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<div class=3DSection1>

<p class=3DMsoTitle><span style=3D'font-size:18.0pt'>Lesson 2.4</span><span
style=3D'font-size:8.0pt'>F&#8217;08</span><span style=3D'font-size:18.0pt'=
><o:p></o:p></span></p>

<p class=3DMsoTitle align=3Dleft style=3D'text-align:left'><span style=3D'f=
ont-size:
18.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoSubtitle><span style=3D'mso-bidi-font-size:18.0pt'>Objectives=
:<span
style=3D'mso-spacerun:yes'>&nbsp; </span>To </span>study multiplication and
division of whole </p>

<p class=3DMsoSubtitle><span style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp; </span>numbers and their
properties.<span style=3D'mso-bidi-font-size:18.0pt'><o:p></o:p></span></p>

<p class=3DMsoTitle><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><i style=3D'mso-bidi-font-style:normal'><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Principles and Standar=
ds</span></i><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'> page 111<o:p></o:p></=
span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<h1 align=3Dcenter style=3D'text-align:center'><b style=3D'mso-bidi-font-we=
ight:normal'>Models
for Multiplication<o:p></o:p></b></h1>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.5in;text-align:ce=
nter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>1.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Repeated Addition =
Model.<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>Suppose we purchase a box of cookies.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>The box has 3 rows of cookies and =
each
row contains 5 cookies.<span style=3D'mso-spacerun:yes'>&nbsp; </span>How m=
any
cookies are in the box?<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>Set model.<span style=3D'mso-spacerun:yes'>&nbsp;
</span></span><span style=3D'font-size:18.0pt'><!--[if gte vml 1]><v:shapet=
ype
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<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><span style=3D'mso-ta=
b-count:
3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
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span
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src=3D"T101Lesson2.4doc_files/image002.gif" v:shapes=3D"_x0000_i1045"><![en=
dif]><o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><span style=3D'mso-ta=
b-count:
3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><=
span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span><!--[if gte vml 1]><v:=
shape
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src=3D"T101Lesson2.4doc_files/image002.gif" v:shapes=3D"_x0000_i1047"><![en=
dif]><!--[if gte vml 1]><v:shape
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src=3D"T101Lesson2.4doc_files/image002.gif" v:shapes=3D"_x0000_i1048"><![en=
dif]><o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><span style=3D'mso-ta=
b-count:
3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><=
span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp; </span><o:p></o:p></spa=
n></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center;text-indent:=
.5in'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>Number Line Model<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>3(5)<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
><o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'>________________________________________<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.5in;text-align:ce=
nter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>2.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The Array Model</s=
pan></b><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>Suppose Steve, as part of his biology research,
planted 5 rows of bean seeds and each row contains 6 seeds.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>How many seeds did he plant in his
rectangular plot?<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
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</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D23
src=3D"T101Lesson2.4doc_files/image004.gif" v:shapes=3D"_x0000_i1049"><![en=
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<table class=3DMsoTableGrid border=3D1 cellspacing=3D0 cellpadding=3D0 alig=
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ext .5pt;
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space:
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t 1.0pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:1=
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  <p class=3DMsoNormal style=3D'mso-element:frame;mso-element-frame-hspace:=
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t 1.0pt;
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<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =
</span></span><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1068" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1068"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1069" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1069"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1070" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1070"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1071" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1071"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1072" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1072"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1073" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1073"><![en=
dif]><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><span style=3D'mso-tab=
-count:
4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1074" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1074"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1075" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1075"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1076" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1076"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1077" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1077"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1078" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1078"><![en=
dif]><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1079" type=3D"#_x0000_t75" style=3D'width:18pt;height:27pt'>
 <v:imagedata src=3D"T101Lesson2.4doc_files/image005.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D24 height=3D36
src=3D"T101Lesson2.4doc_files/image006.jpg" v:shapes=3D"_x0000_i1079"><![en=
dif]><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><span style=3D'mso-tab=
-count:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style=3D'mso-tab=
-count:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>6 columns<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><b style=3D'mso-bidi-font-w=
eight:
normal'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Definiti=
on of
Multiplication of Whole Numbers<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>For any whole numbers a and n<sub><!--[if gte vm=
l 1]><v:shape
 id=3D"_x0000_i1080" type=3D"#_x0000_t75" style=3D'width:11.25pt;height:11.=
25pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image007.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D15 height=3D15
src=3D"T101Lesson2.4doc_files/image008.gif" v:shapes=3D"_x0000_i1080"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1080"
  DrawAspect=3D"Content" ObjectID=3D"_1296384643">
 </o:OLEObject>
</xml><![endif]-->0, <o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span class=
=3DSpellE><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>na</span></span><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'> =3D a + a + a + a + a=
 +&#8230;+
a<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span><span style=3D'font-size:14.0pt'>n terms<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>If n =3D 0, then 0<sub><!--[if gte vml 1]><v:sha=
pe
 id=3D"_x0000_i1081" type=3D"#_x0000_t75" style=3D'width:9pt;height:9.75pt'=
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1081"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
081"
  DrawAspect=3D"Content" ObjectID=3D"_1296384644">
 </o:OLEObject>
</xml><![endif]-->a =3D 0.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>The number n<sub><!--[if gte vml 1]><v:shape id=
=3D"_x0000_i1082"
 type=3D"#_x0000_t75" style=3D'width:9pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1082"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
082"
  DrawAspect=3D"Content" ObjectID=3D"_1296384645">
 </o:OLEObject>
</xml><![endif]-->a, read &#8220;n times a&#8221;, is called the <b
style=3D'mso-bidi-font-weight:normal'><u>product</u></b> of <b style=3D'mso=
-bidi-font-weight:
normal'>n </b>and <b style=3D'mso-bidi-font-weight:normal'>a</b>.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>The numbers <b style=3D'mso-bidi-f=
ont-weight:
normal'>n </b>and<b style=3D'mso-bidi-font-weight:normal'> a</b> are called=
 <b
style=3D'mso-bidi-font-weight:normal'><u>factors</u></b><u>.<o:p></o:p></u>=
</span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.5in;text-align:ce=
nter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>3.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The Cartesian Prod=
uct
Model<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>At Sue&#8217;s Ice Cream Shop, one can order eit=
her
a sugar cone or waffle cone and one of three flavors&#8212;vanilla, chocola=
te,
or strawberry.<span style=3D'mso-spacerun:yes'>&nbsp; </span><o:p></o:p></s=
pan></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.5in;text-align:ce=
nter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>TREE DIAGRAM<o:p></o:p></span></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.5in;text-align:ce=
nter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'><o:p>&nbsp;</o:p></span></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.5in;text-align:ce=
nter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'><o:p>&nbsp;</o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp; </span>Vanilla<span
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp; </span>sugar-vanilla<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>Sugar cone<span style=3D'mso-tab-count:2'>&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </=
span>chocolate<span
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =
</span>sugar-chocolate<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp; </span>Strawberry<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>sugar-straw=
berry<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp; </span>Vanilla<span
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp; </span>waffle-vanilla<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>Waffle cone<span style=3D'mso-tab-count:2'>&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>chocol=
ate<span
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =
</span>waffle-chocolate<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp; </span>Strawberry<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>waffle-stra=
wberry<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'>Let A=3D{sugar(s), waffle(w)} and let B=3D{vanil=
la(v),
chocolate(c), strawberry(<span class=3DSpellE>st</span>)}, then the Cartesi=
an
product A X B gives the ways an ice cream cone can be ordered at Sue&#8217;=
s.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:.5in'><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><span style=3D'mso-tab=
-count:
4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Flavors<o:=
p></o:p></u></span></p>

