We have begun our unit on multiplication
We have begun our unit on multiplication.
Today's problem (Feb 20):
Activation: We tried out a multiplication trick you can do with your fingers. The students have been asked to teach the trick to parents as their homework.
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Then they were asked...
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They found many ways to represent 5 x 3:
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Today's problem:
48 batches of cookies can be baked at a time. Mr. Wendler made 6 batches of cookies. How many cookies does he have to share with the class?
Some students used repetitive addition to solve the problem:
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Some students doubled up batches and then added (more effecient):
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Some students rojunded off 48 to 50 (a friendlier number), did the repetitive addition, and then subtracted the extras. Very creative!
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Some students broke 48 into the expanded form (40 + 8) and then multiplied each part (the tens and the ones) by 6, and then added the two answers together:
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Some students used the traditional approach:
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Consolidation: We focused on the strategy that used repetitive addition. We looked at how and why it worked, and then named this strategy the "Stacking Strategy" because you stack all the numbers and add them:
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Today's Problem (Feb 26):
Activation: First the students were asked how these numbers were relevant to multiplication. This is what they came up with:
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The problem: The students were asked to pull out the important information...
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Some students used the stacking strategy:
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Some students used repetitive addition, but chunked together larger numbers (more efficient) by adding groups of 3 instead of 1 at a time:
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Some students rounded 29 to 30 (a friendly number) and added that 9 times. Then they subtracted 9 to get the answer:
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Some students put 29 into its expanded form, and then multiplied the 10's and the 1's by 9 (seperately):
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Some students multiplied 29 x 10 (instead of 9) because 10 is a very friendly number, and then they subtracted 29. Very simple and efficient:
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Some students used the traditional strategy:
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Consolidation: We focused our discussion on the strategy that broke up 29 into it's expanded form, and then did the multiplication. We talked about why this makes it easy to multiply (friendly numbers), and where errors might occur (the addition part). It was a good discussion:
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The students named this strategy the "Split Second" strategy because firts, the number is "split" into its expanded form, and second, you do the multiplication.
Today's Problem (Feb 27):
Activation: We reviewed some of the strategies (inlcuding the Split Second strategy from the last problem) the students have come up with to solve multiplication problems. We also made some connections between measurement of area and multiplication.
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The problem:
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Some students used the Stacking strategy to solve the problem:
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Some students used "doubling" in addition to the Stacking strategy:
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Some students rounded off the number first, then did the work, then adjusted the total at the end:
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Some students very creatively were able to use the connections we made with area, to solve the problem:
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Some students used the Split Second strategy (in this case splitting 168 into 50, 50 , 30, 30, 4 and 4:
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Some students used the Split Second strategy by breaking up the number into it's place values (expanded form):
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Consolidation: We focused our discussion on how students can use rounding off to help make the problem easier to solve. In this case, in order to round 168 to 170 you have to add 2. You have do that to all 7 groups of 168 (2x7) for a total of 14 added to the total. So at the end you just remove the 14 from the total to get the answer:
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The students called this strategy the Take Back strategy, but whatever numbers you give to round off, you have to take back at the end:
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Today's Question (Feb 28):
Activation: We focused on the idea of connecting area to multiplication that came up last class. The students were asked about arrays, and then asked to connect a multiplication question with some base 10 blocks:
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The problem:
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Some students used the Stacking strategy:
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Some students used the Splitting strategy:
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Some students focused on area:
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Some students used the traditional strategy:
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Some students used Napier's Bones!
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Consolidation: We focused on the group that used area to solve the problem. We had one group explain how they did it, and then we solved using the strategy in two different ways. The students named the strategy "Add in the Box".
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Today's problem (Mar 20):
Activation: We took up the homework (focusing on three different multiplication strategies). We had a brief discussion comparing (similarities and differences) the strategies.
The problem:
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Some students used the Stacking strategy:
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Some students used the Split Second strategy:
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Some students used the Add in the Box strategy:
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Some students used a traditional strategy:
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Consolidation: We had the students who used the traditional strategy explain how they solved the problem. They explained the pattern they followed (first they multiplied the bottom ones by the top ones, then they multiplied the bottom ones by the top tens). We then stretched those 2 steps out a little to better understand them and we called this the "Traditional Long" strategy. We then compared it to the Split Second strategy and the Box strategy and noticed that they are all VERY similar. The only mathematical difference the students found was that with the traditional strategy you focus on the ones (PVC) first and then the tens (PVC), but with the other two strategies you focus on the tens first, and then the ones.
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Good work.
Today's problem (Mar 22)
Activation: We reviewed the Traditional Long strategy:
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The problem:
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Some students used variations of the Stacking strategy:
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Some students used the Box strategy:
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Some students used the Traditional Long strategy:
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Some students used the Traditional (short) strategy:
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Consolidation: We looked at how the Traditional strategy is and the Traditional Long strategy are connected.
Today's Problems (Mar 26):
Napier's Bones:
Today we learned about Napier’s Bones. John Napier, a Scottish mathematician in the early 1600’s, invented a unique method of doing multiplication. It allows the students to multiply large digits, without using the “place value holders” needed when using the traditional strategy. Using a chart (similar to a multiplication chart), the first number is written at the top (one digit per column) and the second number is written on the right hand side (one digit per row). This allows each digit of one number to be multiplied by each digit of the second number (similar to the place value strategy). The answers are written in each box. This method automatically lines up the numbers on a diagonal in their correct place value column (ones, tens, hundreds, etc…). The answers in each box are then added up diagonally (remember to carry if necessary) and the answer is found at the bottom.
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Here it what it looks like:
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Today's problem (Mar 27):
Activation: We took up our homework
Then Mr. Wendler introduced a new multiplication strategy called STICKS. It looks like this:
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Here is a bit of an explanation:
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Today's problem:
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Some students used Napier's Bones:
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Some students used the Traditional Long strategy:
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Some students used the Traditional strategy:
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Some students used Sticks:
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Consolidation: The students were asked which strategy STiCKS reminded them of. Most students made a connection between STICKS and the ADD IN THE BOX (or Magic Squares) strategy.
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