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

©Bill Atwood 2014

On Amazon, markers can be found as low as $0. 63 each 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: 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

Examples What follows are some sample questions that relate to understanding multiplication, area, division, fractions, as well as some multiplication fact work for grade 3. 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

©Bill Atwood 2014

©Bill Atwood 2014

©Bill Atwood 2014

On the graph paper, draw a rectangle that is 4 inches long and 3 inches wide (3 x 4). Label the dimensions (sides) with numbers (3 in. and 4 in.) 4 in 3 in Erase! ©Bill Atwood 2014

On the graph paper, draw a rectangle that is 6 inches long and 2 inches wide (6 x 2). Label the dimensions (sides) with numbers (6 in. and 2 in.) 6 in 2 in Erase! ©Bill Atwood 2014

On the graph paper, draw a rectangle that is 6 inches long and 4 inches wide (6 x 4). Label the dimensions (sides) with numbers (6 in. and 4 in.) How many little square units inside this shape? (area) 6 in Write 2 number sentences that show your thinking. 24 in2 4 in Don’t erase! 6 x 4 = 24 4 x 6 = 24. ©Bill Atwood 2014

Using your 4 by 6 rectangle, show 4 groups of 6. 4 x 6 = 24 ( 4 groups of 6) 6 6 4 in 6 4 x 6 = 6 + 6 + 6 +6 24 = 24 ( 4 groups of 6) 6 Just erase the inside part! ©Bill Atwood 2014

Using your 4 by 6 rectangle, show 6 groups of 4. 6 x 4 = 24 ( 6 groups of 4) 6 in 4 in 4 4 4 4 4 4 6 x 4 = 4 + 4 + 4 + 4 + 4 + 4 24 = 24 ( 6 groups of 4) Erase! ©Bill Atwood 2014

On the graph paper, draw a rectangle that is 8 inches long and 3 inches wide (8 x 3). Label the dimensions (sides) with numbers (8 in. and 3 in.) What is the area of the rectangle? 8 in Write a 2 number sentences that show your thinking. 3 in 24 in2 3 x 8 = 24 8 x 3 = 24 Don’t erase! ©Bill Atwood 2014

Using your 3 by 8 rectangle, show 3 groups of 8. 3 x 8 = 24 ( 3 groups of 8) 8 in 8 3 in 8 3 x 8 = 8 + 8 + 8 24 = 24 ( 3 groups of 8) 8 Just erase the inside part! ©Bill Atwood 2014

Can you show eight groups of three? Write a number sentence that shows this. 8 in 3 in 3 3 3 3 3 3 3 3 8 x 3 = 24 ( 8 groups of 3) 8 x 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 24 = 24 ( 8 groups of 3) Erase! ©Bill Atwood 2014

Just erase the inside part! Draw a rectangle that has an area of 15 square inches and a width of 3 inches. Label the side lengths. Show 3 groups of 5 5 in Write a number sentence that shows this. 3 in 3 15 in2 3 3 3 3 3 x ? = 15 3 x 5 = 15 ( 3 groups of 5) Just erase the inside part! ©Bill Atwood 2014

Just erase the inside part! Draw a rectangle that has an area of 12 square inches and a width of 3 inches. Label the side lengths. Show 4 groups of 3 4 in Write a number sentence that shows this. 3 in 3 3 3 3 4 x 3 = 12 ( 4 groups of 3) Just erase the inside part! ©Bill Atwood 2014 ©Bill Atwood 2014

Show three groups of four. 3 x 4 = 12 ( 3 groups of 4) 4 in 4 3 x 4 = 4 + 4 + 4 ( 3 groups of 4) 3 in 4 4 Erase! ©Bill Atwood 2014

On the graph paper, draw a rectangle that is 7 inches long and 3 inches wide (7 x 3). Label the dimensions. 7 in Write 2 number sentences that show this math fact. 3 in 3 x 7 = 21 7 x 3 = 21 7 + 7 + 7 = 21 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 Don’t Erase! ©Bill Atwood 2014

Show that it’s possible to break 7 into two parts and to show 3 x 7 = (3 x 5) + (3 x 2) Think of it as a candy bar broken into 2 parts 5 in 7 in 2 in 6 in2 3 in 15 in2 3 x 5 = 15 3 x 2 = 6 7 in 15 + 6 = 21 3 in 21 in2 3 x 7 = (3 x 5) + (3 x 2) 21 = 15 + 6 21 = 21 Erase! ©Bill Atwood 2014

