Grade by Grade
C. Algebra · Patterns, Variables, Coding and Modelling

Creating and Translating Patterns with Shapes and Numbers

C1.2About 35 minutes
Learning goals
  • I can create my own repeating, growing and shrinking patterns.
  • I can translate a shape pattern into a number pattern.
  • I can translate a number pattern into a shape pattern.
  • I can explain why two patterns that look different follow the same rule.

Words to know

create
To make something new, like your own pattern.
translate
To show the same pattern in a different way, like changing shapes into numbers.
representation
One way to show a pattern: with shapes, numbers, letters, actions or a table.
pattern structure
The way a pattern is built, like AB, ABB, or grows by 2.

Remember from Grade 1

You learned to translate repeating patterns. Clap, snap, clap, snap can become 1, 2, 1, 2 or A B A B. The things change, but the rule stays the same.

This year you will translate growing and shrinking patterns too, and go back and forth between shapes and numbers.

Translating a repeating pattern

Here is a shape pattern:

🟥 🔵 🔵 🟥 🔵 🔵 🟥 🔵 🔵

Give each shape a number. Square is 1, circle is 2:

1 2 2 1 2 2 1 2 2

With letters, it is an ABB pattern. All three show the same pattern structure.

ShapesNumbersLetters1A2B2B1A2B2B1A2B2Bcore = square, circle, circle → 1 2 2 → A B B
The same pattern three ways. Each square becomes 1 or A, and each circle becomes 2 or B. The dashed lines split the cores.
ShapesNumbersLettersActions
🟥 🔵 🔵1 2 2A B Bjump, clap, clap
🔺 🔺 🟩5 5 0A A Bstomp, stomp, spin
⭐ 🌙 ☀️3 6 9A B Chop, touch toes, wave
Each row shows one core in four different ways. Any numbers can be used, as long as the same shape always gets the same number.

Translating a growing pattern

To translate a growing pattern made of shapes into numbers, count the shapes in each term.

Look at these L shapes made of squares.

Term 1Term 2Term 3Term 4
Term 1 has 3 squares. Term 2 has 5. Term 3 has 7. Term 4 has 9. Each new term adds 1 square going up and 1 square going across.
Term1234
Number of squares3579
The shape pattern translated into a number pattern: 3, 5, 7, 9. It grows by 2.
Worked example

From shapes to numbers

Translate this growing pattern into numbers. What is the rule?

🧱🧱 | 🧱🧱🧱🧱🧱 | 🧱🧱🧱🧱🧱🧱🧱🧱 | 🧱🧱🧱🧱🧱🧱🧱🧱🧱🧱🧱

  1. Count the bricks in term 1: 2.
  2. Count term 2: 5. Count term 3: 8. Count term 4: 11.
  3. Write the number pattern: 2, 5, 8, 11.
  4. Find the jump: 2 to 5 is 3. 5 to 8 is 3. 8 to 11 is 3.

The number pattern is 2, 5, 8, 11. The rule is start at 2 and add 3 each time.

Worked example

From numbers to shapes

Show the number pattern 10, 8, 6, 4 with shapes.

  1. The pattern is shrinking. It goes down by 2 each time.
  2. Term 1: draw 10 circles: ⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪
  3. Term 2: draw 8 circles: ⚪⚪⚪⚪⚪⚪⚪⚪
  4. Term 3: draw 6 circles: ⚪⚪⚪⚪⚪⚪
  5. Term 4: draw 4 circles: ⚪⚪⚪⚪
  6. Check: each term has 2 fewer circles than the one before.

A shrinking pattern of circles: 10, 8, 6, 4. You could also use blocks, coins or tally marks.

Creating your own pattern

To create a pattern, first choose a rule. Then build it.

  • Repeating: choose a core, like big square, small square, triangle. Repeat it at least 3 times.
  • Growing: choose a start and a jump, like start at 1, add 4. Build 1, 5, 9, 13.
  • Shrinking: choose a start and a jump, like start at 20, take away 5. Build 20, 15, 10, 5.
Worked example

Make a pattern and translate it

Aiyana makes a repeating pattern with buttons: big, big, small, big, big, small. Translate it into numbers and letters.

  1. Find the core: big, big, small.
  2. Choose numbers: big = 7, small = 3. The numbers are 7 7 3 7 7 3.
  3. Choose letters: big = A, small = B. The letters are A A B A A B.
  4. Check: the same thing always gets the same number or letter.

