The student's strategy of making a table to show seven days, the money earned for walking the dog, feeding the pony, the total money, and comparing that total to $2.25 works to solve this task. The student's answer, "not correct," is correct. The student uses an alternative strategy of generalizing and applying rules to solve the same task and verifies that her/his answer is correct.
The student demonstrates correct understanding of the underlying concepts of the task. The student's table shows seven days, a running total of feeding the dog earnings, feeding the pony earnings and total money. The student also compares her/his total money to $2.25. The student then generalizes two rules, 5 * d = g and 20 * d = p and uses the two rules to extend the task to other days and to verify that the data on her/his table and answer is correct.
The student correctly uses the mathematical terms money and days from the task. The student also correctly uses the terms table, "totol" (total), week, more, "paterns" (patterns), dollar, quarter, nickel, dime, rules, key. The student correctly uses the mathematical notation $.05, $.10, $.15, $.20, $.25, $.30, $.35, $.20, $.40, $.60, $.80, $1.00, $1.20, $1.40, $.50, $.75, $1.25, $1.50, $1.75, $2.00, $2.25, 1/4, 3/4, 1/2. The student correctly uses the symbolic notation 5 * d = g, and, 20 * d = p, with all variables defined in a key.
The student solves the task and makes the mathematically relevant Practitioner observations, "7 days is a week," "day 8 is $2.00," "day 9 is $2.25," "Ben needs $.50 more money," "paterns day +1, dog +$.05, pony +$.20, total money +$.25." The student also states, "It ($.25) is a quarter," and, "$.05 is a nickel." The student makes Expert connections. The student relates money to fractions by stating, "I Know $.25 is 1/4 of a dollar," "$.50 is 1/2 of a dollar," "$.75 is 3/4 of a dollar," "... a nickel and 1/2 of a dime." The student states, "rules to how I am right." The student generalizes the rule, 5 * d = g, defines the variables in a key, and uses the rule to find the total dog money earned for days two, seven, and 10. The student generalizes the rule, 20 * d = p, defines the variables in a key, and uses the rule to find the total pony money for days four, seven, and one hundred.
The student's use of a table is appropriate and accurate. All necessary labels and money notation are provided and the entered data is correct. The student uses the table to determine two rules that would work to find the total money earned for any number of days that Ben walks the dog or feeds the pony. All variables are defined.