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.
To add the One Penny White Board to your teaching repertoire, just purchase some sheet protectors and white board markers (see the following slides). Net, 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.
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.)
The heavy-weight model works well.
On Amazon, Avery protectors can be found as low as $0.09 each.
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)
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 it for a while. Then say, Check your neighbor s answer, fi if necessary, then hold up your whiteboard. This gets more students involved and allows for more eyes and feedback on the work.
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 eample, 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.
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.
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 a whiteboard with a mistake and say, Now, here is an ecellent mistake one we can all learn from. What mistake is this? Why is this tricky? How do we fi it?
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.
Questions When posing questions for the One Penny Whiteboard, keep several things in mind: 1. Mi low and high level questions 2. Mi the strands (it may be possible to ask about fractions, geometry, and measurement on the same template) 3. Mi in math and academic vocabulary (Calculate the area use an epression determine the approimate difference) 4. Mi 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 or eplain answers
Eamples What follows are some sample questions that relate to understanding measuring liquid volume and masses as outlined in the Massachusetts Curriculum Frameworks that incorporate the Common Core Standards: 3 MD2
Eamples Each of these problems can be solved on the One Penny Whiteboard. To mi 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?
Templates Print the following slides and have students insert it into their One Penny Whiteboards. There are 7 Templates but you should also have a blank side ready for problem solving.
1 ML
2
3 Line Plot of how much water each 3 rd grader drinks per day Key: each represents 1 student 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
4 2 liter 1 liter
5 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 0 liter
6
7 kilograms grams 1 1000 2 3 4
Getting Comfortable with Liters Estimating, using scales, adding, subtracting Insert Template #1
Liters and milliliters are metric units used to measure volume the amount of liquid held in a container (beaker, glass, jar, mug, pitcher )
What metric units are used to measure liquid volume? Liters or milliliters.
What is liquid volume? The amount of liquid in a container like this beaker.
What metric unit would you use to measure the liquid in this beaker? Liters or milliliters ML Ounces, cups, pints, quarts, gallons can be used to measure liquids but are not part of the metric system.
A liter is about 1 quart. Here are 2 quarts of milk and a liter of ginger ale.
A very common size for soda is the 2 liter bottle.
How much is a liter? What common object comes in a liter size? A liter is about equal to 1 quart. Milk comes in this size.
What size soda is this? 2 Liters Abbreviation: Liter = L (l)
For small amounts, you can use a milliliter. 1000 milliliters = 1 liter Abbreviation: ML (ml) = milliliter A milliliter is very small. 5 milliliters = 1 teaspoon. A milliliter is 1/5 of this. This beaker contains 1000 ml (milliliters)
1 ml 1 tsp Often medicine is given in milliliters. When this device if full of medicine it is 1 teaspoon. 1/5 of it is 1 milliliter. A milliliter is very small, you need a special syringe to give an accurate dose. It would be about the amount to fill from the bottom of your thumb to half way up your thumbnail.
How many milliliters are in a liter? 1000 milliliters = 1 liter
About how much liquid is a milliliter? 1/5 of a teaspoon From the tip of your thumb to half way up to your thumbnail.
What is often measured in milliliters? Medicine (you need a special syringe.)
About how many more milliliters need to be added to this beaker to make 1 liter? Approimately 100-125 ml more.
What is the scale on this beaker? (What is it going up by)? It s marked off in 10 ml, but only the multiples of 20 are labeled. (Starts off at 20 not zero or 10) ML
About how many milliliters (ml) of liquid are in this beaker? Approimately 50 ml 48 ML Assume it s eactly 48 ml ML
John said this contained 45 ml. What mistake did he make? He thinks the scale is going up by 5 s. ML
Shade the beaker so it contains approimately 60 ML ML
Shade the beaker so it contains approimately 90 ML ML
Shade the beaker so it contains approimately 70 ML ML
Shade the beaker so it contains approimately 65 ML ML
Shade the beaker so it contains approimately 85 ML ML
Shade the beaker so it contains approimately 95 ML ML
Shade the beaker so it contains Approimately 82 ML ML
Shade the beaker so it contains Approimately 50 ML ML
X off liquid so it contains Approimately 30 ML ML
X off liquid so it contains Approimately 20 ML ML
This beaker has 48 ML. Use shading to add 17 ml to this beaker. How much do you have now? 17 ml 15 ml 2 ml 65 ml 48 ML 50 ML Write a number sentence to show your work. 48ml + 17ml =? 48 + (2 + 15) =? ML (48 + 2) + 15 =? (50) + 15 = 65
80 ml Use shading to add 32 ml to this beaker. How much do you have now? 32 ml 30 ml 2 ml 48 ML 50 ML Write a number sentence to show your work. 48ml + 32ml =? 48 + (2 + 30) =? ML (48 + 2) + 30 =? (50) + 30 = 80 ml
Use shading to subtract 18 ml from this beaker. How much do you have now? 18 ml 8 ml 48 ML 10 ml 30 ml 40 ML Write a number sentence to show your work. 48ml - 18ml =? 48 8 10 =? ML 48-8 - 10 =? 40-10 = 30 ml
Fractions with Liters Number Line Review Insert Template #2
4/4 Divide this container into 4 equal parts. Label them with fractions. ¾ ½ ¼ 0/4
4/4 ⅞ ¾ ⅝ ½ ⅜ ¼ ⅛ 8/8 6/8 4/8 2/8 Divide this container into 8 equal parts. Label them with fractions.
