Simple Patterns

1Summary 重點摘要

Find the repeating part, then continue.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Find the repeating partA pattern is a small part of shapes repeating again and again; to find it, read the shapes and find where the repeat starts, which is the first step of every pattern problem. Example: in ● ○ ● ○ ● ○, the repeating part is ● ○, black then white. Once you find the repeating part, you hold the whole pattern. Take care that the start of the repeating part must be right; reading from the middle of the design shifts the beat, and the rule twists with it, so always read from the very first shape.
2. Step 2: Carry on the patternAfter finding the repeating part, follow it shape by shape to draw what comes next. Example: after ● ○ ● ○, the repeating part says the next shape is ● and the one after is ○. Saying the rule softly while drawing, black, white, black, white, helps you keep the beat. The usual error is not returning to the head of the repeating part, so ● ● follows ● ○ and breaks the rhythm; after drawing, read the whole row from the start to check.
3. Step 3: Patterns in groups of threeThe repeating part need not be two shapes; it can be three or even longer, and the method is the same: find one full stretch first. Example: in △ △ ○ △ △ ○, the repeating part is the three shapes △ △ ○. Read them in groups of three, and the repeated beat sounds very clear. Take care that the order inside a group never moves; △ △ ○ and △ ○ △ are two different patterns. Start counting from the first shape and split the row three at a time.
4. Step 4: Number pattern plus 1Numbers make patterns too; the way is to see how much two neighbouring numbers differ, and so find what is added each time. Example: in 2, 3, 4, 5, each number is 1 more than the one before; it is a plus-1 pattern, so the next number is 5 + 1 = 6. After finding the rule, check one more pair of neighbours to be sure the rule is right. The usual error is deciding from the first two numbers alone; if the third does not fit, the rule is wrong, and every neighbouring pair must be compared again.
5. Step 5: Number pattern plus 2Some patterns add something other than 1 each time, so careful comparison is needed. Example: in 1, 3, 5, 7, 1 plus 2 is 3, 3 plus 2 is 5, and 5 plus 2 is 7; adding 2 each time, the next number is 7 + 2 = 9. These are the odd numbers we have learned, appearing every other number. Take care that the step must be identical all the way for the pattern to hold; if one step differs, start observing again instead of forcing the old idea onto the numbers.
6. Step 6: Number pattern minus 1Patterns can also shrink; first decide whether they grow or shrink, then find how much each step changes. Example: in 10, 9, 8, each number is 1 less than the one before; it is a minus-1 pattern, so the next number is 8 - 1 = 7. The usual mistake is treating a shrinking pattern as a growing one and writing 9 straight after 8; asking first whether the numbers got bigger or smaller builds a habit of judgement that avoids most errors.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Find the repeating part, then continue.
• Circle the repeating group in shape patterns.
• In number patterns, check the gap between neighbours.
• +2 means two more each time.
• Shrinking patterns get smaller each step.