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ng
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0%;
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></div>
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'></div>
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'></div>
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bsolute;
 top:24.5%;left:11.04%;width:83.33%;height:6.75%'><span style=3D'mso-specia=
l-format:
 bullet;position:absolute;left:-6.06%'>&#8226;</span>On your note cards, wr=
ite
 a specific </span><span style=3D'position:absolute;top:31.5%;left:11.04%;
 width:96.06%;height:6.75%'>question that involves a <i>math procedure</i>.
 &#13;</span></div>
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v>
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%;
 left:5.99%;width:91.38%;height:6.75%'><span style=3D'position:absolute;
 top:0%;left:5.53%;width:94.46%;height:100.0%'><span style=3D'mso-special-f=
ormat:
 bullet;position:absolute;left:-5.85%'>&#8226;</span>Answer your question, =
and
 consider:&#13;</span></div>
 <div class=3DB1 style=3D'mso-margin-left-alt:766;mso-text-indent-alt:430;
 position:absolute;top:55.75%;left:13.48%;width:84.83%;height:6.0%'><span
 style=3D'position:absolute;top:0%;left:6.84%;width:93.15%;height:100.0%'><=
span
 style=3D'mso-special-format:bullet;position:absolute;left:-7.34%'>&#8211;<=
/span>What
 would an &#8220;expert&#8221; know and do? &#13;</span></div>
 <div class=3DB1 style=3D'mso-margin-left-alt:766;mso-text-indent-alt:430'>=
<span
 style=3D'position:absolute;top:63.24%;left:19.28%;width:75.84%;height:6.0%=
'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-7.65%'>&#8211;<=
/span>How
 does this compare to what your </span><span style=3D'position:absolute;
 top:69.5%;left:19.28%;width:74.9%;height:6.0%'>students know and do? &#13;=
</span></div>
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pan
 style=3D'mso-special-format:bullet;position:absolute;left:-7.75%'>&#8211;<=
/span>How
 can we bridge that gap?</span></div>
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0%;
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 <div class=3DB2 style=3D'mso-margin-left-alt:1126;mso-text-indent-alt:838'=
></div>
 <div class=3DB3 style=3D'mso-margin-left-alt:1438;mso-text-indent-alt:1198=
'></div>
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'></div>
 <div class=3DB style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:288;
 position:absolute;top:23.25%;left:5.99%;width:88.2%;height:6.0%'><span
 style=3D'position:absolute;top:0%;left:5.73%;width:94.26%;height:100.0%'><=
span
 style=3D'font-size:88%'><span style=3D'mso-special-format:bullet;position:=
absolute;
 left:-6.08%'>&#8226;</span></span><span style=3D'font-size:88%'>Solve:&#13=
;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:29.5%;left:13.48%;width:80.7=
1%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo=
rmat:
 "numbullet3\,1";position:absolute;left:-7.75%'>1.</span></span><span
 style=3D'font-size:86%'>2x - 1 =3D 6&#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:34.75%;left:13.48%;width:80.=
71%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo=
rmat:
 "numbullet3\,1";position:absolute;left:-7.75%'>2.</span></span><span
 style=3D'font-size:86%'>|x &#8211; 3| &lt; 5&#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:40.0%;left:13.48%;width:80.7=
1%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo=
rmat:
 "numbullet3\,1";position:absolute;left:-7.75%'>3.</span></span><span
 style=3D'font-size:86%'>x</span><span style=3D'font-size:57%;position:rela=
tive;
 top:-.45em;mso-text-raise:30%'>2</span><span style=3D'font-size:86%'><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>+ 3x &#8211; 4 =3D 0&#13;</span></=
span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:45.5%;left:13.48%;width:80.7=
1%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo=
rmat:
 "numbullet3\,1";position:absolute;left:-7.75%'>4.</span></span><span
