\doc\web\97\08\samptest.htm Sample WA Assesment Test Questions Home | arthurhu@halcyon.com The sample questions for the 4th grade Washington assessment are in general, much too difficult for the average 4th grader. Many would be difficult even for 6th grade or adult. By contrast, the 7th grade samples are very straightforward applications of material commonly taught in 7th grade, and are certainly much easier relative to grade level, I found them even easier than the 4th grade problems because they did not require clever decoding of language in order to figure out how to use mathematics to get the actual answer Calculators were NOT allowed in this test. Compare these test sample problems with 1996 NAEP Mathematics Objectives, Essential Academic Learning Requirements/Benchmarks (EALR) for the 4th grade, 4th grade NCTM standards

Sample 4th Grade (HA!) WA Assessment Questions

Original Sample Questions (The 7th grade questions are MUCH EASIER than the 4th grade questions!) Reading | Math Flagpole Problem | Marbles Probability Problem | Estimate cards that will fit into a box | Estimate notebook paper in metric | Frequency Histogram | Bird Feeder |

Sample Passage Summary

Students read a short passage, summarized here, explaining what the
word camouflage means and how it works.

Animals in nature have a special way of hiding. The color of their
skin or coat blends with the color of their surroundings and makes
them hard to see. This is called camouflage.

If you want to find out how camouflage works, take some toothpicks of
different colors, including green, natural wood, and red. Scatter
these toothpicks, one color at a time, over a small area of green
grass. Which toothpicks are easiest to see in the grass? Which are
hardest to see?

NOTE: Because most of the reading passages are copyright protected,
only a summary of the passage is reproduced here.

1. In the activity described in the selection, which of these colors
would be easiest to find?

       A. Green 
       B. Natural wood 
       C. Red 

2. What is the author's purpose for writing this selection? Circle a
phrase given below.

   To tell a story

   To explain an idea

   To describe a setting

Explain your choice.

3. Make up an activity different from the one in the selection to
show how camouflage works. Be sure to tell

   (1) what materials you need and

   (2) what steps you will take

My camouflage activity:

Materials to use:

Steps to take:

4. In your own words tell the meaning of the word camouflage.

Task 1: Page 1 | Task 1: Page 2 | Task 1: Page 3 | Task 1: Page 4 |
Task 1: Page 5 | CSL Homepage 


Directions: Today you will do a writing assignment. The magazine
column below, "Advice Column," is meant to give you ideas for the
assignment. Read the column to yourself while it is read to you.

                                                       Advice Column

Dear Guest Advice Columnist,

I have an idea, and I'd like to see what you think about it. I'm a
fourth grader who thinks the school day should be longer. Now, before
you say "What?!" please read the rest of my letter.

If we had a longer school day, we could have more days off! That
would mean longer vacations during the school year or for the summer.
Suppose we went to school one hour more each day. That would make
five hours a week. If there are about four weeks in a month, that
would make 20 hours a month. That's almost two full days each month!

What do you think about my idea? Do you think other kids would like
it? Do you think my principal and teachers would go for it?



In this letter, a fourth grader wants advice about an idea to make
the school day longer. Your writing assignment is to pretend that you
are the advice columnist and will write a letter to the person
explaining what you think about the idea. Is it a good idea? Why or
why not? Think about the advantages and disadvantages of having a
longer school day. Make sure you answer the questions that are at the
end of the person's letter, and explain your answers.

On the next page is a checklist for you to follow in order to do your
best writing. Before you begin writing, read the checklist to
yourself while it is read to you. Read it again before and after you
write your final draft, and put a checkmark in each box when you
think you have done that part of the checklist.

Go On > 

4th grade Math --

Comment - this question requires use of proportionality and
similarity, which is not in any 4th grade textbook, not in anybody's
curriculum list, not in the WA state essential skills manual, and the
NAEP says you're NOT supposed to assess this until the 8th grade.


Eddie wants to find the height of the school flagpole below. The only
measuring tool Eddie has is a 12-inch ruler.

Tell one way Eddie can figure out the height of the flagpole. Explain
all your steps clearly. Use words, numbers, or pictures.

Picture shows building, fire hydrant, and the flagpole casting a
shadow on the ground.

