” Grade 1 is the starting point of mathematics journey and plays an integral role in helping children to understand and befriend basic math concepts such as numbers. The beginning of this long journey lasting over a decade should be firmly established in this grade. Besides, mathematics also encourages children to develop their problem-solving skills and critical abilities.”

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Overall and Specific Expectations

The overall expectations are divided in five main categories each of which contains several subcategories. Every subcategory lists specific expectations for grade 1 in more detail.

Elementry

## 1. Number

### Number Sense:

Students will demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life. They will

### Operations:

Students will use knowledge of numbers and operations to solve mathematical problems encountered in everyday life. They will

## 2. Algebra

### Patterns and Relationships:

Students will identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts. They will

### Equations and Inequalities:

Students will demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts. They will

### Coding:

Students will solve problems and create computational representations of mathematical situations using coding concepts and skills. They will

### Mathematical Modelling:

Students will apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.

## 3. Data

### Data Literacy:

Students will manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life. They will

### Probability:

Students will describe the likelihood that events will happen and use that information to make predictions. They will

## 4. Spatial Sense

### Geometric and Spatial Reasoning:

Students will describe and represent shape, location, and movement by applying geometric properties and spatial relationships to navigate the world around them. They will

### Measurement:

Students will compare, estimate, and determine measurements in various contexts. They will

## 5. Financial Literacy

### Money and Finances:

Students will demonstrate an understanding of the value of Canadian currency. They will

## Evaluation

Objective evaluation is believed to be one of the most essential parts of teaching mathematics. In Genius Math, we use different tools and methods to evaluate the mathematical knowledge of students and their progress. Our evaluation process consists of three stages: before teaching sessions, during teaching sessions and after teaching sessions.

### 1. Initial Assessment Test

Before starting our teaching sessions, we administrate an assessment test to obtain some insights on the strengths and weaknesses of students and their previous math knowledge. This key information helps us to come up with a special plan for every single student.

### 2. Standard Problems

During teaching sessions, we use a combination of different resources providing standard problems that are designed by famous mathematicians all over the world to improve the problem-solving skills of students. Among those resources are Math Kangaroo Contests, CEMC (University of Waterloo), AMC (American Mathematics Competitions), and even IMO (International Mathematics Olympiad), the latter might be considered for those who want to tackle more challenging problems or prepare for math olympiads. We use these problems to design homework, quizzes, and tests for our students based on their grades, needs and goals. As a matter of fact, such problems can be used to unveil the depth of students’ mathematical understanding.

### 3. Final Assessment Test

When teaching sessions are over, students are asked to take another assessment test aiming to show their real progress in mathematics.

### Most Common Challenging Topics

The followings are among the most common challenges students face in grade 1:

1. Mixed operations
2. Patterns
3. Data analysis
4. Symmetry
5. Measurement
6. Graphs

### What We Can Offer

Students have different goals and expectations according to their background, knowledge, or experience. This data along with the result of assessment session help us to design a unique plan for each student. There are different kinds of helps that we offer students in Genius Math:

1. To review and practice their class notes and handouts
2. To be helped with their homework, quizzes, and tests
3. To improve their math skills in general
4. To level up (e.g., moving from B- to B+)
5. To get A+
6. To learn topics beyond curriculum
7. To prepare for math competitions Mixed operation, measurements, and data and graphs are the most challenging topics in first grade.

## Counting and number patterns Any number you can use for counting. Number patterns is a list of numbers that follow a certain sequence or pattern.
Counting review – up to 10
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Count to fill a ten frame
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Counting review – up to 20
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Counting tens and ones – up to 20
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Count on ten frames – up to 40
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Skip-counting by twos
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Skip-counting by fives
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Skip-counting by tens
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Skip-counting by twos and fives
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Skip-counting by twos, fives and tens
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Counting – up to 100
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Counting tens and ones – up to 99
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Counting by twos, fives and tens
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Counting forward – up to 100
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Counting backward – up to 100
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Number lines
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Counting on the hundred chart
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Hundred chart
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Even or odd
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Identify numbers as even or odd
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Even or odd numbers on number lines
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Which even or odd number comes before or after?
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Skip-counting patterns – with tables
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Sequences – count up and down by 1, 2, 3, 5 and 10
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Ordinal numbers
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Writing numbers in words – convert words to digits
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Writing numbers in words – convert digits to words
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Roman numerals I, V, X In the primary grades, students develop an understanding of part-whole concepts – they learn that two or more parts can be combined to create a whole (addition).
Addition facts – sums up to 10
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Ways to make a number – addition sentences
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Make a number using addition – sums up to 10
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Complete the addition sentence – sums up to 10
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Addition word problems with pictures – sums up to 10
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Addition word problems – sums up to 10
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Addition sentences for word problems – sums up to 10
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Addition facts – sums up to 20
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Addition sentences using number lines – sums up to 20
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Addition word problems – sums up to 20
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Make a number using addition – sums up to 20
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Addition sentences for word problems – sums up to 20
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Use models to add a two-digit and a one-digit number – without regrouping
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Add a one-digit number to a two-digit number – without regrouping
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Use models to add a two-digit and a one-digit number – with regrouping
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Add a one-digit number to a two-digit number – with regrouping

