Additive and Multiplicative Models
William earns a daily allowance of $\(3.00\). Julian earns $\(0.01\) on the first day of the month and then the amount is doubled each day thereafter for the remainder of that same month.
Two different representations below show the allowances earned for William and Julian for the first 10 days in a month.
List Representation
- Bill’s Allowance: \(3, 3, 3, 3, 3, 3, 3, 3, 3, 3\)
- Julian’s Allowance: \(.01, .02, .04, .08, .16, .32, .64, 1.28, 2.56, 5.12\)
Table Representation
| Bill | Juan | |||
| Day | Allowance | Day | Allowance | |
| 1 | 3 | 1 | 0.01 | |
| 2 | 3 | 2 | 0.02 | |
| 3 | 3 | 3 | 0.04 | |
| 4 | 3 | 4 | 0.08 | |
| 5 | 3 | 5 | 0.16 | |
| 6 | 3 | 6 | 0.32 | |
| 7 | 3 | 7 | 0.64 | |
| 8 | 3 | 8 | 1.28 | |
| 9 | 3 | 9 | 2.56 | |
| 10 | 3 | 10 | 5.12 | |
- Which boy’s allowance is additive and which boy’s is multiplicative? Explain your reasoning.
- Which representation best shows additive versus multiplicative thinking. Why?