         F    P
         /   /
        /   /

(Geez, can you solve this problem without trigonometry??)

1 - use trigonometry by matching the apparent size of the ruler to
the flagpole, and measuring the distance away as the base of a
triangle with the ruler at the far end

2 - attach the ruler to the rope so that it falls when it hits the top, count
aloud to measure it time it takes to fall to the ground, use the gravitational
constant to solve for the height.

3 - measure the length of the shadow of the fire hydrant, compare
that to the actual height and establish the "scale". Measure the
length of the shadow of the flag pole, and multiply by the same scale
factor. This will only work on a sunny day with a clear shadow.


Look at the four digits below.
       3   1   8   5

Change the order of the digits to make the greatest number possible.
Write the new number on the line.

Use these same digits to make the smallest number possible. Write
that number on the line.

Explain what you had to think about to make your numbers. Use words,
numbers, or pictures.

You have three different bags of marbles. Each bag contains black and
white marbles. Which bag gives you the best chance of picking a white


A - 2 black 1 white
B - 5 black 3 white
C - 2 black 2 white

(you have to count each, make fractions over the total, compare and
reduce fractions 1/3, 3/8, 2/4, and compute probability)
2/4 = 0.5
3/8 = ? but it's smaller than  4/8
1/3 = .33, smaller than 1/2

These would be very difficult fractions to compare for 4th graders.
At this level, they might be expected to compare some fractions by
themselves, but this is combined with a probability problem, making
this a very complex problem.

NCTM standards:
http://www.enc.org/reform/journals/ENC2280/nf_28057s12.htm " Children
also should use reasoning to determine that 1/5 is larger than 1/8 or
1/10 since fifths are larger than eights or tenths.  Students should
recognize that, for example, 3/4 is between 1/2 and 1 and that 1/3 is
large compared to 1/10, about the same size as 1/4, and small
compared to 5/6. They can also explore fractions that are close to 0,
close to 1/2, or close to 1, as in figure 12.4. Experiences with the
relative size of numbers promote the development of number sense. "

That's still a long way from combining this to determine probability,
mixing two different skills in one problem.


Eric plans to use the box shown below to hold his baseball cards.

(box evidently can hold 1 row of cards on end, ruler is provided)

Explain how Eric can estimate the number of cards this box can hold
without putting any cards in the box.


Which of the following is a reasonable estimate of the width of a
sheet of notebook paper?

       A. About 20 millimeters 
       B. About 20 centimeters 
       C. About 20 kilometers 

The right way to do this is imagine how large each of these things
would be, but an adult might attempt to convert 8.5 by 11" to
centimeters, which would require computation and memorizing the
conversion constant instead of just picking the one with the right
approximate units.

Rating - still relatively difficult because it looks like a
conversion problem, and kids are NOT familiar with metric measures.

Students tested different brands of batteries to see how long they
would power the same flashlight. They tested 20 batteries of each
brand.  The students graphed the results below:

Here's the frequency histogram:

Brand A:
      x  xxx
    x xxxxxxxx
0   10   20    30

Brand B:
        x  x xx
        x  x xx
 x xxxx xxxxxxx
0   10   20    30

Brand C:
            xx x 
            xx x
 x xx       xxxx
0   10   20    30

Which brand of battery should you buy if you need your batteries to
last at least 10 hours? Explain your thinking. Use words, numbers, or


1) Unclear as to how this would be scored, this might meet the
standard even though it does not meet the question as well as
the next solution.

Find the highest median
Compute the median by counting halfway (10) from the top, down
Take the one with the highest median
a: halfway point is 19
b: halfway point is between 20 and 21
c: all but 17 are above 22, so 
the median is well above 22

Answer: "C" has the highest median value, assuming that lasting at
least 10 hours means the longest lasting one. In real life, this
would be a safe assumption.

2) (This appears to be the best therefore, only correct solution, it
is a trick question because the one with the highest average life
isn't the one least likely to last less than 10 hours.)

