## C1. Patterns and Relationships

### Specific Expectations

#### Patterns

C1.1

identify and describe the regularities in a variety of patterns, including patterns found in real-life contexts

**regularities:**- repeating patterns: the core repeats
- growing patterns: the pattern grows in a predictable way
- shrinking patterns: the pattern shrinks in a predictable way

**patterns found in real-life contexts:**- the arts: dance, music
- nature: flowers, honeycombs
- clothing: fabrics, uniforms, regalia
- addresses: pattern of going up by twos or fours
- calendar structures: weeks, 13 moons
- daily routines: get up, have breakfast, get dressed, comb your hair, brush your teeth, and so on
- cultural practices and the culture of daily life: religious holidays and practices; statutory holidays; the way we do certain things, like taking the school bus (walk to the bus stop, wait at the bus stop, wait for the bus to stop and the doors to open, enter the bus and find a seat, …)
- physical activity schedules according to the seasons, such as hockey or skating in the winter, track and field in the summer
- seasons: spring, summer, fall, winter, repeat

**patterns found in words:**- stories
- poems
- rap, spoken word
- song lyrics

**patterns found in numbers:**- counting sequence going up by one each time
- hundreds chart:

- Human activities, histories, and the natural world are made up of all kinds of patterns, and many of them are based on the regularity of an attribute.
- The regularity of attributes may include colour, shape, texture, thickness, orientation, or materials.

*Note*

- Students can engage in mathematics and patterns through the contexts, cultural histories, and stories of various cultures.
- Patterns do not need to be classified as repeating or otherwise in Grade 1. Instead, focus on the attributes that are being used in patterns.

Start a pattern wall. Have students add to it throughout the year as they collect pictures, make diagrams, or use words to describe the patterns that they find in real life, including patterns that are personally relevant.

Provide pairs of students with a picture of a pattern, and ask them to describe what makes it a pattern. Ask students to find another pair that has the same kind of pattern and describe what is the same. Then, have each pair find another pair that has a different kind of pattern and describe what is different.

Consider having students start a “learning log”, which could travel with them throughout the grades. One section of the log could be about patterns. They could revisit this learning log and keep adding to it as they learn about different kinds of patterns.

Invite community partners, such as First Nation, Métis, or Inuit beadworkers, sewers, weavers, and fashion designers, to share patterns. Some examples may include beading, henna or mehndi, kolam, and hair braiding or weaving. This provides an opportunity to discuss the historical and cultural context of the local community, and respectful representations of cultural histories and identities. (See the examples for this expectation).

C1.2

create and translate patterns using movements, sounds, objects, shapes, letters, and numbers

**patterns using:**- movements, such as:
- right 3, up 4, right 3, up 5, right 3, up 6, …

- sounds, such as:
- clap, clap, snap; clap, clap, snap; clap, clap, snap, …

- everyday objects, such as:

- movements, such as:

- shapes, such as:

- letters, such as:
- AAB, AAB, AAB, AAB, ...

- number sequences, such as:
- 2, 4, 6, 8, 10, …, 50
- 5, 10, 15, 20, 25, …, 50

**translating patterns:**- a sound pattern: clap, clap, snap, snap; clap, clap, snap, snap; clap, clap, snap, snap, …
- translated into a letter pattern:
- AABB, AABB, AABB, …

- translated into a number pattern:
- 2 [As], 2 [Bs]; 2 [As], 2 [Bs]; 2 [As], 2 [Bs], ...

- translated into a letter pattern:
- a movement pattern: jump, turn; jump, turn, turn; jump, turn, turn, turn, …
- translated into a number pattern:
- 1, 2; 1, 2, 2; 1, 2, 2, 2, …

- translated into a number pattern:
- a word pattern: dog, dog, cat; dog, dog, cat, cat; dog, dog, cat, cat, cat, …
- translated into a letter pattern:
- AAB, AABB, AABBB, …

- translated into a number pattern:
- 2 [dogs], 1 [cat]; 2 [dogs], 2 [cats]; 2 [dogs], 3 [cats], ...

- translated into a letter pattern:

- a sound pattern: clap, clap, snap, snap; clap, clap, snap, snap; clap, clap, snap, snap, …

- The same pattern structure can be represented in various ways.
- Patterns can be created by changing one or more attributes.

*Note*

- When patterns are translated, they are being re-represented using the same type of pattern structure (e.g., AB, AB, AB… to red-black, red-black, red-black).

