ymath.haifa.ac.ilymath.haifa.ac.il/images/stories/part3/teachers/articles/...mathematics

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1 Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009 by the National Council of Teachers of Mathematics, Inc. www.nctm.org . All rights reserved. NCTM is not responsible for the accuracy or quality of the translation ا ا ا ت ا ي اآ ا- http://mathcenter-k6.haifa.ac.il A Framework for Analyzing Geometric Pattern Tasks : Susan N. Friel and Kimberly A. Markworth : Mathematics Teaching in the Middle School, 15 (1), August 2009, pp. 24-33 : ) ( . . " " Blanton and Kaput (2005) " " ) . 413 .( Blanton and Kaput (2005) . ) NCTM 2000 ( . ) ( . . Driscoll ) 1999 ( " : ) input ( ) output ( ) " . 2 .( . . . ) ( . . ) NCTM 2000 ( ) Billings, Tiedt, and Slater 2007/2008 .(

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Page 1: ymath.haifa.ac.ilymath.haifa.ac.il/images/stories/part3/teachers/articles/...Mathematics

1

Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009

by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

� ا����ا����� � ا�������ت �� ا�� ��-ا� �آ� ا����ي ��� ����� http://mathcenter-k6.haifa.ac.il

�� ���� ��� ����������� � �� A Framework for Analyzing Geometric Pattern Tasks

���� :Susan N. Friel and Kimberly A. Markworth

�� �: Mathematics Teaching in the Middle School, 15 (1), August 2009, pp. 24-33

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Page 2: ymath.haifa.ac.ilymath.haifa.ac.il/images/stories/part3/teachers/articles/...Mathematics

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Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009

by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009

by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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Page 5: ymath.haifa.ac.ilymath.haifa.ac.il/images/stories/part3/teachers/articles/...Mathematics

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by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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Page 6: ymath.haifa.ac.ilymath.haifa.ac.il/images/stories/part3/teachers/articles/...Mathematics

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by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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Page 7: ymath.haifa.ac.ilymath.haifa.ac.il/images/stories/part3/teachers/articles/...Mathematics

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by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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NCTM is not responsible for the accuracy or quality of the translation

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by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009

by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009

by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

� ا����ا����� � ا�������ت �� ا�� ��-ا� �آ� ا����ي ��� ����� http://mathcenter-k6.haifa.ac.il

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=>;د:ت ا�9!(ل ا�$$�7 ا���� ر45

)T – !"#$ا� @A ل;�BCد ا,-n (

x :T = n<��ت 1

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x : T = n + 1<��ت 3

x : T = n + 4<��ت 4

}�ت 5{������ت; n: أ�4A^ ا� Dح�ف; 1: :n ;اء��Bع ا> t� :T = 2n + 1

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<ع ا�; x: 4n + 4<��ت �� ا� ح�ط; x: n2<��ت �� ا� �آ� 10t� T= n2 + 4n + 4: �<��ت

}�ت 11{� :n ;ت����� :5n + 1 ;اء��Bع ا> t� :T = 6n + 1

x :T = 3n - 2<��ت 12

<ع ا��<��ت ; x :8n + 8<��ت ����ء ; x :4n + 1<��ت =<داء 13t� :T = 12n + 9

x :T= n2 + 2n + 2<��ت 14

�?��4ت 15 :T = 3n + 1

16 o�[ا� ���[� :T = 4n + 2

17 � [�4� ^>� T = 3n + 1: و

x :T = n2<��ت 18

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Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009

by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

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Translated and reprinted with permission from Mathematics Teaching in the Middle School, copyright © 2009

by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

NCTM is not responsible for the accuracy or quality of the translation

� ا����ا����� � ا�������ت �� ا�� ��-ا� �آ� ا����ي ��� ����� http://mathcenter-k6.haifa.ac.il

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