Strategy: Find the lowest probability of battery lasting less than 10
hours Count the total number of x's, then count the number that fall
below 10 hours. Ignore the number above 10 hours, that's not actually
relevant to the answer.

a: 1 below 10
c: 3 below 10
d: 3 below 10

Answer: A has the lowest probability of not lasting at least 10
hours, compared to 3 out of 20 for the other two. This is counter to
the intuitive assumption that the one with the highest median will
has the lowest probability of short life.

(What the heck is this? Most high schoolers only see frequency
histograms in advanced science classes, not in normal math and
certainly not in the 4th grade. You have to interpret intermediate x
tic marks, ask if they're just asking for the battery with the
longest average, which is just about impossible to computer, or
median, which you could eyeball as giving the edge to the last one
since all but 3 x's are above 20, but a much larger fraction of the
others is below 20)

Rating - way inappropriate for 4th graders.


Bird Feeder Sample Math Problem

Teachers say the math section of the new fourth-grade test is
particularly difficult, requiring students to read story type problems
and answer questions with words, numbers and drawings. Many
problems require a number of steps to reach the correct answer. This
question is typical:

Problem: Your class project is to build a bird feeder. Explain how
you could use the information given to find the total cost of the
materials. use words, numbers, or pictures.



## = concrete in ground

Parallel projection 3D picture: bird sits on a tray on post,

dimension lines drawn 60 inches tall from top to bottom of post,

bottom of post is in cutaway of ground in cement.

Top view: Screws attach to post drawn in dotted lines, dimension
lines are set on tray bottom 2 feet square, tray frame made of wooden

|               |
|     x  x      |
|     x  x      |
|               |

x = screw

Item     cost per unit
Wooden post  $2.50 per foot
Strips for 
tray frame   $1.00 per foot
Tray bottom  $6.00
tools, screws, nails, wood glue, and cement mix - donated by

Example problem shows a bird house with a platform of a certain size,
and material at a certain cost. The solution was not just to get the
right answer, in fact, the explanation was graded more important than
a right answer. 

Times 5 by 2.50 and get $12.50 for the wooden post.  For each side of
the tray, times 4 by 2 and get 8.  the tray bottom (sic) is $6 and
the rest is donated by parent. You add $12.50, 48 and $6 together and
get a total of $26.50

source: Washington State Commision on Student Learning

Comment - you have to deal with english foot / inch conversion the
answer is wrong, you have to divide 60 inches by 12 to get 5 feet,
and remember the conversion factor. The answer does not tell what
part of the table 4 by 2 (4 sides by 2 feet per side strip) comes
from. For a tray, you have to know enough 3D geometry to know that it
has a bottom and 4 sides.  

You also have to be trained to read 3-view construction drawings, and
the meaning of dotted lines, and dimension arrows, something most
kids don't get until they take mechanical drawing in high school, and
something boys and whites are better at than girls or minorities. You
have to know how posts attach to screws, how wooden "strips" attach
to a "frame", how a post is set into cement, and how to read a table.
In short, there's no way this is fourth grade material, I imagine
even an average 50th percentile 10th grader would be hard pressed to
get this one completely correct.

If a fourth grader understands the basic four functions of plus,
minus, multiplication and division, that should be plenty without
having to master shop as well.

Skills - 





division 60 inches by 12 inches = 5 feet by hand or memory

reading 3D projection drawing

reading top view, reading number of screws from

dimension lines in 3D and top view

hidden lines

screw attachment

cement achoring


tray geometry

strips for tray edger

reading table

english foot / inch conversion
(the 7th grade brick sample tells you 12in = 1 ft,
the 4th grade question does not!)


- Way inappropriate.


What numbers do W, X and Y probably represent on the number line?

0                     600

A w=100, x=200, y=500
B w=150, x=300, y=400
c w=150  x=300, y=525

Solution - X is pretty obviously halfway, 600 / 2 = 300. W seems
halfway between 0 and X, so 300 / 2 = 150.  If y were 400, it would
be 1/3 of the way between x and y, but it looks just a little beyond
2/3, so more likely 525.


This sort of logic, requiring proportional thinking, fractions and
division is way beyond what 4th graders should be familiar with. 
The NAEP guide says they're supposed to be able to fill in whole
number sequences, not this sort of stuff.