 style=3D'font-size:86%'>2x + 3y &lt; 6&#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:50.74%;left:13.48%;width:80.=
71%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo=
rmat:
 "numbullet3\,1";position:absolute;left:-7.75%'>5.</span></span><span
 style=3D'font-size:86%'>3x + 4y =3D 14, and y =3D -(5/2)x&#13;</span></spa=
n></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:56.0%;left:13.48%;width:80.7=
1%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%;visibility:hidden'><span
 style=3D'mso-special-format:"numbullet3\,1";position:absolute;left:-7.75%'=
>6.</span></span><span
 style=3D'font-size:86%;display:none'>&#13;</span></span></div>
 <div class=3DB style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:288;
 position:absolute;top:61.5%;left:5.99%;width:88.2%;height:6.0%'><span
 style=3D'position:absolute;top:0%;left:5.73%;width:94.26%;height:100.0%'><=
span
 style=3D'font-size:88%'><span style=3D'mso-special-format:bullet;position:=
absolute;
 left:-6.08%'>&#8226;</span></span><span style=3D'font-size:88%'>Consider:&=
#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:67.75%;left:13.48%;width:80.=
71%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo=
rmat:
 bullet;position:absolute;left:-7.75%'>&#8211;</span></span><span
 style=3D'font-size:86%'>What would an &#8220;expert&#8221; know and do? &#=
13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
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9.28%;
 width:81.08%;height:5.25%'><span style=3D'font-size:86%'><span style=3D'ms=
o-special-format:
 bullet;position:absolute;left:-7.15%'>&#8211;</span></span><span
 style=3D'font-size:86%'>How does this compare to what your students </span=
></span><span
 style=3D'position:absolute;top:77.25%;left:19.28%;width:74.9%;height:5.25%=
'><span
 style=3D'font-size:86%'>know and do?&#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"80 20 0";mso-margin-left-alt:76=
6;
 mso-text-indent-alt:430;position:absolute;top:82.5%;left:13.48%;width:80.7=
1%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:7.19%;width:92.=
8%;
 height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo=
rmat:
 bullet;position:absolute;left:-7.75%'>&#8211;</span></span><span
 style=3D'font-size:86%'>How can we bridge that gap?</span></span></div>
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ype of
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14%;
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oncepts,
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sition:
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hallow
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ovice
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 style=3D'position:absolute;top:0%;left:4.6%;width:95.39%;height:100.0%'><s=
pan
 style=3D'mso-special-format:bullet;position:absolute;left:-4.83%'>&#8211;<=
/span>Solve:
 2x - 1 =3D 6&#13;</span></div>
 <div class=3DB1 style=3D'mso-margin-left-alt:611;mso-text-indent-alt:395;
 position:absolute;top:47.25%;left:12.92%;width:81.27%;height:6.0%'><span
 style=3D'position:absolute;top:0%;left:4.6%;width:95.39%;height:100.0%'><s=
pan
 style=3D'mso-special-format:bullet;position:absolute;left:-4.83%'>&#8211;<=
/span>Solve:
 |x &#8211; 3| &lt; 5&#13;</span></div>
 <div class=3DB1 style=3D'mso-margin-left-alt:611;mso-text-indent-alt:395;
 position:absolute;top:54.75%;left:12.92%;width:81.27%;height:6.0%'><span
 style=3D'position:absolute;top:0%;left:4.6%;width:95.39%;height:100.0%'><s=
pan
 style=3D'mso-special-format:bullet;position:absolute;left:-4.83%'>&#8211;<=
/span>Solve:
 x<span style=3D'font-size:67%;position:relative;top:-.45em;mso-text-raise:=
30%'>2</span><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>+ 3x &#8211; 4 =3D 0&#13;</span></=
div>
 <div class=3DB1 style=3D'mso-margin-left-alt:611;mso-text-indent-alt:395;
 position:absolute;top:62.25%;left:12.92%;width:81.27%;height:6.0%'><span
 style=3D'position:absolute;top:0%;left:4.6%;width:95.39%;height:100.0%'><s=
pan
