About 20 two-sided (white and red) tokens Four or five variable counters (such as pennies) Warning: The boards we are using limit the numbers we can handle, as you will see below. In this unit, some concepts that underlie algebra will be introduced. We will use variable counters with two boards to find numbers in such problems as "I am thinking about a number p. Three times p equals 2 times p plus 5. What is my number?" We use the two boards to represent the two expressions on either side of an equals sign, and whatever we do to an expression on one board, we do to the expression on the other board. Let's try it on the problems below, and then make up some more.
Here's how it may look using the boards: My number is the green triangle. My number plus 7 = 10. I subtract 7 from both sides (both boards). I regroup 10 as 5 + 5. My number equals 5 minus 2. I regroup 5 as 3 + 2. 2 minus 2 is zero, so my number equals 3. Let's check. I'm thinking of three. When you add seven to it, do you get 10? Yes!
Here's how it may look using the boards: My number is the green triangle. My number doubled plus 1 = 9. I subtract 1 from both sides (both boards). I half both sides by moving all tokens down one row. My number equals 4. Let's check. I'm thinking of four. When you double it and add one, do you get 9? Yes!
Now let's just put configurations of tokens on the two boards and regroup as far as we can! Number Board index |