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Baroody, A. J. (2003). The development of adaptive expertise and flexibility:

The integration of conceptual and procedural knowledge. In A.J.Baroody

& A.Dowker (Eds.), The development of arithmetic concepts and skills

(pp. 1-33). Mahwah, NJ: Erlbaum.

Behm, S., & Lloyd, G. (2009). Factors influencing student teachers use of

mathematics curriculum materials. In J. Remillard, B. Herbel-Eisenmann,

., & G. Lloyd (Eds.), Mathematics teachers at work: Connecting

curriculum materials and classroom instruction. New York: Routledge,

Taylor and Francis.

Berry J., Graham E. & Smith A. (2005) Classifying Students Calculator

Strategies. The International Journal for Technology in Mathematics

Education, 12(1), 15-31.

Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D. (2004). Proofs

through exploration in dynamic geometry environments. International

Journal of Science and Mathematics Education, 2(3), 339-352.

Clement, D. (2007). Curriculum research: Towards a framework for

Research-based Curricula. Journal for Research in Mathematics

Education, 38(1), 35-70.

Connecticut State Department of Education (2006). A Guide to Curriculum

Development: Purposes, Practices, Procedures.

http://www.sde.ct.gov/sde/cwp/view.asp?a=2618&q=321162

Grant, T., Kline, K., Crumbaugh, C., Kim, O., & Cengiz, N. (2009). How can

curriculum materials support teachers in pursuing student thinking during

whole group discussions? In J. Remillard, B. Herbel-Eisenmann, ., & G.

Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum

materials and classroom instruction. New York: Routledge, Taylor and
http://www.sde.ct.gov/sde/cwp/view.asp?a=2618&q=321162http://www.sde.ct.gov/sde/cwp/view.asp?a=2618&q=321162


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Francis.

Jackiw, N. & Sinclair, N. (2009). Sounds and pictures: dynamism and duality

in Dynamic Geometry. ZDM, 41(4), 413-426.

Mullis, I.V.S., Martin, M.O., & Foy, P. (with Olson, J.F., Preuschoff, C.,

Erberber, E., Arora, A., & Galia, J.). (2008).TIMSS 2007 International

Mathematics Report: Findings form IEAS Trends in International

Mathematics and Science Study at the Fourth and Eight Grades.Chestnut

Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

National Council of Teachers of Mathematics (2000). Principles and standards

for school mathematics.Reston: Va, NCTM.

National Council on Education and the Disciplines (2001). Mathematics and

Democracy: The case for quantitative literacy. The Woodrow Wilson

National Fellowship Foundation.

OECD Education (2006). Assessing scientific, reading and mathematical

literacy: A framework for PISA 2006. OECD.

Ruthven, K., Deaney, R., & Hennessy, S. (2009). Using graphing software to

teach about algebraic forms: A study of technology-supported practice in

secondary-school mathematics. Educational Studies in Mathematics,

71(3), 279-297.

Schoenfeld, A. (1994). What do we know about mathematics curricula?

Journal of Mathematical Behavior, 13, 55-80.

Sdrolias, K.A., & Triandafillidis, T.A. (2007). The transition to secondary school

geometry: can there be a chain of school mathematics? Educational

Studies in Mathematics, 67(2), 159-169.

Stein, M., & Kim G. (2009). The role of mathematics curriculum materials in
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large scale urban reform: An analysis of demands and opportunities for

teacher learning. In J. Remillard, B. Herbel-Eisenmann, ., & G. Lloyd

(Eds.), Mathematics teachers at work: Connecting curriculum materials

and classroom instruction.New York: Routledge, Taylor and Francis.

Weiss, I.R., Knapp, M.S., Hollweg, K.S., & Burrill, G. (2001). Investigating the

Influence of Standards: A Framework for Research in Mathematics,

Science, and Technology Education. Center for Education, National

Research Council.

(2009). 12

2009

( 2020).

, V, 28.5.2009, 2009/C 119/02.


