Module 3: Posttest

What fractional part of the set of dots is red? (Check all that apply)

1/4 3/12

William says that he has discovered a method that always works when comparing fractions. He states that he just looks at the denominator and "the fraction with the larger denominator is smaller because the whole is divided into more pieces, therefore each piece is smaller." How would you respond to William? All answers correct!

I'd praise him, but point out that while this explanation works in some cases, it might not always work for all fractions. I'd discourage him from using this explanation because it would confuse the rest of the class. I'd discourage him from using this explanation because it would confuse the rest of the class. I'd tell him that I'd like him to concentrate on learning the standard methods for comparing fractions. I'd let him use this explanation, as it works for all fractions.

Your class is learning the parts of a whole definition of fractions. Scott, a second grade student, is asked to explain what the 5 in the fraction 2/5 means. He says that the "5 is the whole." How would you respond to Scott? All answers correct!

I'd praise him, but point out that while this explanation works in this case, it might not always work for all fractions. I'd discourage him from using this explanation because it would confuse the rest of the class. I'd ask him to explain how he figured this out and why he thinks it works for all fractions. I'd tell him that I'd like him to concentrate on learning the standard parts of a whole definition of fractions. I'd let him use this explanation, as it works for all fractions.

Celia states that she has found an easier way to divide fractions. For example, suppose that she is given 2 and 1/2 divided by 1/4. She says "2 and 1/2 is like $2.50 and 1/4 is like a $0.25, therefore this question is really like asking how many quarters there are in $2.50."

It is mathematically correct for all cases.

William says that he has discovered a method that always works when comparing fractions. He states that he just looks at the denominator and "the fraction with the larger denominator is smaller because the whole is divided into more pieces, therefore each piece is smaller." What do you think about William's reasoning?

It works in some cases, but it would not work in general.

A teacher is working with a group of elementary students and wants to teach the concept of fractions using fraction tiles. Which representational model would be MOST appropriate when using this tool?

Linear model.

Cindy is comparing the fractions 3/12 and 5/20. Which of the following statement(s) are TRUE?

None of these statements are true.

Suppose that you have a closed number line having the length of one unit. The number line is divided into 8 segments that are equal in length. A red dot appears in the middle of the fifth segment. What location on the would the red dot represent?

None of these.

A teacher is working with a group of elementary students and wants to teach the parts of whole definition of fractions by using color counter. Which attribute of color counters should the teacher emphasize?

Number of counters in sets and subsets.

When you divide a fraction by another fraction the answer is always smaller than one.

Sometimes true.

Four students are discussing fractions as parts of a whole in real world contexts specifically, with the gender makeup of the 25 students in class. Student A proposes, we can use the fraction 13/12 since "13 is the number of boys in class and 12 is the number girls in class." Student B says that we can use the fraction 12/13 since "fractions are parts of a whole and the bigger number is always used in the denominator." Student C insists that "The whole in this context could be 25 because that is the total number of students in the class. So, we can use the fraction 12/25 for girls and 13/25 for boys." Student D responds, "I think you all are right." Which student(s) do you think is/are correct when using fractions to represent the gender make up of the class?

Student C

Alice gave ½ of her candy to Billy. Billy gave 1/4 of the candy that he received from Alice to Carter. How could you find what fraction of Alice's candy Carter received?

Take one half and multiply by one fourth.

Raymond, a third grade student, took a piece of paper and divided it into 6 equal-sized regions. He then shaded two of the regions green. Jian, another third grade student, took a piece of paper the same size as Raymond's and divided it into 12 equal-sized pieces. He then shaded four of the regions blue. You tell the class that both Raymond and Jian have shaded fractional parts of their paper. You then ask the class whether Raymond or Jian shaded more of their piece of paper. Bobby says that "Jian shaded more because he shaded 4 regions." What do you think about Bobby's reasoning?

This is not mathematically correct.

Which of the following word problems BEST illustrates what 1/4 divided 1/2 means?

You are making some homemade taffy and the recipe calls for 1/4 cups of butter. How many sticks of butter will you need? (Each stick = 1/2 cup).

Which of the following word problems BEST illustrates what 1/4 divided 2 means?

You want to split 1/4 pie evenly between two families. How much pie should each family get?

Sally is comparing the fractions 3/8 and 1/2. Which of the following statement(s) are TRUE?

3/8 < 1/2 because four eighths is more than three eighths. 3/8 < 1/2 because when you cross multiply 8 x 1 is larger than 3 x 2.

Suppose that 6 pieces of candy represent 2/3 of a whole bag of candy. How many pieces of candy were in the whole bag?

9 pieces of candy.

A teacher is working with a group of elementary students and wants to teach the concept of fractions using fraction circles. Which representational model would be MOST appropriate when using this tool?

Area model