Purely Amateur Attempt at Comparing the WIAT-III 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 WIAT-II 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 1-20

12

one-to-one 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 1-10

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