Rating: not appropriate


Pat needs 30 ounces of chocolate chips for the least amount
of money. Which is a good first step he could use to
solve the problem?

X 1.20 for 12 oz
Y 1.75 for 16 oz

A Find the total price of the bags he decides to buy

B Find how many bags of each brand would be needed

C Find the price per ounce for each bag

Well, if you work this one out, you'd need 3 bags of x or 36 oz to
get 30, the cost would be $3.60 if you multiply by hand or 2 bags of
Y, to get 32 oz, or $3.50 if you multiply that out. B would be more
precise becase you might have to buy more chocolate than you needed
even if it cost less per pound. Because it only asks for a strategy,
you don't actually need to do the division to figure out how many
bags you need.

Normally, you shop by the per-pound price, and if you follow (c), you
would need a calculator to figure out that (b) was more expensive, or
eyeball that 1.2/12 is less than 1.75/16.

Rating - this is not a very good asessment of basic math skills
because it's really about solving a problem that does not fit
very well into division or basic maht.

Leon tossed a coin in the air 20 times to see how it would land.
He got heads 12 times. What is the probability of Leon
getting tails on the next toss

a) 12 out of 20
b) 8 out of 20
c) 1 out of 2

The answer is (c) because a coin has equal probablity of either
side, regardless of what happened before. It is an independent

Rating - not appropriate because 4th graders are not taught about
independent / dependent events, NAEP framework says this should
NOT be assesed. Clever kids will figure this one out though.


7th Grade questions from the web page

Mr.Morales wants to cover the 20 ft. by 8 ft. wall of his family room
with brick. The face of the brick chosen is 7 1/2 in. by 3 1/2 in.,
and the mortar space between the bricks is 1/2 in. wide.

How many bricks will Mr. Morales need altogether to completely cover
the wall? Explain in detail how you found your answer. (1 ft. = 12

(hey, they tell you how many in in a foot in 7th but not 4th grade!)


A store is advertising juice at 6 cartoons for $1.98. You only want
to buy 4 cartons. What will you pay for the 4 cartons?

     A. $0.99 
     B. $1.32 
     C. $1.65 
     D. $2.97 

Solution - You have to apply 4 / 6 or 2/3 times 1.98, estimate that

1.98 is about 2.00. Multiply the top of the ratios gives 4, divide by
3 is 4/3, $1.32 is the closest to this result.

Comments - requires proportional thinking, and multiplying by a
fraction. Very, very few kids in the 4th grade are able to compute


Rating - not appropriate for 4th grade.


Last week your friend bought a jacket on sale for $59.95. She tells
you that the jacket was 25% off the regular price. This week, you see
the same store selling that jacket at a regular price of $79.99.

Use estimation to explain to your friend whether she got a 25%
discount on her jacket. Show how you found your estimate.

If the numbers 2/5, 0.26, 1/4, 0.275, and 255/1000 were ordered from
least to greatest, which of these would be the middle number?

     A. 0.26 
     B. 0.275 
     C. 255/1000 
     D. 1/4 

(This is only slightly harder than the 4th grade probability problem,
maybe even simpler because it's only one task)

A bagel store makes charts to help them predict sales for the
following week. Last week, 200 shoppers came into the store and
bought the following number of bagels.

Type    Sold
Plain   146
Onion   40
Raisin  111
Egg     95

Suppose 300 shoppers come in to this store next week. Based on the
chart, explain how you could predict how many of each kind of bagel
will be sold. Explain your answer using words, numbers, and/or

(proportional thinking, easy)

Task 6

The letter A represents an even number, and the letter B represents
an odd number. Which of the following statements is true?

     A. The sum of A + B is an even number 
     B. The sum of A + B is an odd number 
     C. You cannot tell if the sum is even or odd without knowing one of the numbers 
     D. You cannot tell if the sum is even or odd without knowing both of the numbers 

(this is SOOO easy)

Task 7

A report on the life span of a type of turtle shows the data graphed

1000                            750                       390

20     40     60     80    100   120   140  160    180    200

Based on these data, what would you expect to be the number of years
to which the oldest turtle would live? Explain your reasoning in
detail. You may write or draw on the graph to help explain your

(draw an extrapolation on the chart, easy)