Getting Started 
Misconception/Error The student thinks the parts of a ratio should be multiplied or divided. 
Examples of Student Work at this Level The student said:
 The ratio 2:1 â€śmeans multiplication.â€ť
 The ratio 2:1 means â€ś2 x 1 because of the two dots.â€ť
 The ratio means â€śto divide.â€ť

Questions Eliciting Thinking What is a ratio?
Why did you multiply (or divide) the two parts of the ratio?
Why do you think 2:1 means to multiply (or divide)? 
Instructional Implications Provide direct instruction on ratios. Describe ratios as comparisons of two quantities and point out that the 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., â€śfor each,â€ť â€śfor every,â€ť and â€śperâ€ť) when interpreting ratios or describing their meaning. Give the student additional opportunities to write and interpret ratios in the context of a variety of problems.
Clarify the difference between the colon and the multiplication dot. 
Moving Forward 
Misconception/Error The student can identify parts of a given ratio, but does not recognize the parts of the related ratio. 
Examples of Student Work at this Level The student says the ratio 7/22 represents the students who prefer doing homework before school to students who prefer doing homework after school. The student does not recognize the significance of the number 22 in the problem.
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Questions Eliciting Thinking What does the ratio 7/15 represent? If seven students prefer to do homework before school and 15 prefer to do homework after school, how many students are there all together?
Why do you think 7/22 represents the same thing? What does the number 22 represent in the problem?
What is the difference between 22 and 15? 
Instructional Implications Make explicit the difference between parttopart and parttowhole ratios. Use visuals to help the student recognize the difference between these two types of ratios.
Model how to write a parttowhole ratio from a parttopart ratio and vice versa. Provide the student with additional practice problems.
Consider using MFAS task Writing Ratios (6.RP.1.1). 
Almost There 
Misconception/Error The student can identify the parts of a given ratio, but cannot explain the meaning of the ratio using ratio language. 
Examples of Student Work at this Level For the ratio 2:1, the student says the two â€śis how much red paint,â€ť and the one â€śis the blue paint.â€ť
For the ratio 7/22, the student says the seven is â€śthe number of students who prefer to do homework after school,â€ť and the 22 is â€śthe number of total students.â€ť
For the ratio 2:1, the student says â€śthere is 2 red paints and 1 blue paint.â€ť

Questions Eliciting Thinking If the ratio 2:1 refers to two parts of red paint and one part of blue paint, is that all there can be? Can it also mean four parts of red paint and two parts of blue paint?
Describe the ratio in question one using more detail. Be more specific.
What do you mean by two red paints?
What does a ratio tell you? 
Instructional Implications Model explaining the meaning of ratios in the context of problems. Use ratio language (e.g., â€śfor each,â€ť â€śfor every,â€ť and â€śperâ€ť) when interpreting ratios or describing their meaning. Have the student practice writing descriptions of ratios using ratio language.
Explore using ratios to find missing values in problem contexts (e.g., ask the student to find the number of boys in a class when the ratio of the number of girls to the number of boys is 3:2 and the number of girls is 12). Encourage the student to make drawings or use manipulatives to solve problems such as these rather than setting up and solving proportions. 
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 explains the meaning of 2:1 using ratio language such as â€śfor every two red parts, there is one blue part.â€ť
The student describes the ratio 2:1 using a multiplicative comparison. The student says, â€śIt means double the amount of red paint as opposed to blue paint.â€ť
The student recognizes the significance of 22 in the problem. The student interprets the ratio 7/22 to mean seven students who prefer to do homework before school out of the whole class of 22 students.

Questions Eliciting Thinking How did you determine there are 22 students in the class?
If the ratio was written in the form 7 to 22, would it mean the same thing?
How would you write the ratio of the total number of students to the number of students who prefer doing homework after school? 
Instructional Implications Challenge the student to find how many parts of red there would be if there were five parts blue.
Introduce unit rates. Define unit rate and model how to find a unit rate.
Pair the student with a Moving Forward partner. Have the student explain parttopart and parttowhole ratios to the Moving Forward partner. 