 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum                      Exploring Communication  Introduction | Problem: Shaded/Unshaded Circles | Solution: Shaded/Unshaded Circles | Talking About the Problem | Representing Fractions with Rods | Other Denominators | Modeling Operations | Try It Yourself: Cuisenaire Rods | Problem Reflection | Summary | Your Journal    Use this Interactive Activity to work on the problems that follow, which let you use the rods to try out addition and subtraction with fractions.

In this activity, focus on how you are communicating your thinking as you work through each problem below. How might you respond if someone asked you to explain your approach?

Problem 1

 Question: Which rod(s) would you use as a unit to do computations with fourths? Explain your reasoning. Show Answer
 Our Answer: You could use a purple rod as "1." You could also use a brown rod, or a combination of rods; two purples would work (4 + 4 = 8), as would an orange and a red (10 + 2 = 12, which is also a multiple of 4). The bottom line is, the rod you choose as "1" must have an all-purple train. (For example, the combination of an orange rod and a red rod can be represented by a train of three purple rods: 4 + 4 + 4 = 12.) Question: Which rod(s) would you use as a unit to do computations with thirds? Explain your reasoning. Show Answer
 Our Answer: You could use a light-green rod to represent "1." You could also use a dark-green rod or a blue rod, or a combination of rods that will contain a light-green train. For example, an orange and a red (10 + 2 = 12, which is also a multiple of 3) would work, as would a black and a brown (7 + 8 = 15). Question: Which rod(s) would you use as a unit to do addition and subtraction with fourths and thirds? Explain your reasoning. Show Answer
 Our Answer: You could use two dark-green rods because combined they represent 12, which is a common multiple of 3 and 4. You could also use three purple rods, or four light-green rods, or an orange and a red rod; all of these options are the same length and represent 12. (Note: When using the orange/red combo to represent "1," the light-green rod will represent 1/4, and the purple rod will represent 1/3.) Just be sure that any rod you choose has both a light-green train for thirds and a purple train for fourths, since 12 is a common multiple of 3 and 4. Question: How are the combinations of rods you can use related to multiples of fourths and thirds? Think of the language you are using as you communicate this answer. Show Answer
 Our Answer: The total value of the unit would have to be a common multiple of 3 and 4. For example, any unit that is equivalent to 12 white rods would work, since 12 is a common multiple of 3 and 4. Problem 2

Make the model for thirds and fourths, then answer the questions that follow:

 Question: How would you model 2/3 + 1/4? Show Answer
 Our Answer:  Question: How would you explain the process you used to model this computation? Show Answer
 Our Answer: This model uses the orange/red combo as "1." Therefore, the white rod is 1/12, the light-green rod is 1/4, the purple rod is 1/3, the brown rod is 2/3, etc. The sum of 2/3 and 1/4 (brown plus light green) is 11/12. Problem 3

Continuing to use the model for thirds and fourths, please answer the following questions:

 Question: How would you model 3/4 - 2/3? Show Answer
 Our Answer:  Question: How would you explain the process you used to model this computation? Show Answer
 Our Answer: This model uses the orange/red combo as "1." Therefore, the white rod is 1/12, the light-green rod is 1/4, the purple rod is 1/3, the brown rod is 2/3, and the blue rod represents 3/4. The difference of 3/4 and 2/3 (blue minus brown) is one white rod, or 1/12.  Reflect on these problems       Teaching Math Home | Grades 6-8 | Communication | Site Map | © |        