3/3 Divide this container into 3 equal parts. Label them with fractions. 2/3 1/3 0/3
3/3 5/6 2/3 3/6 1/3 1/6 0/6 Divide this container into 6 equal parts. Label them with fractions. 6/6 4/6 1/2 2/6
Problem Solving with Liters Using bar models and number sentences
This is a 3 liter beaker of water. Michael drank 4 of these these beakers. How much water did he drink? Think: You need to find the total. Draw a bar. 3 L Now, add in the information: 4 beakers Now, add in 3 liters in each beaker 3 4 = 12 liters Total liters? 3 3 3 3 12 liters
This is a 2 liter beaker of water. Michael drank 5 of these these beakers. How much water did he drink? 2 L Think: You need to find the total. Draw a bar. Now, add in the information: 5 beakers Now, add in 2 liters in each beaker 2 5 = 10 liters Total liters? 2 2 2 2 2 10 liters
This is a 2 liter beaker of water. Michael drank 3 of these beakers every day for a week. How much water did he drink? 2 L Think: You need to find the total. Draw a bar. 2 liters 3 days = 6 liters per day? Liters each day 2 2 2 6 Each day? Liters each Week 42 6 6 6 6 6 6 6 6 liters 7 = 42 liters Each week
Use a blank for the following slides
How much liquid is in each of these beakers? ML ML ML 100 milliliters
Jessie thinks the beaker on the right has more liquid. Why does he think that? Why is he wrong? ML ML ML It looks more because the liquid is higher in the beaker. However, it is skinny and so it s not more. The wide ones have the same amount. You can see by the labels all have 100m.
How much liquid it this all together? Use a number sentence to show your thinking. 100 3 = 300 ml or 100ml + 100ml + 100ml = 300ml
Sam is trying to fill the beaker on the right to the 200 ml mark. He only has a 25 ml beaker to fill it with. How many 25 ml will it take? 25 ml 25 ml 25 ml 25 ml 25 ml ML ML ML It will take 4 25 ml beakers to fill it to the 200 ml mark 100 +? = 200? = 100 25 = 100 = 4
This beaker contains 8 liters. How many 2 liter beakers could it fill? Use a number sentence to show your work. Think: You know the total. You need to find the parts. How many 2 s are in 8? Draw a bar. 8 liters 2 liters =? 8 liters 2 liters = 4 8 liters 2 2 2 2 8 liters
This beaker contains 12 liters of liquid. How many 3 liter beakers could it fill? Think: You know the total. You need to find the parts. Draw a bar. 3 = 12 12 liters 3 liters = 4 This can mean how many 3 s in 12 12 liters 3 3 3 3 12 L How many 3 s are in 12?
To hike in the desert you need 4 liters of water each day. This container holds 4 liters. How many would be needed for on a seven day hike? Think: You need to find the total water. Draw a bar. Now, put on the 7 days. Then add in the 4 liters per day.? Total liters 4 4 4 4 4 4 4 4 L 4 liters 7 days =? 28 liters for a week long trip
During ordinary life, each person should drink 2 liters of water everyday. How much water should you drink in a week? Think: You need to find the total. You know 7 days and 2 liters each day. Draw a bar. 2 liters 7 days =? 14 liters per week 2 L? Total liters 2 2 2 2 2 2 2
The total amount of liquid in these 3 beakers is 15 liters. The red beaker has 2 liters. The green beaker has 4 liters. How much does the blue beaker contain? Use a number sentence to show your work. Think: You know the total. You need to find a part. Draw a bar. Put on what you know. 15 ml 2 4? 2 + 4 + = 15 6+ = 15 = 9
This beaker contains 450 ml. George thinks it contains 405 ml. Why is he wrong? He thinks it goes up by 5 not 50!
