Emergent Math in the Lumber Primes (K/1)

We arrived back on Monday to discover that the heavy wet snow that fell over November break damaged several of our tarp shelters. We were able to fix and re-hang a few of the smaller tarps, but the large tarp over our main meeting area has a large tear through one side and will need to be replaced. This setback provided not only a good opportunity for teachers to model flexibility and purposeful work, but also a chance to engage the children in a meaningful and authentic experience of using math to solve an important problem.

After morning meeting, teachers asked for volunteers to help measure the length of the space beneath our main tarp so that we would know how long the new tarp should be. Children grabbed the flexible measuring tapes from our tool tower and helped stretch them out across our meeting area. Each person in line then read the final number on their measuring tape while a teacher wrote the numbers down on the board. The first four children in line were able to unfurl their measuring tapes completely, and called out the number 60. The final person in line only had to unroll her measuring tape until it reached the number 27.

During lunch time we told the Lumber Primes community that we had a problem. The numbers on the board told us how long the new tarp needed to be in inches: 60 inches + 60 inches + 60 inches + 60 inches + 27 inches, but what we actually  needed to know was how many feet long the tarp should be. We explained that we know that 12 inches equals 1 foot, and asked the class what we should do next. One student suggested we just keep adding 12's together, so that's where we began.

This is a complicated problem, and what we wanted was for children to practice adding 10's and 1's, so we took it slow, and used visual representations of the number 12 for our addition problems.

First we used our 10's and 1's magnets to represent two 12's side by side and asked how many 10's there were all together (2) and how many 1's there were together (4). Then children identified that two 10's actually  means 20, and when you add 4 more you get 24. 

Next, we added a third group of 12, and the process was repeated. The children identified three 10's and six 1's, which means 30 plus six more. We repeated this process until there were five groups of 12 on the board. For this final step, the children identified five 10's, which means 50. Then, it was time to look at the 1's. After counting by 2's students erupted into excitement when they discovered that there was actually another hidden group of 10, and 50+10 equals exactly 60!

Teachers explained that since we counted five sets of 12, what we found out was that each full measuring tape (60 inches long) was actually 5 feet long. We counted by 5's for each of the full measuring tapes and ended up with 20 feet.

But there was still that pesky 27 inches left. Students remembered that 12 + 12 = 24 (and we double checked by counting 10's and 1's yet again). So that was two more feet, plus an extra 3 inches.

The next math problem to solve was 20 + 2, so we used the "counting on" strategy, starting with 20 and counting up two more, giving us 22 feet (plus that extra three inches).

The final problem of the day was: None of the tarps we can buy are exactly 22 feet and 3 inches long. If we buy one that is 30 feet, will that be long enough?

Many children said "yes" because 30 is bigger than 22. It's always important to double-check when you doing math, so we confirmed this fact by thinking about how many tens are in each number. The number 30 has three tens in it, while the number 22 only has two tens!