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Math · Grade 3 Math

Chapter 7: Shapes and Problem Solving

Patterns and Explaining Them

Spotting a pattern is half. Saying why is the other half.

Lesson
4
Time
About 13 minutes
0 of 7 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

The tables are full of patterns. Every one of them has a reason.

An example

Adding two odd numbers always gives an even answer. Each odd number has one left over, and the two leftovers pair up.

Patterns let you predict

Once you know why, you can say what comes next without working it out.

But check it

A pattern that holds for three examples might fail on the fourth. The reason is what makes it safe.

Describe the rule, not just the next term

Given 4, 8, 12, 16, saying "20 comes next" is only half the work. The rule is "add 4 each time", or "these are the multiples of 4". A rule lets you find the hundredth term; a next-number guess does not.

Explaining why the pattern happens

The multiples of 4 are all even because 4 is even, so every multiple is a number of even groups. That is an explanation, not just an observation. Being able to say why is what separates spotting a pattern from understanding one.

Test your rule before trusting it

Once you think you have the rule, test it on a term you have not used yet. Patterns can look convincing from three examples and then fail on the fourth. Checking against a value you did not build the rule from is the only honest test.

Step 2: Try It Yourself

Tap and try it out.

Tap a square. Every square with the same total lights up.
Addition chart. Rows are the first number, columns are the second, and each cell is their total.
+012345
0
1
2
3
4
5

Tap any square to see its number sentence.

Step the rows up by one and watch the product grow by the row size.

4 × 6 = 24

4 rows of 6 makes 24.

Step 3: Watch an Example

One step at a time.

Watch Leo Explain a Growing Pattern

Leo notices each answer in the 6 times table is 6 more than the last.

  1. Step 1

    He checks a few: 6, 12, 18, 24. Each is 6 more.

Step 4: Your Turn

Practice makes it stick.

The Next One

Problem 1 of 2

The 7 times table goes 7, 14, 21, 28. What comes next?

Odd and Odd

Problem 2 of 2

Is 7 + 9 odd or even?

Find and Explain

1 of 3

The 8 times table goes 8, 16, 24. What comes next?

2 of 3

Is 6 + 8 odd or even?

3 of 3

Is 5 + 8 odd or even?

Step 5: Quick Check

Show what you know.

Question 1 of 2

The 9 times table goes 9, 18, 27. What comes next?

Question 2 of 2

Why is spotting a pattern not enough?

What You Learned

  • Every pattern in the tables has a reason.
  • Knowing the reason lets you predict safely.
  • A pattern without a reason might fail on the next case.