 
Purely Amateur Attempt at Comparing the
WIATIII and WJ III Math Tests
Sequence of
Math Development adapted from Smith, C. R. (1994), Learning Disabilities:
The interaction of learner, task, and setting (Fourth Edition).
New York: Allyn & Bacon 
Tables Comparing the WIATII Math
Reasoning Test Items to the WJ III Applied
Problems Test Items 

TASK 
WIAT 
WJ III 
Middle School 
masters order of operations in complex
problems 


multiplies / divides two fractions 


adds subtracts, multiplies divides decimals
to the thousands 


understands real, rational, irrational
numbers and different number bases 


calculates square and cube roots 


estimates percentages / proportions 

50 
calculates discount, sales tax, restaurant
tip 


understands simple interest, compound
interest, percent increase/decrease 

52, 57 
understands angles (complementary,
supplementary, adjacent, straight, congruent) 


calculates volume of a cylinder 


calculates arc / circumference of circle 

58, 61, 62, 63 
understands eqilatera1, isosceles, scalene,
obtuse figures 


graphs coordinates, transformations,
rotations, equations with two variables 

59 
solves equations by substitution 


learns about probability, permutations,
factorial notation, frequency, normal curve, 
66, 67 
60 
learns Pythagorean theorem 

56 
deepens understanding of previously taught
skills and concepts 
65 
55 

TASK 
WIAT 
WJ III 
Fifth Grade 
multiplies three digit numbers (962 x 334) 


can work harder division problems (102 + 32) 

45 
adds, subtracts, multiplies mixed numbers 


divides a whole number by a fraction 

47 
represents fractions as decimals, ratios,
percents 


adds, subtracts, multiplies, with decimals 


understands use of equations, formulas,
"working backward" 
58, 59 

estimates products/quotients 


learn about exponents, greatest common
factor, bases, factors, composite numbers, integers 


understands percent, ratios 
60, 61 
49 
understands mean, median, mode 
64 

measures area and circumference of a circle 


measures perimeter and areas of triangles and
parallelograms, volume of cube 
62 
41, 51, 53, 54 
performs metric conversions 


uses compass, protractor 


reads scale drawings 



TASK 
WIAT 
WJ III 
Fourth Grade 
adds columns of 3 or more numbers 


multiplies three digit by two digit numbers (
348 x 34 ) 


performs simple division ( 44/22 ) 
54 

reduces fractions to lowest terms 


adds/subtracts fractions with different
denominators ( 3/4 + 2/3 ) 
55 
42 
adds/subtracts decimals 


converts decimals to percents 
53, 57 
43 
counts/makes change for up to $20.00 
63 

estimates time 

46 
can measure time in hours, minutes, seconds 
52 
44 
understands acute, obtuse, right angles 


computes area of rectangles 


identifies parallel, perpendicular,
intersecting lines 


calculates weight in tons, length in
meters, volume in cubic centimeters 

48 
Solves simple probability problems 
56 


TASK 
WIAT 
WJ III 
Third Grade 
understands place value to thousands 
32 

adds and subtracts four digit numbers (e.g.,
1,017 978) 


learns multiplication facts to 9 x 9 
50 
34 
solves simple multiplication and division
problems ( 642 x or ÷ 2 ) 

37, 40 
reads complex charts and tables 
42 

counts by 4s, 1000s 


geometry (identifies hexagon, pentagon) 


introduction to fractions adds / estimates /
orders simple fractions 
43, 46, 47 
39 
understands mixed numbers 

39 
reads fractions of an inch 
45, 51 

understands diameter, radius, volume, area 
41 

understands decimals 


begins to learn about negative numbers,
probability, percentage, ratio 
34 

solves harder number story problems

48, 49 
40 

TASK 
WIAT 
WJ III 
Second Grade 
identifies / writes numbers to 999 


adds / subtracts two / three digits with &
without regrouping (e.g., 223 + 88, 124 16) 


multiplies by 2, 3, 4, 5 
38, 39 
31 
counts by 3s, 100s 
37 

reads / writes Roman
numerals to XII 


counts money and makes change up to $10.00 
35, 44 
32, 33, 36 
recognizes days of the week, months, and
seasons of the year on a calendar 
33 

tells time to five minutes on a clock with
hands 
22, 28 

learns basic measurements (inch, foot, pint,
pound) 

38 
recognizes equivalents ( e.g., two quarters =
one half, four quarts = one gallon) 
30 

divides area into 2/3, 3/4, 10ths 


graphs simple data 
36 


TASK 
WIAT 
WJ III 
First Grade 
counts / reads / writes /orders numbers to 99 
19 

begins learning addition and subtraction
facts to 20 


performs simple addition/subtraction problems
(e.g., 23 + 11) 
26, 31 
27, 28, 29, 30 
understands multiplication as repeated
addition 


counts by 2s, 5s and 10s 
23 

identifies odd / even numbers 


estimates answers 


understands 1/2, 1/3, 1/4 
29, 40 

gains elementary knowledge of calendar and
time 
21 

understands schedules 


reads digital clock 


understands measurement (cup, pint, etc.,
inch, cm, etc. ) and money (value of quarter, etc.) 
16, 20, 27 
26, 27, 29 
solves simple number story problems 


reads bar graphs and charts. 
24, 25 


TASK 
WIAT 
WJ III 
Kindergarten 
matches / sorts / names objects by size,
color and shape 
3, 5 
1, 2, 7, 8, 11, 12 
recites and recognizes numbers 120 
12 

onetoone correspondence 


counts / adds up to nine objects 
1, 8, 10 
3, 4, 5, 6, 13 
knows addition / subtraction facts to six 
9, 11, 13 
9, 10, 16, 17, 18, 20 
evaluates objects by quantity, dimensions,
size (e.g., more/less, longer/shorter, tall/tallest) 
2, 3, 4, 17 

writes numbers 110 


understands concepts of addition and
subtraction 
9, 11, 13 
14, 15, 18, 17, 20, 22, 23 
knows symbols +, , = 


recognizes whole vs half 


understands ordinals (first, 5th) 
14, 15 

learns beginning concepts of weight, time (
e.g., before/after) 


understands lunch is at 12:00 


tells time to the hour 


money (knows value of pennies, nickels,
dimes), and temperature (hotter/colder) 

19, 21 
aware of locations ( e.g., above/below,
left/right, nearest/farthest) 

24, 25 
interprets simple maps, graphs and tallies.

6, 7 