On the graph paper, draw a rectangle that is 6 inches long and 4 inches wide (6 x 4). Label the dimensions and the area. 6 in Write 2 number sentences that show this math fact. 4 in 24 in2 4 x 6 = 24 6 x 4 = 24 Don’t Erase! ©Bill Atwood 2014

Erase! Write 2 addition sentences 6 + 6 + 6 + 6 = 24 4 + 4 +4 + 4 + 4 + 4 = 24 6 in 6 6 4 in 24 in2 6 6 Erase! ©Bill Atwood 2014

Show that it’s possible to break 6 into two parts to show 4 x 6 = (4 x 5) + (4 x 1) Think of it as a candy bar broken into 2 parts 4 in2 4 in 20 in2 4 x 5 = 20 6 in 4 x 1 = 4 20 + 4 = 24 4 in 24 in2 4 x 6 = (4 x 5) + (4 x 1) 24 = 20 + 4 24 = 24 Erase! ©Bill Atwood 2014

Use an area model to show that 3 x 7 = (3 x 5) +( 3 x 2) 7 in 3 in Erase! ©Bill Atwood 2014

Use an area model to show that 5 x 8 = (5 x 5) + (5 x 3) 8 in 5 in Erase! ©Bill Atwood 2014

Use an area model to show that 6 x 7 = (6 x 6) + (6 x 1) 7 in 6 in Erase! ©Bill Atwood 2014

On the graph paper, draw a 4” by 5” rectangle. Label the side lengths On the graph paper, draw a 4” by 5” rectangle. Label the side lengths. What is the area? 20 in2 Divide this candy bar into 4 equal parts. How many squares are in each part? 5” 5 5 in each part 5 4” 5 5 Write the number sentence for this operation. 20 ÷ 4 = 5 Erase! ©Bill Atwood 2014

On the graph paper, draw a 3” by 8” rectangle. Label the side lengths On the graph paper, draw a 3” by 8” rectangle. Label the side lengths. What is the area? 24 in2 Divide this candy bar into 3 equal parts. How many squares are in each part? 8” 8 8 in each part 3” 8 8 Write the number sentence for this operation. 24 ÷ 3 = 8 Erase! ©Bill Atwood 2014

It’s possible to break this problem: 24 ÷ 3 = 8 into this problem: (18 + 6) ÷ 3 = 8 Divide (18 ÷ 3) = 6 Think of it as diving a candy bar in 2 steps! Divide the 18 into 3 pieces then the 6 into 3 pieces! Now divide (6 ÷ 3) = 2 It’s the distributive property! 24 ÷ 3 = 8 (18 + 6) ÷ 3 = 8 (18 ÷ 3) + (6 ÷3) = 8 6 + 2 = 8 8 = 8 So there would be 8 squares in each ⅓ piece. 6” 8” 2” 18 in2 6 in2 2 in2 24 in2 2 in2 3” 6 6 6 2 in2 Erase! ©Bill Atwood 2014 ©Bill Atwood 2014

On the graph paper, draw a 3” by 6” rectangle. Label the side lengths On the graph paper, draw a 3” by 6” rectangle. Label the side lengths. What is the area? 24 in2 Divide this candy bar into 3 equal parts. How many squares are in each part? 6” 3” Write the number sentence for this operation. 18 ÷ 3 = 8 Erase! ©Bill Atwood 2014 ©Bill Atwood 2014

Shade ½ of the rectangle. On the graph paper, draw a rectangle that is 8 inches long and 2 inches wide (8 x 2). Shade ½ of the rectangle. 8 in 2 in 8 in 2 in Erase! ©Bill Atwood 2014

Shade ¼ of the rectangle. On the graph paper, draw a rectangle that is 8 inches long and 2 inches wide (8 x 2). Shade ¼ of the rectangle. There is more than 1 way to do it… 8 in 2 in 8 in 2 in Erase! ©Bill Atwood 2014

Shade ½ of the rectangle. On the graph paper, draw a rectangle that is 4 inches long and 2 inches wide (4 x 2). Shade ½ of the rectangle. 4 in 2 in 4 in 2 in ©Bill Atwood 2014

Shade ¼ of the rectangle. On the graph paper, draw a rectangle that is 4 inches long and 2 inches wide (4 x 2). Shade ¼ of the rectangle. 4 in 2 in 4 in 2 in ©Bill Atwood 2014

Shade 1/3 of the rectangle. On the graph paper, draw a rectangle that is 6 inches long and 1 inches wide (6 x 1). Shade 1/3 of the rectangle. 6 in 1 in ©Bill Atwood 2014

