Next students need to expand their understanding of numbers to addition and subtraction facts to 20. For most of the Chinese teachers interviewed by Ma this was a critical area. Now students begin to tackle two digit numbers. Students should have increased experience with number families so that they can see that 17 +3 =20, 3+17 = 20 and also that 20-17 = 3 and 20 -- 3 = 17. The most important examples are the ones that cross 10: 7+8=15, 8+7=15, 7=15-8, and 8=15-7. Students should see that 8+7=8+ (2+5) = (8+2) +5=10+5=15.The Chinese teachers viewed working with the number to 20 as critical. If students didnn’t understand doing subtraction numbers within 20 how could they tackle higher numbers? In their view early exploration with lower numbers would form the basis of expanding students’ abilities in a way that would guarantee success. 6
Here we might use two-sided counters. Each child would be given a different amount under 20 and they would be asked to toss their counters on their desks and record the number of each color. They would continue this trying to find as many combinations as possible. Students would then be asked to discuss what they learned. The class would also prepare a chart showing the different possible combination for each number of coins.
Many of my students have also benefited from using a number line on which they plot the composing and decomposing of numbers under twenty.