1. 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

2. 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

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5. On Amazon, markers can be found as low as $0. 63 each
On Amazon, markers can be found as low as $0.63 each. (You might even get a better deal with a bulk discount. Consider “low odor” for students who are sensitive to smells.)
©Bill Atwood 2014

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

7. On Amazon, Avery protectors can be found as low as $0.09 each.
©Bill Atwood 2014

8. 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.
Coming soon: more templates at
©Bill Atwood 2014

9. 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

10. 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 fifths of class): 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

11. 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

12. 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/struggling, give another question. They will work more quickly with a second chance. Anytime there is an issue, clarify and then pose another similar problem. Have students help each other!
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

13. 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

14. Questions
When posing questions for the One Penny Whiteboard, keep several things in mind:
Mix low and high level questions
Mix the strands (it may be possible to ask about fractions, geometry, and measurement on the same template)
Mix in math and academic vocabulary (Calculate the area… use an expression… determine the approximate difference)
Mix verbal and written questions (project the written questions onto a screen to build reading skills)
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.)
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

15. Examples
What follows are some sample questions that address fractions concepts and Data: Common Core Standards:
3NF 1-3 and 3MD 3-4.
Each of these questions 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.
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

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18. Teachers: Print the following slides (as needed) and then have students insert whichever one you need into their whiteboards.
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20. 1
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23. Title:
Pictograph Key
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24. Title: Pictograph Key 3 MD 3 Day Number of Day # Monday Tuesday
Wednesday
Thursday
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28. 3 NF 1    
How many equal sections is this line divided into?
Show them with arrows.
4 equal sections
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29. 3 NF 2
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Imagine you were in a one kilometer race. The starting line is zero and the finish line is 1. Use thick lines to divide your race into 4 equal sections.
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30. 3 NF 2
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Every ¼ of a kilometer, the race has a water station. Write the fraction (1/4, 2/4, 3/4, 4/4 ) above each water station.
Now add in 0/4 above the number line.
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©Bill Atwood 2014
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31. 3 NF 3B
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Explain to your neighbor why 2/4 and 1/2 are equal fractions.
Possible answers:
They are the same distance from zero.
They are at the same point on the number line.
The fourths are smaller units so you must go to 2/4 to equal ½.
2 out of 4 is half way of the race; it is the same as 1 out of 2.
Don’t erase
©Bill Atwood 2014