7 7 3 7 7 3 and AAB AAB. All three show the same AAB structure.

Check your translation

Line up the two patterns, one under the other. Each part of the first pattern should match one part of the second. For a growing pattern, check that the jump is the same in both.

Just for fun

What if your day was a pattern: snack, snack, nap, snack, snack, nap? That's an AAB pattern… and a very good afternoon! 😴

Your turn

1

Translate into numbers (🟡 = 1, 🟣 = 2): 🟡 🟣 🟣 🟡 🟣 🟣

2

Translate into letters: 🐻 🐻 🐟 🐻 🐻 🐟

3

Translate into numbers: ⭐ | ⭐⭐⭐ | ⭐⭐⭐⭐⭐ | ⭐⭐⭐⭐⭐⭐⭐

4

Draw the number pattern 4, 5, 6, 7 with squares. How many squares are in term 3?

5

Create a repeating pattern with an ABC structure using shapes.

6

Do 1 2 1 2 1 2 and 🍎 🍌 🍎 🍌 🍎 🍌 have the same structure?

Hands-on activity

Pattern translator

You need: about 30 small things (Lego, buttons, coins, cereal or pasta), paper and a pencil.

  1. A grown-up builds a repeating pattern with the objects. You translate it into numbers on paper, then into actions.
  2. Switch! You build one, and the grown-up translates it.
  3. Now build a growing pattern with towers of Lego or piles of pasta. Write the number of pieces under each term.
  4. Last: the grown-up says a number pattern like 2, 4, 6, 8. You build it with objects.

What to look for: the same object always gets the same number, and growing patterns have the same jump in both versions.

More practice: warm-up

1

Translate into letters: 1 1 2 1 1 2

2

What does translate a pattern mean?

3

Translate into numbers: 🟩 | 🟩🟩 | 🟩🟩🟩 | 🟩🟩🟩🟩

4

Translate into shapes (A = 🔺, B = 🟦): A B A B

5

Translate into numbers (clap = 5, stomp = 0): clap, clap, stomp, clap, clap, stomp

More practice: on your own

1

Translate into numbers and find the rule: 🔷🔷🔷🔷🔷🔷🔷🔷🔷 | 🔷🔷🔷🔷🔷🔷 | 🔷🔷🔷

2

Which number pattern matches 🔵 🔵 🟥 🔵 🔵 🟥?

  • A: 1 2 1 2 1 2
  • B: 4 4 9 4 4 9
  • C: 4 9 9 4 9 9
3

Show the number pattern 3, 6, 9, 12 with towers of cubes. How many cubes are in the 4th tower? What is the jump?

4

Create a growing pattern that starts at 5 and grows by 5. Write the first 4 terms.

5

Maya says hop, hop, spin, hop, hop, spin translates to 1 2 1 2 1 2. Is she right?

Challenge

1

The L-shape pattern has 3, 5, 7, 9 squares. If it keeps going, how many squares are in term 6? Explain.

2

Create a repeating pattern where two attributes change, then translate it into letters.

3

Leo's towers have 20, 16, 12, 8 blocks. Ana's towers have 4, 8, 12, 16 blocks. How are these patterns alike? How are they different?

Check your understanding

Quiz

1.

Which number pattern matches 🌲 🍁 🍁 🌲 🍁 🍁?

2.

Translate into numbers: 🟦🟦 | 🟦🟦🟦🟦 | 🟦🟦🟦🟦🟦🟦

3.

What does it mean to translate a pattern?

4.

Which pattern has the same structure as A B B A B B?

5.

Which shape pattern shows 7, 5, 3, 1?

6.

A pattern starts at 1 and grows by 4. What are the first 3 terms?

For parents and teachers

Translating a pattern helps children see the structure (the rule) underneath, separate from what it is made of. This year, children translate growing and shrinking patterns between shapes and numbers, not only repeating ones.

Common mistakes

  • Changing the structure while translating (ABB becomes AB). Line the two patterns up, one under the other.
  • Miscounting large terms. Encourage touching each object or grouping by 2s or 5s.
  • Making a "growing pattern" with uneven jumps (2, 5, 6, 10). Ask: What is your rule? Does every term follow it?

How to help

  • Use any small objects: coins, Lego, pasta, crayons.
  • Take turns: one person builds, the other translates.
  • Ask your child to explain their own pattern's rule before you guess it.