Grade by Grade
C. Algebra · Patterns, Equality and Coding

Number Patterns to 50

C1.4About 35 minutes
Learning goals
  • I can find patterns on a 50 chart.
  • I can make number patterns by counting by 1s, 2s, 5s and 10s.
  • I can describe how numbers in a pattern are related, like "each number is 10 more".
  • I can use a pattern to find all the ways to make a number.

Words to know

50 chart
A chart that shows the numbers 1 to 50 in rows of 10.
skip count
To count by jumping over numbers, like 2, 4, 6 or 5, 10, 15.
ones digit
The digit on the right of a number. In 37, the ones digit is 7.
tens digit
The digit on the left of a two-digit number. In 37, the tens digit is 3.
relationship
How two things are connected, like "this number is 1 more than that one".

Numbers love patterns!

Numbers follow patterns too. When you count 1, 2, 3, 4, 5, each number is 1 more than the number before. That is a pattern!

Today you will find number patterns all the way up to 50.

12345678910
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
The 50 chart: the numbers 1 to 50 in 5 rows of 10.

Patterns on the 50 chart

Going across a row (→): each number is 1 more. 21, 22, 23, 24...

Going down a column (↓): each number is 10 more. 4, 14, 24, 34, 44.

The last column: 10, 20, 30, 40, 50. These are the numbers we say when we count by 10s!

Worked example

Look down a column

Look at the column that starts with 7: 7, 17, 27, 37, 47. What pattern do you see?

  1. Look at the ones digit (the right digit) of each number: 7, 7, 7, 7, 7. It stays the same.
  2. Look at the tens digit (the left digit): 7 has no tens (0), then 1, 2, 3, 4. It goes up by 1 each time.
  3. Going down one row adds one ten, so each number is 10 more than the one above it.

The ones digit is always 7. The tens digit goes up by 1. Each number is 10 more than the one before.

Skip counting patterns

Skip counting makes number patterns.

Count byPatternRule
2s2, 4, 6, 8, 10, 12, 14, 16, 18, 20Start at 2. Add 2 each time.
5s5, 10, 15, 20, 25, 30, 35, 40, 45, 50Start at 5. Add 5 each time.
10s10, 20, 30, 40, 50Start at 10. Add 10 each time.
Skip counting patterns to 50

Look at the ones digit

When you count by 5s, the ones digit goes 5, 0, 5, 0, 5, 0. That is an AB repeating pattern hiding inside a growing pattern!

When you count by 2s from 2, the ones digit goes 2, 4, 6, 8, 0 and then starts again.

05101520253035404550+5+5+5+5+5
Counting by 5s on a number line. Every jump is the same size: +5.
Each full ten frame has 10 hockey sticks. 1 frame is 10, 2 frames are 20, 3 frames are 30. Each new frame adds 10.

Patterns that show how numbers are made

Here is a cool pattern. Let's find all the ways to make 6 using two numbers.

First numberSecond numberTotal
066
156
246
336
426
516
606
Ways to make 6. The first number goes up by 1. The second number goes down by 1. The total stays 6.
Worked example

Use the pattern to make 10

Use a pattern to find all the ways to make 10 with two numbers.

  1. Start with 0 + 10.
  2. Make the first number 1 more and the second number 1 less: 1 + 9.
  3. Keep going: 2 + 8, 3 + 7, 4 + 6, 5 + 5, 6 + 4, 7 + 3, 8 + 2, 9 + 1, 10 + 0.
  4. Stop when the first number is 10. The pattern helps you not miss any!

0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5, 6 + 4, 7 + 3, 8 + 2, 9 + 1, 10 + 0. That is 11 ways.

Worked example

Make your own number pattern

Ava starts at 3 and adds 10 each time. Write her pattern up to 50.

  1. Start: 3.
  2. 3 + 10 = 13.
  3. 13 + 10 = 23.
  4. 23 + 10 = 33.
  5. 33 + 10 = 43. The next one would be 53, which is more than 50, so stop.

3, 13, 23, 33, 43. The ones digit stays 3 and the tens digit goes up by 1.

Your turn

1

Continue: 30, 32, 34, ___, ___

2

Continue: 15, 20, 25, ___, ___

3

Continue: 9, 19, 29, ___, ___

4

Count back: 50, 45, 40, ___, ___

5

On the 50 chart, what number is right below 26?

6

What is the rule? 41, 42, 43, 44, 45

7

Finish the pattern for making 5: 0 + 5, 1 + 4, 2 + 3, ___, ___, ___

8

Liam says the ones digit of every number when you count by 10s from 10 is 0. Is he right?

Just for fun

Why was 6 afraid of 7?

Because 7, 8, 9! (Say it out loud: seven ate nine.)

Hands-on activity

Colour the 50 chart

You need: paper, a pencil and two crayons (or small coins or cereal pieces to cover numbers).

  1. Write or print a 50 chart (5 rows of 10).
  2. Count by 5s. Colour every number you say with one crayon (5, 10, 15 ... 50).
  3. What shape does the colouring make? (Two straight columns going down!)
  4. With the other crayon, put a dot on every number when you count by 2s.
  5. Which numbers have both colours? (10, 20, 30, 40, 50.) Why do you think that is?

Bonus: Play "stairs": hop on a step for every number when counting by 2s to 20. How many hops? (10)

More practice: warm-up

1

Continue: 11, 12, 13, ___, ___

2

Count by 10s. What comes next? 10, 20, 30, ___

3

On the 50 chart, what number comes right after 39?

4

Count the socks by 2s: 🧦🧦 🧦🧦 🧦🧦 🧦🧦

5

True or false? When you count by 5s from 5, you say the number 12.

More practice: on your own

1

Continue: 6, 16, 26, ___, ___

2

What is the rule? 20, 22, 24, 26

3

On the 50 chart, what number is right above 33?

4

Each hand has 5 fingers. Count the fingers by 5s: ✋ ✋ ✋ ✋ ✋ ✋

5

Finish the pattern for making 7: 0 + 7, 1 + 6, 2 + 5, ___, ___, ___, ___, ___

Challenge

1

Find the mistake! Zoe counts by 10s from 20: 20, 30, 40, 41. What went wrong? Fix it.

2

Mo starts at 8 and adds 10 each time. Write his pattern up to 50. What stays the same?

3

Use a pattern to find all the ways to make 8 with two numbers. How many ways are there?

Check your understanding

Quiz

1.

What number comes next? 25, 30, 35, ___

2.

On the 50 chart, the numbers 2, 12, 22, 32, 42 are in a column. What stays the same?

3.

Which pattern counts by 2s?

4.

What is missing? 0 + 4, 1 + 3, ___, 3 + 1, 4 + 0

5.

What number comes next? 18, 20, 22, ___

6.

On the 50 chart, what number is right below 17?

For parents and teachers

This lesson connects patterns with place value and addition facts. Noticing that the ones digit stays the same when you add 10 helps later with mental math.

Common mistakes

  • Saying 30, 31, 32 when counting by 10s from 20 (switching to counting by 1s). Use a 50 chart and point to each number in the column.
  • Confusing the tens digit and the ones digit. Use the words the left digit and the right digit, and show with bundles of 10 straws or ten frames.
  • Missing a pair when finding ways to make a number. Show how the "one goes up, one goes down" pattern keeps the list organized.

How to help

  • Count by 2s, 5s and 10s while walking, climbing stairs or putting away groceries.
  • Count shoes in pairs (2s), fingers on hands (5s) and loonies in stacks of 10.
  • Ask: What do you notice? What stays the same? What changes?