©Bill Atwood 2014
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32. 3 NF 3D
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Write a number sentence that shows ¼ is less than ½ . Circle the fractions, then explain to your neighbor why this is true.
1/4 < 1/2 or 1/2> 1/4
½ is further from zero on the number line.
¼ is a smaller part of the race than ½.
Fourths are a smaller unit than halves because the mile has been cut into 4 equal parts. Halves have only been cut into two equal parts.
©Bill Atwood 2014
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33. 3 NF 3D
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Write a number sentence that shows 3/4 is greater than 2/4 . Circle fractions. Explain to your neighbor why this is true.
2/4 < 1/2 or 3/4> 1/4
3/4 is further from zero on the number line.
¾ is a larger part of the race than 2/4.
Both fractions are fourths but 3 fourths has more fourths than 2 fourths. 2/4 = 1/ but 3/4 > 1/2
©Bill Atwood 2014
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34. 4 NF 2
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Write a number sentence that shows this. Circle the fractions. Explain to your neighbor why ¾ is greater than ½.
1/2 < 3/4 or 3/4> 1/2
3/4 is further from zero on the number line.
¾ is a larger part of the race than 1/2.
Fourths are a smaller unit than halves but in this case you ran 3 fourths which is more than half of the race. 2 fourths would be half, but ¾ is more than half.
©Bill Atwood 2014
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35. 3 NF 3D
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Write a number sentence that compares two fractions on this number line. There are many answers.
2/4 = 1/2
0/4 < 1/4
1/4 < 2/4
2/4 < 3/4
3/4 < 4/4
4/4 > 0/4
0/4 < 2/4
1/4 < 3/4
2/4 < 4/4
3/4 > 0/4
4/4 > 1/4
0/4 < 3/4
1/4 < 4/4
2/4 > 0/4
3/4 > 1/4
4/4 > 2/4
0/4 < 4/4
1/4 > 0/4
2/4 > 1/4
3/4 > 2/4
4/4 > 3/4
©Bill Atwood 2014
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36. GRADE 4
4 NF 3
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Mark says he like to think of a 1 kilometer race as a 4 short distances. He says, 4/4 = 1/4 + 1/4 + 1/4 + 1/4
Is this true? Can you write an equation that breaks 3/4 into unit fractions of 1/4 +… 3/4 = ____________
3/4 = 1/4 + 1/4 + 1/4
©Bill Atwood 2014
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37. GRADE 4
4 NF 3
1/4
0/4
2/4
3/4
4/4
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Can you write a similar equation for 2/4 = ____
2/4 = 1/4 + 1/4
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38. 1/4 0/4 2/4 3/4 4/4 Carlos ran ½ of a mile race.
3 NF 3D
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Carlos ran ½ of a mile race.
Mary ran ¼ of a 10 mile race.
Even thought ½ is greater than ¼, Mary ran further than Carlos. Why? Turn to your neighbor and explain.
Even though ½ is greater fraction, they ran in different races. The ten mile race is ten times longer, so even though Mary only ran ¼ of it, she ran more than Carlos. When you compare fractions you must be talking about the same WHOLE.
©Bill Atwood 2014
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39. 1/4 0/4 2/4 3/4 4/4 Jacob ran ¾ of his race.
3 NF 3D
1/4
0/4
2/4
3/4
4/4
©Bill Atwood 2014
Jacob ran ¾ of his race.
Marta ran ½ of her race. Marta ran much farther than Jacob. How can this be? Write one idea on your white board.
Marta’s race must have been a greater distance because Jacob ran ¾, he ran more of his race, but his race must have been shorter. Maybe he ran a race that was only 10 feet. Marta’s race was maybe a mile. When you compare fractions, you must be comparing to the same WHOLE!
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40. 1/4 0/4 2/4 3/4 4/4 Erase the white board. ©Bill Atwood 2014

