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 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 because you just need to add the numerators.
The student says the first equation is false because it would have to be for the equation to be true. However, the student is unable to recognize that equals . 
Questions Eliciting Thinking Does equal ? Why or why not?
When adding fractions with different denominators, what should we 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 is true?
How many hundredths is equal to? 
Instructional Implications Explain how tenths and hundredths are related. Use 10 by 10 grids to show that shading in three rows of ten can represent both three tenths and thirty hundredths. Use the grids to model the equation .
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. 
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 . The student makes one of the following (or similar) errors:
The student adds and says the sum is .
loading video
Â
The student adds numerators to numerators and denominators to denominators and determines the sum is .

Questions Eliciting Thinking What do you notice about and ?
You determined that the first equation is true because equals . Can you apply that same thinking to this second equation?
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?
How many hundredths is equivalent to? Can you show me that on this 10 by 10 grid?
When adding fractions with different denominators, what should we be certain to do? Do both denominators need to be the same number in order to add the fractions? 
Instructional Implications Explain the rationale for rewriting fractions with common denominators by referencing the meaning of the numerator and denominator. For example, when adding 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 means there are seven of these units called â€śtenths.â€ť However, means there are two 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 as . Then guide the student to add to 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. 
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 using similar reasoning.
loading video
Â
loading video
Â

Questions Eliciting Thinking Does = ? How do you know?
Can we add the denominators if they are not alike? Why or why not?
How can we create equivalent fractions?
Can you use what we worked on in this first problem to help you determine the sum in the second problem?
Can you shade on this grid? How many hundredths is that?
To how many hundredths is equivalent? 
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 is equivalent to and . The student uses similar reasoning to correctly find the sum of and as .
loading video
Â

Questions Eliciting Thinking Can you find ? What would you do first?
How many tenths is equivalent to?
How could you explain to another student how you would add two fractions with different denominators?
How many thousandths is equal to? How many tenthousandths? Do you notice a pattern? 
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: ; ; ; . Encourage the student to write out each step of work.
Consider using the MFAS task Seven Tenths. 