<h1><span style=3D'mso-tab-count:6'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>v<span style=3D'mso-tab-count:2'>&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>c<span
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp; </span><span class=3DSpellE>st</span></h1>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
>Types
of cones<span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp; </span>s<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>(<span
class=3DSpellE>s,v</span>)<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>(<sp=
an
class=3DSpellE>s,c</span>)<span style=3D'mso-tab-count:1'>&nbsp;&nbsp; </sp=
an><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n>(<span
class=3DSpellE>s,st</span>)<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><span
style=3D'mso-tab-count:5'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>w<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span>(<span class=3DSpellE>=
w,v</span>)<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>(<span
class=3DSpellE>w,c</span>)<span style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>(<span
class=3DSpellE>w,st</span>)<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'>n(A
X B) =3D 2(3) =3D 6<o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Alternat=
ive
Definition of Multiplication of Whole Numbers<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'>For
finite sets A and B, in n(A) =3D a and n(B)=3D b then<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;</span>a<sub><!--[if gte vml 1]><v:shape i=
d=3D"_x0000_i1083"
 type=3D"#_x0000_t75" style=3D'width:9pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1083"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
083"
  DrawAspect=3D"Content" ObjectID=3D"_1296384646">
 </o:OLEObject>
</xml><![endif]-->b =3D n( A X B).<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<h2><b style=3D'mso-bidi-font-weight:normal'><u><span style=3D'mso-bidi-fon=
t-style:
italic'>PROPERTIES OF WHOLE NUMBER MULTIPLICATION<o:p></o:p></span></u></b>=
</h2>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp;</span><b=
>Closure
property of multiplication of whole numbers.<o:p></o:p></b></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp; </span>F=
or any
whole numbers a and b, a b is a unique whole number.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><b><span style=3D'font-si=
ze:18.0pt;
mso-bidi-font-size:12.0pt'>Commutative property of whole numbers</span></b>=
<span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp; </span>F=
or any
whole numbers a and b,<span style=3D'mso-spacerun:yes'>&nbsp; </span>a b =
=3D b a.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<h4 style=3D'margin-left:0in'>Associative property of multiplication of who=
le
numbers</h4>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp; </span>F=
or any
whole numbers a, b and c, (a b) c =3D a ( b c).<o:p></o:p></span></p>