Demonstrate a pattern using a series of claps and snaps. Ask students to represent this pattern using concrete materials, using letters, and using numbers. Discuss the connections between the representations.

Have students create three different patterns using three different representations (e.g., all letters, all numbers, all movements). Have them exchange their patterns with a partner, who then represents each pattern using a different representation.

Have students create patterns to show the relationships between the values of coins. For example, 1 dime has the same value as 2 nickels, 2 dimes have the same value as 4 nickels, 3 dimes have the same value as 6 nickels, and so on.

C1.3

determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in patterns

**extending patterns in both directions:**- What shape comes before 1 and after 10?

**making near and far predictions:**- What shape is in the 12th position? What shape is in the 14th position? What shape is in the 20th position?

**identifying missing elements in pictorial representations and numerical sequences of patterns:**- What shape is in the 6th position?

- Patterns can be extended because they are repetitive by nature.
- Pattern rules are generalizations about a pattern, and they can be described in words.
- Patterns can be extended in multiple directions, by showing what comes next or what came before.
- To make a near prediction about a pattern is to state or show what a pattern will look like just beyond the given representation of that pattern. The prediction can be verified by extending that pattern.
- To make a far prediction about a pattern is to state or show what a pattern will look like well beyond the given representation of that pattern. Often calculations are needed to make an informed prediction or to verify a prediction.
- To identify missing elements of patterns is to complete a representation for a given pattern by filling in the missing parts.

*Note*

- In order to extend, predict, or determine missing elements in patterns, students need to generalize patterns using pattern rules.
- Rules can be used to verify predictions and to critically analyse extensions and solutions for missing elements.

Provide students with patterns that they can extend in multiple directions. For example:

- Extend the pattern to the right, and show the next three shapes.
- Extend the pattern to the left, and show the three shapes that came before.

Provide students with opportunities to make near and far predictions and then justify those predictions. For example:

- Predict which shape will be in the 12th position in the pattern. Justify your prediction.
- Predict which shape will be in the 15th position in the pattern. Justify your prediction.
- Predict which shape will be in the 20th position in the pattern. Justify your prediction.

Provide students with patterns that have missing elements, and have them strategize to determine those missing elements. For example:

- 3, 5, ___, ___, 11, ___, …
- 4, ___, 8, ___, 12, ___, …
- Which shape is in the 6th position?

C1.4

create and describe patterns to illustrate relationships among whole numbers up to 50

**using a hundreds chart to show how skip counting by 2 makes a pattern:**

**creating a pattern to show the relationship between the place-value digits:**- when the tens place goes down by 1, the ones place goes up by 10:

37 = | 3 tens | + 7 ones |

37 = | 2 tens | + 17 ones |

37 = | 1 tens | + 27 ones |

37 = | 0 tens | + 37 ones |

**creating patterns to show the relationship between addition and subtraction facts:**

0 + 7 = 7 |
7 − 7 = 0 |

1 + 6 = 7 |
7 − 6 = 1 |

2 + 5 = 7 |
7 − 5 = 2 |

3 + 4 = 7 |
7 − 4 = 3 |

4 + 3 = 7 |
7 − 3 = 4 |

5 + 2 = 7 |
7 − 2 = 5 |

6 + 1 = 7 |
7 − 1 = 6 |

7 + 0 = 7 |
7 − 0 = 7 |

- There are patterns in numbers and the way that digits repeat from 0 to 9.

*Note*

- Creating and analysing patterns that involve decomposing numbers will support students in understanding how numbers are related.
- Creating and analysing patterns involving addition and subtraction facts can help students develop fluency with math facts, as well as understand how to maintain equality among expressions.

Ask students to pick a number less than 50 and rename it in as many ways as they can using a pattern of tens and ones:

37 = | 3 tens | + 7 ones |

37 = | 2 tens | + 17 ones |

37 = | 1 tens | + 27 ones |

37 = | 0 tens | + 37 ones |

Have students create an ordered list to write the addition and subtraction facts for any number up to 10. Ask them to identify any patterns they notice:

0 + 7 = 7 |
7 − 7 = 0 |

1 + 6 = 7 |
7 − 6 = 1 |

2 + 5 = 7 |
7 − 5 = 2 |

3 + 4 = 7 |
7 − 4 = 3 |

4 + 3 = 7 |
7 − 3 = 4 |

5 + 2 = 7 |
7 − 2 = 5 |

6 + 1 = 7 |
7 − 1 = 6 |

7 + 0 = 7 |
7 − 0 = 7 |