Getting Started 
Misconception/Error The student does not understand what it means to write a ratio. 
Examples of Student Work at this Level The student:
 Writes only one part of each ratio.
 Multiplies two numbers from the table together and says their product is the ratio.

Questions Eliciting Thinking What is a ratio?
What do your answers mean?
How did you find these numbers? How do they represent the ratios you were asked to write? 
Instructional Implications Provide instruction on the concept of a ratio. Describe ratios as comparisons of two quantities and explain that the compared quantities may or may not contain the same units of measure. Emphasize the meaning of ratios in context and the use of ratio language (e.g., “for each,” “for every,” and “per”) when interpreting ratios. Be sure to explain the conventions typically used in writing ratios. Give the student additional opportunities to write and interpret ratios in the context of a variety of problems.
Consider using manipulatives and drawings to model ratios. Emphasize the multiplicative relationship between the parts of the ratio and ask the student to write ratios in various equivalent forms (e.g., given the ratio 2:10, write other equivalent ratios such as 1:5 and 3:15) that reflect the modeled ratios. Guide the student to observe that one part of the ratio is always a constant multiple of the other part (e.g., for equivalent ratios 2:10, 1:5, and 3:15, the second part is always five times the first part). 
Moving Forward 
Misconception/Error The student incorrectly determines parts of some of the ratios. 
Examples of Student Work at this Level The student writes ratios but some or all contain incorrect quantities.

Questions Eliciting Thinking How did you determine the quantities in your ratio?
How would you calculate the total number of boys surveyed?
How would you calculate the number of students preferring strings? 
Instructional Implications Explain the difference between parttopart and parttowhole ratios. Ask the student to use the table to calculate each row and column total and explain what each represents. Then guide the student to revise any incorrectly written ratios on his or her paper. Explicitly relate the verbal descriptions of ratios given in the problems to the elements of the ratios. Ask the student to use the table to write other parttopart and parttowhole ratios.
If needed, review the conventions for writing ratios and address any issues with the form in which ratios are written. 
Almost There 
Misconception/Error The student makes a minor error when writing a ratio. 
Examples of Student Work at this Level The student makes one easily corrected error while all other work is correct. For example, the student:
 Writes ratios in an unconventional manner such as “30 and 19.”
 Selects one incorrect value for one part of one ratio.
 Writes one ratio in the wrong order.
 Makes a calculation error when summing the total number of boys.

Questions Eliciting Thinking What are the conventions for writing ratios? How are ratios typically written?
How did you decide which number to put first in each ratio?
I think you made a mistake in this ratio. Can you check your work and correct the error? 
Instructional Implications Provide feedback to the student concerning any calculation errors and allow the student to correct the errors. If needed, review the conventions for writing ratios and allow the student to revise his or her answers.
Explain how the description of a ratio is related to the order in which the numbers are written in the ratio. Encourage the student to pay close attention to the way ratios are described in problems. Provide the student with a variety of contexts in which ratios are described and ask the student to write ratios in multiple ways, varying the order of the quantities in the ratios. 
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 correctly writes each of the three ratios: 30:19, 32:93, and 23:38. The student is able to explain how he or she determined each ratio when asked.

Questions Eliciting Thinking How does question two differ from question three?
What determines the order in which a ratio is written? 
Instructional Implications Give the student a parttowhole ratio and ask him or her to write a parttopart ratio. Have the student explain the process he or she used to write the new ratio.
Pair the student with a Moving Forward classmate and ask the student to explain the difference between parttopart and parttowhole ratios. Have the student describe additional ratios for the Moving Forward partner to write. 