Counting 11 to 20

1Summary 重點摘要

Teens are ten plus ones, e.g. 11 is ten plus one.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Ten ones make a tenCount the sticks one by one; when you reach 10, wrap them with a band into one bundle, and that bundle is 1 ten, the starting point of understanding bigger numbers. Why tie them? Once 10 ones are seen as one whole, counting big numbers becomes far faster. Example: a full bundle of 10 sticks stays tied; later, whenever you see one bundle, you know it means 10 without opening and counting again. Take care that a bundle holds exactly 10 sticks, no more and no fewer, or every number after will come out wrong.
2. Step 2: Ten and one make elevenOne ten plus one more one makes 11, the first two-digit number we meet. Example: 1 bundle stands for 10, and 1 loose stick beside it gives 10 + 1 = 11, read as eleven. The 1 in the tens place means 1 ten, and the 1 in the ones place means 1 one; the two 1s mean different things. The usual mistake is thinking both 1s are equal; in fact the left 1 is ten times the right 1, and position decides a digit's value, which is the very idea of place value.
3. Step 3: Ten plus some onesOne ten plus a few ones makes a teens number, the shared rule of every number from 11 to 19. Example: 10 + 3 = 13, 10 + 7 = 17, 10 + 9 = 19. The number of loose sticks is the ones digit, and the ones digit tells you the name of the number. With this rule, a full ten plus a few ones can be read at once. Take care that 10 + 10 is not a teens number, because it holds two tens and is already 20, whose name changes to twenty.
4. Step 4: Two tens make twentyTwo bundles of 10 sticks each make 2 tens, written 20. Example: 10 + 10 = 20, read as twenty. With two tens and no loose sticks, the ones place has nothing, so we write 0 there; 20 holds two tens, which is what makes it different from the teens numbers. The common error is writing 20 as 2 and dropping the ones 0; that 0 holds the place and shows there are no loose sticks, so it must be written, for without it 20 turns into a completely different number.
5. Step 5: Count on past 20Do not stop counting at 20; keep counting on, so that the order from 11 to 20 is truly mastered. Example: after 18 comes 19, after 19 comes 20, and we can go on to 21 and 22. When the order is firm in your mind, you can count on from any number, and your counting grows steady. The usual mistake is going from 19 straight to 21 and skipping 20; every number must follow in order with none left out, and counting back through the list once is a good check.
6. Step 6: From sticks to digitsTo write the number from sticks, count the bundles first and the loose sticks next; this is the way back from real things to written digits. Example: 1 bundle plus 4 loose sticks is 10 + 4 = 14, written as 14; the 1 is in the tens place for 1 ten, and the 4 is in the ones place for 4 ones. The tens and the ones together make the whole number. Take care of the order, bundles first; treating the loose sticks as tens writes a completely different number, for 4 bundles and 1 loose stick is 41, not 14.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Ten ones bundle into one ten.
• Teens = one ten + some ones.
• Twenty = two tens.
• After 19 comes 20; keep the order.
• Write tens first, then ones.