Special Educator Program
SpEd 625
Brownbridge
Informal Math Probes 2
Fractions, Decimals, Percent/Ratio, Time, Money,
Measurement, Graphs/Charts, Geometry
Student Pages
Sources:
Stein, M., Silbert, J., & Carnine, D. (1997). Designing effective mathematics instruction: A direct
instruction approach (3rd ed.). Merrill/Pearson Publishing.
and
Stein, M., Kinder, D., Silbert, J., & Carnine, D. (2006). Designing effective mathematics
instruction: A direct instruction approach (4th ed.). Merrill/Pearson Publishing.
1
PRETEST
Student
Date
FRACTIONS
Complete these fraction questions in the space provided. If you make an error, just cross
out the wrong answer and print the correct answer. Let’s begin.
Circle the picture that shows 2/4.
Circle the picture that shows 4/4.
Circle the picture that shows 4/3.
Circle the picture that shows 3/2.
In the circle show:
3/4 =
2/3 =
3/2 =
Read the following fractional numbers.
2
1
––
4
3
2
––
5
3
7 ––
9
Read the following fractional numbers.
2 1/3
4 2/5
6½
Write these fractions.
Two-thirds
=
––
Five-halves
=
––
Four-fifths
=
––
Rewrite each of the following as a mixed number.
12
––
5
=
8
––
3
=
21
––
9
=
2
PRETEST
Student
Date
Rewrite each whole number as a fraction.
9
=
––
6
=
––
8
=
––
1
=
––
1
=
––
3
=
––
=
––
9
Write the equivalent fractional number by supplying the numerator.
2
––
5
=
3
––
4
––
10
=
2
––
3
––
12
Use the correct symbol in the blank to make the statement true: More than >, Less than
< , equal to =.
4
––
3
is
7
––
7
1
is
1
5
––
6
is
1
Circle the larger fraction in each pair.
2
––
3
4
––
5
or
4
––
5
or
3
––
4
2
––
7
or
1
––
2
Add the following fractions. Reduce your answers to simplest terms, if necessary.
3
––
5
+
4
––
6
2
––
4
1
––
5
6
––
10
3
––
5
+
=
2
––
5
––
+
2
––
5
=
+
2
––
3
=
+
4
––
5
=
1
––
2
+
3
––
6
+
3
––
10
=
––
2
––
6
1
+ ––
2
=
––
=
3
PRETEST
Student
2
––
3
+
2
––
4
+
1
––
6
=
3
––
4
+
1
––
2
+
2
––
5
=
2
7 ––
4
+
1
3 ––
4
=
3
2 ––
5
+
1
4 ––
5
=
+
1
2 ––
2
=
3
4 ––
4
Date
Subtract the following fractions.
3
2
––
–
3
––
4
=
––
––
3
3
5
2
–
––
4
=
––
5
–
4
––
–
7
2
––
2
––
––
––
=
––
1
––
3
=
7
1
=
––
–
––
2
3
Subtract the following mixed fractions. Reduce your answers to lowest terms, if
necessary.
4
––
7
5
–
2
––
7
2
1 ––
3
=
––
8
–
9
–
3
2 ––
5
=
–
1
4 ––
2
=
7
3
2
––
5
–
1
2
––
5
=
=
4
PRETEST
Student
Date
Multiply the following fractions.
3
––
5
2
x ––
3
= –– or
––
2
––
5
x
3
––
5
=
––
2
––
2
x
3
––
5
= –– or ––
Multiply each fraction by the whole number and state your answer as a whole number.
2
––
3
x
2
––
5
x
6
3
––
5
=
14
x 20
2
––
9
=
1
––
3
=
x 15
=
3
––
7
x
12
=
x 8 =
Multiply these mixed fractions; reduce your answers to simplest terms.
3
7 ––
4
x
1
3 ––
2
=
3
2 ––
5
x
4
=
5
x
1
2 ––
2
=
Divide these fractions; reduce your answers to simplest terms.
3
––
4
÷
2
––
5
=
5
––
6
÷
2
––
3
=
7
––
9
÷
1
––
3
=
Divide these fractions; reduce your answers to simplest terms.