How many 50 ml beakers could you fill with this? Show total on a bar. 50 = 450 450 50 = 9 = 450 ml 50 50 50 50 50 50 50 50 50
Line Plots and Problem Solving with Liters (insert line plot template) 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
Line Plot of how much water each 3 rd grader drinks per day Key: each represents 1 student 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
How many students drink 1 liter per day? Key: each represents 1 student 3 Students 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
How many students drink 1/2 liter per day? Key: each represents 1 student 6 Students 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
What was the most common amount that students drink? Key: each represents 1 student 1/2 liter is most common 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
How many students drink more than 1 liter per day? Key: each represents 1 student 5 Students 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
How many students drink less than 1 liter per day? Key: each represents 1 student 7 Students 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
How was the largest amount of water that a student drank? Key: each represents 1 student The largest amount was 3 liters. 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
How much water was drunk in all? TOTAL: 3 + 3 + 4 + 1/2 + 5 = 15 1/2 LITERS 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 3 whole liters Key: each represents 1 student 1 + 1 + 1 = 3 whole liters 1 1/2 + 1 1/2 + 1 1/2 = (1 + 1 + 1) + 1/2 + 1/2 + 1/2= 4 and 1/2 liters 3 + 2 = 5 liters 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
5 new students were added to the data set. See the tally chart. Than add them to the line plot. Liters Students 0 liters I 1/2 liters 0 1 liters IIII Key: each represents 1 student 0 liters 1/2 liter 1 liter 1 1/2 liters 2 liters 2 1/2 liters 3 liters
More Fractions with Liters Insert graduated cylinder template #4
Finish marking off this beaker. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter
Shade this beaker so has 1 liter. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter
Shade this beaker so it contains 1 1/2 liters. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter
Shade this beaker so it contains 3 1/2 liters. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter
Shade this beaker so it contains 4 1/5 liters. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter
Shade this beaker so it contains 5 2/5 liters. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter
Insert template #5 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 0 liter
This is a large 6 liter bottle. Divide it into 6 equal sections so you can tell how much water is in the bottle. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
6 liter 5 liter 4 liter 3 liter 2 liter 1 liter When this bottle has 6 liters it is full. When it has 1 liter it is 1/6 full. Label the right edge with fractions up to 6/6. 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
When this bottle has 6 liters it is full. When it has 1 liter it is 1/6 full. Label the edges with fractions up to 6/6. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
Shade this beaker so it 1/6 full. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
Shade this beaker so it 1/2 full. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
Shade this beaker so it 5/6 full. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
Shade this beaker so it 1/3 full. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
Shade this beaker so it 2/3 full. 6 liter 5 liter 4 liter 3 liter 2 liter 1 liter 6/6 5/6 4/6 3/6 2/6 1/6 0 liter 0/6
What fraction is shaded? 6 liter 5 liter 3/6 or 1/2 4 liter 3 liter 2 liter 1 liter 0 liter
What fraction is shaded? 6 liter 5 liter 1/6 4 liter 3 liter 2 liter 1 liter 0 liter
What fraction is shaded? 6 liter 5 liter 6/6 = 1/1 = 1 4 liter 3 liter 2 liter 1 liter 0 liter
6 liter 5 liter Carla drank 1/2 of a bottle. Marie drank 2/6 of a bottle. Who drank more? Draw a second bottle to show your thinking. 6/6 5/6 1/2 > 2/6 Carla drank more! 4 liter 3 liter 2 liter 1 liter Carla Marie 1/2=3/6 2/6 4/6 3/6 2/6 1/6 0 liter
6 liter 5 liter Frank Frank drank 4/6 of a bottle. Mary drank 2/3 of a bottle. Who drank more? Draw a second bottle to show your thinking. Mary 6/6 5/6 4/6 = 2/3 They drank same amount 4 liter 3 liter 2 liter 1 liter 1/3 4/6=2/3 1/3 4/6 3/6 2/6 1/6 0 liter