<h4><o:p>&nbsp;</o:p></h4>

<h4>Identity property of multiplication of whole numbers</h4>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp; </span>T=
here
is a unique whole number 1 such that for any whole number a,<span
style=3D'mso-spacerun:yes'>&nbsp; </span>a<sub><!--[if gte vml 1]><v:shape =
id=3D"_x0000_i1084"
 type=3D"#_x0000_t75" style=3D'width:9pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1084"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
084"
  DrawAspect=3D"Content" ObjectID=3D"_1296384647">
 </o:OLEObject>
</xml><![endif]-->1=3D a =3D 1<sub><!--[if gte vml 1]><v:shape id=3D"_x0000=
_i1085"
 type=3D"#_x0000_t75" style=3D'width:9pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1085"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
085"
  DrawAspect=3D"Content" ObjectID=3D"_1296384648">
 </o:OLEObject>
</xml><![endif]-->a. ( 1 is a multiplicative identity)<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<h4>Zero multiplication of whole numbers</h4>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp; </span>F=
or any
whole number a, a<sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1086" type=
=3D"#_x0000_t75"
 style=3D'width:9pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image011.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1086"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
086"
  DrawAspect=3D"Content" ObjectID=3D"_1296384649">
 </o:OLEObject>
</xml><![endif]-->0 =3D 0 =3D 0<sub><!--[if gte vml 1]><v:shape id=3D"_x000=
0_i1087"
 type=3D"#_x0000_t75" style=3D'width:9pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image012.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1087"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
087"
  DrawAspect=3D"Content" ObjectID=3D"_1296384650">
 </o:OLEObject>
</xml><![endif]-->a.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Distributive property =
of
multiplication over addition<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'>4(3 + 4) =3D ( 3 + 4) + ( 3 + 4) + <span
style=3D'mso-spacerun:yes'>&nbsp;</span>( 3 + 4) + ( 3 + 4)</span><span
style=3D'font-size:8.0pt'>( repeated addition)<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
8.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt'>=3D <span
style=3D'mso-spacerun:yes'>&nbsp;</span>( 3+3+3+3)+(4+4+4+4) </span><span
style=3D'font-size:8.0pt'>(Commutative and associative)</span><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'> =3D 4(3) +4(4)<o:p></=
o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'>Therefore<span style=3D'mso-spacerun:yes'>&nbsp;
</span>4(3 + 4) =3D 4(3) +4(4)<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Distribu=
tive
property of multiplication over addition<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp; </span>F=
or any
whole numbers a, b and c, a(b + c) =3D <span class=3DSpellE>ab</span> + ac.=
<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'>EXAMPLE-<span style=3D'mso-spacerun:yes'>&nbsp;
</span>Model 3(x + 2y + 3z)<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<table class=3DMsoTableGrid border=3D1 cellspacing=3D0 cellpadding=3D0 alig=
n=3Dleft
 style=3D'border-collapse:collapse;border:none;mso-border-alt:solid windowt=
ext .5pt;
 mso-yfti-tbllook:480;mso-table-lspace:9.0pt;margin-left:6.75pt;mso-table-r=
space:
 9.0pt;margin-right:6.75pt;mso-table-anchor-vertical:paragraph;mso-table-an=
chor-horizontal:
 margin;mso-table-left:left;mso-table-top:13.6pt;mso-padding-alt:0in 5.4pt =
0in 5.4pt;
 mso-border-insideh:.5pt solid windowtext;mso-border-insidev:.5pt solid win=
dowtext'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border:solid windowtext =
1.0pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>x<o:p=
></o:p></span></p>
  </td>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border:solid windowtext =
1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>2y<o:=
p></o:p></span></p>
  </td>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border:solid windowtext =
1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>3z<o:=
p></o:p></span></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:1'>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border:solid windowtext =
1.0pt;
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:s=
olid windowtext .5pt;
  padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>x<o:p=
></o:p></span></p>
  </td>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border-top:none;border-l=
eft:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>2y<o:=
p></o:p></span></p>
  </td>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border-top:none;border-l=
eft:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>3z<o:=
p></o:p></span></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:2;mso-yfti-lastrow:yes'>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border:solid windowtext =
1.0pt;
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:s=
olid windowtext .5pt;
  padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>x<o:p=
></o:p></span></p>
  </td>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border-top:none;border-l=
eft:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>2y<o:=
p></o:p></span></p>
  </td>
  <td width=3D96 valign=3Dtop style=3D'width:1.0in;border-top:none;border-l=
eft:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal style=3D'text-align:justify;mso-element:frame;mso-el=
ement-frame-hspace:
  9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
  mso-element-anchor-horizontal:margin;mso-element-top:13.6pt;mso-height-ru=
le:
  exactly'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>3z<o:=
p></o:p></span></p>
  </td>
 </tr>
</table>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'>Each of the following is an example of one of the
properties for multiplication of whole numbers.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Fill in the blank to complete the =
statement,
identify the property that is illustrated.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp; </span>1.
4 x 5 =3D 5 x _____<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp; </span>2.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>6(3 + 2) =3D (3 + 2) _____<o:p></o=
:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp; </span>3.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>5(2 + 9) =3D 10 + ______<o:p></o:p=
></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp; </span>4.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>6 x (7 x 2) =3D ( 7 x ___) x 2<o:p=
></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp; </span>5.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>(4 + 7) x 0 =3D ______<span
style=3D'mso-spacerun:yes'>&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp;</span><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp;</span><o=
:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Order of
Operation<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'>TRY THESE:<span style=3D'mso-tab-count:2'>&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Compute<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;
</span>1. <span style=3D'mso-spacerun:yes'>&nbsp;</span>3 + 4<sub><!--[if g=
te vml 1]><v:shape
 id=3D"_x0000_i1088" type=3D"#_x0000_t75" style=3D'width:9pt;height:9.75pt'=
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1088"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
088"
  DrawAspect=3D"Content" ObjectID=3D"_1296384651">
 </o:OLEObject>
</xml><![endif]-->2<span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
>2.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>3 + 16<sub><!--[if gte vml 1]><v:s=
hape
 id=3D"_x0000_i1089" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.=
75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image013.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1089"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
089"
  DrawAspect=3D"Content" ObjectID=3D"_1296384652">
 </o:OLEObject>
</xml><![endif]-->2<sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1090" typ=
e=3D"#_x0000_t75"
 style=3D'width:9pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D12 height=3D13
src=3D"T101Lesson2.4doc_files/image010.gif" v:shapes=3D"_x0000_i1090"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
090"
  DrawAspect=3D"Content" ObjectID=3D"_1296384653">
 </o:OLEObject>
</xml><![endif]--> 8<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-size:=
18.0pt'>3.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>6<sup>2</sup> - 3(5) &#8211; 18 <s=
ub><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1091" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.=
75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image015.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1091"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
091"
  DrawAspect=3D"Content" ObjectID=3D"_1296384654">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>2(3)<span
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp; </span><span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
>4.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>2<sup>2</sup> + 3<sup>2</sup> &#82=
11; (
4 &#8211; 2)<sup>2</sup>.<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><span style=3D'mso-ta=
b-count:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.75in;text-indent:.25in'><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:18.0pt'>Division of Whole Numbers</span></=
b><span
style=3D'font-size:18.0pt'><o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:40.5pt;text-align:=
center;
text-indent:-22.5pt;mso-list:l0 level1 lfo2;tab-stops:list 40.5pt'><![if !s=
upportLists]><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'><span style=3D'mso-list:Ignore'>1.<span style=3D'font:7.0pt "Times =
New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span></b><![endif]><b style=3D'mso-bidi-font-weight:normal'=
><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Repeated subtraction m=
odel.<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'>If
we have 15 cookies and want to package them in boxes that hold 5 cookies ea=
ch,
how many boxes are needed?<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1092" t=
ype=3D"#_x0000_t75"
 style=3D'width:198.75pt;height:15.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image016.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D265 height=3D21
src=3D"T101Lesson2.4doc_files/image017.gif" v:shapes=3D"_x0000_i1092"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
092"
  DrawAspect=3D"Content" ObjectID=3D"_1296384655">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp; </span></p>