 style=3D'mso-special-format:bullet;position:absolute;left:-4.83%'>&#8211;<=
/span>Solve:
 2x + 3y &lt; 6&#13;</span></div>
 <div class=3DB1 style=3D'mso-margin-left-alt:611;mso-text-indent-alt:395;
 position:absolute;top:69.75%;left:12.92%;width:81.27%;height:6.0%'><span
 style=3D'position:absolute;top:0%;left:4.6%;width:95.39%;height:100.0%'><s=
pan
 style=3D'mso-special-format:bullet;position:absolute;left:-4.83%'>&#8211;<=
/span>Solve:
 3x + 4y =3D 14 and y =3D -(5/2)x&#13;</span></div>
 <div class=3DB style=3D'mso-margin-left-alt:323;position:absolute;top:77.5=
%;
 left:5.99%;width:88.2%;height:6.75%'><span style=3D'position:absolute;
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dden'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-6.8%'>&#8226;</=
span></span><span
 style=3D'mso-special-format:lastCR;display:none'>&#13;</span></span></div>
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 top:2.96%;left:44.04%;width:48.18%;height:11.85%'><span style=3D'mso-hansi=
-font-family:
 Arial'>1a) What is the goal of the procedure?&#13;</span></div>
 <div class=3DO style=3D'mso-char-wrap:0;mso-kinsoku-overflow:0;position:ab=
solute;
 top:14.81%;left:44.04%;width:50.43%;height:11.85%'><span style=3D'mso-hans=
i-font-family:
 Arial'>1b) What sort of answer should I expect?&#13;</span></div>
 <div class=3DO style=3D'mso-char-wrap:0;mso-kinsoku-overflow:0;position:ab=
solute;
 top:26.66%;left:44.04%;width:48.18%;height:11.85%'><span style=3D'mso-hans=
i-font-family:
 Arial;color:blue'>2a) How do I carry out the procedure?&#13;</span></div>
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solute;
 top:38.51%;left:44.04%;width:48.7%;height:11.85%'><span style=3D'mso-hansi=
-font-family:
 Arial'>2b) What other procedures could I use?&#13;</span></div>
 <div class=3DO style=3D'mso-char-wrap:0;mso-kinsoku-overflow:0;position:ab=
solute;
 top:50.37%;left:44.04%;width:48.18%;height:11.85%'><span style=3D'mso-hans=
i-font-family:
 Arial'>3)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>Why does the
 procedure work?&#13;</span></div>
 <div class=3DO style=3D'mso-char-wrap:0;mso-kinsoku-overflow:0;position:ab=
solute;
 top:62.22%;left:44.04%;width:48.18%;height:11.85%'><span style=3D'mso-hans=
i-font-family:
 Arial'>4)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>How can I ve=
rify
 my answer?&#13;</span></div>
 <div class=3DO style=3D'mso-char-wrap:0;mso-kinsoku-overflow:0;position:ab=
solute;
 top:74.07%;left:44.04%;width:55.61%;height:11.85%'><span style=3D'mso-hans=
i-font-family:
 Arial'>5)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>When is this=
 the
 &#8220;best&#8221; procedure to use?&#13;</span></div>
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solute;
 top:85.92%;left:44.04%;width:55.95%;height:11.85%'><span style=3D'mso-hans=
i-font-family:
 Arial'>6)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>What else ca=
n I
 use this procedure to do?</span></div>
 </div>
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 <div class=3DO3 style=3D'mso-margin-left-alt:1008'></div>
 <div class=3DO4 style=3D'mso-margin-left-alt:1296'></div>
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flow:
 0'><span style=3D'position:absolute;top:5.0%;left:3.55%;width:93.07%;heigh=
t:
 11.5%'><span style=3D'font-family:"Comic Sans MS";mso-ascii-font-family:"C=
omic Sans MS";
 mso-hansi-font-family:"Comic Sans MS";font-size:244%;color:black;mso-color=
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 3;mso-special-format:lastCR;display:none'><b><i>&#13;</i></b></span></span=
></div>
 </div>
 <div v:shape=3D"_x0000_s12309" class=3DT><span style=3D'position:absolute;
 top:5.75%;left:-2.62%;width:105.61%;height:6.75%'><span style=3D'font-size=
:73%'><b>Framework
 for Procedural Understanding <br>
  </b></span></span><span style=3D'position:absolute;top:12.75%;left:5.43%;
 width:89.32%;height:6.75%'><span style=3D'font-size:73%'><b>(or, Eight Alg=
ebraic
 Habits of Mind)</b></span><span style=3D'font-size:91%;mso-special-format:=