2
––
3
÷
4
=
5
PRETEST
Student
3
––
5
÷
2
=
2
––
4
÷
7
=
Date
Divide these mixed fractions; reduce your answers to simplest terms.
1
3 ––
2
÷
3
=
1
2 ––
5
÷
2
=
1
7 ––
2
÷
4
=
Read each story problem aloud and write the answer in the space provided. If you need
help reading the problem, please ask.
Bill ran 2 ¾ miles on Monday and 3 ¼ miles on Tuesday. How many
miles did he run altogether?
Jack had 4 2/8 pounds of nails. Bill had 2 3/8 pounds of nails. How much
more did Jack have?
Bob worked 2 1/2 hours on Monday and 3 hours on Tuesday. How many
hours did he work altogether?
There are 15 children in the class. Two-thirds are boys. How many boys
in the class?
Jack has to study for 30 hours. He has done half of the studying. How
many hours did he study?
Ann's coach told her to run 3/4 of a mile a day. How many miles will she
run in 5 days?
6
PRETEST
Student
Date
Bill painted ½ the wall. Jane painted ¼ of the wall. How much of the wall
have they painted together?
Tom ate 1/3 of the pie of the pie, and Jack ate 1/2 of the pie. How much
of the pie did they eat?
Two girls picked 5 ½ pounds of cherries. They want to split up the
cherries equally. How much will each one get?
Bill has 35 inches of ribbon. He wants to make shorter ribbons. If each
ribbon is ½ “ long, how many ribbons can he make?
Write all the numbers that are factors of each of the following.
12
8
Write the lowest common multiple for each of the following.
Find the lowest common multiple of 6 and 4
Find the lowest common multiple of 5 and 10
Find the lowest common multiple of 5 and 2
Find the lowest common multiple of 3, 6 and 4
Find the lowest common multiple of 2, 4 and 5
Find the lowest common multiple of 2, 5 and 10
Write the greatest common factor of each of the following.
8 and 12
4 and 8
12 and 15
7
PRETEST
Student
Date
DECIMALS
Complete these decimal questions in the space provided. If you make an error, just
cross out the wrong answer and print the correct answer. Let’s begin.
Circle the correct decimal for each of the following:
five-tenths (5/10)
5
.05
.5
four-hundredths (4/100)
4
.04
.4
seventy-hundredths (7/100)
70
.70
.07
five-thousandths (5/1000)
.05
.5
.005
.500
ninety-thousandths (90/1000)
.90
.900
.090
.009
Circle the equivalent fraction for each of the following.
.75
=
1
––
4
.8
=
4
––
5
8
––
8
1
––
8
2
––
5
=
1
––
4
2
––
3
6
––
7
1
––
6
.67
5
––
7
2
––
3
3
––
4
Write these fractions as decimal numbers. Round to the nearest hundredth.
5
––
100
=
5
––
10
=
19
–––
100
=
342
––––
1000
=
60
––––
1000
=
5
––––
1000
=
2
––
5
=
3
––
4
=
3
–––
10
=
=
4
––
6
=
2
–––
9
=
3
––
7
Circle the correct mixed decimal number for each of the following:
five and three-tenths
.53
5.03
5.3
ten and four-hundredths
1.04
10.04
10.4
eighteen and six-hundredths
18.6
1.86
18.06
8
PRETEST
Student
Date
Rewrite these mixed fractions as mixed decimal numbers; round off to the nearest
hundredth.
14
10 –––
100
=
3
3 ––
5
=
3
16 ––
10
=
18
40 –––
100
=
1
7 ––
4
=
Rewrite these numbers in order, beginning with the smallest:
18.8
10.10
10.3
10.03
Write these problems in columns and solve them.
8.23 + 12.1 + 6
=
7 + .3 + 45
=
.08 + 4 + .6 =
Write these problems in columns and solve them.
5 – 3.2
=
8 – .34
=
7 – .3
=
Multiply these decimal numbers.
7.14
x
.5
214.0
x
.7
.1
x
.7
.02
x
.8
Multiply each decimal number by 10, 100 or 1000.
10 x 34.2
100 x 34.52
10 x 34.52
1000 x 34.52
10 x 83.267
1000 x 83.267
100 x 83.267
10 x 943.782
9
PRETEST
Student
Date
Divide these numbers and write the answer to the nearest hundredth.