Find the area of this shape. ©Bill Atwood 2014 ©Bill Atwood 2014

Find the area of this shape. ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Find the area of this shape. ©Bill Atwood 2014

Find the area of this shape. ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Find the area of this shape. ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Find the area of this shape. ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Find the area of this shape. ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Write the fact family for 6 x 4 = 24 ©Bill Atwood 2014

Fact Work: 5’s; 9’s; squares; The rest (10 facts) ©Bill Atwood 2014

Square field. Side is 5 ft. Area? Rectangular field. 5 x 2 = 10 3 x 5 = 15 __ x 5 = 45 9 5 x 4 = x 5 = 10 20 8 x 5 = 40 2 5 x 7 = 35 5 x 5 = 25 5 x __ = 35 7 5 x 6 = 30 1 x 5 = 5 __ x __ = 25 5 5 Find the product of 5 and 8 40 Square field. Side is 5 ft. Area? 25 ft2 Rectangular field. L = 9 ft. W = 5 ft. Area? 45 ft2 ©Bill Atwood 2014

Rectangular field area = 45 L = ___ ft. W = __ ft 5 x 2 = 10 3 x 5 = 15 __ x 5 = 45 9 5 x 4 = 20 8 x 5 = __ x 5 = 10 40 2 5 x 7 = 35 5 x 5 = 25 5 x __ = 35 7 5 x 6 = 30 1 x 5 = 30 __ x __ = 25 5 5 Product is 40. Factors? 8 x 5; 4 x 10; 2 x 20, 80 x 1 80 x ½ … Area of square is =25 ft2 S = ? S = 5 ft Rectangular field area = 45 L = ___ ft. W = __ ft 9 5 ©Bill Atwood 2014

5 x __ = 15 5 x __ = 20 5 x __ = 25 5 x __ = 30 5 x __ = 35 Show the missing factor(s) with your fingers 5 cm 5 x __ = 15 3 2 cm 10 cm2 5 x __ = 20 4 5 cm 3 cm 5 x __ = 25 15 cm2 5 5 x __ = 30 6 5 cm 5 x __ = 35 7 4 cm 20 cm2 __ x __ = 25 5 5 5 ©Bill Atwood 2014

5 x __ = 10 5 x __ = 0 5 x __ = 55 5 x __ = 45 5 x __ = 5 5 x __ = 60 Show the missing factor with your fingers 5 x __ = 10 2 5 x __ = 0 5 x __ = 55 11 5 x __ = 45 9 5 x __ = 5 1 5 x __ = 60 12 ©Bill Atwood 2014

Show the product with your fingers Show the product with your fingers. Use your left hand for tens place and right hand for ones place. Make a fist for zeroes. 5 x 2 = 10 3 x 5 = 15 5 x 4 = 20 8 x 5 = 40 5 x 7 = 35 5 x 5 = 25 5 x 6 = 30 1 x 5 = 5 ©Bill Atwood 2014

35 ÷ 5= 7 30/5 = 6 __ x 5 = 45 9 45 ÷ 5 = x 5 = 10 9 20/5 = 4 2 15 ÷ 5= 3 40/5 = 8 5 x __ = 35 7 25 ÷ 5 = 5 10/5 = 2 __ x __ = 25 5 5 8 rows of five chairs, how many chairs? 40 chairs Forty-five pieces of gum. Five people sharing How many pieces each? 9 pieces each 30 mile race. Water stop every 5 miles. How many water stops? 6 w.s. ©Bill Atwood 2014

The Nines… ©Bill Atwood 2014

Square field. Side is 9 ft. Area? 9 x 2 = ☐ 3 x 9 = ☐ ☐ x 9 = 27 9 x 4 = ☐ 8 x 9 = ☐ ☐ x 9 = 18 9 x 7 = ☐ 5 x 9 = ☐ 5 x ☐ = 45 9 x 6 = ☐ 1 x 9 = ☐ ☐ x ☐ = 81 Find the product of 9 and 8 Square field. Side is 9 ft. Area? Rectangular field. L = 9 ft. W = 3 ft. Area? ©Bill Atwood 2014