lastCR;
 display:none'>&#13;</span></span></div>
 <div v:shape=3D"_x0000_s12310" class=3DO1>
 <div style=3D'position:absolute;top:23.25%;left:15.16%;width:50.74%;height=
:5.25%'><span
 style=3D'font-size:133%'>Solve: 2x - 1 =3D 6&#13;</span></div>
 <div style=3D'position:absolute;top:28.49%;left:15.16%;width:50.74%;height=
:5.25%'><span
 style=3D'font-size:133%'>Solve: |x &#8211; 3| &lt; 5&#13;</span></div>
 <div style=3D'position:absolute;top:33.75%;left:15.16%;width:50.74%;height=
:5.25%'><span
 style=3D'font-size:133%'>Solve: x</span><span style=3D'font-size:89%;posit=
ion:
 relative;top:-.45em;mso-text-raise:30%'>2</span><span style=3D'font-size:1=
33%'><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>+ 3x &#8211; 4 =3D 0&#13;</span></=
div>
 <div style=3D'position:absolute;top:39.25%;left:15.16%;width:50.74%;height=
:5.25%'><span
 style=3D'font-size:133%'>Solve: 2x + 3y &lt; 6&#13;</span></div>
 <span style=3D'position:absolute;top:44.5%;left:15.16%;width:51.12%;height=
:5.25%'><span
 style=3D'font-size:133%'>Solve: 3x + 4y =3D 14 and y =3D -</span></span><s=
pan
 style=3D'position:absolute;top:49.75%;left:15.16%;width:50.74%;height:5.25=
%'><span
 style=3D'font-size:133%'>(5/2)x</span></span></div>
 <div v:shape=3D"_x0000_s12311" class=3DO style=3D'position:absolute;top:86=
.0%;
 left:3.37%;width:87.64%;height:4.0%'>Adapted from NCTM&#8217;s Navigating
 through Algebra in Grades 9-12</div>
</p:slide></div>

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0%;
 left:5.99%;width:88.2%;height:9.25%'>Benefits of Understanding</div>
 <div v:shape=3D"_x0000_s54275" class=3DB><span style=3D'position:absolute;
 top:24.25%;left:9.73%;width:84.45%;height:6.0%'><span style=3D'font-size:8=
8%'><span
 class=3DBB style=3D'position:absolute;left:-4.43%'>&#8226;</span></span><s=
pan
 style=3D'font-size:88%'>If existing knowledge is understood, new </span></=
span><span
 style=3D'position:absolute;top:30.5%;left:9.73%;width:93.25%;height:6.0%'>=
<span
 style=3D'font-size:88%'>knowledge is easier to learn and understand.<span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span></span></span><span
 style=3D'position:absolute;top:36.75%;left:9.73%;width:84.45%;height:4.0%'=
><span
 style=3D'font-size:56%'>(Hiebert &amp; Carpenter, 1992) &#13;</span></span>
 <div style=3D'position:absolute;top:41.5%;left:5.99%;width:88.2%;height:4.=
0%'><span
 style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;height:100.0%'><=
span
 style=3D'font-size:56%;visibility:hidden'><span class=3DBB style=3D'positi=
on:absolute;
 left:-4.43%'>&#8226;</span></span><span style=3D'font-size:56%;display:non=
e'>&#13;</span></span></div>
 <span style=3D'position:absolute;top:47.0%;left:9.73%;width:92.69%;height:=
6.0%'><span
 style=3D'font-size:88%'><span class=3DBB style=3D'position:absolute;left:-=
4.04%'>&#8226;</span></span><span
 style=3D'font-size:88%'>Knowledge that is understood is more robust </span=
></span><span
 style=3D'position:absolute;top:53.0%;left:9.73%;width:87.82%;height:6.0%'>=
<span
 style=3D'font-size:88%'>and can be used flexibly within and across </span>=
</span><span
 style=3D'position:absolute;top:59.25%;left:9.73%;width:87.45%;height:6.0%'=
><span
 style=3D'font-size:88%'>different contexts. </span><span style=3D'font-siz=
e:56%'>(Carpenter
 &amp; Lehrer, 1999; Hiebert &amp; </span></span><span style=3D'position:ab=
solute;
 top:65.5%;left:9.73%;width:84.45%;height:4.0%'><span style=3D'font-size:56=
%'>Carpenter,
 1992; Van Hiele, 1986)<br>
  </span></span><span style=3D'position:absolute;top:69.5%;left:9.73%;width=
:84.45%;
 height:4.0%'><span style=3D'font-size:56%'><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>&#13;</span></span><span
 style=3D'position:absolute;top:74.5%;left:9.73%;width:93.82%;height:5.25%'=
><span
 style=3D'font-size:75%'><span class=3DBB style=3D'position:absolute;left:-=
3.99%'>&#8226;</span></span><span
 style=3D'font-size:75%'>Students should use procedures &#8220;flexibly,
