The One Penny Whiteboard - Collins Education Associates files 4.29.2013/Math/g3... · One Penny...

The One Penny Whiteboard Ongoing, “in the moment” assessments may be the most powerful tool teachers have for improving student performance. For students to get better at anything, they need lots of quick rigorous practice, spaced over time, with immediate feedback. The One Penny Whiteboards can do just that.

©Bill Atwood 2014

To add the One Penny White Board to

your teaching repertoire, just purchase some sheet protectors and white board markers (see the following slides). Next, find something that will erase the whiteboards (tissues, napkins, socks, or felt). Finally, fill each sheet protector (or have students do it) with 1 or 2 sheets of card stock paper to give it more weight and stability.

©Bill Atwood 2014

©Bill Atwood 2014

On Amazon, markers can be found as low as $0.63 each. (That’s not even a bulk discount. Consider “low odor” for students who are sensitive to smells.)

©Bill Atwood 2014

I like the heavy-weight model. ©Bill Atwood 2014

On Amazon, Avery protectors can be found as low as $0.09 each.

©Bill Atwood 2014

One Penny Whiteboards and The Templates

The One Penny Whiteboards have advantages over traditional whiteboards because they are light, portable, and able to contain a template. (A template is any paper you slide into the sheet protector). Students find templates helpful because they can work on top of the image (number line, graph paper, hundreds chart…) without having to draw it first. For more templates go to www.collinsed.com/billatwood.htm) ©Bill Atwood 2014

Using the One Penny Whiteboards

There are many ways to use these whiteboards. One way is to pose a question, and then let the students work on them for a bit. Then say, “Check your neighbor’s answer, fix if necessary, then hold them up.” This gets more students involved and allows for more eyes and feedback on the work.

©Bill Atwood 2014

Using the One Penny Whiteboards Group Game

One way to use the whiteboards is to pose a challenge and make the session into a kind of game with a scoring system. For example, make each question worth 5 possible points.

Everyone gets it right: 5 points Most everyone (4 fifths): 4 points More than half (3 fifths): 3 points Slightly less than half (2 fifths): 2 points A small number of students (1 fifth): 1 point

Challenge your class to get to 50 points. Remember students should check their neighbor’s work before holding up the whiteboard. This way it is cooperative and competitive.

©Bill Atwood 2014

Using the One Penny Whiteboards Without Partners

Another way to use the whiteboards is for students to work on their own. Then, when students hold up the boards, use a class list to keep track who is struggling. After you can follow up later with individualized instruction.

©Bill Atwood 2014

Keep the Pace Brisk and Celebrate Mistakes

However you decide to use the One Penny Whiteboards, keep it moving! You don’t have to wait for everyone to complete a perfect answer. Have students work with the problem a bit, check it, and even if a couple kids are still working, give another question. They will work more quickly with a second chance. Anytime there is an issue, clarify and then pose another similar problem. Celebrate mistakes. Without them, there is no learning. Hold up mistakes and say, “Now, here is an excellent mistake–one we can all learn from. What mistake is this? Why is this tricky? How do we fix it?”

©Bill Atwood 2014

The Questions Are Everything!

The questions you ask are critical. Without rigorous questions, there will be no rigorous practice or thinking. On the other hand, if the questions are too hard, students will be frustrated. They key is to jump back and forth from less rigor to more rigor. Also, use the models written by students who have the correct answer to show others. Once one person gets it, they all can get it.

©Bill Atwood 2014

Questions When posing questions for the One Penny Whiteboard, keep several things in mind:

1. Mix low and high level questions 2. Mix the strands (it may be possible to ask about fractions,

geometry, and measurement on the same template) 3. Mix in math and academic vocabulary (Calculate the area… use

an expression… determine the approximate difference) 4. Mix verbal and written questions (project the written questions

onto a screen to build reading skills) 5. Consider how much ink the answer will require and how much

time it will take a student to answer (You don’t want to waste valuable ink and you want to keep things moving.)

6. To increase rigor you can: work backwards, use variables, ask “what if”, make multi-step problems, analyze a mistake, ask for another method, or ask students to briefly show why it works

©Bill Atwood 2014

Examples What follows are some sample questions that relate to understanding measuring time as outlined in 3 MD1.

©Bill Atwood 2014

©Bill Atwood 2014

Slides 20-41 deal with writing and telling time to the nearest minute. Slides 41-63 are solving word problems with adding and subtracting time intervals and using a number line diagram. Slides 63-75 problems with 2 clocks. Slides 76 -88 are line plot problems with time. The last 5 slides review fractions on a clock/circle.

©Bill Atwood 2014

Examples Each of these problems can be solved on the One Penny Whiteboard. To mix things up, you can have students “chant” out answers in choral fashion for some rapid fire questions. You can also have students hold up fingers to show which answer is correct. Sometimes, it makes sense to have students confer with a neighbor before answering. Remember, to ask verbal follow-ups to individual students: Why does that rule work? How do you know you are right? Is there another way? Why is this wrong?