<table class=3DMsoTableGrid border=3D1 cellspacing=3D0 cellpadding=3D0
 style=3D'border-collapse:collapse;border:none;mso-border-alt:solid windowt=
ext .5pt;
 mso-yfti-tbllook:480;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-inside=
h:
 .5pt solid windowtext;mso-border-insidev:.5pt solid windowtext'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes;
  height:17.25pt'>
  <td width=3D34 valign=3Dtop style=3D'width:25.8pt;border:solid windowtext=
 1.0pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:1=
7.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1093"=
 type=3D"#_x0000_t75"
   style=3D'width:15pt;height:15.75pt' o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D21
  src=3D"T101Lesson2.4doc_files/image019.gif" v:shapes=3D"_x0000_i1093"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
i1093"
    DrawAspect=3D"Content" ObjectID=3D"_1296384656">
   </o:OLEObject>
  </xml><![endif]--></p>
  </td>
  <td width=3D34 valign=3Dtop style=3D'width:25.8pt;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:17.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1094"=
 type=3D"#_x0000_t75"
   style=3D'width:15pt;height:15.75pt' o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D21
  src=3D"T101Lesson2.4doc_files/image019.gif" v:shapes=3D"_x0000_i1094"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
i1094"
    DrawAspect=3D"Content" ObjectID=3D"_1296384657">
   </o:OLEObject>
  </xml><![endif]--></p>
  </td>
  <td width=3D34 valign=3Dtop style=3D'width:25.8pt;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:17.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1095"=
 type=3D"#_x0000_t75"
   style=3D'width:15pt;height:15.75pt' o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D21
  src=3D"T101Lesson2.4doc_files/image019.gif" v:shapes=3D"_x0000_i1095"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
i1095"
    DrawAspect=3D"Content" ObjectID=3D"_1296384658">
   </o:OLEObject>
  </xml><![endif]--></p>
  </td>
  <td width=3D34 valign=3Dtop style=3D'width:25.8pt;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:17.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1096"=
 type=3D"#_x0000_t75"
   style=3D'width:15pt;height:15.75pt' o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D21
  src=3D"T101Lesson2.4doc_files/image019.gif" v:shapes=3D"_x0000_i1096"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
i1096"
    DrawAspect=3D"Content" ObjectID=3D"_1296384659">
   </o:OLEObject>
  </xml><![endif]--></p>
  </td>
  <td width=3D34 valign=3Dtop style=3D'width:25.8pt;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:17.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1097"=
 type=3D"#_x0000_t75"
   style=3D'width:15pt;height:15.75pt' o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D21
  src=3D"T101Lesson2.4doc_files/image019.gif" v:shapes=3D"_x0000_i1097"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
i1097"
    DrawAspect=3D"Content" ObjectID=3D"_1296384660">
   </o:OLEObject>
  </xml><![endif]--></p>
  </td>
 </tr>
</table>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1098" t=
ype=3D"#_x0000_t75"
 style=3D'width:132.75pt;height:15.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image020.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D177 height=3D21
src=3D"T101Lesson2.4doc_files/image021.gif" v:shapes=3D"_x0000_i1098"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
098"
  DrawAspect=3D"Content" ObjectID=3D"_1296384661">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp; </span><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><o:p></o:p></span></p>

