Then, to make it easier to find and compare numbers, pairs also filled in the first row and benchmark/landmark numbers (multiples of 5 and 10) on each chart.
Today we played an adaptation of a game we learned a few weeks ago, Changing Places on the 10,000 Chart. Students were given a start number, drew Change Cards (which told them to add or subtract a multiple of 10, 100, or 1000), then wrote equations to describe what happened as a result of the Change Cards. The students were able to write the numbers that resulted from the Change Cards on the class chart. Some students used the U.S. Standard Addition Algorithm, but many used what they have discovered about adding and subtracting multiples of 10, 100, and 1,000 to perform the operations mentally.
One way we can think about 10,000 is ten 1000s. Since there are ten 100s in each thousand, we can also think of 10,000 as one hundred 100s. Yesterday we wrote letters to third graders proving how many 10s are in 10,000! Since there are 10 tens in every hundred, there are 100 tens in one thousand. And since there are ten thousands in 10,000, there are one thousand 10s in 10,000.
This week, we've also started discussing some habits of successful problem-solvers called Mathematical Practices. Successful problem-solvers are able to reason abstractly, or think using numbers and mathematical symbols. We can answer the same questions using equations:
How many 100s are in 10,000?
100 x 100 = 10,000
How many 1,000s are in 10,000?
10 x 1,000 = 10,000
How many 10s are in 10,000?
10 x 10 = 100 (There are ten 10s in one hundred.)
10 x 100 = 1,000 (There are 100 tens in one thousand.)
10 x 1,000 = 10,000 (There are 1,000 tens in ten thousand.)
I'm so proud of our students' perseverance this week, which also happens to be another Mathematical Practice we introduced!
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