Getting Started 
Misconception/Error The student is unable to determine that the first equation is true. 
Examples of Student Work at this Level The student says that the first equation is false and that it should be Â because the numerators should be added and then the denominators should be added.
The student says that the first equation is false and that it should be Â because you just need to add the numerators.
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Questions Eliciting Thinking What do you know about the fraction ?
To how many hundredths is Â equal?
When adding fractions with different denominators, what should you be certain to do? Do both denominators need to be the same number in order to add the fractions?
What do you know about the denominators 10 and 100? How many times greater is the denominator 100 than the denominator 10? Can we use that to determine if the equation Â + Â = Â is true?
Is of a pizza the same as of a pizza?
When we add fractions with unlike denominators, what do we need to do first? 
Instructional Implications Explain how tenths and hundredths are related. Use 10 by 10 grids to show that shading in two rows of 10 can represent both two tenths and twenty hundredths. Use the grids to model the equation Â + Â = .
Guide the student through the process of adding fractions with the same denominator (beginning with tenths). Use 10 by 10 grids to explain why the denominators are not added.
Provide the student with a set of matching cards that include equivalent fractions written with denominators of 10 and 100 (one fraction per card). Challenge the student to find all of the pairs of equivalent fractions.
Consider the use of context when working with fractions of denominators 10 and 100. Context can allow the student to visualize and model the action and consequently can help the student see why one cannot add fractions with unlike denominators. 
Moving Forward 
Misconception/Error The student is unable to add fractions with denominators of 10 and 100. 
Examples of Student Work at this Level The student may be able to determine that the first equation is true but is unable to apply that reasoning to find the sum of Â and . The student makes one of the following (or similar) errors:
 The student adds Â + Â and says the sum is .Â
 The student adds numerators to numerators and denominators to denominators and determines the sum is .Â

Questions Eliciting Thinking What do you notice about Â and ?
To how many hundredths is Â equivalent? Can you show me that on a 10 by 10 grid?
You determined that the first equation is true because Â equals . Can you apply that same thinking to this second equation?
When adding fractions with different denominators, what should you be certain to do? Do both denominators need to be the same number in order to add the fractions?
How did you determine that the denominator in this second equation should be 100? If you multiplied 10 x 10 to get the denominator of 100, were you supposed to do any operations on the numerator? 
Instructional Implications Explain the rationale for rewriting fractions with common denominators by referencing the meaning of the numerator and denominator. For example, when adding Â to , explain to the student that the denominator, â€śa tenth,â€ť is like a unit of measure; it describes the number of equal parts into which the whole has been divided. The numerator of each fraction indicates the number of tenths so Â means there are two of these units called â€śtenths.â€ť However, Â means there are eight of these units called â€śhundredths.â€ť Since the units, tenths and hundredths, are different, the fractions cannot be added as written. Use fraction grids to model for the student rewriting Â as . Then guide the student to add Â to Â emphasizing that the fractions can now be added since their denominators are the same.
Continue to expose the student to the use of 10 by 10 grids to model adding fractions with numerators of 10 and 100. Encourage the student to observe that each tenth is equal to 10 hundredths and to create fractions with common denominators when adding fractions with denominators of 10 and 100.
Model tenths and hundredths using dimes () and pennies () to illustrate the use of common denominators.
Consider the use of context when working with fractions of denominators 10 and 100. Context can allow the student to visualize and model the action and consequently can help the student see why one cannot add fractions with unlike denominators.
Provide the student with a tenths grid and ask the student to shade in of the grid. Next, use that same grid to crate a hundredths grid by horizontally partitioning the square into ten equal parts that bisect the vertical tenths. Connect for the student that the is now also represented as . 
Almost There 
Misconception/Error The student is able to correctly add the given fractions only after prompting to determine that the first equation is true. 
Examples of Student Work at this Level The student needs prompting from the teacher to determine that the first equation is true and is then able to add Â and Â using similar reasoning.

Questions Eliciting Thinking Can you use what we worked on in this first problem to help you determine the sum in the second problem?
Can you shade Â on this grid? How many hundredths is that?
How many hundredths is Â equivalent to?
Does Â = ? How do you know?
Can we add the denominators if they are not alike? Why or why not?
How can we create equivalent fractions? 
Instructional Implications Provide the student with a set of matching cards that include equivalent fractions written with denominators of 10 and 100 (one fraction per card). Challenge the student to find all of the pairs of equivalent fractions.
Continue to provide practice for the student in adding fractions with denominators of 10 and 100. Begin by encouraging the student to represent each fraction on 10 by 10 grids and then guide the student to complete addition problems without the use of the grids. 
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 that the first equation is true because Â is the same as Â so Â + Â = . The student uses similar reasoning to correctly find the sum of Â and Â as .
The student first converts each fraction to a decimal (0.08 and 0.2) and adds to get a sum of 0.28. The student then converts 0.28 to a fraction (). The student uses a similar strategy to correctly add Â andÂ .

Questions Eliciting Thinking How many tenths is Â equivalent to?
How would you explain to another student how to add two fractions with different denominators?
Can you find Â + ? What would you do first? 
Instructional Implications Provide opportunities for the student to solve addition and subtraction word problems that involve unit fractions with unlike denominators. Guide the student through the process of finding a common denominator and rewriting each fraction with that denominator in order to add or subtract.
Challenge the student to extend his or her understanding of equivalent fractions by solving the following equations: Â + x = ; Â â€“ Â = x; Â + x = ; Â â€“ Â = x. Encourage the student to write out each step of work.
Consider using the MFAS task AddingÂ Five Tenths. 