Getting Started |
Misconception/Error The student is unable to distinguish between the two parts of the problem and interprets the problem as a one-step problem. |
Examples of Student Work at this Level The student subtracts 4 from 14 and concludes that Trish has 10 marbles left in her bag.
The student subtracts four from six and concludes that Trish has two marbles left in her bag. |
Questions Eliciting Thinking How many blue marbles did Sam have? Can you use some of the manipulatives to show me? How many red marbles did Sam have? Can you use some of the manipulatives to show me? How many marbles did Sam have in all?
How many marbles did Trish have? Can you use some of the manipulatives to show me? What did Trish do with some of the marbles in her bag? Can you show me using your manipulatives? |
Instructional Implications Guide the student in using counters, linking cubes, or marks on paper to model two-step problems making each step explicit. Provide feedback at each step.
Expose the student to a variety of strategies used by his or her peers. This can be done by asking Level III and Level IV students to share their strategies with the class. |
Moving Forward |
Misconception/Error The student distinguishes between the two parts of the problem and determines an appropriate strategy to solve one part but is unable to successfully implement a strategy to solve the other part. |
Examples of Student Work at this Level The student understands the first step is to add 14 and 6 but then adds rather than subtracts four.
The student incorrectly subtracts 6 from 14 as a first step but then correctly subtracts four from this result. |
Questions Eliciting Thinking You determined that Trish has 20 marbles. Did she put four marbles into the bag or take four marbles out of the bag? Should you add four or subtract four?
Can you reread the first sentence of the problem? How many marbles does Sam have all together? Now reread the second sentence. How many marbles does Trish have? |
Instructional Implications Guide the student in using counters, linking cubes, or number lines to model the step of the problem the student was unable to successfully complete. Then, ask the student to solve a similar problem providing feedback as necessary.
Have the student use Counting On to find the sum using a number line to model Counting On. Ask the student to show one other way to find the total number of marbles Sam has. |
Almost There |
Misconception/Error The student determines successful strategies for solving both parts of the problem but makes minor errors when implementing one or both strategies. |
Examples of Student Work at this Level The student correctly adds: 14 + 6 = 20, but then makes an error when subtracting four from 20: 20 - 4 = 17.
The student writes: 14 + 6 = 20 - 4 = 16, showing values that are not equal. |
Questions Eliciting Thinking Can you check your answer? Does everything look right? Can you show me how you got 17?
Your thinking is correct but we need to look at how you wrote your solution. What is the value of 14 + 6? What is the value of 20 - 4? Are those values the same? |
Instructional Implications Ask the student to present and explain his or her solution to the class demonstrating how he or she determined the answer to each part of the problem.
Ask the student to represent each step of the problem with an equation, carefully checking each result. Then, ask the student to interpret the result in each equation in light of the context of the problem:
14 + 6 = 20 (Sam had 20 marbles in all.) 20 = 20 (Trish had 20 marbles.) 20 - 4 = 16 (Trish now has 16 marbles in her bag.)
Provide opportunities for the student to solve a variety of two-step problems and to explain his or her strategies and solutions. |
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 solves both steps of the problem correctly. The student is able to clearly explain his or her strategy and is confident in his or her answer. |
Questions Eliciting Thinking The problem tells us Sam had blue marbles and red marbles. It also tells us Trish removed four blue marbles from her bag. Do we know anything else about the color of Trish's marbles? Do we need to know? Why or why not? |
Instructional Implications Provide opportunities for the student to solve a variety of two-step problems and to explain his or her strategies and solutions.
Ask the student to explain how the strategies used by one or more other students differ from the way he or she solved the problem. Have the student determine if the strategies of others are more, less, or equally easy to implement than the strategy he or she used.
Provide opportunities for students to solve two-step word problems with larger numbers particularly ones that will require regrouping (e.g., 27 + 45 or 32 - 19). |