Identify Hidden Features of Patterns

Students analyze generated number patterns to discover features not stated in the rule, such as noticing that all terms are odd, every other term is even, the sequence always grows by the same amount, or the units digits cycle. They explain why these features occur based on the rule.

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Grade 4 · Patterns and Rules · question 1 of 3

0 of 20

20 rungs. A star at the top.

3, 5, 7, 9 are all odd. Which of these lists is all odd too?

5, 7, 9, 11

4, 6, 8, 10

6, 8, 10, 12

3, 6, 9, 12

How it is taught

0:00 of 3:53

A hidden feature is true of the terms but not written in the rule.

Check several terms before you name the feature.

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.

The rule is add 4, starting at 7: 7, 11, 15, 19. What do you notice? — All odd. 7 is odd, and adding 4, an even number, keeps every number odd.

Rule: Start at 3, add 4

Today we'll be pattern detectives. We'll find hidden features — things the rule never told us.

Here's our rule: start at three, then add four each time.

Our first term is three.

Add four: three plus four is seven.

Add four again: seven plus four is eleven.

Keep going: eleven plus four is fifteen.

And one more: fifteen plus four is nineteen.

Now let's look at our pattern: three, seven, eleven, fifteen, nineteen. What do you notice?

Every single term is odd! The rule never said that — it's a hidden feature.

Why? We started with three, an odd number. Adding four — an even number — keeps it odd every time.

Here's another hidden feature: the ones digits make a pattern of their own — three, seven, one, five, nine.

Great detective work! A rule can hide lots of features. Always look closer.

Grade 4 · Spotting features the rule didn't tell us

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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