5 ) 32.45
7 ) 215.6
2 ) .85
9
) .036
9 ) .36
9 ) .0036
2 )3
5 ) 3.1
4 ) 21
7
) 3.1
9 )7
3 )2
.2 ) 23.74
.5 ) 13
.2 ) 14.26
.50 ) 275
.05 ) .345
.02 ) 3.1
.05 ) 2
Round off these numbers to the nearest whole number.
8.342
=
7.812 =
Round off these numbers to the nearest tenth.
8.34
9.961
=
=
19.942 =
9.782
=
29.981
=
9.782
=
Round off these numbers to the nearest hundredth.
8.346
=
14.993
=
14.996 =
29.9982 =
10
PRETEST
Student
Date
PERCENTAGE
Complete these percentage questions in the space provided. If you make an error, just
cross out the wrong answer and print the correct answer. Let’s begin.
Write these percentages as decimals for each of the following:
45 %
=
15 %
=
6%
=
1%
=
Convert these decimal numbers to percentages:
.32
=
.6 =
3.4
=
Convert these fractions to percentages:
3
––
5
4
––––
9
=
5
––
4
=
5
––––
3
=
3
–––
7
=
=
7
––––
10
=
Determine the percentage of each number:
8 % of 20
=
25 % of 12
=
130 % of 50
=
Read each story problem aloud and write the answer in the space provided. If you need
help reading the problem, please ask.
Bill took 20 basketball shots. He made 12. What is his shooting
percentage?
Ann has 15 friends; 9 of her friends are from Texas. What percentage of
her friends are from Texas?
Jill earned $80 in May. In June she earned 30% more than she did in
May. How much did Jill earn in June?
Tim borrowed $200. He must pay 9% interest. How much must he pay back
altogether?
11
PRETEST
Student
Date
I got A’s on 5 tests and B's on 4 tests. What percent of the tests did I get A's
on?
There are 4 boys and 6 girls. What percent of the class is boys?
Bill has 5 blue pens and 15 red pens. What percent of the pens are blue?
12
PRETEST
Student
Date
TIME
Complete these problems about time in the space provided. If you make an error, just
cross out the wrong answer and print the correct answer. Let’s begin.
Circle the clock that shows 7:25.
Circle the clock that shows 4:03.
Circle the clock that shows 2:53.
Check the correct time from the choices.
quarter after 10
half-past 10
half-past 9
10 minutes before 6
quarter after 6
half-past 6
6 o’clock
quarter to 7
quarter after 3
quarter after 4
quarter after 5
quarter to 4
Express the time as minutes after the hour:
____ minutes after ____
____ minutes after ____
____ minutes after ____
13
PRETEST
Student
____ minutes after ____
____ minutes after ____
Date
____ minutes after ____
Express the time as minutes before the hour:
____ minutes before ____
____ minutes before ____
____ minutes before ____
14
PRETEST
Student
Date
MONEY
Complete these problems about money in the space provided. If you make an error, just
cross out the wrong answer and print the correct answer. Let’s begin.
Write the value (¢ and decimals) of the coins in the space provided.
$
$
___¢
___¢
____
$ ____
___¢
___¢
____
$ ____
Write the value (¢ and decimals) of the coins in the space provided.
___¢
$ ____
___¢
$ ____
___¢
$ ____
15
PRETEST
Student
Date
Write the value (¢ and decimals) of the coins in the space provided.
___¢
$ ____
___¢
$ ____
___¢
$ ____
Write the correct numerical representation of money values.
Write four dollars & six cents.
Write nine dollars & thirty cents.
Write one dollar & five cents.
Add or subtract these amounts:
$ 1.32
$ 4.78
$ 15.00
$ 9.00
$ 10.00
+ $ 2.43
+ $6.92
– $1.35
– $ 8.20
– $ 6.16
16
PRETEST
Student
Date
Determine the correct change:
You bought a soda that costs 20 ¢. You give the clerk a half dollar. The clerk gives
you this change. Is it correct?
You bought a soda that costs 27 ¢. You give the clerk 35 ¢. The clerk gives you this
change. Is it correct?
