Getting Started 
Misconception/Error The student is unable to use proportional reasoning to find equivalent ratios. 
Examples of Student Work at this Level The student does not have a clear strategy to scale up the quantities in the recipe. The student:
 Repeats back numbers given in the problem (e.g., cup flour and 16 cookies) saying, â€śItâ€™s what the recipe calls for.â€ť
 Says, â€śShe will need one cup of flour because there will be one cup of sugar.â€ťÂ
 Scales up the recipe using addition, e.g., since = 1, the student adds to to get the amount of flour needed.
 Adds the new (or old) amount of sugar to flour, writing 1 + .
 Uses different operations for each part of the problem (e.g., sugar: Â Ă— 4; flour: ; cookies: 16 + 4).
 Triples all quantities of flour, sugar and the number of cookies, saying, â€śWe need three more batches of everything.â€ť
 Sets up a proportion but uses all three given quantities in one proportion rather than setting up two separate proportions â€“ one comparing the sugar with flour and another comparing the number of cookies with flour.

Questions Eliciting Thinking What does proportionally increase mean?
What operation is typically used when scaling up a quantity or a value proportionally?
How can you tell if the relationship between the amounts of sugar and flour is proportional? 
Instructional Implications Review the concept of ratio and encourage the student to use a ratio table to write and explore patterns in equivalent ratios. Guide the student to use multiplication (rather than repeated addition) to generate equivalent ratios, e.g., if the ratio 1:3 means for every blue cube, there are three red cubes, then there will always be three times more red cubes than blue cubes. Have the student practice writing equivalent ratios using multiplication. Point out that associated values in ratio tables are related by a constant ratio and define this ratio as the constant of proportionality. Give the student additional ratio tables to calculate the constant of proportionality and use it to find missing values.
Demonstrate how to find the constant of proportionality in word problems and how to use it to find other pairs of proportional values. Initially use whole number quantities, but transition the student to quantities given by rational numbers. Review operations with fractions, as needed. Eventually, introduce the student to other strategies for finding an unknown value in a proportional relationship such as writing a proportion. 
Making Progress 
Misconception/Error The student shows evidence of proportional reasoning, but makes computational errors. 
Examples of Student Work at this Level The student:
 Performs fraction operations incorrectly when multiplying Â Ă— 4 or changing from an improper fraction to a mixed number.
 Leaves the answer in decimal form of 2.67, unable to convert it to a mixed number to keep it in problem context.
 Rounds which impacts the results of subsequent computations.

Questions Eliciting Thinking Can you show me how you multiplied by 4?
Is equivalent to 0.7 exactly (or and 2.6)? What will happen to your answer when you use an estimated value in the calculation? Can you perform the same operation using fractions? 
Instructional Implications Review operations with fractions, as needed. Guide the student to use the form of the numbers given in the problem when deciding which form to use in the answer. Discuss applications in which the use of fractions (or decimals) is more appropriate, e.g., amounts of money are typically written with decimals, but quantities in recipes are typically written in fraction form.
Make the student aware of the error that is introduced when rounding repeating decimals. Explain that if rounding is going to occur, it is best to round only once in the last step of the problem.
Expose the student to the various strategies used by classmates at the Got It level. Provide additional opportunities for the student to use proportional reasoning to find missing values. 
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 uses proportional reasoning to determine that 2 cups flour will be needed and the new recipe will yield 64 cookies.
The student may solve the problem by:
 Writing a proportion and solving.
 Adding the original amount of each ingredient to the original quantity four times.
 Using a picture to show proportional amounts.
 Multiplying each amount by the constant of proportionality which is four.Â

Questions Eliciting Thinking How did you know where to place each value in your proportion?
Could you use multiplication instead of repeated addition?
How did you know to multiply by four? 
Instructional Implications Ask the student to determine the amount of each ingredient when making batch, 3 batches, or a total of 40 cookies.
Consider using other MFAS 7.RP.1.3 tasks to give students practice with proportional reasoning and percent. 