<TestItem CLASS="ssmc" METHOD="list">

<Stem>
  <Paragraph><Sentence>
 You have an excellent recipe for chocolate chip cookies. By the end of a week, you've shared the 
 recipe with four of your friends. During the second week, each of your friends share the recipe 
 with four of their friends, so that sixteen new people now know about the recipe. During the third week, 
 each of these 16 people share the recipe with four new friends.

  </Sentence></Paragraph>

  <Paragraph><Sentence>
 Assuming this pattern continues, how many new friends will get the recipe during the 4th week?
  </Sentence></Paragraph>
</Stem>
<Distractor_list>
  <Distractor><Paragraph><Sentence>1,024</Sentence></Paragraph></Distractor>
  <Distractor><Paragraph><Sentence>64</Sentence></Paragraph></Distractor>
  <Distractor><Paragraph><Sentence>256</Sentence></Paragraph></Distractor>
  <Distractor><Paragraph><Sentence>32</Sentence></Paragraph></Distractor>
  <Distractor><Paragraph><Sentence>16</Sentence></Paragraph></Distractor>	
</Distractor_list>
<key TYPE="SSMC">
    <response  SCORE="0" EVIDENCEVAL="0">
        <observable>1</observable>
        <feedback TYPE="Student">Sorry, that's not right, but you are close. You correctly figured out how many new friends will get the recipe in week 5. In week 4, there will be 4<sup>4</sup> = 256 new recipes out there.</feedback>
        <feedback TYPE="Teacher">The student probably raised the exponent
 by one too many. Instead of calculating the number of new friends who get the recipe in week 4 (4<sup>4</sup> = 256), the student calculated the number of new friends who get the recipe in week 5: 4<sup>5</sup> = 1,024</feedback>
    </response>
    <response  SCORE="0" EVIDENCEVAL="0">
        <observable>2</observable>
        <feedback TYPE="Student">Sorry, that's not right, but you are close. You correctly figured out how many new friends would hear about the recipe in week 3. In week 4, there will be 4<sup>4</sup> = 256 new recipes out there.</feedback>
        <feedback TYPE="Teacher">The student probably raised the exponent
 by one too few. Instead of calculating the number of new friends who get the recipe in week 4 (4<sup>4</sup> = 256), the student calculated the number of new friends who get the recipe in week 3: 4<sup>3</sup> = 64</feedback>
    </response>
    <response  SCORE="1" EVIDENCEVAL="1">
        <observable>3</observable>
        <feedback TYPE="Student">Correct, good job!</feedback>
        <feedback TYPE="Teacher">Student has answered correctly: 4<sup>4</sup> = 256.</feedback>
    </response>
    <response  SCORE="0" EVIDENCEVAL="0">
        <observable>4</observable>
        <feedback TYPE="Student">Sorry, that's not right. By the end of week 3, 16 * 4 = 64 new friends have the recipe. So by the end of week 4, more than 64 new friends must have the recipe. In fact, by week 4, there will be 4<sup>4</sup> = 256 new recipes out there.</feedback>
        <feedback TYPE="Teacher">The student probably multiplied 16 (the number of new friends who get the recipe in month 2) by 2.</feedback>
    </response>
  <response  SCORE="0" EVIDENCEVAL="0">
        <observable>5</observable>
        <feedback TYPE="Student">Sorry, that's not right. If four additional friends got the recipe each month, 
        your answer would be correct. But each month, each person gives the recipe to four new friends. 
        In week 4, there will be 4<sup>4</sup> = 256 new recipes out there.</feedback>
        <feedback TYPE="Teacher">The student multiplied 4 * 4 = 16, instead of raising 4 to the 4th power (4<sup>4</sup> = 256).</feedback>
    </response>
  </key>	
<Metadata>
    <AeL ItemNode="tVerbalRuleExtendModelGeometric1b" Difficulty="1">
        <PMNode LINK="true">ExtendGeometric</PMNode>
	<PMNode LINK="true">VerbalRuleGeometric</PMNode>
	<PMNode>ModelGeometric</PMNode>
    </AeL>
</Metadata>
 
</TestItem>