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2

125

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133/474

2

126

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cm.

.

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134/474

2

127

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.

.

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.

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135/474

2

128

:

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, 1 m;

: Kg g.

() () ()

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4 , 900 , :

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15 L1,5 L

4 L0,5 L


136/474

2

129

12

; , .

(http://nrich.maths.org/content/03/03/penta1/clock.swf)

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137/474

2

130

()

,

. .

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( )

6 , :

.

15 m

9m

2700 cm

250 cm

() 27 m.

() 1500 cm.

() 2,5 m.

2.6


138/474

2

131

() 900 cm.

,

.

.

;

0,6kg

145 g

56 g

260 g

3,6 kg

45 g

() ,

.

() 1 kg;

()

, ;

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.

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3000 cm 150 cm 15 m 1300 cm 2,8 m 30 m


139/474

2

132

58

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0,35

7 .


140/474

2

133

7

7

7

7

7

,

..

:

1 ,:

.

20/06/1995

3/12/2001

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M2.8


141/474

2

134

28/10/1990

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2010 .

2010 2010 2010

8 8 8

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M2.9


142/474

2

135

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.

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143/474

2

136

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.

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.

;

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1 .

, ;

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.

() 80 = _____ _____

() 3 = __________

() 1 = _________

() 20 = ______

2.11

7 , :

.

() ()

.

2.12


144/474

2

137

() ()

4oC

34oC

4oC

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145/474

2

138

: ..

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25 cm

2

. 1 cm2.

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2 .

() :

() :

() :

,

;

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1,5 L

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875 g

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25 m

25 cm


146/474

2

139

4 .

() ()

()

2.5

6 . 32 cm, 0,29 m

57 cm. .

.

1.()

2.()

3.

()

4.()

5. ()

6.

()

2.6


147/474

2

140

7 7,50 20.

.

2.7

8 18 2001 18/6/2001.

;

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.

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10 ,

.

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.

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148/474

2

141

11 >,


149/474

2

142

:

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150/474

3

143

3

:

1 (mm, cm, m, km), (Kg, g), (L, ml) (m

3, cm

3).

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151/474

3

144

.

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152/474

3

145

() 100 ml

.

2 , :

;

.

() 5 km = ___________ m

() 4,1 kg = __________g

() 5,5 cm = __________ km

() 3,75 L = _________ ml

() 650 cm = ________ m

() 96 ml = ________ L

3.2

3 , , :

() ,

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.

.

() .

1

2

3

_______________________________________________________

3.3


153/474

3

146

_______________________________________________________

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.

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4 , :

24 cm2

.

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.

1 = 1 cm2


154/474

3

147

1 24 cm

2

2 24 cm

2

3 24 cm

2

4 24 cm

2

()

6 cm2, 8 cm

2, 12

cm2, 15 cm2, 16 cm2, 18 cm2 .

.

1 = 1 cm2


155/474

3

148

1 6 cm

2

2 6 cm

2

3 8 cm

2

4 8 cm2

5 12 cm

2

6 12 cm

2

7 12 cm

2

8 15 cm

2

9 15 cm

2

10 16 cm

2

11 16 cm

2

12 16 cm

2

13 18 cm

2

14 18 cm

2

15 18 cm

2

()

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______________________________________________________

______________________________________________________

()

.

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______________________________________________________

5 , :

() .

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3

.

(

)

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)

3.5


156/474

3

149

()

, .

____________________________________________________________

________________________________________________

6 , , , :

,

.

() =___ () =____ () =____

.

() 20, () 45

, () 70

, () 122

() 157

.

3.6


157/474

3

150

:

() 4

1 :

() : .

7

, :

.

:

4,39

:

13,31

:

M3.7


158/474

3

151

21,49

:

59,99

/

.

() 52 : _________________________.

() 2

1 : _______________________.

() 4

1 : ___________________________.

() 5

1 : _____________________________.

