BOX 5–4 Progress Map for Counting and Ordering

Following (below and on the next two pages) is the lower portion of a counting and ordering progress map. The map shows examples of knowledge, skills, and understandings in the sequence in which they are generally expected to develop from grades one through five. This type of map is useful for tracking the progress of an individual child over time. An evaluation using tasks designed to tap specific performances on the map can provide a “snapshot” showing where a student is located on the map, and a series of such evaluations is useful for assessing a student’s progress over the course of several years.



Uses unitary ratios of the form 1 part to X parts

(the ratio of cordial to water was 1 to 4)

Understands that common fractions are used to describe ratios of parts to whole

(2 in 5 students ride to school. In school of 550, 220 ride bikes)

Uses percentages to make straightforward comparisons

(26 balls from 50 tries is 52%; 24 from 40 tries is 60%, so that is better)

Uses common equivalences between decimals, fractions, and percentages

(one-third off is better than 30% discount)

Uses whole number powers and square roots in describing things

(finds length of side of square of area 225 sq cm as a square root of 225)


Counts in decimal fraction amounts (0.3, 0.6, 0.9, 1.2, …)

Compares and orders decimal fractions

(orders given weight data for babies to two decimal places)

Uses place value to explain the order of decimal fractions

(which library book comes first—65.6 or 65.126? why?)

Reads scales calibrated in multiples of ten

(reads 3.97 on a tape measure marked in hundredths, labeled in tenths)

Uses the symbols =, <, and > to order numbers and make comparisons

(6.75 < 6.9; 5 × $6 > 5 × $5.95)

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