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Generate Number Patterns from a Given Rule

Students apply a given mathematical rule (e.g., 'add 6 starting from 0' or 'multiply by 3 starting from 2') to generate a sequence of numbers. They practice applying the rule repeatedly and recording the sequence correctly.

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Generate Number Patterns from a Given Rule

Grade 4 · Patterns and Rules · question 1 of 3

0 of 20

20 rungs. A star at the top.

Eli lines up backpacks in piles on the school bus. The smallest pile has 1 backpack. Each bigger pile has 2 more backpacks than the pile before it. How many backpacks are in pile 7?

How it is taught

0:00 of 3:47

A rule tells you how to get the next term.

The starting value is term number 1.

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.

  1. Read the rule off 2 numbers side by side: 9 − 4 = 5, so the rule is add 5.
  2. Use the rule to find a missing number: 19 + 5 = 24.
  3. 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.

3, 7, 11, ___ — 15. Each number is 4 more than the one before, so 11 + 4 = 15.

Rule: start at 0, add 6

Today we'll build a number pattern by following a rule.

Here's our rule: start at zero, then add six each time.

First, write down the starting number — zero.

Now follow the rule. Zero plus six is six.

Add six again. Six plus six is twelve.

Keep going. Twelve plus six is eighteen.

Eighteen plus six is twenty-four.

One more time. Twenty-four plus six is thirty.

Build a number pattern!Follow the rule, one step at a time.RULEStart at 0, then add 60+66+612+618+624+630Every term is a multiple of 6 — all even numbers.PATTERN0, 6, 12,18, 24, 30rule: start at 0, add 6
Grade 4 · Following a rule to build a number pattern

Look closely — every number we made is a multiple of six, and they're all even!

Our pattern is zero, six, twelve, eighteen, twenty-four, thirty. Awesome pattern building!

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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