help all learners. Those who are severely struggling and those who require extension will both benefit from these resources,

There is a explicit focus on teaching geometry in relation to measurement.

A focus on manipulatives allows for learners to retain geometric ideas that may not be obvious from just reading and view content on paper (Booker

et al., 2010).

All resources purchased are flat packed for easy delivery. All that you are required to have is scissors and glue!Slide7

Definition List

As the main issue in geometry is derived from not comprehending the terminology, the ‘Definition List’ is the “go to” resource for learners. It consists of many of the commonly used words that are encountered during the study of measurement and geometry and can easily be glued into the front of a learners work book to ensure they always have access to a handy glossary.Slide8

Definition Cube and equation cube

The ‘Definition Cube’ is derived from the definition list and primarily focuses on the terminology that students will be facing when learning measurement and geometry.

Similar to the definition cube, the equation cube has a different equation printed on each face. These equations are related to the measurement of both 2D and 3D shapes

. Euler’s formula is also included to extend learners who require it.Slide9

Shape windows

The shape windows are a set of three windows that allow learners to identify the properties of each shape. This is accomplished by turning over each flap,

w

hich reveals what the shape looks like and some brief information about the shape in relation to properties that can be measured.Slide10

Shape Memory Game

A game of memory is simple. All cards are placed facedown. The player flips over two cards at a time. If they match, the learner gets to collect them. If they do not, the cards are returned to face down position. This continues until all cards are removed from play.

This variation of the game has students match an image of a shape to its name. Only then can they remove the cards.

The aim of this activity is to allow learners to connect the names of shapes with the correct shapes. Booker et al. (2010) identifies the naming of shapes to be an area of concern, especially when terms such as “polygon”, “isosceles” and “equilateral” are introduced, for example. Therefore, a well defined base knowledge of shapes is essential for further learning

.Slide11

I have, who has Game

This simple game gets learners to answer each others questions. Each card has the answer to a question and a question itself. This forms a chain and allows learners to work collaboratively to work through all questions presented,

Collaborative learning helps “learners accept responsibility for their learning through active involvement (

proactiveness

); that they become dynamically engaged with their learning (participation); and that learning is the result if meaningful interaction” (Brady, 2007)

Like the previous activity, the aim of this is to allow learners to connect the names of shapes with the correct

shapes.Slide12

Task cards

The task cards are designed with only basic instructions for learners to follow. This provides learners are given the opportunity to explore different geometric concepts. The task cards are varied and are appropriate to be implemented for a large range of learners. This allows learners to extend their knowledge by practicing problem solving skills, which is considered an essential skill in life (Marzano & Pickering, 1997).Slide13

Website

The website is a repository of useful hyperlinks that will allow learners to play games to support their development of geometric understandings. Access to the website can be found here:

http

://shapelyunderstandings.weebly.com

/

“Digital

technologies, such as spreadsheets, dynamic geometry software and computer algebra software, can engage students and promote understanding of key concepts

.” (ACARA, 2015)

Teachers are able to access the website to download the resources for free.Slide14

Conclusion

The Shapely Understandings Resource package is a great way to supplement your teaching practice.

Great for struggling learners and learners who need that extra push, Shapely Understandings is your one stop for a collection of great geometric resources.

Available for free download from the official website:

http://shapelyunderstandings.weebly.com/

THANK YOU FOR YOUR TIMESlide15

References

Australian Curriculum Assessment and Reporting

Authority (ACARA).

(

2010).

Mathematics

. Retrieved from http

://

www.australiancurriculum.edu.au/mathematics/rationale

Booker

, G., Bond, D., Sparrow, L., & Swan, P. (2010).

Teaching primary mathematics

(4th ed.).

Frenchs Forest

, NSW: Pearson.

Brady

, L. (2006).

Collaborative learning in action.

Frenchs Forest, NSW: Pearson Education

Australia

.

Marzano, R. J., & Pickering, D. J. (with

Arrendondo

, D. E.,

Paynter

, D. E., Blackburn, G.

J.,Brandt

, R.

S

.,

Moffet

,

C

. A., Pollock, J. E., & Whistler, J. S.). (1997).

Dimensions of learning teacher’s manual

(

2nd ed.).

Alexandria

, VA: Association for Supervision and Curriculum Development.

Siemon

, D.,

Beswick

, K., Brady, K., Clark, J.,

Faragher

, R. & Warren, E. (2011).

Teaching

mathematics: Foundations

to

middle years

.

South Melbourne, VIC: Oxford University Press.