41. ©Bill Atwood 2014
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42. 3 NF 2
0/8
1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8
Use thick lines to divide this number line into eight equal sections. Label each 0/8, 1/8, 2/8, 3/8…
Don’t erase
©Bill Atwood 2014

43. 3 NF 2
0/8
1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8
Another way to think about this problem is to first divide the line into halves (2 sections)
Then divide the line into fourths (1/4’s = 4 sections).
Then divide the line into eighths (1/8’s = 8 sections).
Don’t erase
©Bill Atwood 2014
©Bill Atwood 2014

44. 1/2 = 2/4 = 4/8 They are at the same distance from zero!
3 NF 3A + B
2/8
4/8
6/8
8/8
0/8
1/8
3/8
5/8
7/8
1/4
3/4
4/4
2/4
Write a number sentence that shows two equal fractions on this number line. Explain why to your neighbor.
1/2 = 2/4 = 4/8 They are at the same distance from zero!
8/8 = 4/4 = 1/1 All one whole unit away from zero.
2/8 = 1/4. Eighths are smaller units but you have two eighths so that equals one fourth.
©Bill Atwood 2014
©Bill Atwood 2014
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45. 3 NF 3C
2/8
4/8
6/8
8/8
0/8
1/8
3/8
5/8
7/8
Write a number sentence that compares two fractions. Use > < = (be prepared to explain)
8/8 > 7/8
©Bill Atwood 2014
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46. A Put the letter A over 2/8. 2/8 4/8 6/8 8/8 0/8 1/8 3/8 5/8 7/8
3 NF 2 A
2/8
4/8
6/8
8/8
0/8
1/8
3/8
5/8
7/8
Put the letter A over 2/8.
©Bill Atwood 2014
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47. B Put the letter B over 4/8. 2/8 4/8 6/8 8/8 0/8 1/8 3/8 5/8 7/8
3 NF 2 B
2/8
4/8
6/8
8/8
0/8
1/8
3/8
5/8
7/8
Put the letter B over 4/8.
©Bill Atwood 2014
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48. C Put the letter C over 7/8. 2/8 4/8 6/8 8/8 0/8 1/8 3/8 5/8 7/8
3 NF 2 C
2/8
4/8
6/8
8/8
0/8
1/8
3/8
5/8
7/8
Put the letter C over 7/8.
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49. 3 NF 3C v
0/8
1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8 v 1
1 = 8/8
Why is this true?
They are in the same place on the number line.
©Bill Atwood 2014
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50. 3 NF 3B v
0/8
1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8 v
4/8 = 1/2
Why is this true?
4/8 has smaller pieces but you have 4 of them.
©Bill Atwood 2014
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51. 3 NF 3D
2/8
4/8
6/8
8/8
0/8
1/8
3/8
5/8
7/8
5/8 > 3/8 Why is this true?
Since 8th’s are the same size and 5/8 has more eighths than 3/8.
5/8 is farther away from zero.
5/8 is more than half and 3/8 is less than half.
©Bill Atwood 2014
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52. GRADE 4
4 NF 3
1/8
0/8
Write and equation which breaks 4/8 into all unit fractions of 1/8.
4/8 = 1/8 + 1/8 + 1/8 + 1/8
Erase
©Bill Atwood 2014
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53. 1
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54. 3 NF2A
0/3
1/3
2/3
3/3 1
This is 1 mile race. It starts at 0 and ends at 1.
Use thick lines to break this race into 3 equal sections (1/3’s).
Label the race with 0/3, 1/3, 2/3..
Don’t erase
©Bill Atwood 2014
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55. 1/3 0/3 2/3 3/3 1 One way to draw thirds Find the 1/2 point
3 NF2
0/3
1/3
2/3
3/3
1/2 1
One way to draw thirds
Find the 1/2 point
Move a little to the left and and little to right of 1/2.
©Bill Atwood 2014
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56. 3 NF2B
0/3
1/3
2/3
3/3 X 1
At 2/3 of a mile, there is a water station.
Put an X on 2/3 of mile.
Don’t erase
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57. 3 NF 3C
0/3
1/3
2/3
3/3 F 1
The finish line is at 3/3. Put an F at 3/3 of a mile.
Don’t erase
©Bill Atwood 2014
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58. C 1/3 of the race 1/3 0/3 2/3 3/3 1 Don’t erase
3 NF2
0/3
1/3
2/3
3/3 C 1
Shaquille ran to Point C.
How much of the race did he complete?
1/3 of the race
Don’t erase
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59. C 2/3 of the race more. 1/3 0/3 2/3 3/3 1 1/3 1/3 Don’t erase
3 NF 2B
4 NF 3
0/3
1/3
2/3
3/3 C 1
1/3
1/3
What fraction of a mile does he have to go?
2/3 of the race more.
Don’t erase
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60. 1/3 < 2/3 or 2/3 > 1/3. S < K or K > S 1/3 0/3 2/3 3/3 1 S
3 NF 3C
0/3
1/3
2/3
3/3 1 S K
Shaquille ran to Point S. Kenny ran to point K. Who ran further? Write a number sentence which compares these distances.
1/3 < 2/3 or 2/3 > 1/3.
S < K or K > S
Erase
©Bill Atwood 2014
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61. 1 This is 1 Kilometer race. It starts at 0 and ends at 1.
3 NF2 1
This is 1 Kilometer race. It starts at 0 and ends at 1.
Use thick lines to break this race into 6 equal sections.
Label the race with 0/6, 1/6, 2/6, 3/6...
©Bill Atwood 2014