<table class=3DMsoTableGrid border=3D1 cellspacing=3D0 cellpadding=3D0
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ext .5pt;
 mso-yfti-tbllook:480;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-inside=
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 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes;
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  <td width=3D31 valign=3Dtop style=3D'width:23.1pt;border:solid windowtext=
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  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:1=
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  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
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endif]></sub><!--[if gte mso 9]><xml>
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<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1104" t=
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</v:shape><![endif]--><![if !vml]><img width=3D91 height=3D21
src=3D"T101Lesson2.4doc_files/image023.gif" v:shapes=3D"_x0000_i1104"><![en=
dif]></sub><!--[if gte mso 9]><xml>
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</xml><![endif]--><span style=3D'mso-tab-count:1'> </span></p>

<table class=3DMsoTableGrid border=3D1 cellspacing=3D0 cellpadding=3D0
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h:
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  height:17.25pt'>
  <td width=3D31 valign=3Dtop style=3D'width:23.1pt;border:solid windowtext=
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  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:1=
7.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1105"=
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  <td width=3D31 valign=3Dtop style=3D'width:23.1pt;border:solid windowtext=
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  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1106"=
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   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
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  src=3D"T101Lesson2.4doc_files/image019.gif" v:shapes=3D"_x0000_i1106"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
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  </xml><![endif]--></p>
  </td>
  <td width=3D31 valign=3Dtop style=3D'width:23.1pt;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:17.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1107"=
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endif]></sub><!--[if gte mso 9]><xml>
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  </td>
  <td width=3D31 valign=3Dtop style=3D'width:23.1pt;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
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   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D21
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endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
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  </td>
  <td width=3D31 valign=3Dtop style=3D'width:23.1pt;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:17.25pt'>
  <p class=3DMsoNormal><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1109"=
 type=3D"#_x0000_t75"
   style=3D'width:15pt;height:15.75pt' o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image018.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D21
  src=3D"T101Lesson2.4doc_files/image019.gif" v:shapes=3D"_x0000_i1109"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
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  </xml><![endif]--></p>
  </td>
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</table>

