Metric Measurements, Fractions and Number Lines
Students will be able to calculate fractions of metric units using number lines.
- Ask, “What two numbers can we multiply together to get 100?” Note how these are called factors of 100.
- Mention to your class that any factor for a given number divides that number evenly.
- Demonstrate by writing a multiplication fact family for 100 as: 4 x 25 = 100, 25 x 4 = 100, 100/4 = 25. Hence, 4 and 25 divide 100 evenly.
- Allow your class to think, pair and share their thoughts on any other factors for 100.
- Have your students share whole class, confirm and post the factors for 100 as: 1, 2, 4, 5, 10, 20, 25, 50, 100.
- Tell your students that finding factors, will be one strategy used to find fractions and equivalent measurements to 100.
Explicit Instruction/Teacher modeling(10 minutes)
- Preview and explain how the metric system is based on partitions (or divided into equal parts) of 100. The factors for 100 that we previously listed all divide a number line of 100 units evenly, with no remainder. We call this a base-ten system, like our money system.
- Show your class an open number line labeled 0 to 100 and ask, “How might we find ¾ of a 100 meter number line?”
- Have your students think, pair and share their thoughts with the whole class. If your class uses math journals, this would be a good time for them to use them.
- During student responses, note any academic terms for future reference.
- Share with your class that finding fractions of 100 on a number line can be achieved in four steps!
Step one for finding ¾ of 100 meters: Draw an open number line, beginning at 0 and ending at 100 meters.
Step two: Look to the denominator of the fraction to calculate how many partitions are needed for the number line (in this case, it’s 4.). From our factor list, we know four is a factor of 100, so draw and partition an open number line into four equal parts (...including the endpoint!)
Step three: Calculate partition increments: 100/4 =25, so there will be four partitions in 25 meter increments. Then, label the number line at 25m, 50m (25 + 25), 75m (25 + 25 + 25) and 100m (25 + 25 + 25 + 25).
Step four: Skip count partitions by the numerator amount. Skip three out of four partitions from zero (25, 50, arriving at 75), to calculate ¾ of 100. So, ¾ of 100 meters is 75 meters.
Guided Practice(10 minutes)
- Repeat the four-step procedure with your students to calculate and illustrate 6/10 of 100 centimeters and answer any clarifying questions.
- The result should be 6/10 of 100 cm is 60cm.
Independent working time(15 minutes)
- Hand out and preview the Finding Fraction Equivalents for Metric Measurements worksheet.
- Answer any clarifying questions and have your students complete the exercises.
- Print and post the four-step procedure for students to reference. Direct students with a study-buddy partner to the poster as needed, to follow the procedure step-by-step.
- print sheets of number lines pre-partitioned by factors of 100 for students to use
- Students can convert metric measurements to greater or lesser metric units, (i.e. meters to centimeters or meters to kilometers) by using a metric conversion chart.
- Students can try finding fractions of numbers that aren’t 100 (but still divide evenly), like ¾ of 40.
- Interactive whiteboards are a great resource to use in tandem with the Online Ruler reference in the media section.
- Computers with Internet access and a projector make for a great set-up to display the online ruler, listed in the suggested media section. Students can interact with the number line repeatedly on a whiteboard with erasable markers.
- Show your students three fractions and an open number line (where one has a denominator factor of 100.)
- Ask your students to point out which fractions that would work on a number line that is 0-100.
Review and closing(10 minutes)
- Review the answers for Finding Fraction Equivalents for Metric Measurements, whole class, allowing students to call on peer assistance when needed.
- Pose and discuss the question, “What are the advantages and disadvantages of using a number line to express equivalent fractions for metric measurements?”