 accurately, </span></span><span style=3D'position:absolute;top:80.0%;left:=
9.73%;
 width:98.31%;height:5.25%'><span style=3D'font-size:75%'>efficiently, and
 appropriately&#8221; </span><span style=3D'font-size:56%'>(National Resear=
ch
 Council, 2001)</span><span style=3D'font-size:63%;display:none'>&#13;</spa=
n></span>
 <div style=3D'position:absolute;top:86.0%;left:5.99%;width:88.2%;height:4.=
0%'><span
 style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;height:100.0%'><=
span
 style=3D'font-size:56%;visibility:hidden'><span class=3DBB style=3D'positi=
on:absolute;
 left:-4.43%'>&#8226;</span></span><span style=3D'font-size:56%;mso-special=
-format:
 lastCR;display:none'>&#13;</span></span></div>
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%;
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op:24.5%;
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bsolute;
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pan
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what
 impact does it have on student </span><span style=3D'position:absolute;
 top:38.5%;left:9.73%;width:84.45%;height:6.75%'>learning?&#13;</span><span
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'><span
 class=3DBB style=3D'position:absolute;left:-4.43%'>&#8226;</span>Algebra t=
ests
 given to students in 9 </span><span style=3D'position:absolute;top:54.25%;
 left:9.73%;width:101.12%;height:6.75%'>participating classrooms and 5
 comparison </span><span style=3D'position:absolute;top:61.25%;left:9.73%;
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5%;
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 Assessment Tasks</span></div>
 <div v:shape=3D"_x0000_s23555">
 <div class=3DB1 style=3D'mso-margin-left-alt:624'></div>
 <div class=3DB2 style=3D'mso-margin-left-alt:864'></div>
 <div class=3DB3 style=3D'mso-margin-left-alt:1104'></div>
 <div class=3DB4 style=3D'mso-margin-left-alt:1392'></div>
 <div class=3DB style=3D'mso-margin-left-alt:384'><span style=3D'position:a=
bsolute;
 top:24.25%;left:12.73%;width:82.2%;height:6.0%'><span style=3D'font-size:8=
8%;
 color:#006600'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-8.2%'>&#8226;</span></span><span style=3D'font-size:88%;color:#00660=
0'>3.1)
 What is the value of the expression <br>
  </span></span><span style=3D'position:absolute;top:30.5%;left:12.73%;
 width:81.46%;height:6.0%'><span style=3D'font-size:88%;color:#006600'><span
 style=3D'mso-tab-count:1;width:4.09%'> </span>(x+1)(x+2) when </span><span
 style=3D'font-size:88%;color:#006600'><i>x</i></span><span style=3D'font-s=
ize:
 88%;color:#006600'> =3D -4?&#13;</span></span></div>
 <div class=3DB style=3D'mso-margin-left-alt:384'><span style=3D'position:a=
bsolute;
 top:38.0%;left:12.73%;width:84.45%;height:6.0%'><span style=3D'font-size:8=
8%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-7.98%'>&#8226;<=
/span></span><span
 style=3D'font-size:88%'>3.2) Could (x+1)(x+2) ever be a negative <br>
  </span></span><span style=3D'position:absolute;top:44.25%;left:12.73%;
 width:81.46%;height:6.0%'><span style=3D'font-size:88%'><span style=3D'mso=
-tab-count:
 1;width:4.09%'> </span>number? Explain.&#13;</span></span></div>
 <div class=3DB style=3D'mso-margin-left-alt:384;position:absolute;top:51.7=
4%;
 left:5.99%;width:88.2%;height:6.0%'><span style=3D'mso-special-format:nobu=
llet;
 display:none'>&#8226;</span><span style=3D'font-size:88%;display:none'>&#1=
3;</span></div>
 <div class=3DB style=3D'mso-margin-left-alt:384'><span style=3D'position:a=
bsolute;
 top:59.25%;left:12.73%;width:84.08%;height:6.0%'><span style=3D'font-size:=
88%;
 color:#006600'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-8.01%'>&#8226;</span></span><span style=3D'font-size:88%;color:#0066=
00'>3.3)
 Solve this equation for </span><span style=3D'font-size:88%;color:#006600'=
><i>x</i></span><span
 style=3D'font-size:88%;color:#006600'>. Show your <br>
  </span></span><span style=3D'position:absolute;top:65.5%;left:12.73%;
