Aims of this phase of a longitudinal mathematics achievement investigation were to (1) detect individual and group differences in math achievement among a sample of fourth-year children, (2) monitor changes in math skills since a 1981 math investigation, and (3) identify limits of children's understanding of mathematical concepts. (The math test itself was designed to be additionally suitable for use in 1983.) An item bank was assembled by combining those items which the fewest children answered correctly on the 1981 test with items assessing skill in operations for counting numbers at fourth-year level and above. Items tested content area skill and three aspects of problem structure: number size, position of the answer box or missing element, and problem format. The resulting test consisted of six subscales, including addition, subtraction, multiplication, concepts, word problems, and number problems paralleling the word problems. Altogether, 692 children in 33 fourth-year classes were tested; subjects attended 5 Mt. Druitt schools and 3 contrast schools. Findings indicated significant achievement differences between subsamples and among schools on all subscales and on the total test. Longitudinal change was found on the 11 items common to the 1981 and 1982 tests, and sample-wide error patterns emerged from the data. The test and instructions for administration are appended. (RH)