Transcript PowerPoint

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. (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.
2.
3.
4.
5.
6.
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)
Write 2 number
sentences that show
your thinking.
6 in
4 in
24 in2
Don’t erase!
©Bill Atwood 2014
6 x 4 = 24
4 x 6 = 24.
Using your 4 by 6 rectangle, show 4 groups
of 6.
4 in
6 in
6
6
6
6
4 x 6 = 24
( 4 groups of 6)
4 x 6 = 6 + 6 + 6 +6
24 = 24
( 4 groups of 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
6x4=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?
Write a 2 number
sentences that show
your thinking.
3 x 8 = 24
8 x 3 = 24
8 in
3 in
24 in2
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
3 in
8
8
8
3x8 =8+8+8
24 = 24
( 3 groups of 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)
8x3 =3+3+3+3+3+3+3+3
24 = 24
( 8 groups of 3)
Erase!
©Bill Atwood 2014
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
3 in32
3 in 3 15
3 3
Just erase the inside part!
©Bill Atwood 2014
Write a number
sentence that shows
this.
3 x ? = 15
3 x 5 = 15
( 3 groups of 5)
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
3 in 3 3 3
3
Write a number
sentence that shows
this.
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 in
3 x 4 = 12
( 3 groups of 4)
4 in
4
4
4
3x4=4+4+4
( 3 groups of 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)
3 in
5 in
7 in 2 in
in2
6 in2
15
3 x 5 = 15
3x2=6
15 + 6 = 21
7 in
3 in
Think of it as a candy bar
broken into 2 parts
21 in2
Erase!
©Bill Atwood 2014
3 x 7 = (3 x 5) + (3 x 2)
21
= 15 +
6
21
= 21
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
4 in
Write 2 number
sentences that show
this math fact.
24 in2
4 x 6 = 24
6 x 4 = 24
Don’t Erase!
©Bill Atwood 2014
Write 2 addition sentences
6 + 6 + 6 + 6 = 24
4 + 4 +4 + 4 + 4 + 4 = 24
4 in
6 in
6
246 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)
5 in 6 in 1 in
4 in
20 in2
4
in2
Think of it as a candy bar
broken into 2 parts
4 x 5 = 20
6 in
4 in
4x1=4
20 + 4 = 24
24 in2
Erase!
©Bill Atwood 2014
4 x 6 = (4 x 5) + (4 x 1)
24
= 20 + 4
24
= 24
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. What is the area? 20 in2
Divide this candy bar into 4 equal parts. How
many squares are in each part?
5 in each part
4”
5”
5
5
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. What is the area? 24 in2
Divide this candy bar into 3 equal parts. How
many squares are in each part?
8”
8 in each part
3”
8
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
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
Think of it as diving a candy bar
in 2 steps! Divide the 18 into 3
pieces then the 6 into 3 pieces!
6” 8”
3” 6
Erase!
2”
18 in2 62 in
in22
2
6 246in 2 in2
2 in2
©Bill Atwood 2014
©Bill Atwood 2014
So there would
be 8 squares in
each ⅓ piece.
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
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
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
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
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
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
Find the area of this shape.
©Bill Atwood 2014
Find the area of this shape.
©Bill Atwood 2014
Find the area of this shape.
©Bill Atwood 2014
Find the area of this shape.
©Bill Atwood 2014
Find the area of this shape.
©Bill Atwood 2014
Find the area of this shape.
©Bill Atwood 2014
Write the fact family for 6 x 4 = 24
Write the fact family for 7 x 8 = 56
Write the fact family for 7 x 6 = 42
Write the fact family for 6 x 8 = 48
©Bill Atwood 2014
Fact Work:
5’s; 9’s; squares;
The rest (10 facts)
©Bill Atwood 2014
5 x 2 = 10 3 x 5 =
5 x 4 = 20 8 x 5 =
5 x 7 = 35 5 x 5 =
5 x 6 = 30 1 x 5 =
15 __
9 x 5 = 45
2 x 5 = 10
40
25 5 x __
7 = 35
5 __
5 = 25
5 x __
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
5 x 2 = 10 3 x 5 =
5 x 4 = 20 8 x 5 =
5 x 7 = 35 5 x 5 =
5 x 6 = 30 1 x 5 =
Product is 40.
Factors?