©Bill Atwood 2014

Examples

Copy the following graph paper samples and have students insert it into their One Penny Whiteboards.

©Bill Atwood 2014

©Bill Atwood 2014 ©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x

Line Plot of Bedtimes for 15 third graders.

x Key: each represents 1 student

Show 7:15 PM on the clock. Label the time.

7:15 PM

Quarter past seven in the evening.

©Bill Atwood 2014 Erase!


8:30 PM

Half past eight in the evening


©Bill Atwood 2014


9:05 PM


5 min after 9PM



3:33 PM


©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014


9:58 PM


2 min before 10PM

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014


6:13 PM


13 minutes past 6 PM 13 min after 6 PM

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014


4:38 PM


22 minutes before 5:00 PM

What time is this?

9:55

Joe thinks it is 10:55. Why is this wrong?


5 minutes till 10 5 min before 10

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Show 8:56 AM on the clock. Label the time.

8:56 AM


Why is this not 9:56?

4 minutes before 9:00 AM

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Show 11:14 AM on the clock. Label the time.

11:14 AM


About a quarter past 11 AM


What time is it?

11:05


5 minutes past 11

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

What time is it?

11:25


©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

What time is it?

2:32


A little after half past 2

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

What time is it?

9:28


It’s almost 9:30

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

What time is it?

1:02


Just a little after 1 O’Clock

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

What time is it?

12:58


2 minutes before 1:00

©Bill Atwood 2014

What time is it?

6:58

Erase!

2 minutes before 7:00

Fred said it was 7:58. What would 7:58 look like?

©Bill Atwood 2014

What time is it?

9:15

Erase!

Quarter past 9:00

©Bill Atwood 2014

What time is it?

7:15

Erase!

Quarter past 7:00

©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

What time is it?

2:15


Quarter past 2:00

Draw the time that is 15 minutes later.

Show the time is 9:55

9:55 + 15 minutes = 10:10

©Bill Atwood 2014

©Bill Atwood 2014

Brian school starts at 8:15 AM. There are 2 hours and 30 minutes until recess. How long until recess?


One way to solve this is to use the clock. Draw 8: 15 AM on the clock.

Since recess is 2 hours away, imagine adding two hours to the hour hand.


Then add 30 minutes to the minute hand. Since adding the 30 minutes doesn’t take you to a new hour, you’re done!

Recess is at 10: 45. (Since it’s 10:45 you might want to adjust the hour hand a little.)



There is another way to solve this problem using a number line.


First, use your finger to divide the number line into about 10 equal sections. (it doesn’t have to be perfect!)

Think of the time line or as a clock that has been unrolled! (Like a Fruit Roll Up)

Time moving this way….


Next, mark off the beginning time on the first notch of your number line.

8:15 Am


Time moving this way….


Now, count off by 15 minutes until you get to 9:15 AM. That’s 1 hour. Mark that on the time line.

8:15 Am

8:30 Am

8:45 Am

9:00 Am

9:15 Am


1 hr


You can keep going until you get up to 2 hours and 30 minutes!

8:15 Am

8:30 Am

8:45 Am

9:00 Am

9:15 Am

10:30 Am

9:30 Am

9:45 Am

10:00 Am

10:15 Am

10:45 Am

1 hr 1 hr 30 min



Recess is at 10:45

8:15 Am

8:30 Am

8:45 Am

9:00 Am

9:15 Am

10:30 Am

9:30 Am

9:45 Am

10:00 Am

10:15 Am

10:45 Am

1 hr 1 hr 30 min



8:15 Am

8:30 Am

8:45 Am

9:00 Am

9:15 Am

10:30 Am

9:30 Am

9:45 Am

10:00 Am

10:15 Am

10:45 Am

1 hr 1 hr 30 min

Of course, you don’t have always label every 15 minute interval. Just use the number line to help you find the new time.

©Bill Atwood 2014

Use a number line to find the elapsed time!


Sally’s school starts at 9:45 AM. Her first two classes last 2 hours and 45 minutes. How long until recess?

9:45 AM

10:45 Am 12 pm

11:45 Am

12:15

1 hr 1 hr 45 min

12:30

There are 2 hours and 45 minutes until recess!

©Bill Atwood 2014

8:15 Am

8:30 Am

8:45 Am

9:00 Am

9:15 Am

10:30 Am

9:30 Am

9:45 Am

10:00 Am

10:15 Am

10:45 Am

You might need practice just labeling the line and counting by 15 minutes.

11:00 Am

With your partner, practice counting up and back from 8:15 to 11:00. Go by 15 minutes.


8:45 Am 9:45

10:45

11:45

12:45 pm 5:45 1:45

2:45 3:45

4:45 6:45

Now try counting by 1 hour. Start at 8:45 AM and go up to 8:45 PM.

7:45

With your partner, practice counting up and back from 8:00 to 11:00. Go by 15 minutes.

