4.12_v1
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“Planning contingently” in formative assessment means that teachers will consider the range of evidence they might likely see in advance of a lesson, and be ready with instructional strategies—for individuals, small groups, or the whole class—that allow for in-the-moment responses to the evidence as it arises. Since we can never know just how students will understand new content, planning contingently may involve considering a broad range of possible next steps. In this first NowComment prompt, you will consider what the teacher planned, not only what evidence students might give, but also how to respond to six possible commons issues that might arise. |
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COMMON CORE STATE STANDARDS
G-GMD: Explain volume formulas and use them to solve problems. |
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Standards for Mathematical Practice:
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Learning Goal:
Solve volume and area problems |
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Success Criteria
Before the lesson, students work individually on a task designed to reveal their current understanding and difficulties.
THE TASK |
 
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The teacher introduces the above task and helps the student to understand the problems and their context:
“In the questions, the term ‘fair price’ means that the amount you get should be in proportion to the amount you pay. So for example, if a pound of cookies costs $3, a fair price for two pounds will be $6. Read through the questions and try to answer them as carefully as you can. Show all your work so that I can understand your reasoning.”
The teacher has thought about the following six common issues that may arise and has planned questions and prompts he/she will provide to students if these issues arise. |
| Common Issues | Questions and Prompts |
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Assumes the diagrams are accurate representations
For example: The student writes “I’ve counted the candy. The larger circle has more than twice the amount of candy that the smaller one has.” Or: The student writes “Three small pizzas fit into the large one.” |
The pictures are not accurate. How can you use math to check that your answer is accurate? |
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Fails to mention scale
For example: The student calculates the areas of the two pizzas but not the scale of increase. |
How can you figure out the scale of increase in area/volume using your answers? |
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Focuses on non-mathematical issues
For example: The student writes “It takes longer to make three small pizzas than one large one. The large one should cost $8.” |
Now consider a fair price from the point of view of the customer. Are three small pizzas equivalent to one big one? How do you know? |
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Makes a technical error
For example: The student substitutes the diameter into the formula instead of the radius. Or: The student makes a mistake when calculating an area or volume. |
What does r in the formula represent? Check your calculations. |
| Simply triples the price of the pizza or doubles the price of a cone of popcorn | Do you really get three times as much pizza? Do you really get twice as much popcorn? |
| Correctly answers all the questions The student needs an extension task. | If a pizza is made that has a diameter four times (ten times/n times) bigger, what should its price be? How do you know? Can you use algebra to explain your answer? If a cone of popcorn has a diameter and height four times (ten times/n times) bigger, what should its price be? How do you decide? Can you use algebra to explain your answer? |
Integrating Reading Science and English Language Development
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