Write the coins you would need to make 27 ¢.
Write the coins you would need to make 79 ¢.
Write the coins you would need to make 43 ¢.
Read each story problem aloud and write the answer in the space provided. If
you need help reading the problem, please ask.
Jack had $6.00. He spent $3.25. How much does he have left?
If you had $4.00 and you got $2.15 more, how much would
you have?
Jan buys a shirt for $2.85. She gives the clerk a $5 bill. How
much change does she get back?
You buy 3 pencils for 15 ¢ each and 5 pencils for 10 ¢ each. How
much do you spend?
You buy 4 pens for 30 ¢ each and 2 erasers for 12 ¢ each. How
much do you spend?
17
PRETEST
Student
Date
You buy 5 pens for 15 ¢ each and 3 erasers for 8 ¢ each. How
much do you spend?
Bill wants to buy pencils that cost 7 ¢ each. He has 2 dollar bills
and a dime. How many pencils can he buy?
Bill has 3 quarters. If spoons cost 5 ¢ each, how many spoons
can he buy?
Bill has 3 half dollars. If spoons cost 5 ¢ each, how many spoons
can he buy?
Bill wants two hamburgers with cheese – one with fries, one
without fries – a large soda, and two large ice cream cones. How
much will all that cost?
Hamburger
Ice cream
plain
35 ¢
cheese
50 ¢
small
50 ¢
bacon
70 ¢
large
60 ¢
20 ¢
Sundae
Fries – add
Soda
small
30 ¢
med.
40 ¢
large
50 ¢
Cone
small
60 ¢
large
80 ¢
A 6 oz. package of rice made by ABC Company costs 96 ¢. A 5oz. package made by the XYZ company costs 90 ¢. Which
package of rice is the best buy? Tell why.
18
PRETEST
Student
Date
MEASUREMENT
Complete these problems about measurement in the space provided. If you make an
error, just cross out the wrong answer and print the correct answer. Let’s begin.
Complete each of the following:
About how long is a spoon?
6 inches
6 feet
6 yards
About how tall is a person?
5 inches
5 feet
5 yards
About how much does a cat weigh?
8 ounces
8 pounds
8 tons
About how much does a car weigh?
2 ounces
2 pounds
2 tons
About how long is a pen?
8 mm
8 cm
8m
8 km
About how long is a car?
2 mm
2 cm
2m
2 km
About how much does a pencil weigh?
75 mg
75 g
75 kg
About how much does a newborn baby weigh?
4 mg
4g
How much water can we put in a baby bottle?
250 ml
250 dl
How much milk would a basketball hold?
3 ml
3 dl
75 cg
4 kg
250 l
3l
4 cg
250 kl
3 kl
Check or “x” the correct length for each ruler section below.
2 inches
3 inches
2 ½ inches
3 ½ inches
3 inches
3 ¼ inches
2 ¾ inches
2 ¼ inches
Complete the following:
Put a W over 2 ¼ inches
Put an X over 1 ½ inches
Put a Y over 2 3/8 inches
Put a Z over 3 5/16 inches
Check or “x” the correct answer.
4 feet 5 inches
+ 3 feet 8 inches
8 feet 3 inches
8 feet 1 inch
7 feet 3 inches
3 weeks 4 days
– 1 week 6 days
1 week 8 days
2 weeks 8 days
1 week 5 days
19
PRETEST
Student
Date
Check or “x” the correct answer.
A kilogram equals:
A hectogram equals:
1 gm
1 gm
10 gm
10 gm
100 gm
100 gm
1,000 gm
1,000 gm
A dekaliter equals
1l
10 l
100 l
1,000 l
A milliliter equals:
1/10 of a liter
1/100 of a liter
1/1000 of a liter
A decimeter equals:
1/10 of a meter
1/100 of a meter
1/1000 of a meter
A centigram equals:
1/10 of a gram
1/100 of a gram
1/1000 of a gram
Complete each of the following:
There are: ____ inches in a foot
4 feet = ____ inches
____ feet in a yard
2 yards = ____ feet
There are: ____ ounces in a pound
There are: ____ cups in a pint
____ pounds in a ton
____ pints in a quart
There are: ____ millimeters in a centimeter
There are: ____ meters in a kilometer
There are: ____ milliliters in a liter
36 inches = ____ feet
____ quarts in a gallon
____ centimeters in a meter
____ grams in a kilogram
____ liters in a kiloliter
What is the area of a room 8 feet long and 10 feet wide?