15 __
9 x 5 = 45
2 x 5 = 10
40 __
25 5 x __
7 = 35
30 __
5 = 25
5 x __
8 x 5; 4 x 10; 2 x 20, 80 x 1
80 x ½ …
Area of square is =25 ft2 S = ?
Rectangular field area = 45
5 ft
9 ft. W = __
L = ___
©Bill Atwood 2014
S = 5 ft
Show the missing factor(s) with your fingers
2
cm
5 x __
3 = 15
5 cm
5 x __
4 = 20
5 x __
7 = 35
5 = 25
__
5 x __
3
cm
__
5 = 25
__
6 = 30
5 cm
15 cm2
5 cm
4
cm
5x
5x
10 cm2
©Bill Atwood 2014
20 cm2
Show the missing factor with your fingers
5 x __
2 = 10
5 x __
0 =0
5x
5x
__
11 = 55
__
9 = 45
5 x __
1 =5
5 x 12
__ = 60
©Bill Atwood 2014
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 =
5 x 4 = 20 8 x 5 =
5 x 7 = 35 5 x 5 =
5 x 6 = 30 1 x 5 =
©Bill Atwood 2014
15
40
25
5
35 ÷ 5= 7
45 ÷ 5 = 9
15 ÷ 5= 3
25 ÷ 5 = 5
30/5 =
20/5 =
40/5 =
10/5 =
6
4
8
2
__
9 x 5 = 45
2 x 5 = 10
5 x __
7 = 35
5 = 25
5 x __
__
8 rows of five chairs, how many chairs?
40
chairs
Forty-five pieces of gum. Five people sharing
9 pieces each
How many pieces each?
30 mile race. Water stop every 5 miles.
6 w.s.
How many water stops?
©Bill Atwood 2014
The Nines…
©Bill Atwood 2014
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
3 cm
Imagine a square:
Side = 3 cm
3 cm
Area = 9 cm2
9
2
cm
©Bill Atwood 2014
6m
6m
Side= 6 m
Area = 36 m2
©Bill Atwood 2014
7m
7m
Side= 7 m
Area = 49 m2
©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
2
cm
__ cm
Area = 16
__ cm Side = 4 cm
Area =
16 cm2
©Bill Atwood 2014
2
miles
__ cm
Area = 9
__ cm Side = 3 miles
9
2
cm
©Bill Atwood 2014
2
ft
Area = 100
Side = 10 ft
©Bill Atwood 2014
2
m
Area = 81
Side = 9 m
©Bill Atwood 2014
2
km
Area = 64
Side = 8 km
©Bill Atwood 2014
2
m
Area = 144
Side = 12 m
©Bill Atwood 2014
2
m
Area = 121
Side = 11 m
©Bill Atwood 2014
2
m
Area = 169
Side = 13 m
©Bill Atwood 2014
2
ft
Area = 49
Side = 7 ft
©Bill Atwood 2014
2
m
Area = 1
Side = 1 m
©Bill Atwood 2014
2
m
Area = 4
Side = 2 m
©Bill Atwood 2014
Be Careful
Not all numbers
have a whole
number square
root!
2
m
Area = 10
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 $15.50. 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
7:15 PM
Quarter past seven
in the evening.
Show 7:15 PM on the clock. Label the time.
©Bill Atwood 2014
8:30 PM
Half past eight in
the evening
Show 8:30 PM on the clock. Label the time.
©Bill Atwood 2014
9:55
What time is this?
Joe thinks it is 10:55. Why is this wrong?
Erase!
©Bill Atwood 2014
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. 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
Imagine the clock is a pizza. Shade 3/4 of the pizza.
©Bill Atwood 2014
Imagine the clock is a pizza. Shade 4/4 of the pizza.
©Bill Atwood 2014
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
Imagine the clock is a pizza. Shade 2/3 of the pizza.
What section is not shaded?
©Bill Atwood 2014
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
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
Imagine the clock is a pizza. Show 1/2 = 2/4
©Bill Atwood 2014
Imagine the clock is a pizza. Show 1/2 = 6/12
©Bill Atwood 2014
Imagine the clock is a pizza. Show 1/2 > 1/3
©Bill Atwood 2014
Imagine the clock is a pizza. Show 1/3 > 1/6
©Bill Atwood 2014
Imagine the clock is a pizza. Show 1/3 + 1/3 = 2/3
©Bill Atwood 2014
Imagine the clock is a pizza. Show 12/12 – 1/12 = 11/12
©Bill Atwood 2014