<p class=3DMsoNormal><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'><o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:40.5pt;text-align:=
center;
text-indent:-22.5pt;mso-list:l0 level1 lfo2;tab-stops:list 40.5pt'><![if !s=
upportLists]><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'><span style=3D'mso-list:Ignore'>2.<span style=3D'font:7.0pt "Times =
New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span></b><![endif]><b style=3D'mso-bidi-font-weight:normal'=
><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Set (partition) model.=
<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>If we have 12 cookies and want to give an equal
number of cookies to each of 3 friends, how many cookies should each friend
receive?<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><sub><!--[if gte vml 1]><v=
:shape
 id=3D"_x0000_i1110" type=3D"#_x0000_t75" style=3D'width:159.75pt;height:15=
.75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image024.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D213 height=3D21
src=3D"T101Lesson2.4doc_files/image025.gif" v:shapes=3D"_x0000_i1110"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
110"
  DrawAspect=3D"Content" ObjectID=3D"_1296384674">
 </o:OLEObject>
</xml><![endif]--></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><sub><!--[if gte vml 1]><v=
:shape
 id=3D"_x0000_i1111" type=3D"#_x0000_t75" style=3D'width:189.75pt;height:15=
.75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image026.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D253 height=3D21
src=3D"T101Lesson2.4doc_files/image027.gif" v:shapes=3D"_x0000_i1111"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
111"
  DrawAspect=3D"Content" ObjectID=3D"_1296384675">
 </o:OLEObject>
</xml><![endif]--><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt=
'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:40.5pt;text-indent:-22.5pt;mso-li=
st:l0 level1 lfo2;
tab-stops:list 40.5pt'><![if !supportLists]><span style=3D'font-size:18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-list:Ignore'>3.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span></span><![endif]><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Missing factor model<s=
pan
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span style=3D'font-size:18=
.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:40.5pt'><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'>18 </span><sub><!--[if gte vml 1]><v:shape id=3D=
"_x0000_i1112"
 type=3D"#_x0000_t75" style=3D'width:14.25pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image028.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D19 height=3D17
src=3D"T101Lesson2.4doc_files/image029.gif" v:shapes=3D"_x0000_i1112"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
112"
  DrawAspect=3D"Content" ObjectID=3D"_1296384676">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span><span
style=3D'font-size:18.0pt'>6 =3D x<span style=3D'mso-tab-count:3'>&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>6
</span><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1113" type=3D"#_x0000=
_t75"
 style=3D'width:6.75pt;height:9.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image030.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D9 height=3D13
src=3D"T101Lesson2.4doc_files/image031.gif" v:shapes=3D"_x0000_i1113"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
113"
  DrawAspect=3D"Content" ObjectID=3D"_1296384677">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span><span
style=3D'font-size:18.0pt'>x =3D 18<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-spacerun:yes'>&nbsp; </span><=
span
style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.25in;text-align:c=
enter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>Definition of Division of Whole Numbers<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>For any whole numbers a and b with b not equal to
zero,<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
class=3DGramE>a</span> </span><sub><!--[if gte vml 1]><v:shape id=3D"_x0000=
_i1114"
 type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image032.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1114"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
114"
  DrawAspect=3D"Content" ObjectID=3D"_1296384678">
 </o:OLEObject>
</xml><![endif]--><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt=
'><span
style=3D'mso-spacerun:yes'>&nbsp;</span>b =3D c <span class=3DSpellE>iff</s=
pan> <span
class=3DSpellE>bc</span> =3D a, <b>c is unique</b>.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>a is called the <b style=3D'mso-bidi-font-weight=
:normal'><u>dividend</u></b>,
b is called the <b style=3D'mso-bidi-font-weight:normal'><u>divisor</u></b>=
 and c
is called the <b style=3D'mso-bidi-font-weight:normal'><u>quotient</u></b>.=
<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>Is the set of whole numbers closed under divisio=
n?<span
style=3D'mso-spacerun:yes'>&nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>Divide<span style=3D'mso-spacerun:yes'>&nbsp;
</span>314 <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1115" type=3D"#_x=
0000_t75"
 style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image033.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1115"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
115"
  DrawAspect=3D"Content" ObjectID=3D"_1296384679">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>31=3D c<span
style=3D'mso-spacerun:yes'>&nbsp; </span><span style=3D'mso-tab-count:1'> <=
/span><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;</span>31c =3D 314<span
style=3D'mso-spacerun:yes'>&nbsp; </span>?<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<table class=3DMsoTableGrid border=3D1 cellspacing=3D0 cellpadding=3D0
 style=3D'border-collapse:collapse;border:none;mso-border-alt:solid windowt=
ext .5pt;
 mso-yfti-tbllook:480;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-inside=
h:
 .5pt solid windowtext;mso-border-insidev:.5pt solid windowtext'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td width=3D197 valign=3Dtop style=3D'width:2.05in;border:solid windowtex=