 width:81.46%;height:6.0%'><span style=3D'font-size:88%;color:#006600'><span
 style=3D'mso-tab-count:1;width:4.09%'> </span>steps.<span
 style=3D'mso-spacerun:yes'>&nbsp; </span>5x &#8211; 6 =3D 4x + 3&#13;</spa=
n></span></div>
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Will
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me
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0%;
 left:5.99%;width:88.2%;height:9.25%'>Quantifying Understanding</div>
 <div v:shape=3D"_x0000_s26630">
 <div class=3DB><span style=3D'position:absolute;top:24.5%;left:9.73%;width=
:84.83%;
 height:6.75%'><span class=3DBB style=3D'position:absolute;left:-4.41%'>&#8=
226;</span>Task-specific
 rubrics are needed for </span><span style=3D'position:absolute;top:31.5%;
 left:9.73%;width:94.0%;height:6.75%'>evaluating the degree of understandin=
g:
 <br>
  </span><span style=3D'position:absolute;top:38.5%;left:9.73%;width:84.45%;
 height:6.0%'><span style=3D'font-size:88%'>(0 =3D no, 1 =3D low, 2 =3D mod=
erate, 3 =3D
 high)&#13;</span></span></div>
 <div class=3DB1 style=3D'position:absolute;top:45.75%;left:11.04%;width:83=
.14%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.1=
7%;
 height:100.0%'><span style=3D'font-size:86%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.74%'>&#8211;</span></span><span style=3D'font-size:86%'>T=
asks
 3.1 &amp; 3.2&#13;</span></span></div>
 <div class=3DB1 style=3D'position:absolute;top:52.25%;left:11.04%;width:83=
.14%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.1=
7%;
 height:100.0%'><span style=3D'font-size:86%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.74%'>&#8211;</span></span><span style=3D'font-size:86%'>T=
asks
 3.3 &amp; 3.4&#13;</span></span></div>
 <div class=3DB1 style=3D'position:absolute;top:58.5%;left:11.04%;width:83.=
14%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.1=
7%;
 height:100.0%'><span style=3D'font-size:86%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.74%'>&#8211;</span></span><span style=3D'font-size:86%'>T=
ask
 3.15 and 3.16&#13;</span></span></div>
 <div class=3DB><span style=3D'position:absolute;top:65.25%;left:9.73%;widt=
h:84.45%;
 height:6.0%'><span style=3D'font-size:88%'><span class=3DBB style=3D'posit=
ion:absolute;
 left:-4.43%'>&#8226;</span></span><span style=3D'font-size:88%'>What do you
 notice about the student </span></span><span style=3D'position:absolute;
 top:71.5%;left:9.73%;width:84.45%;height:6.0%'><span style=3D'font-size:88=
%'>responses?&#13;</span></span></div>
 <div class=3DB style=3D'position:absolute;top:79.0%;left:5.99%;width:88.2%;
 height:6.75%'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.=
75%;
 height:100.0%'><span style=3D'visibility:hidden'><span class=3DBB
 style=3D'position:absolute;left:-4.43%'>&#8226;</span></span>&#13;</span><=
/div>
 <div class=3DB1 style=3D'position:absolute;top:87.5%;left:11.04%;width:83.=
14%;
 height:6.0%'><span style=3D'mso-special-format:nobullet;display:none'>&#82=
11;</span><span
 style=3D'mso-special-format:lastCR;display:none'>&#13;</span></div>
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 <div class=3DB><span style=3D'position:absolute;top:24.25%;left:9.73%;widt=
h:99.43%;
 height:6.0%'><span style=3D'font-size:88%'><span class=3DBB style=3D'posit=
ion:absolute;
 left:-3.76%'>&#8226;</span></span><span style=3D'font-size:88%'>3.15) If 3=
x + 4y
 =3D 14, and y =3D -(5/2)x, what is the </span></span><span style=3D'positi=
on:absolute;
 top:30.5%;left:9.73%;width:84.45%;height:6.0%'><span style=3D'font-size:88=
%'>value
 of x?&#13;</span></span></div>
 <div class=3DB style=3D'position:absolute;top:38.0%;left:5.99%;width:88.2%;
 height:6.0%'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.7=
5%;
 height:100.0%'><span style=3D'font-size:88%;visibility:hidden'><span class=
=3DBB
 style=3D'position:absolute;left:-4.43%'>&#8226;</span></span><span
 style=3D'font-size:88%;display:none'>&#13;</span></span></div>
 <div class=3DB1 style=3D'position:absolute;top:45.25%;left:11.04%;width:98=
