The Investigation below poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find.
Click on the Read Me file below to open the investigation in a Word file:
Read Me - Four-Digit Numbers Instructions (Word Format)
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Calculator Investigation 1.1: Four Digit Numbers
Starting Points for Investigations
- Choose any four-digit number, reverse its digits, add the two numbers, and try dividing by 11. For example,
7582 + 2857 = 10,439
which is divisible by 11 (that is, there is a remainder of zero when it is divided by 11). Try this process for some other four-digit numbers. Note: Zero is divisible by 11. Based on your investigation, write T for true or F for false under the number 4 in the table below. - Try this process for several two-digit numbers and several three-digit numbers and write T or F above the numbers 2 and 3 in the table.
- Make a conjecture based on your results for two-digit, three-digit, and four-digit numbers. Then check several five, six, seven, and eight-digit numbers to see if your conjecture holds.
Number of digits 2 3 4 5 6 7 8
Divisible by 11 (T or F)