Patterns (II): ABAB & AABB

1Summary 重點摘要

ABAB: R,B,R,B. AABB: R,R,B,B.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Circle the repeating partTo find a pattern, first find the part that keeps repeating and circle it with a pencil. For example, in red blue red blue red blue, circle 'red blue'; that part appears again and again, which is an AB pattern. Circle from the beginning and check group by group to make sure every group is identical. Once the repeating part is found, the pattern is half solved. A common mistake is to take 'red blue red' as the repeating part; after that, every later step goes wrong. The way to check is to slide the circled part along the line once and see whether it fits everywhere; only then is the repeating part genuine.
2. Step 2: Continue an AB patternAfter finding the repeating part, fill in following its order. For example, the repeating part of △ ○ △ ○ △ is '△ ○'; after △ it is ○'s turn, so the next shape is ○. To fill further, return to the start of the part: after ○ comes △ again. After filling, read the line once more to check that it flows smoothly. A common mistake is to take the last three shapes as the repeating part, or to forget the cycle and put △ after △. Remember that a pattern plays like a loop: whenever you reach the end of the part, go back to its beginning and continue. Fill and read at the same time, and the chain will not break.
3. Step 3: AABB patternAn AABB pattern repeats in pairs of two: for example red red blue blue red red blue blue, with repeating part 'red red blue blue'. Circle the repeating part and you can see that after blue blue comes red red. Each shape appears twice in a row; this is the mark of AABB, and what separates it from ABAB is how many times each shape appears in a row. A common mistake is to circle 'red blue' as if it were an AB pattern. Before circling, count whether each shape appears once or twice in a row; only then circle, and the repeating part will not be misread.
4. Step 4: Missing in the middleWhen a gap hides in the middle of the shapes, circle the repeating parts before and after it, then work out what is missing. For example, in red blue __ blue red blue, circle 'red blue' from the start; the third position follows red blue, so by the order it should be red, and after filling, the rest reads blue red blue exactly. Read from the start after filling to be sure the pattern is not broken. A common mistake is to guess from only the one or two shapes next to the gap. A middle gap needs clues from both sides: the answer is right only when both sides agree; if just one side fits, check again.
5. Step 5: Number pattern +2Numbers have patterns too: 5, 7, 9, 11 - each number is 2 more than the one before it. This is an add-2 pattern, and the next number is 11 + 2 = 13. Find the gaps between neighbouring numbers first: 7 − 5 = 2, 9 − 7 = 2, 11 − 9 = 2; the equal differences show the rule is add 2. Once the rule is found, filling on becomes easy. A common mistake is to conclude from the first pair alone; in 5, 7, 10 the differences are not equal, so there is no add-2 rule after all. Check that at least two neighbouring pairs have the same difference before trusting a rule.
6. Step 6: Tens patternSome number patterns add 10 each time: 30, 40, 50 - the ones digit stays the same and the tens digit grows by 1, so the next number is 60. These jump-by-ten patterns are often used in counting and addition, so practise them well. When finding one, look at the ones digit for changes first, then at the tens: in 30, 40, 50 the ones are all 0, and the tens 3, 4, 5 grow by 1 each step. A common mistake is to slip a place while jumping by tens, going from 30 to 50, or to confuse adding 10 with adding 1 and write 31, 32. Count aloud a few times - thirty, forty, fifty, sixty - and the next term becomes obvious at a glance.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Circle the repeating part first.
• AB = taking turns one by one.
• AABB = going in pairs.
• Gaps follow the same repeating part.
• Number patterns: check the step size.