.5%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:3.04%;width:96.=
76%;
 height:100.0%'><span style=3D'font-size:86%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.14%'>&#8211;</span></span><span style=3D'font-size:86%'>0:
 Blank or no honest effort (e.g. &quot;I don't know (IDK.)&quot;)&#13;</spa=
n></span></div>
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 style=3D'position:absolute;left:-3.23%'>&#8211;</span></span><span
 style=3D'font-size:86%'>1: Two or more mistakes present OR an incomplete, =
</span></span><span
 style=3D'position:absolute;top:56.99%;left:14.04%;width:80.71%;height:5.25=
%'><span
 style=3D'font-size:86%'>illogical, confusing, or way off track response.&#=
13;</span></span></div>
 <div class=3DB1 style=3D'position:absolute;top:63.5%;left:11.04%;width:86.=
51%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:3.46%;width:96.=
32%;
 height:100.0%'><span style=3D'font-size:86%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.59%'>&#8211;</span></span><span style=3D'font-size:86%'>2=
: Only
 one mistake with an attempted answer.&#13;</span></span></div>
 <div class=3DB1 style=3D'position:absolute;top:69.75%;left:11.04%;width:83=
.14%;
 height:5.25%'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.1=
7%;
 height:100.0%'><span style=3D'font-size:86%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.74%'>&#8211;</span></span><span style=3D'font-size:86%'>3:
 Correct answer is provided.&#13;</span></span></div>
 <div class=3DB style=3D'position:absolute;top:76.5%;left:5.99%;width:88.2%;
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5%;
 height:100.0%'><span style=3D'font-size:88%;visibility:hidden'><span class=
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 <div class=3DB style=3D'mso-line-spacing:"90 20 0"'><span style=3D'positio=
n:absolute;
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8%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-4.13%'>&#8226;<=
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</span><span
 style=3D'position:absolute;top:29.5%;left:9.73%;width:91.19%;height:6.0%'>=
<span
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n></span><span
 style=3D'position:absolute;top:35.0%;left:9.73%;width:84.45%;height:6.0%'>=
<span
 style=3D'font-size:88%'>equations? &#13;</span></span></div>
 <div class=3DB style=3D'mso-line-spacing:"90 20 0";position:absolute;top:4=
2.0%;
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%;
 left:4.24%;width:95.75%;height:100.0%'><span style=3D'font-size:88%;visibi=
lity:
 hidden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4=
.43%'>&#8226;</span></span><span
 style=3D'font-size:88%;display:none'>&#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"90 20 0";position:absolute;top:=
48.5%;
 left:11.04%;width:98.5%;height:5.25%'><span style=3D'position:absolute;
 top:0%;left:3.04%;width:96.76%;height:100.0%'><span style=3D'font-size:86%=
'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.14%'>&#8211;<=
/span></span><span
 style=3D'font-size:86%'>0: Blank or no honest effort (e.g. &quot;I don't k=
now
 (IDK.)&quot;)&#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"90 20 0"'><span style=3D'positi=
on:absolute;
 top:54.5%;left:14.04%;width:92.88%;height:5.25%'><span style=3D'font-size:=
86%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.22%'>&#8211;<=
/span></span><span
 style=3D'font-size:86%'>1: Response is vague, illogical, confusing, or way=
 off </span></span><span
 style=3D'position:absolute;top:59.25%;left:14.04%;width:79.96%;height:5.25=
%'><span
 style=3D'font-size:86%'>track.&#13;</span></span></div>
 <div class=3DB1 style=3D'mso-line-spacing:"90 20 0"'><span style=3D'positi=
on:absolute;
 top:65.0%;left:14.04%;width:92.88%;height:5.25%'><span style=3D'font-size:=
86%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.22%'>&#8211;<=
/span></span><span
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220;it
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