Seven Tenths

Getting Started

The student cannot correctly rewrite  as an equivalent fraction with a denominator of 100.

The student says  is equivalent to  and adds  +  to get .

Do you know how to find fractions that are equivalent to a given fraction?

How can you create a fraction that is equivalent to ? What would you need to do to both the numerator and denominator?

Is  equivalent to ? How do you know?

What does the word equivalent mean?

Is of a pizza the same as of a pizza?

Can we add fractions that are not divided into the same size pieces?

Using fraction grids, model for the student how to rewrite a fraction with a denominator of 10 as a fraction with a denominator 100. Using the tenths grid, have the student shade . Then have the student create a hundredths grid by drawing 10 horizontal lines bisecting the vertical lines. Now have the student counts the total number of squares and the total shaded squares to determine the fraction of shaded squares. Make a connection to show how the two are equal and that nothing else was shaded or erased. After modeling with fraction grids, show the student that a fraction can be written in an equivalent form by multiplying both the numerator and denominator by the same value. Use fraction grids to model the relationship between  and . Relate the model to the numerical procedure for rewriting fractions in an equivalent form. Provide the student with additional opportunities to add a pair of fractions in which one has a denominator of 10 and the other has a denominator of 100 such as  + . The teacher should observe if the student converts  to .

Provide opportunities for the student to practice rewriting fractions in an equivalent form using the denominators 10, 100, and 1000.

Consider using an MFAS task which assesses the student’s understanding of equivalent fractions.

Making Progress

The student does not recognize the need to rewrite  as  before adding it to .

The student rewrites  as  but says the sum of  and  is . In the context of an addition problem, the student forgets to adjust the numerator proportionally and adds  to .



The student rewrites  as  but does not recognize the need to rewrite  as  when adding  to . He or she adds numerators to numerators and denominators to denominators and says the sum is .



The student is able to express  as  but is unable to use  to add  + . He or she writes  as the answer.

What must be true of two fractions before they can be added?

Why must fractions have like denominators in order to add them?

How could you use the work you did in the first part to help you find the sum of the fractions in the second part?

If I had  of a pizza and added  of a pizza and just added the numerators and denominators, what would the sum be? That is right, the sum would be . Does that seem reasonable? Is  less than or more than ?

Is of a pizza the same as of a pizza?

Can we add fractions that are not divided into the same size pieces?

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, “a tenth,” 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 “tenths.” However,  means there are 23 of these units called “hundredths.” 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.

Provide the student with a problem in context and help the student reason about the denominators and the need for rewriting fractions so they have the same denominator. For example, present the student with a problem such as: Mario has  of a medium cheese pizza and  of a medium pepperoni pizza left from a party. How much pizza does Mario have left from the party? In this example, if the student adds  +  by adding across the numerators and denominators, the sum of  is less than . Help the student understand that this is not reasonable because  is also equivalent to  so the sum of  and  cannot be less than .

Got It

The student provides complete and correct responses to all components of the task.

The student is able to correctly rewrite  as . When asked to find the sum of  and , the student converts  to  and says the sum is .

What fraction with a denominator of 10 is equivalent to ?

How could you determine the sum of  and ? What do you think you would need to do?

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:  + x = ;  –  = x;  + x = ;  –  = x. Encourage the student to write out each step of work.

Consider using the MFAS task Tenths and Hundredths.