• • • • A year in a 5th grade Singapore-based math classroom. • • • • Follow two master teachers through a year of daily lessons in 5th grade. Corrinne is from Singapore, and Kathleen is from the US, with years of experience teaching in Germany. Together, they have created a hybrid approach using Singapore Math, European math, and the best practices from American constructivist teaching.

Question #1: Fractions. Everyone was able to solve this problem correctly! This is huge. Fractions matter.

Students are still learning to simplify their answers, but that will come with practice. They can see the equivalencies on their fraction templates.

Question #2: Multiplication. Almost everyone got these problems correct, too. The diamonds are mildly challenging, and involve multiplication practice for those who need it.

Question #3: Area Model. 85% got this correct. Some got blocks to check during the quiz. Our hope is that simple 2-digit problems can soon be done mentally. The top row of this drawing equals 280 (28×10), plus the 28 below it. 280 + 20 + 8 = 308.

Question #4 Multiply/Divide by 10, 100. About 2/3 got this correct at this point. A handful of students still haven’t processed the concept adequately. (See 3rd example, below). To remediate, struggling students absolutely need to use blocks to see what’s happening, and then record it. Nothing is as effective as what they can see, using blocks. They also need to talk about what’s happening as they exchange the blocks. For example, “1 times 100 means the one morphs from a single block into a 100-flat. Now it’s in the 100’s column. It moved 2 place values bigger.”

Question #5 Challenge. About half of the students got (a) and (b) correct at this point.

Only 5 students got (c) correct – it’s challenging. Long method: it would be possible to put 47 dots in the column on the right, then exchange them 5 at a time for one in the next column. Short method: Since each column is 5 times as large as the last, they are labeled 25, 5 and 1.