() 10

1 : _______________________________.


159/474

3

152

,

..

:

1 , :

2 13 ,

.

2 13

:

6:57 9:10

M3.8

2 , :

()

.

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::

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160/474

3

153

() ,

;

______________________________________________________

______________________________________________________

() ,

;

______________________________________________________

______________________________________________________

3 , , :

.

() 3 = _____

() 1 = ______ = _______

()5

1 = _____ = _________

7

.

.

3.10


161/474

3

154

7

;

Chichen Itza,

,

800 ..

,

, 1931 ..

, 200 ..

, 1460 ..

, 9 ..

,

, 70 ..

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162/474

3

155

, , 7000

.. ;

4 , :

.

.

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14:32 15:15

09:05 10:25

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3.11

5 , :

7:00 .. -4oC. 12:00 ..

7oC. 7:00 ..

3oC.

7:00 . .

7 ..

3.12


163/474

3

156

: ..

1

1kg, 2kg, 6kg 8kg, 13 kg;

3.1

2 4 L 8 . (ml)

;

5,34 kg.

, 650g

.

;

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4

.

1 cm2.

3.4

5 ,

.

() ()

3.5

6

, .

3.6


164/474

3

157

()

()

360. .

7

.

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0, 1, 3

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-

,

,

20 10

.

-

20

:

()

3.7

() _______ () _______

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= ____

= ____

= ____

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= ____

= ____


165/474

3

158

2

1 20

()

5

1 10

() 50

() 1

8 .

() 4:35 ..

() 12: 20 ..

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.

.

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3.8

:

:

:

:


166/474

3

159

12:35

13:35

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()

.

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, 12:35 ..

;

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() 4 25 .

12:35 ..,

;

9 25 cm2.

4 cm,

;

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.

3.9

10 >,


167/474

3

160

12 2oC 500 m

. ,

, 7oC

3oC,

. , ,

:

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C.

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C.

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C.

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C.

;

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168/474

3

161

:

1 , :() 180 g, ;

() 375 g, ;

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15 .

7 11 .

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,


169/474

3

162

;

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170/474

4

163

4

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,

9 .

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171/474

4

164

..

:

1 , , :

0,15 kg, 0,55 kg, 1 kg, 3 kg, 9 kg,

27 kg. 34,30 kg;

4.1

2

, :

,

.

() 17 m, 17 040 000 cm, 17 400 000 005 mm

() 435 678 g, 4,32 kg, 432 g, 0,50

() 4788 ml, 47,6 L, 489 654 ml

mm, cm, m km. .

mm cm m km

- 72

- 504000

1105,76

1261000

4.2

3 , :

.

() () ()

4.3

=___cm

= ___cm2

=___cm

= ___cm2

=___cm

= ___cm2


172/474

4

165

,

1 cm.

7 ,

.

4 , ,

:

233 m

146 m.

.

4.4


173/474

4

166

,

330 ml

6 cm.

5 , , :

() 8

, .

, 16, 24, 36 48

.

:

()

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______________________________________________________

______________________________________________________

.

4.5


174/474

4

167

() ()

8cm 4 ,

. .

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, .

(http://illuminations.nctm.org/ActivityDetail.aspx?ID=9)

4.6


175/474

4

168

7 , , , :

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, ;

(http://users.ira.sch.gr/thafounar/classB/lessons/LehghtCircle/lenghtCircle.htm

) ,

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;

(http://illuminations.nctm.org/ActivityDetail.aspx?ID=116)

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176/474

4

169

,

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,

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:

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.

.

4.9

2 , :

4 cm. ,

. ;

4.10


177/474

4

170

: ..

1

20,32 cm 30,48 cm.

4

1,

(cm);

4.1

2 130 26,5g. kg ;

1 m.

, 5 Km;

.

() 43 mm = _____ cm

() 8 = ______ kg

() 378 ml = _____ L

() 3,24 km = ______ cm

() 45,94 Kg = ______ g

() 33 m = _____ cm

() 654,2 km = _____ mm

4.2

3 .