62. 0/6 2/6 6/6 3/6 4/6 1/3 0/3 2/3 5/6 3/3 1/6 1 Don’t erase
3 NF 2
0/6
2/6
3/6
4/6
6/6
0/3
1/3
2/3
5/6
3/3
1/6
1/2 1
One way to draw sixths
Find the 1/2 point then move a little to the left and and little to right of 1/2. Add the 1/3’s.
Since 1/6 is half of 1/3, add in the sixths. Sixths are smaller than thirds, they have been divided into twice as many pieces!
Cut the thirds into two pieces! Then label.
Don’t erase
©Bill Atwood 2014
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63. 3 NF 3A + B
0/6
2/6
3/6
4/6
6/6
0/3
1/3
2/3
5/6
3/3
1/6
1/2 1
Write two equations to show equal fractions.
2/6 = 1/3
4/6 = 2/3
3/6 = 1/2
6/6 = 3/3
Don’t erase number line
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64. 0/6 2/6 6/6 3/6 4/6 1/3 0/3 2/3 5/6 3/3 1/6 1 Erase Why is 2/6 = 1/3?
3 NF 3A + B
0/6
2/6
3/6
4/6
6/6
0/3
1/3
2/3
5/6
3/3
1/6
1/2 1
Why is 2/6 = 1/3?
They are the same point on the number line.
They are the same distance from zero.
Sixths are smaller than thirds but you have 2/6 so that = 1/3.
Erase
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65. 4 1 This is a 4 mile race. Cross off the 1 and change it to a 41
This is a 4 mile race.
Cross off the 1 and change it to a 4
©Bill Atwood 2014

66. 1 2 3 4 1 Don’t erase This is a 4 mile race.1
This is a 4 mile race.
Add in lines to show 1 mile, 2 miles, and 3 miles.
Don’t erase
©Bill Atwood 2014
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67. 3 NF 3D 1 2 3 4 1
1/1
2/1
3/1
4/1
If you think of 1 mile as a whole. Then the fraction for 1 mile is 1/1. The fraction for 2 miles is 2/1.
What is the fraction for 3 miles?
3/1
What is the fraction for 4 miles?
4/1
What is the fraction for 10 miles?
10/1
Erase
©Bill Atwood 2014
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68. 1
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69. This is a ruler with 1/4 inches. You can use it to measure things.
This caterpillar is about 3/4 of an inch long.
©Bill Atwood 2014

70. 1
1/4
1/2
3/4
Imagine this is an inch. Add thick lines to this inch to show 1/4, 1/2, and 3/4
Don’t erase
©Bill Atwood 2014
©Bill Atwood 2014

71. 3 MD 4 1
1/4
1/2
3/4
A third grade science class measured the lengths of 10 caterpillars in the trees near their school. The data is in the column below. Use X’s to make a line plot with this data.
Size of Caterpillare in inches
Number of caterpillars
1/4 inch long 2
1/2 inch long 4
3/4 inch long 5
1 inch long 1
©Bill Atwood 2014
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72. X X X X X X X X X X X X 1 1/2 3/4 1/4 Don’t erase 3 MD 41
1/4
1/2
3/4
Size of Caterpillar in inches
Number of caterpillars
1/4 inch long 2
1/2 inch long 4
3/4 inch long 5
1 inch long 1
Don’t erase
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73. X X X X X X X X X X X X 1 1/2 3/4 1/4 Don’t erase
3 MD 4 X X X X X X X X X X X X 1
1/4
1/2
3/4
Which size caterpillar was most common? Circle it.
The 3/4 inch size was the most common size for caterpillars in this sample.
Don’t erase
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74. X X X X X X X X X X X X 1 1/2 3/4 1/4 Don’t erase
3 MD 4 X X X X X X X X X X X X 1
1/4
1/2
3/4
How many caterpillars were less than 1/2 inch? Circle them.
Only 2 caterpillars were less than 1/2 of an inch.
Don’t erase
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75. X X X X X X X X X X X X 1 1/2 3/4 1/4 Don’t erase
3 MD 4 X X X X X X X X X X X X 1
1/4
1/2
3/4
How many caterpillars were greater than 3/4 inch?
Only 1 caterpillar was longer.
Don’t erase
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76. X X X X X X X X X X X X 1 1/2 3/4 1/4 Erase
3 MD 4 X X X X X X X X X X X X 1
1/4
1/2
3/4
How many more caterpillars were 3/4 inches long than 1/2 inch long?
There is 1 more caterpillar = 1
Erase
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77. ©Bill Atwood 2014

