Elapsed Time and Measurement

1. Elapsed Time and Measurement MSP March Session 3/16/11 Agree or disagree? “Learning to tell time has little to do with time measurement.”

2. Site Visits • March 21—Wise Co. School Board 3:00 • March 23—Richlands Middle 3:45 • March 28—Washington Co. School Board 3:30 • March 30—Wythe Co. School Board 3:30 • April 6-- Pulaski Elementary 3:00

3. Measurement • Speaking in general terms, measurement is one of the most useful and practical mathematical strands International data from TIMSS and NAEP consistently indicate that students are weaker in the area of measurement than any other topic in a curriculum (Thompson & Preston, 2004). Some attribute learning both customary and metric is the problem. It can certainly be a contributing factor However the most likely culprit is a function of how it is taught Namely a reliance on worksheets and pictures and too little hands on A focus on skills with less attention to concepts

4. To Measure requires 3 steps • 1. Decide on the attribute to be measured. • 2. Select a unit that has an attribute • 3. compare units by filling, covering, matching, etc. • The number of units required to match is the measure

5. Big Ideas • Meaningful measurement and estimation of measurement depend on a personal familiarity with the unit of measure being used. • Estimation of measures and development of benchmarks helps prevent errors and increases familiarity with frequently used units. • Area, Perimeter, and Volume are related. (and better taught with measurement)

6. Connections across strands • Early measurement is a very meaningful context for counting. • Measuring important objects in a familiar environment connects ideas of number to the real world • Multiples of ten are used by young children in non-standard measures. The metric system is built on the base ten system • Measurement formulas are themselves functions • Measurement provides data from which generalizations and functional relationships can be made

7. Cont. • The need for increased precision leads to fractional parts of units • Benchmarks in estimating measures promotes multiplicative thinking. Used in scale drawings. Proportions are used to find unknown measures of similar figures • Measures help to describe shapes and angular measures play a significant role in the properties of shapes • Statistics are often described in terms of measures

8. Time • Time can be one of the most difficult to teach because it cannot be seen or felt as other types of measure • It is more difficult for students to comprehend units of time or how they are matched against a given time period or duration (i.e. elapsed time is the hardest to teach!)

9. Duration • Can be thought as duration of an event from beginning to end • Students should compare events of different durations • Ex. Which spinner spins longer? Which class period is shorter? (The issue here is that most of the time all begin at the same time) • This pushes the focus on the ending rather than the duration itself • Have to move on to comparing 2 events not starting at the same time • Requires the use of the same unit of measurement from beginning to end of both events (although it may not be presented that way)

10. Informal duration • Activities for students: Stacking ten blocks one at a time and unstacking them Printing the alphabet Untying and tying a shoe Students need a feel for seconds, minutes, and hours Make an effort to note long and short daily events Have students time daily routines such as brushing teeth (2 minutes), riding to school, time spent on homework etc.

11. Be Ready for the Bell! • Give students a recording sheet with a set of clock faces. • Secretly set a timer to go off on the hour, half hour, or minute • When the bell rings, students should look up and record the time on the clock face in numerals • Elapsed time can be incorporated by more than one timer ring and discussing the time between the rings

12. Clock Reading—not that elementary… Learning to read a clock has more to do with the skills of reading a dial instrument than with time measurement and duration. Students are first taught to read an analog clock and begin with hour, then ½ hour, ¼ hour, 5 minute intervals, minute intervals They are shown pictures of clocks set to exact times This makes reading 2:33 and 6:58 accurately a challenge

13. Digital? • Does provide ease of reading but does not relate time well • To know that 7:58 is near 8:00, a child must know 7 precedes 8 on a clock face, 60 minutes in an hour means that 58 is close to 60 (or a new hour beginning) and that 2 minutes is not very long. • This kind of thinking is not developed at an early enough level and reading a clock accurately (analog or digital) is challenging all the way through

14. Some suggestions • 1. Begin with a one-handed clock but use lots of approximate language. “Its about 7 o’clock,” It’s a little past 9 o’clock,” Its halfway between 2 o’clock and 3 o’clock.” • 2. Discuss what happens to both hands as one moves. Then go to specifics like where would the hour hand be if the minute hand is ____? • 3. Teach time after the hour in 5 minute intervals first, then go to more precise readings • Have a digital and analog clock. Cover one and uncover the other. Have students read one and predict what the other will look like (or read) • A one-handed clock blackline master will be up on the MSP site