8:45


8:45 Am 9:15

9:45

10:15

10:45 1:15 11:15

11:45 12:15 PM

12:45 1:45

Now try counting by 30 Min. Start at 8:45 AM 2:45 PM.

2:15 2:45


8:35 Am 8:40

8:45

8:50

8:55 9:20 9:00

9:05 9:10

9:15 9:25

Now try counting by 5 Min. Start at 8:35 AM 9:35 PM.

9:30 9:35




Olivia’s piano lesson starts at 3:45 and ends at 5:15. How long is her lesson?

3:45 PM

4:45 Pm

1 hr

5 Pm

5:15 Pm

30 Min

1 hr and 30 min!




Carlos plays chess from 1:15 until 3:30. How long does he play?

1:15 PM

2:15

1 hr 1 hr

2 hr and 15 min!

3:15 3:30

15 min


Use a number line!


Jamal loves to read. He reads before school from 7:15 until 8:00. Then he reads after school from 3:00 until 4:15. He also reads in bed from 8:00 until 8:45? How much does he read in all?

7:15 Am

3:00 pm

45 min 1 hr

2 hr and 45 min!

4:00 4:15

45 min

7:30 7:45 8:00 8:45

15 min

8:00


Use a number line!


Jacob practices basketball a lot. He works on shooting from 7:15 until 7:45. Then after school he works on dribbling from 3:15 until 3:45. Later he works on layups from 6:30 until 7:15. How much time does Jacob spend on basketball?

7:15 Am

3:30

30 min 30 min

1 hr and 45 min

6:30 6:45 7:15 7:45 3:15

7:15

45 min

7:00 3:45


10 min + 25 min + 15 min = 50 min


Min needs to know what time to wake up. He must be at the school bus at 8:15 AM. It takes him 10 minutes to brush his teeth; 25 minutes to eat breakfast; and 15 minutes to walk to the bus. What time should he wake up?

7:25 Am

7:45

8:15 – 50 min = 7:25

7:55 8:00 7:30 7:35 7:40

8:15 8:05 7:50

8:10

Bus leaves Work backwards


45 min + 30 min = 75 min 75 minutes = 60 min + 15 min


Chi wants to get to the movie on time. The movie starts at 7:15 PM. It takes 45 minutes to drive to the theatre and 30 minutes to get the tickets and the popcorn. What time should she leave?

7:15 – 75 min = 5:50

5:50 5:55 7:15 6:10 6:15

60 min 15 min

©Bill Atwood 2014

Sarah’s Bed Time Jeff’s Bed Time

Find the difference between these two bedtimes.



Sarah’s bed time = 8:15 Jeff’s bed time = 9:45



8:15 Am

8:30 Am

8:45 Am

9:00 Am

9:15 Am

9:30 Am

9:45 Am

1 hr 30 min



8:15 Am

8:30 Am

8:45 Am

9:00 Am

9:15 Am

9:30 Am

9:45 Am

1 hr 30 min

1 hour 30 minutes difference. Or 90 Min.



On the second clock show 6:55.



On the second clock show a time 10 minutes later.



On the second clock show a time 10 minutes earlier.



On the second clock show a time 2 hours earlier.



On the second clock show a time 1 hour later.

©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x




8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



How many students had a bed time of 8:45?

6 students

©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



How many students had a bed time later than 9:00 PM?

2 students

©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



How many students had a bed time earlier than 8:45 PM?

3 students


8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



What was the most common bedtime?

8:45 PM

©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



What time was the earliest bed time?

8:35 PM

©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



What time was the latest bed time?

9:20 PM

©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



What time was the difference between the earliest and latest bed times?

45 min

45 min

©Bill Atwood 2014

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



The 9:20 bedtime was lowered to 9:05. What is the difference between earliest and latest now?

30 min

30 min


8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



Martha joined the class. Her bedtime was 25 minutes later 8:45. What time was her bedtime? Put it on the line plot.

9:10 PM

x

5min 10min 15min 20min

25min


8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



Latoya joined the class. Her bedtime was 15 minutes earlier than 9:20. Add her bedtime to the line plot.

x


8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



How many more students have a bedtime at 8:45 than 8:40?

6 - 2 = 4 4 more students

8:35 PM

8:40 8:45 8:50 8:55 9:20 9:00 9:05 9:10 9:15 9:25 9:30 9:35

x x

x x x x

x x x x x x x

x x



Shelly’s bedtime is exactly half way between 8:50 and 9:20. What time is her bedtime?

30 min

15 min 15 min

Shelly’s bedtime is 9:05


Divide the clock into 2 equal parts. Label each part with fractions.

1/2 1/2



1/4 1/4

1/4 1/4



1/8 1/8

1/8 1/8

1/8 1/8

1/8

1/8



1/3 1/3

1/3



1/6

1/6

1/6

1/6

1/6

1/6

The One Penny Whiteboard - Collins Education Associates files 4.29.2013/Math/g3... · One Penny...

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