Lesson: Comparing and Ordering Fractions, Mixed Numbers, and Decimals
Introducing the Concept
Introduce this concept by relating it to comparing and ordering whole numbers or to comparing and ordering fractions. You can refer to the models described in Comparing and Ordering Fractions and make a set of decimal models that are the same size.
Materials: student-made fraction kits, wax paper or 6-inch squares of tracing paper, millimeter rulers
Preparation: Provide each student with 6-inch squares of tracing paper that they can see through. Have them get out their matching fraction kits.
Prerequisite Skills and Concepts: Students should be able to compare and order whole numbers and fractions. They should have a good grasp of what a decimal number is and how to determine the denominator for the related fraction.
- Say: Take one of your paper squares and carefully fold it in half. Line up the bottom of the ruler on the edge of the paper. Now line up the 7.5-cm mark with the center fold. Put a dot at these measures: 1.5 cm, 3 cm, 4.5 cm, 6 cm, 7.5 cm, 9 cm, 10.5 cm, 12 cm, and 13.5 cm. Repeat at the opposite edge of the paper until you have two dots at each measure. Draw a line the full length of the paper, going through each pair of dots.
- Ask: The parts of your square should be about equal. Let's assume they are. How many equal parts are in the whole?
There are ten parts. Work with students to make 10 identical paper squares. Color one tenth in one square, two tenths in the next square, and so forth. Keep one square clean just in case you need it. - Ask: What does one square represent?
Students should recognize that one square is one whole. - Ask: What does one part represent? (
)
Students may identify one part of the ten equal-size parts as representing. - Ask: Can someone show me two ways to write this number?
Students may write and 0.1 on the chalkboard.
For all other comparisons in this lesson, have students write fraction and decimal representations on the board. - Say: Look at both your fraction kit and your decimal kit. Place your five-tenths square over your one-half square.
- Ask: How do the fractions compare?
Students may notice that since the same part of each square is colored in,
= 
= 0.5. - Say: Place your five-tenths square over your four-eighths square.
- Ask: How do the fractions compare?
Students should notice that since the same part of each square is colored in,
= 
= = 0.5.
Continue in this vein, helping students to compare by using the terms greater than and less than as well as equal to and not equal to.
- Say: Mix up your fraction and decimal squares. Take the first four squares from the top of your stack and put the rest out of the way. Put the squares in order from least to greatest.
- Ask: Can you write the names of your numbers from least to greatest, using both fraction and decimal notation?
This should be an easy task. If it is not, find some time later to work with any student who is having trouble. - Ask: Can you use your fraction squares to help you put these numbers in order from least to greatest?
, 0.5, 
, 1, 1.3
This will be a more challenging task, but students should be able to pick out the appropriate models and use them to order their fractions. - Say: Work with a partner. Mix up your kits and stack them, then take four squares and work together to put them in order. Do this three times.