t 1.0pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:1=
2.0pt'>31
  </span><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1116" type=3D"#_x00=
00_t75"
   style=3D'width:6.75pt;height:9.75pt' o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image034.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D9 height=3D13
  src=3D"T101Lesson2.4doc_files/image031.gif" v:shapes=3D"_x0000_i1116"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
i1116"
    DrawAspect=3D"Content" ObjectID=3D"_1296384680">
   </o:OLEObject>
  </xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span><span
  style=3D'font-size:18.0pt'>10</span><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
  12.0pt'><o:p></o:p></span></p>
  </td>
  <td width=3D197 valign=3Dtop style=3D'width:2.05in;border:solid windowtex=
t 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:1=
2.0pt'><span
  style=3D'mso-spacerun:yes'>&nbsp;</span>31 </span><sub><!--[if gte vml 1]=
><v:shape
   id=3D"_x0000_i1117" type=3D"#_x0000_t75" style=3D'width:6.75pt;height:9.=
75pt'
   o:ole=3D"">
   <v:imagedata src=3D"T101Lesson2.4doc_files/image035.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D9 height=3D13
  src=3D"T101Lesson2.4doc_files/image031.gif" v:shapes=3D"_x0000_i1117"><![=
endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_=
i1117"
    DrawAspect=3D"Content" ObjectID=3D"_1296384681">
   </o:OLEObject>
  </xml><![endif]--><span style=3D'font-size:18.0pt'>11<o:p></o:p></span></=
p>
  </td>
  <td width=3D197 valign=3Dtop style=3D'width:2.05in;border:solid windowtex=
t 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:1=
2.0pt'><o:p>&nbsp;</o:p></span></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:1;mso-yfti-lastrow:yes'>
  <td width=3D197 valign=3Dtop style=3D'width:2.05in;border:solid windowtex=
t 1.0pt;
  border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:s=
olid windowtext .5pt;
  padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:1=
2.0pt'><span
  style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>310<o:p></o:p></span></p>
  </td>
  <td width=3D197 valign=3Dtop style=3D'width:2.05in;border-top:none;border=
-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:1=
2.0pt'><span
  style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span>341<o:p></o:p></span=
></p>
  </td>
  <td width=3D197 valign=3Dtop style=3D'width:2.05in;border-top:none;border=
-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:1=
2.0pt'><o:p>&nbsp;</o:p></span></p>
  </td>
 </tr>
</table>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>314 <sub><!--[if gte vml 1]><v:shape id=3D"_x000=
0_i1118"
 type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1118"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
118"
  DrawAspect=3D"Content" ObjectID=3D"_1296384682">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>31 =3D 10 w=
ith a
remainder of 4.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Therefore div=
ision
is not closed<o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.25in;text-align:c=
enter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>Division Algorithm<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>Given any whole numbers a and b with b<sub><!--[=
if gte vml 1]><v:shape
 id=3D"_x0000_i1119" type=3D"#_x0000_t75" style=3D'width:14.25pt;height:14.=
25pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image037.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D19 height=3D19
src=3D"T101Lesson2.4doc_files/image038.gif" v:shapes=3D"_x0000_i1119"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
119"
  DrawAspect=3D"Content" ObjectID=3D"_1296384683">
 </o:OLEObject>
</xml><![endif]--> 0, there exists unique whole numbers q(quotient) and r
(remainder) such that<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nb=
sp;
</span>a =3D <span class=3DSpellE>bq</span> + r with 0 </span><sub><!--[if =
gte vml 1]><v:shape
 id=3D"_x0000_i1120" type=3D"#_x0000_t75" style=3D'width:15.75pt;height:18p=
t' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image039.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D21 height=3D24
src=3D"T101Lesson2.4doc_files/image040.gif" v:shapes=3D"_x0000_i1120"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
120"
  DrawAspect=3D"Content" ObjectID=3D"_1296384684">
 </o:OLEObject>
</xml><![endif]--><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt=
'><span
style=3D'mso-spacerun:yes'>&nbsp;</span>r &lt; b.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>When the remainder is zero we say the b divides =
a,
or a is divisible by b, or b is a divisor of a.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><b style=3D'mso-bidi-font-=
weight:
normal'><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>Example<=
/span></b><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>:<span
style=3D'mso-spacerun:yes'>&nbsp; </span>If 118 is divided by a number and =
the
remainder is 8, what are the possible divisors?<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbs=
p; </span>118
=3D <span class=3DSpellE>bq</span> + 8<span style=3D'mso-spacerun:yes'>&nbs=
p;&nbsp;
</span><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp; </span>b
&gt; 8<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span class=3DGramE><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>b</span><sub><!--[if g=
te vml 1]><v:shape
 id=3D"_x0000_i1121" type=3D"#_x0000_t75" style=3D'width:33.75pt;height:44.=
25pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image041.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D45 height=3D59
src=3D"T101Lesson2.4doc_files/image042.gif" v:shapes=3D"_x0000_i1121"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
121"
  DrawAspect=3D"Content" ObjectID=3D"_1296384685">
 </o:OLEObject>
</xml><![endif]--></span><span style=3D'font-size:18.0pt;mso-bidi-font-size=
:12.0pt'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.25in;text-align:c=
enter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>Relating Multiplication and Division<o:p></o:p></span></b></p>

