By Ann Lawrence
Those classes express the right way to maximize guideline that prepares scholars for formal algebra. via a sequence of investigations that support scholars make connections among mathematics and algebra, scholars construct skillability with key algebraic strategies - styles, features, and variables. They use a number of representations together with types, drawings, tables, graphs, phrases, and emblems. classes contain a expertise part with feedback for instructing with graphing calculators.
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Additional info for Lessons for Algebraic Thinking, Grades 6-8
If the starting value of the coins in my pocket is ten cents, and I use my rule, the final value is sixteen cents. ” Several hands were raised and I called on Amrita. “Amrita, use the rule to predict the final value of the coins if the starting value is twenty cents,” I said, writing 20 in the table. Amrita promptly offered twenty-six as the final value, and I verified that her answer followed my rule. Now the table contained the information shown below. Starting Value Using the Rule Final Value 6 12 5 11 10 16 20 26 “We now have two correct predictions,” I reminded the class, “so anyone can volunteer to guess my rule if you think you know it.
When I announced four cents as the starting value, Maury confidently gave the corresponding final value as eleven cents, the correct amount using my rule. At this point, I repeated the procedure we used in the first round of the game, including the following steps: 1. “Think time” for everyone before a rule is offered 2. Confirmation of the correct rule: Final value = 2 × starting value + 3 3. Writing the rule and substituting in that rule for each row in the center column of the T-chart, as shown here: Starting Value Using the Rule Final value = 2 ؋ starting value + 3 Final value = (2 ؋ s) + 3, 2 • s + 3, or 2s + 3 Final Value 5 2(5) + 3 = 13 13 10 2(10) + 3 = 23 23 1 2(1) + 3 = 5 5 12 2(12) + 3 = 27 27 0 2(0) + 3 = 3 3 9 2(9) + 3 = 21 21 4 2(4) + 3 = 11 11 23 CCC 6-8 Algebra 1 (1-38) 24 8/6/02 Functions and Graphing 4:39 PM Page 24 4.
After we found out Chip did not guess the correct rule, I tried to think of other ways to get from six to twelve. ” Sally added, “I went backwards from twelve to six. Since the difference between them was six, I tried adding six to the starting value. ” I noted that everyone should keep the suggestions offered by Chip, Amrita, and Sally in mind to see whether those strategies were useful in the next rounds of the game, then began Round 2 of Guess My Rule. ” CCC 6-8 Algebra 1 (1-38) 8/6/02 4:39 PM Starting Value Page 23 Using the Rule Functions and Graphing Final Value 5 13 No one offered to make a prediction, so I asked for a new starting value.