What is the volume of a box 6 inches long, 8 inches wide
and 4 inches high?
Fill in the correct answers.
20 meters = ____ centimeters
500 kilometers = ____ meters
46 grams = ____ kilograms
5000 centigrams = ____ grams
3.6 meters = ____ centimeters
2.7 liters = ____ deciliters
20
PRETEST
Student
Date
GRAPHS, CHARTS, MAPS & STATISTICS
Complete these problems about graphs, charts, maps & statistics in the space provided.
If you make an error, just cross out the wrong answer and print the correct answer. Let’s
begin.
How many points did Bill score on Monday?
On which day did Bill score the least?
How many points did Ann earn?
How many more points did Ann earn than Jim?
1998
x x x
1999
x x
x = 10 babies
How many babies were born in 1998?
3
40
30
35
How many more babies were born in 1998 than in 1999?
21
PRETEST
Student
How many points did Ann score?
How many points did Bill score?
Date
15
19
17
20
20
15
19
16
How many points did Ann score on Wednesday?
How many points did Ann score on Monday?
20
22
28
25
15
10
9
12
How many babies were born in 1988?
30
3
40
35
Who is the heaviest player on the team?
How much heavier is Tanya than Tammy?
How much younger is Tammy than Jill?
22
PRETEST
Student
Date
Bill’s Work in School and at Home
How many hours of school work did Bill do in February?
In which month did Bill do more school work than housework?
Jill & Mary – Miles Run
On which days did Jill run more than Mary?
How many miles did Jill run on Wednesday?
On which days did Mary run more than Jill?
Who ran the most miles? How many more miles than the other?
23
PRETEST
Student
Date
Read and interpret the following maps & schedules and answer the questions.
C
C
A
C
B
C
1 inch = 10 miles
If city A is 2 inches from city B on the map, how much is the distance in miles
between A and B?
If city C is 2 ½ inches from city B on the map, how far apart are cities C and B?
When will Bus C arrive at 41st Street??
How long does it take Bus B to get from 34th Street to 64th Street?
What time would you leave downtown if you want to be at 64th
Street just before 10 o’clock?
Mrs. James gave a test to the 9 students in her class. The marks are written below:
What is the range of scores?
What is the median score?
What is the mode of scores?
Jill plays basketball. She scores 8 points in one game, 2 points the next
game, 6 points the next game, and 4 points in the last game. How many
points did Jill average per game?
24
PRETEST
Student
Date
GEOMETRY
Complete these problems about geometry in the space provided. If you make an error,
just cross out the wrong answer and print the correct answer. Let’s begin.
Mark each circle with a “/” or “x”.
Mark each rectangle with a “/” or “x”.
Mark each triangle with a “/” or “x”.
Mark each square with a “/” or “x”.
Mark each cube with a “/” or “x”.
Mark each sphere with a “/” or “x”.
Mark each cone with a “/” or “x”.
Mark each picture with a “/” or “x” that shows a diameter.
25
PRETEST
Student
Date
Mark the picture with a “/” or “x” that shows a radius of a circle
Mark each pyramid with a “/” or “x”.
Mark each cylinder with a “/” or “x”.
Mark each right triangle with a “/” or “x”.
Mark each isosceles triangle with a “/” or “x”.
Mark each equilateral triangle with a “/” or “x”.
Mark each scalene triangle with a “/” or “x”.
Put a “P” over the pentagon, and “H” over the hexagon, and a “O” over the octagon..
Circle each group of parallel lines.
Circle each group of perpendicular lines.
Circle each parallelogram.
26
PRETEST
Student
Date
For each example, write the letter name of the angle.
Find the perimeter of this square.
Find the area of this rectangle.
4”
3”
4”
6”
Draw the line segment CD.
A
C
D
B
What is the volume of a figure that is 5 inches long, 3 inches wide, and 6 inches high?
27