() () ()

,

100 cm2

.

,

100 cm.

4.3

4

.

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178/474

4

171

,

720 mm3.

To .

.

5 .

,

8 mm.

4.5

15 cm


179/474

4

172

6 ;

() () ()

4.6

7 , 20 cm

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4.7

8 . .

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.

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13.

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4.9

9 64 cm3.

6 cm,

4.10


180/474

4

173

;

.


181/474

4

174

:

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(cm) (cm) (cm)

(cm

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)

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4 6 12.

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cm2.


182/474

4

175

5 , :

.

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183/474

5

176

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184/474

5

177

..

:

1.

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2. ,:

,

50 m 60 m.

.

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).

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185/474

5

178

.

4. 180,

68 cm.

m

M5.6

5. ,

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60 m 50 m,

.

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6. , ,

:

(-2,3) (4,7).

.

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7. , :

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km

, . (

365 ).

5.8


186/474

5

179

, :

8. , :

4 m 5 m 3 m.

;

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);

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5.10

2.

, :

(

)

5.11


187/474

5

180

.

580km.

8:20 ..

40,

4:15.. ;


188/474

5

181

1. .

M5.3

2. .

,

: 2,20 mx 1,10 m, 65 cmx 65 cm,

1,20 mx 0,75 m

1:50

M5.6


189/474

5

182

:

1 ,

.

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2200, 300

4800 .

() ,

.

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.

2000 635 . 2000

2008 35 .

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,, :

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,

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190/474

6

183

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.

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.

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.


191/474

6

184

,

10. ()

.

11.

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, :

120

.

40 m

. ,

;

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2.

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.

8km

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1370( ) 5km.

6.2


192/474

6

185

.

;

3. ,

, :

450,

2 m ( ). (

)

5m, .

6. 3

4. , ,

, :

(1, 2) =

, (3, 7) =

, ( 2,5) =

) +

3 8 +

)

.

(2,-3). 2-3+5=0

3+2-7=0.

.

6.4


193/474

6

186

5.

, :

R=.

, , .

, R.

6.8

6.

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,

;

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, ..

:

1.

.

6.10


194/474

6

187

1. AB

f(x) = 5x g(x) = 5x. f(x)

[0, 2] f(x) = 0 g(x) = 0 [, 2].

.

6.2

2. 234m

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)

.

)

, ,

.

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3. 29 cm2

45.

.

6.9

4. () .

(-1/2, 1), (2, -1), (6, 4).

.

.

.

6.10


195/474


196/474

6

189

Ferris Luna Parks.

http://www.ies.co.jp/math/java/trig/kanran/kanran.html

o . :

h = a(bt + c) + d

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197/474

7

190

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198/474

7

191

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.

,

.

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M7.1

2. ,

, :

.

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M7.3


199/474

7

192

A1

A2

A3

A4

A5

A6

A7A8

A9

A10

A11

A12

B1

B2

B3

B4

B5B6

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.

M6.4

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.

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200/474

7

193

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201/474

7

194

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2cm, 3cm 4cm. 36cm.

;

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2 1,3 3

= =

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.

M7.2

4. = 50cm2. M7.4


202/474

7

195

8cm.

.

:

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2-4+2-8+4=0 =1

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3 149637000km,

.

=2.

.

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203/474

7

196

4 ().

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204/474

8

197

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205/474

8

198

00 1 2

12

2

x

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f(x)dx h (y y ) (y y ... y ) + + + + +

7. Simpson

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x

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=f(x) (,)

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10.

=

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.

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x

= f(t) = g(t) t [t1, t2]

=

2

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t

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dx d

dtdt dt

+

12. ,

.

13. .


206/474

8

199

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, =2

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.

M8.3

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()

()

2 .

M8.5

5.

, :

()

M8.5

-1 1 2 3

1

2

3

4

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