@pwharris I see that the 4 was halved to 2 in the expression on the right, which means we can double 5.5 to 11 to maintain balance on both sides because each expression would be equal to 22.
@pwharris I’m thinking about 1/2 as 4/8 in order to identify the number of counts the unit 1/8 and the left side of the equation, which would be 11/8, and since 8/8 equals 1, the missing addend in this balanced equation would be 3/8.
@pwharris I would describe this process as the removal in parts strategy on an open number line. I would also show students the adding up strategy as another option for solving using a number line.
@pwharris I figured it out this way: 10% of 75 is 7.5, and 2% of 7.5 is 1.5. So, I can identify 88% of 75 with the following (7.5 x 8) + (1.5 x 4), which is 66.
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@LaSalleEd This is true sometimes. If both are 3-digit numbers, then yes, the number with the 7 in the hundreds place will always be larger. But, if the numbers have more than 3 digits, the number with the 7 in the hundreds place may not always be the larger number.
@pwharris The adjusting strategy can be tricky for third grade students since whatever adjustment is made to the subtrahend, whether adding to or removing from, has to be done again as a final step to get back to the original problem. Interested to see how others model/represent this.
@pwharris I would first make a point to provide students with a name for this strategy so they can name it when explaining their process. When debriefing as a whole group, “adding one number in parts” can be modeled on an open number line or as a series of expressions.