1.
|
Can
my students use numbers to compare quantities and describe
relationships between quantities?
|
|
|
Example Grade
K-3:
|
a.
|
How
many scissors do we need to get so that everyone at the table has
one? How many containers of juice do we need to bring on our
field trip so every one in the class can have one?
|
|
|
IV-3.5
|
|
|
|
|
|
|
|
|
b.
|
About
how many lima beans do you think are in this clear plastic cup?
If it takes 13 beans to fill it up to here (half way), how
many beans do you think the cup would hold if we filled it up? If the cup holds 24 lima beans, how many pinto beans do you
think it would hold?
|
|
|
Example Grade
3-4:
|
Using
dimes, pennies, nickels, quarters, fifty-cent pieces, and dollars,
in how many ways can you make $1.25?
|
|
|
IV-3.5
|
|
|
Example Grade
5-6:
|
Look
at the graph of favorite foods of the students in last year’s
class. What fraction
of the class liked hot dogs best?
Did more or less than 50% of the class like pizza?
Is the percent who liked pizza closer to 50% or 75%?
In this kind of a graph, is a person limited to one choice?
Why?
|
|
|
IV-3.5
|
|
|
|
|
Example Grade
7-8:
|
Use
your calculator to change
… into decimals.
Which fractions terminate and which don’t?
Can you make any predictions from your results?
|
|
|
IV-3.5
|
|
2.
|
Can
my students use the place value system to express numbers in
expanded form?
|
|
|
Example Grade
K-3:
|
a.
|
Here
is a pile of counters (36 or so).
How can you organize them in some way so that your friends
can tell how many there are without counting by ones?
Is there another way?
Another way? Which way helped your friends tell the fastest?
|
|
|
IV-1.2
|
|
|
|
|
|
|
|
|
b.
|
Determine
the number of objects in each of the jars (macaroni, beans,
polished rocks, etc.). Organize
as you count so that you and a friend can tell how many you have
as you go along without having to count by ones.
Arrange the objects in such a way that you can tell how
many tens and ones you have.
|
|
|
|
|
|
|
|
|
c.
|
Using
the beans and cups, interlocking cubes, bean sticks, place value
materials, show me 56, 32, 129.
|
|
|
Example Grade
3-4:
|
If
you have 4 hundreds, 2 thousands, 8 ones, and 0
tens, how can you write it?
How could you model it with materials?
|
|
|
IV-1.2, 2.1
|
|
|
Example Grade
5-6:
|
|
|
|
IV-1.2
|
|
|
|
|
|
Use
this 10 by 10 grid to stand for one.
Show one tenth, one hundredth.
How could you show .34, .26, .231?
How do the squares on the grid relate to money?
How would you show the same amounts with money instead of
squares on the grid?
|
|
|
|
|
|
Example Grade
7-8:
|
a.
|
Why
does your science book list the speed of light as 1.86 x 105 miles
per second? How far
does light travel in one year?
|
|
|
IV-1.2
|
|
|
|
|
|
|
|
|
b.
|
103
is how much bigger than 10-3?
|
|
3.
|
Can
my students use basic number facts along with relationships
between addition, subtraction, multiplication and division to
obtain more numerical information?
|
|
|
Example Grade
K-3:
|
a.
|
Make
up stories that go with the following number sentences:
|
|
|
IV-1.4, 3.5
|
|
|
|
|
8
+ 2 = 10
9
- 4 = 5
|
|
|
|
b.
|
How
many different ways can you show the quantity of ten?
Can you think of any ways that use a minus sign?
|
|
|
|
|
|
|
|
|
c.
|
If
I tell you
|
|
|
|
|
|
|
|
|
|
14
+ 10 = 24, what is 14 + 9?
6 + 2 = 8, what is 36 + 2?
|
|
|
|
|
|
|
|
|
d.
|
Here
is a pile of 29 beads. How
many groups of ten do you think you could make with these?
How many piles of 5? How
many piles of 9?
|
|
|
Example Grade
3-4:
|
a.
|
If
I tell you…
11.6
+ 4.3 is 15.9, what is 116 + 43?
6
x 9 = 54, what is 7 x 9?
|
|
|
IV-1.4, 3.5
|
|
|
|
|
|
|
|
|
|
b.
|
How
can knowing 2 x 6 help you figure out 2 x 60,
2
x 600, 2 x 6000?
|
|
|
Example Grade
5-6:
|
a.
|
Demonstrate
2/3 of twelve with counters, graph paper, symbols, drawing
pictures, and words.
|
|
|
IV-1.4, 3.5
|
|
|
|
|
|
|
|
|
|
b.
|
5
x 2.2 is 11; what is 1/5 of 11?
Why?
|
|
|
|
|
|
|
|
|
c.
|
Our
class of thirty needs four dozen buns. The price of buns is $.89
for a package that contains eight buns. How many packages do we
need to buy? How much will it cost?
|
|
|
|
|
|
|
|
|
d.
|
Do
you get the same answer if you add first and then multiply or
multiply first and then add?
|
|
|
|
|
|
|
|
|
|
4
x 5 + 7 = ?
5
+ 7 x 4 = ?
|
|
|
Example Grade
7-8:
|
a.
|
If
I multiply 35 by 5 and then divide the product by 5, do I get 35?
Why? If I add
10% to 35 and then subtract 10% of the result from 35, do I get
35?Why?
|
|
|
IV-1.4, 3.5
|
|
|
|
|
|
|
|
|
|
b.
|
If
13 x .17 = 2.21, what is 14 x .17?
|
|
|
|
|
|
|
|
|
c.
|
If
you got these answers on your calculator, would you think they
were reasonable? Why
or why not?
|
|
|
|
|
|
|
|
|
|
234
x 600 = 2408
90 x 20 = 1800
|
|
4.
|
Can
my students determine an appropriate degree of precision needed in
calculating a number?
|
|
|
Example Grade
K-3:
|
Which
things are easy to count exactly, and which things are hard?
|
|
|
IV-2.5
|
|
|
|
|
|
|
|
|
Number
of chairs at the table
Objects
in the jar
Scoops
of rice in the jar (Did everyone come up with the same exact
count? Why or why not?)
|
|
|
Example Grade
3-4:
|
Which
call for estimates and which call for exact answers?
|
|
|
IV-2.5
|
|
How
much your groceries will cost?
How
long it will take you to get to the park?
How
much it will cost to buy the red bike in the window?
How
much tax you owe on the book you bought?
|
|
|
Example Grade
5-6:
|
About
what percent of students in our school wear glasses?
We found 417 out of 1,343.
The calculator says 0.310498883.
How do you report this?
|
|
|
IV-2.5
|
|
|
Example Grade
7-8:
|
The
odometer says you went 427.2 miles.
You took 8 hours and 15 minutes.
After you do some calculations, the calculator says
51.781818. How would
you report the average speed? If the original measurements were in tenths, what degree of
accuracy should you report?
|
|
|
IV-2.5
|
|
|
|