15. Elapsed Time • Required by most states beginning in grade 3 • Noon and midnight pose greatest challenges. Students have a harder time passes from AM to PM and vice versa • Student must know minutes in an hour and hours in a day. They also have to understand on a basic level 12-hour time versus 24 hour time. • According to NAEP stats, only 26% of 4th graders and 55% of 8th graders could successfully solve a problem involving the conversion of one measure of time to another

16. Elapsed Time cont. • Figuring the time between 8:15 AM and 11:45 AM is a multi-step task no matter which way you attempt it • Keeping track of intermediate steps is difficult • Deciding what to do first is difficult • Most students count the hours, but what to do about the minutes?? • Proposing a single method or algorithm is not helpful • Then students must deal with AM and PM issues. Is this a case of spanning across that divide or not?

17. Elapsed Time cont. • With AM and PM its less about whether the students know what actually happens on the clock at noon and midnight (because they actually do!) • It is trouble counting the intervals • Elapsed time gets compounded by finding ending or starting times given the elapsed time. • In general, I have had the most success with blank or modified number lines.

18. An example: • Work this problem as you normally would: • School began late today at 10:45 AM. If you get out at 3:30PM, how much time will you be in school today? • How did you do this? Would you talk it out with students? Use a clock?

19. School began late today at 10:45 AM. If you get out at 3:30PM, how much time will you be in school today? • Same problem solved with a number line:

20. This time try using a number line…and think about possible variations that could be made • The game begins at 11:30 AM. If it lasts 2 hours and 15 minutes, when will it be over?

21. Measurement: Introducing Standard units • One of the biggest errors in measurement instruction is the failure to separate the 2 main objectives we strive to teach: • 1. understanding the meaning and technique of measuring a particular attribute (i.e. weight) • 2. learning about the standard units commonly used to measure the attribute (i.e. kg, g, lb etc) • We tend to focus on how to measure instead of what unit to use when and if other options exist. • This is where we see a disconnect in children recognizing that a meter and yard are similar in measure or a kg is the closest metric equivalent to a pound in customary.

22. What we should set as objectives: • 1. Familiarity with the unit—it is important students know common units of measure and when to use them • Its more important that a student know approximately how much 1 liter of water is or be able to estimate a shelf as 5 ft. long than being able to measure it to the nearest 1/8th inch. • 2. ability to select an appropriate unit—Students need to know what is reasonable. They only get this through hands-on experience! • Its also about precision! We never talk about this. We might measure an open field with the intent of sowing grass seed differently than we would measure a window in our house to be fitted with a new pane of glass, or a room for new flooring. • 3. Knowledge of relationships between units—students should know common relationships between units that are used. Tedious conversion exercises do little to enhance measurement sense

23. Develop Familiarity • Give students a model of a standard unit and have them find objects that measure about the same as the unit • Ex. Rope that is 1 meter in length. • A Styrofoam cup that has close to a fluid ounce in it. • An object that weighs about 1 pound • This can take on many forms and be taken in depth at all levels

24. Unit relationships • Both Customary and Metric have units that are rarely used in everyday life! • Use the ones that are necessary to make valuable connections across systems! • Students must simply be told what the relationships are and instruction must be devised to reinforce this • In our grade band, knowing basic relationships becomes more important than knowing how many cubic centimeters are in a liter.

25. Cont. • Customary has very few patterns or rules to guide students, unlike metric that is set up on the base 10 system (and uses powers of 10) • Exact conversions should be avoided • Students just need to know that a liter is a “gulp more” than a quart (SWVA language there!) A meter is a bit longer than a yard Kilograms are a little lighter than a pound (which makes me weigh less in Europe!)

26. Estimation • This is the key to it all. • Students must estimate measurements. • This begins with choosing a unit • Build this with tasks! • Can you throw a ball 15 meters? • Does this suitcase weigh 5 pounds? Can you lift it? • About how long is our playground fence? • About how tall am I? • Scavenger hunts are great~

27. More to come! • Site visits are next! • I plan to cover more fraction computation, measurement techniques, area and volume introduction, and (of course) some SOL review strategies as we near the end of the year. • I will see you on your appointed date/time! • Questions?