Generate Shape Patterns from a Given Rule

Students extend geometric or visual patterns by applying a stated rule, such as adding a specific number of shapes each step or rotating a shape. They draw or identify the next elements in the pattern.

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Grade 4 · Patterns and Rules · question 1 of 3

0 of 20

20 rungs. A star at the top.

Step 1: 6 · Step 2: 9 · Step 3: 12 · Step 4:

How it is taught

0:00 of 4:24

A shape pattern follows a rule from step to step.

A repeating core can be as simple as two shapes taking turns.

Read it: A rule makes a pattern

Start at 4 and add 5: 4, 9, 14, 19, 24. The same rule grows a tile pattern: 4 tiles, then 9, then 14. The rule only says add 5, but the numbers also go odd, even, odd, even.

Read the rule off 2 numbers side by side: 9 − 4 = 5, so the rule is add 5.
Use the rule to find a missing number: 19 + 5 = 24.
Step 6 is 5 adds after step 1: 5 adds of 5 is 25, and 4 + 25 = 29.

Every jump on the line is the same size, so any 2 numbers side by side show the rule.

Step 1 is the start, and each step after it adds 1 more group, so step 6 has 5 adds.

Adding 5, an odd number, turns each number over from odd to even and back. The rule never said that.

Find the add, use it again and again, and look for what the rule did not say.

Doubling to jump ahead, and saying step 6 is 2 × 14 = 28.

Step 6 is step 1's 4 and 5 adds of 5: 4 + 25 = 29. Only step 1 holds the 4.

A pattern has 11 tiles in step 1, and each step adds 8 tiles. How many tiles are in step 10? — 83. Step 10 is 9 adds after step 1: 9 × 8 = 72, and 11 + 72 = 83.

Rule: add 2 triangles each step

A shape pattern is a row of shapes that grows by a rule. Today we'll use the rule to figure out what comes next.

Here's our rule: each step adds two more triangles than the step before.

Step one starts with just this one triangle.

Grade 4 · Use a rule to draw the next step in a shape pattern

Step two has three triangles — that's two more than step one.

Step three has five triangles — two more again. The rule is working!

So what should step four look like? Let's use the rule.

Step three had five, so we add two more. One… two.

Now let's count the triangles in step four: one, two, three, four, five, six, seven.

Step four has seven triangles. When you know the rule, you can keep the pattern going forever!

Now you try. Count the corners of this shape. How many corners?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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