<h1><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></b></h1>

<h1><span style=3D'font-size:18.0pt'>Division is in the inverse of multipli=
cation.<o:p></o:p></span></h1>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>Subtraction is the in=
verse of
addition.<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>Multiplication is rep=
eated
addition.<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>Division is repeated
subtraction.<o:p></o:p></span></p>

<h1 align=3Dcenter style=3D'text-align:center'><b style=3D'mso-bidi-font-we=
ight:normal'>Division
by 0 and 1<o:p></o:p></b></h1>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:18.0pt'>TRY THESE<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>1.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>2 </span><span style=3D'font-size:=
18.0pt;
mso-bidi-font-size:12.0pt'><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1=
027"
 type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1027"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
027"
  DrawAspect=3D"Content" ObjectID=3D"_1296384686">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>0 =3D ___<s=
pan
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
>2.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>0 <sub><!--[if gte vml 1]><v:shape=
 id=3D"_x0000_i1028"
 type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1028"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
028"
  DrawAspect=3D"Content" ObjectID=3D"_1296384687">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>2 =3D ___<s=
pan
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span>3.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>0 <sub><!--[if gte vml 1]><v:shape=
 id=3D"_x0000_i1029"
 type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1029"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
029"
  DrawAspect=3D"Content" ObjectID=3D"_1296384688">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>0 =3D ___<s=
pan
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'>4.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>5 <sub><!--[if gte vml 1]><v:shape=
 id=3D"_x0000_i1030"
 type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1030"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
030"
  DrawAspect=3D"Content" ObjectID=3D"_1296384689">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>1 =3D ___<s=
pan
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
>5.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>8 <sub><!--[if gte vml 1]><v:shape=
 id=3D"_x0000_i1031"
 type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.75pt' o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1031"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
031"
  DrawAspect=3D"Content" ObjectID=3D"_1296384690">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>1 =3D ___</=
span><span
style=3D'font-size:18.0pt'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'margin-left:.25in;text-align:c=
enter'><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;mso-b=
idi-font-size:
12.0pt'>Rules<o:p></o:p></span></b></p>

<p class=3DMsoNormal style=3D'margin-left:40.5pt;text-indent:-22.5pt;mso-li=
st:l2 level1 lfo3;
tab-stops:list 40.5pt'><![if !supportLists]><span style=3D'font-size:18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-list:Ignore'>1.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span></span><![endif]><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>n<sub><!--[if gte vml =
1]><v:shape
 id=3D"_x0000_i1032" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.=
75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1032"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
032"
  DrawAspect=3D"Content" ObjectID=3D"_1296384691">
 </o:OLEObject>
</xml><![endif]--> 0 is undefined<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:40.5pt;text-indent:-22.5pt;mso-li=
st:l2 level1 lfo3;
tab-stops:list 40.5pt'><![if !supportLists]><span style=3D'font-size:18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-list:Ignore'>2.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span></span><![endif]><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>0<sub><!--[if gte vml =
1]><v:shape
 id=3D"_x0000_i1033" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.=
75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1033"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
033"
  DrawAspect=3D"Content" ObjectID=3D"_1296384692">
 </o:OLEObject>
</xml><![endif]--> n =3D 0<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:40.5pt;text-indent:-22.5pt;mso-li=
st:l2 level1 lfo3;
tab-stops:list 40.5pt'><![if !supportLists]><span style=3D'font-size:18.0pt;
mso-bidi-font-size:12.0pt'><span style=3D'mso-list:Ignore'>3.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span></span><![endif]><span
style=3D'font-size:18.0pt;mso-bidi-font-size:12.0pt'>0<sub><!--[if gte vml =
1]><v:shape
 id=3D"_x0000_i1025" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.=
75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1025"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
025"
  DrawAspect=3D"Content" ObjectID=3D"_1296384693">
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</xml><![endif]--> 0 is indeterminate or undefined<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt;mso-bidi-font-size:12.=
0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'font-size:1=
8.0pt;
mso-bidi-font-size:12.0pt'>4.<span style=3D'mso-spacerun:yes'>&nbsp; </span=
>n <sub><!--[if gte vml 1]><v:shape
 id=3D"_x0000_i1026" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12.=
75pt'
 o:ole=3D"">
 <v:imagedata src=3D"T101Lesson2.4doc_files/image036.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D17 height=3D17
src=3D"T101Lesson2.4doc_files/image014.gif" v:shapes=3D"_x0000_i1026"><![en=
dif]></sub><!--[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
026"
  DrawAspect=3D"Content" ObjectID=3D"_1296384694">
 </o:OLEObject>
</xml><![endif]--><span style=3D'mso-spacerun:yes'>&nbsp;</span>a =3D n<o:p=
></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>Use the distributive =
property
to factor.<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>1.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>3x + 18<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>2.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>7x<sup>2</sup> + 14x<o:p></o:p></s=
pan></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>3.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>3(x + 2) + a(x + 2)<o:p></o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>Class work Bases Acti=
vity 1 <o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>Homework Math XL sect=
ion 2.4
and book work #4, 8, 11, 12, 13, 14, 15, 16a, 19, 21, 23a, 24, 29, 32, 33, =
34,
37, 42<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>DUE BY ______________=
____<o:p></o:p></span></p>

</div>

</body>

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