Joe drank 3 liters. What fraction is left? 6 liter 5 liter 1/2 of bottle 4 liter 3 liter 2 liter 1 liter 0 liter
Joe drank 1 liter. What fraction is left? 6 liter 5 liter 5/6 of bottle 4 liter 3 liter 2 liter 1 liter 0 liter
More Problem Solving With Liters and Fractions
This is a 6 liter bottle. If 3 friends share it equally, how many liters will each person drink? Use a bar model and number sentence. 6 3 = 2 liters 6 total liters 2 2 2
This is a 6 liter bottle. If Dustin drinks 4 bottles, how much will he have drunk? Write a number sentence and a bar model. 6 4 = 24 liters? total liters 6 6 6 6
Insert template #6
Finish marking off this beaker. 10/10 1000 ml 9/10 900 ml 8/10 800 ml 7/10 700 ml 6/10 600 ml 5/10 500 ml 4/10 400 ml 3/10 300 ml 2/10 200 ml 1/10 100 ml
Estimate the amount of water in the beaker. 350 ml 1/10 100 ml
Shade the beaker so it is 1/2 full. How many MLs is this? 500 ML? 1/10 100 ml
If this beaker is at 350 ml, how much must be added to reach 1 liter? 350 + = 1000 ML 1000 ml 350? 650 ml 1/10 100 ml
In the morning this beaker had more liquid. Mary came along and poured out 200 ml. Now it has only 350 ml. How much did it have in the morning? - 200 = 350 ML? Milliliters in AM 200 350 Poured out 550 ml Liquid left 1/10 100 ml
This beaker has 350 ml. Charlie wants it to have 100 ml. How much should he pour out? 350 - = 100 ML 350 Ml before 350 ml 100? Desired amount 250 ml Pour out 1/10 100 ml
Rene drank this amount (350ml) every day for 3 days. How much did he drink? 350 3 = 350 + 350 + 350 =? total 350 ml 350 350 350 350 3 = 1050 ml 1/10 100 ml
Getting Comfortable with Grams, Kilograms, and Mass Insert Scale Template #7 kilog gram 1 1000 rams 2 s 3 4
Kilograms are used for weighing objects or finding Mass (how much matter something has) kilograms grams 1 1000 2 3 4
What are kilograms used for? kilograms grams 1 1000 2 3 4
1 Kilogram is about 2.2 pounds. A dictionary, a pineapple, and a baseball bat each weigh about a kilogram. kilograms grams 1 1000 2 3 4
About how many pounds is a kilogram? What everyday objects weigh a kilogram? kilograms grams 1 1000 2 3 4
There are 1000 little grams in 1 kilogram. A paper clip weighs about a gram. kilograms grams 1 1000 2 3 4
How many grams in a kilogram? What everyday object weighs a gram? kilograms grams 1 1000 2 3 4
Fill out the chart. kilograms grams 1 1000 2 2000 3 3000 4 4000
Draw another kg. on the scale and change the needle and chart. kilograms grams 1 1000 2 2000 3 4
If the needle was here, how many kg would be on scale. Draw them. Record on chart. kilograms grams 1 1000 2 3 3000 4
If the needle was here, add weights to match the needle. kilograms grams 1 1000 2 3 4 1 1/2 1500
Show where the needle would go for these weights. kilograms grams 1 1000 2 3 4 2 1/2 2500
Show where the needle would go for these weights. kilograms grams 1 1000 2 3 4 3 1/2 3500
Bobby has 4 kilograms. How many grams is this? kilograms grams 1 1000 2 3 4 4000
Bobby has 3 kilograms. How many grams is this? kilograms grams 1 1000 2 3 3000 4
Bobby has 1/2 kilograms. How many grams is this? kilograms grams 1 1000 2 3 4 1/2 500
Bobby has 2000 grams. How many kilograms is this? kilograms grams 1 1000 2 3 2000 4
Bobby has 4000 grams. How many kilograms is this? kilograms grams 1 1000 2 3 4 4000
Bobby has 500 grams. How many kilograms is this? kilograms grams 1 1000 2 3 4 1/2 500
Make up your own question
Insert Blank Template for these problems
Think: You know the total! Draw a bar. Put the total on the bar Now find the parts 10 blocks = 200 200 total grams?????????? 20 20 20 20 20 20 20 20 20 20 Now solve: 10 = 200 This apple weighs 200 grams. That is the same as 10 blocks. How much does 1 block weigh?
Red, purple, orange, and yellow weights are all different sizes. What could each weigh in grams? One answer: 100 grams 100 grams Red = 80 Purple = 20 Orange = 40 Yellow = 60
6 apples weigh approimately 1200 grams 1200 total grams?????? 200 200 200 200 200 200 6 = 1200 Approimately how much does 1 apple weigh? 200 grams
These apples weigh 600 grams. Each apple weighs the same amount. How much does one apple weigh?
Scale in pounds Approimately how much does this cat weigh? 40 pounds
Scale in pounds Estimate how much would 3 of these cats weigh? 120 pounds? total pounds 40 40 40
Scale in pounds If the scale read 160 pounds, how many of these cats would be on it? 4 cats 160 total pounds 40 40 40 40
What is the scale on this measuring device? (What does it go by?) It is marked off in 5 s but only the 20 s are labeled!
Make your own questions! 1.