78. Insert this template into your white board.
©Bill Atwood 2014

79. 4/4 1/4 2/4 3/4 Make a bar graph with this information.
3 MD 4
Don’t forget title!
Caterpillar sizes collected by Grade 3
Size of Caterpillar in inches
Number of caterpillars
1/4 inch long 2
1/2 inch long 4
3/4 inch long 5
1 inch long 1
Number of caterpillars.
Add in data. Be neat!
Insert label for axis.
1/4
2/4
3/4
4/4
Label vertical axis (y axis)
Size of caterpillars in inches
Make a bar graph with this information.
Put the sizes along this horizontal axis (x axis).
©Bill Atwood 2014

80. Make a Picto-graph with this information.
3 MD 3
Title:
Make a Picto-graph with this information.
Day
Number of Caterpillars Measured
Pictograph Key
Day
# Measured
Monday 6
Tuesday 8
Wednesday 4
Thursday 5
©Bill Atwood 2014
©Bill Atwood 2014

81. Caterpillars Measured Each Day
3 MD 3
Title:
Caterpillars Measured Each Day
Day
Number of Caterpillars Measured
Monday
Tuesday
Wednesday
Thursday
Pictograph Key
Day
# Measured
Monday 6
Tuesday 8
Wednesday 4
Thursday 5
= 2 caterpillars
©Bill Atwood 2014
©Bill Atwood 2014
©Bill Atwood 2014

82. ©Bill Atwood 2014

83. Use your rule (with 1/4 inches) to measure your thumb
3 MD 4
Use your rule (with 1/4 inches) to measure your thumb
Make an “L” with your hand. Measure the bottom part of the L. Use the inside part of your thumb, not the side with the thumbnail!
©Bill Atwood 2014

84. 3 MD 4
Your teachers will collect data on the tally chart. Then you can make a bar graph or a line plot.
See next slides.
©Bill Atwood 2014
©Bill Atwood 2014

85. Thumb Size # of People 2 inch 2 1/4 2 1/2 2 3/4 3 3 1/4
©Bill Atwood 2014

86. You can use this for a line plot. How long are everyone’s thumbs?
Thumb Size
# of students
You can use this for a line plot. How long are everyone’s thumbs?
©Bill Atwood 2014

87. ©Bill Atwood 2014

88. Erase What is the location of P on this number line? 3/4
©Bill Atwood 2014

89. Erase Label all the lines to the left of P (points less than P) 0/4
1/4
2/4
Label all the lines to the left of P (points less than P)
Erase
©Bill Atwood 2014
©Bill Atwood 2014

90. Erase Q Q is at 4/4. Label Q. ©Bill Atwood 2014 ©Bill Atwood 2014

91. Erase R R is at 1/4. Label R. ©Bill Atwood 2014 ©Bill Atwood 2014

92. Erase W W is at 2/1. Label W. ©Bill Atwood 2014 ©Bill Atwood 2014

93. Erase 1/2 2/4 Use the number line to show that 1/2 = 2/4.
©Bill Atwood 2014
©Bill Atwood 2014
©Bill Atwood 2014
©Bill Atwood 2014
©Bill Atwood 2014
©Bill Atwood 2014

94. Don’t Erase Divide this number line into 1/8ths. ©Bill Atwood 2014

95. Don’t Erase Put an A over 3/8. ©Bill Atwood 2014 ©Bill Atwood 2014

96. Don’t Erase Write a number sentence which compares 3/8 to 3/4.
Turn to a neighbor and explain your thinking.
Don’t Erase
©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