Getting Started |
| Misconception/Error The student is unable to create a model for the situation. |
| Examples of Student Work at this Level The student attempts to model the mudslide with a two-dimensional figure. |
| Questions Eliciting Thinking Can you describe the situation in your own words? What are you being asked to find?
What does model mean? What geometric solid could you use to model the mudslide?
Would the mudslide best be represented by a two-dimensional or a three-dimensional figure? Why? |
| Instructional Implications Clarify the difference between two-dimensional and three-dimensional figures. Remind the student that two-dimensional figures have area while three-dimensional figures have volume. Ask the student to consider the different geometric solids and to identify which one would best model the mud using the information given in the task. Assist the student in sketching and labeling a triangular prism to represent the mudslide.
Provide the student with additional opportunities to model real world situations with geometric solids and then to use the model to find other quantities such as volume or density.
Consider using the MFAS task Size It Up (G-MG.1.1) if not previously used. |
Moving Forward |
| Misconception/Error The student is unable to find the volume. |
| Examples of Student Work at this Level The student creates a model, but:
- Is unable to identify the correct dimensions to find the volume.
- Makes a careless error.
- Does not use the correct formula to find the volume.
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| Questions Eliciting Thinking I think there is an error in your work for the first problem. Can you find it? How would you correct it?
What model did you create to represent the mud? Why did you choose this model? What is the formula for finding volume of a triangular prism?
What is the formula for the volume of any prism? What is the shape of the base of your prism? What is the formula for the area of a triangle? |
| Instructional Implications Review how to find the volume of a triangular prism. Be sure the student understands what each variable in the volume formula represents. Ask the student to identify the shape of the base and the height of the prism model. Assist the student in recalculating the volume of mud.
Provide the student with additional opportunities to model real world situations with geometric solids and then to find the volume of the solid. Consider using the MFAS task Estimating Volume (G-MG.1.1) if not used previously. |
Almost There |
| Misconception/Error The student is unable to use the given density to find the mass. |
| Examples of Student Work at this Level The student determines the volume of the mud is approximately 240  , but:
- Does not attempt to determine the mass.
- Divides the density by the volume.
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| Questions Eliciting Thinking What is density? Do you know the formula for density?
Do you know the density of the mud? Do you know the volume of the mud? How can you find the mass of the mud? |
| Instructional Implications Review with the student the concept of density. Explain that density is the ratio of mass (or a quantity) to volume (or area) and can be found using the formula d =  . Advise the student to be mindful of the units used in both the mass and density measures to be certain they are consistent. Then ask the student to use the given density of mud to calculate the mass of the mud. Provide feedback.
Provide the student with additional opportunities to use the density formula to estimate mass, volume, or density.
Consider using the MFAS tasks Population of Utah (G-MG.1.2) and How Many Trees? (G-MG.1.2) if not already used. |
Got It |
| Misconception/Error The student provides complete and correct responses to all components of the task. |
| Examples of Student Work at this Level The student models the quantity of mud with a triangular prism and determines that the volume of mud is approximately 240 . The student then uses the estimated volume to determine that the mass of the mud is approximately 441,600 kg.
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| Questions Eliciting Thinking Do you think you over- or underestimated the mass of mud? Which might be better in this situation? |
| Instructional Implications For additional experience with modeling, consider using the Illustrative Mathematics tasks A Ton of Snow (https://www.illustrativemathematics.org/illustrations/1794), How Many Leaves on a Tree? (https://www.illustrativemathematics.org/illustrations/1137), or How Thick is a Soda Can? (https://www.illustrativemathematics.org/illustrations/1173).
Consider using the MFAS tasks Population of Utah (G-MG.1.2) and How Many Trees (G-MG.1.2) if not already used. |
