Size and Location of Fractions

Equivalent Fractions

Fraction Comparison

Fraction Concepts and Vocabulary

Using Multiplication and Division to Find Equivalent Fractions

100

Explain or show how you could use a tape diagram to represent sixths.

Show answer on whiteboard.

100

Explain whether or not 3/5 is equivalent to 60/100.

100 divided by 20 equals 5,

60 divided by 20 equals 3,

therefore 3/5 is equivalent to 60/100.

100

Sort the fractions below into the correct category: less than 1/2, equivalent to 1/2. greater than 1/2 but less than 1, greater than 1

3/2

2/3

5/10

6/8

12/4

1/5

2/7

Less than 1/2: 1/5 and 2/7

Equivalent to 1/2: 5/10

Greater than 1/2 but less than 1: 2/3 and 6/8

Greater than 1: 3/2 and 12/4

100

What is vocabulary word for the top part of a fraction that tells how many of the equal parts are being described?

Numerator

100

Using multiplication, show how you would find 2 fractions equivalent to 1/2.

Answers vary.

200

Draw a number line with a point that represents 3/8.

Show on whiteboard.

200

What are 3 fractions that are equivalent to 6/5?

Answers vary.

200

Which option orders the fractions from least to greatest? Explain how you know.

A. 2/7, 7/2, 2/9, 5/9

B. 2/7, 2/9, 5/9, 7/2

C. 2/9, 2/7, 5/9, 7/2

D. 7/2, 5/9, 2/7, 2/9

C. 2/9, 2/7, 5/9, 7/2

200

When the numerator of two fractions is the same, which fraction is going to be larger, the fraction with the larger denominator, or the fraction with the smaller denominator?

Explain why.

The fraction with the smaller denominator because each piece of the whole is going to be larger.

200

Using multiplication, name 3 fractions that are equivalent to 6/12.

Answers vary.

300

Draw a number line with a point that represents 4/5 and 9/10.

Show on whiteboard.

300

How can a number line be used to show whether the following fractions are equivalent?

8/10 and 4/5

A number line would show that every 2 tenths is equivalent to 1 fifth and that it takes 4 x 2 or 8 tenths to make 4/5 so they are equivalent.

300

On a fishing trip, Ms. Loeb, Ms. MacDonald, and Damoni each caught one fish.

Ms. Loeb's fish was 2/5 foot long.

Ms. MacDonald's fish was 7/15 foot long.

Damoni's fish was 1/3 foot long.

Who caught the longest fish? Show how you know.

Ms. MacDonald caught the longest fish.

300

What strategies did we learn about for finding equivalent fractions?

Multiplying or dividing the numerator and denominator by the same number will result in an equivalent fraction.

300

Find two fractions equivalent to 12/4.

Answers vary.

400

Show 8/4 on a number line.

Show answer on whiteboard.

400

Explain why 7/10 and 70/100 are equivalent.

If we put every 10 hundredths into a group, we'd have 10 equal groups in 1 whole, each group being 1 tenth. 70 hundredths is the same size as 7 tenths.

400

Henry’s school is 11/8 miles from his house.

- The library is 13/10 miles from his house.
- The park is 7/9 mile from his house.
- The museum is 14/5 miles from his house.

Which of these places is closer to Henry's house than the school? Explain your reasoning.

The library and park are closer to Henry's house than the school.

The museum is farther from Henry's house than the school.

- The museum is almost 3 miles from his house, while the school is almost 1 ½ miles from his house. So the museum is farther.
- The library is 1 mile and 3/10 of a mile away, while school is 1 mile and 3/8 away. Since the numerators are the same, we can compare the denominator to find out which is further.
- The park is less than 1 mile away and the school is more than 1 mile away, so the school is closer.

400

What is it called when two fractions have the same bottom part?

Why do we care if two fractions have the same bottom part?

A common denominator.

When two or more fractions have a common denominator, it is much easier to compare them.

400

Using division, find two equivalent fractions for 8/12.

Divide by 2: 4/6

Divide by 4: 2/3

500

Draw a number line with a point that represents:

5/12

2/4

1/3

Show on whiteboard.

500

For this set of 3 fractions, identify 2 fractions that are equivalent and explain your reasoning. Then, come up with a third equivalent fraction.

1/4

30/100

3/12

1/4 and 3/12 are equivalent. 30/100 is not equivalent to the other two.

Equivalent fractions vary.

500

Use the numbers 1-12, each only once, to create a set of 3 equivalent fractions.

One number cannot be used. Which number is it?

Sample responses: 2/3 = 4/6 = 8/12

7 cannot be used, because it can't be divided by another number and if you multiply it by 2, it's 14 and that number isn't a choice.

500

What is it called when we compare fractions using what we about the size of fractions?

Using benchmark fractions.

500

Using either multiplication or division, find an equivalent fraction to each of the following:

3/12

6/9

5/3

Answers vary.