The Square Numbers ©Bill Atwood 2014

Imagine a square: Side = 3 cm 3 cm Area = 9 cm2 3 cm 9 cm2 ©Bill Atwood 2014

Side= 6 m 6 m Area = 36 m2 6 m ©Bill Atwood 2014

Side= 7 m 7 m Area = 49 m2 7 m ©Bill Atwood 2014

Side= 8 cm Area = 64 cm2 ©Bill Atwood 2014

Side= 9 in Area = 81 in2 ©Bill Atwood 2014

Side= 4 yd Area = 16 yd2 ©Bill Atwood 2014

Side= 5 m Area = 25 m2 ©Bill Atwood 2014

Side= 3 km Area = 9 km2 ©Bill Atwood 2014

Side= 12 miles Area = 144 miles2 ©Bill Atwood 2014

Area = 16 cm2 __ cm Side = 4 cm __ cm Area = 16 cm2 ©Bill Atwood 2014

Area = 9 miles2 __ cm Side = 3 miles __ cm 9 cm2 ©Bill Atwood 2014

Area = 100 ft2 Side = 10 ft ©Bill Atwood 2014

Area = 81 m2 Side = 9 m ©Bill Atwood 2014

Area = 64 km2 Side = 8 km ©Bill Atwood 2014

Area = 144 m2 Side = 12 m ©Bill Atwood 2014

Area = 121 m2 Side = 11 m ©Bill Atwood 2014

Area = 169 m2 Side = 13 m ©Bill Atwood 2014

Area = 49 ft2 Side = 7 ft ©Bill Atwood 2014

Area = 1 m2 Side = 1 m ©Bill Atwood 2014

Area = 4 m2 Side = 2 m ©Bill Atwood 2014

Area = 10 m2 Side = 3.16227766… m Be Careful Not all numbers have a whole number square root! Area = 10 m2 Side = 3.16227766… m ©Bill Atwood 2014

Number Sense and Subtraction ©Bill Atwood 2014

©Bill Atwood 2014

3, 5 2 6 2, 2 1 5 In the top row, write three thousand, five hundred, twenty six in standard form. In the bottom row, write two thousand, two hundred, fifteen in standard form. In the space below the box, write a number sentence that compares these numbers using < > = ©Bill Atwood 2014

Write six thousand, seven in standard form on the chart. Write this number in expanded form below the box. ©Bill Atwood 2014

Write five thousand, twenty three in standard form on the chart. Write this number in expanded form below the box. ©Bill Atwood 2014

Use the digits 4, 9, 6, 2 and make the largest number possible. Use the digits 4, 9, 6, 2 and make the smallest number possible. (estimate the difference) ©Bill Atwood 2014

Find the difference between 6,320 and 342. Show your work. ©Bill Atwood 2014

Find the difference between 9,020 and 4,746. Show your work. ©Bill Atwood 2014

George wanted to buy a video game that cost $30. 00. He only has $15 George wanted to buy a video game that cost $30.00. He only has $15.50. How much more does he need? Show your work. ©Bill Atwood 2014

Measuring Time and Working with Fractions ©Bill Atwood 2014

©Bill Atwood 2014

©Bill Atwood 2014

Show 7:15 PM on the clock. Label the time. Quarter past seven in the evening. Show 7:15 PM on the clock. Label the time. ©Bill Atwood 2014

Show 8:30 PM on the clock. Label the time. Half past eight in the evening Show 8:30 PM on the clock. Label the time. ©Bill Atwood 2014

Joe thinks it is 10:55. Why is this wrong? Erase! 9:55 What time is this? Joe thinks it is 10:55. Why is this wrong? Erase! ©Bill Atwood 2014

Draw the time that is 15 minutes later. 9:55 + 15 minutes = 10:10 Show the time is 9:55 Draw the time that is 15 minutes later. 9:55 + 15 minutes = 10:10 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 4 equal slices Imagine the clock is a pizza. Show 4 equal slices. Can you prove they are equal sections Shade ¼ of the pizza. ©Bill Atwood 2014

Imagine the clock is a pizza. Shade 2/4 of the pizza. ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Shade 3/4 of the pizza. ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Shade 4/4 of the pizza. ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Shade 3 equal slices. 1/3 of the pizza Imagine the clock is a pizza. Shade 3 equal slices. 1/3 of the pizza. Can you prove they are equal sections? ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Shade 2/3 of the pizza. What section is not shaded? ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 6 equal slices. 1/6 of the pizza Imagine the clock is a pizza. Show 6 equal slices. 1/6 of the pizza. Can you prove they are equal sections? ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 12 equal slices. 1/12 of the pizza Imagine the clock is a pizza. Show 12 equal slices. 1/12 of the pizza. Can you prove they are equal sections? ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 1/2 = 2/4 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 1/2 = 6/12 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 1/2 > 1/3 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 1/3 > 1/6 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 1/3 + 1/3 = 2/3 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014

Imagine the clock is a pizza. Show 12/12 – 1/12 = 11/12 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014 ©Bill Atwood 2014