## Subtraction In the primary grades, students develop an understanding of part-whole concepts – they learn that two or more parts can be separated from a whole (Subtraction).
Subtraction facts – numbers up to 10
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Ways to make a number – subtraction sentences
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Ways to subtract from a number – subtraction sentences
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Make a number using subtraction – numbers up to 10
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Complete the subtraction sentence
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Subtraction word problems with pictures – numbers up to 10
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Subtraction word problems – numbers up to 10
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Subtraction sentences for word problems – numbers up to 10
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Subtraction facts – numbers up to 18
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Subtraction sentences using number lines – numbers up to 18
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Subtraction word problems – numbers up to 18
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Subtraction sentences for word problems – numbers up to 18
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Make a number using subtraction – numbers up to 20
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Related subtraction facts
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Subtraction sentences: true or false?
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Subtract a one-digit number from a two-digit number

## Mixed operations Mixing different basic operations to solve questions and teaching the order of operations which tells us the order to solve steps in expressions with more than one operation.
Addition and subtraction – ways to make a number
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Which sign makes the number sentence true?
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Fact families
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Addition and subtraction facts – numbers up to 10
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Addition and subtraction facts – numbers up to 18
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Add and subtract numbers up to 40
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Addition and subtraction word problems – numbers up to 20
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Addition and subtraction word problems – numbers up to 40
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Ten more or less
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## Comparing Comparing numbers and understanding the concepts of greater than, less than, or equal to.
Comparing – review
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Comparing numbers up to 20
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Comparing numbers up to 100
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Comparison word problems

## Estimation Estimation is a math strategy used to guess a number or quantity. Understanding estimation helps to simplify numbers, making them easier to understand or work with.
Estimate to the nearest ten

## Fractions Fractions help us to understand how many equal parts of a whole we have
Equal parts
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Halves and fourths
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Halves, thirds and fourths
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Make halves and fourths
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Make halves, thirds and fourths
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Make halves and fourths in different ways
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Simple fractions: what fraction does the shape show?

## Two-dimensional shapes Two-dimensional geometry or plane geometry is about flat shapes like triangles and circles. Two-dimensional figures have only two dimensions such as width and height but no thickness. It also known as “2D”.
Name the two-dimensional shape
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Select two-dimensional shapes
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Rhombuses
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Count sides and vertices
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Compare sides and vertices
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Square corners
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Equal sides
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Congruent shapes
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Open and closed shapes
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Flip, turn and slide
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Symmetry
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Compose two-dimensional shapes

## Three-dimensional shapes Having three dimensions such as Height, Width and Depth, like any real-world object is a three-dimensional figure. Three-dimensional geometry is about solid shapes like spheres or cubes. It is also known as “3D”.
Two-dimensional and three-dimensional shapes
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Name the three-dimensional shape
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Cubes and rectangular prisms
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Select three-dimensional shapes
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Count vertices, edges and faces
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Compare vertices, edges and faces
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Identify shapes traced from solids
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Identify faces of three-dimensional shapes
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Shapes of everyday objects I
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Shapes of everyday objects II

## Spatial sense Expressing directions from different locations and understanding and classifying position of things. Spatial sense is an important part in geometry to visualize and the different position of one object to the other in relation to left and right, top and bottom, beside and far from each other.
Above and below
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Beside and next to
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Left, middle and right
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Top, middle and bottom
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Location in a grid

## Data and graphs A collection of facts, such as numbers, measurements or observations is called data. We can create a table with the data. A diagram of values, usually shown as lines is called graph.
Which picture graph is correct?
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Interpret picture graphs
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Which tally chart is correct?
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Interpret tally charts
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Which table is correct?
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Interpret data in tables
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Interpret bar graphs
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Which bar graph is correct?

## Measurement A number that shows the size or amount of something. Measurement is a fundamental component in comparing all physical quantities. There are two main systems of measurement: Metric and US standard.
Long and short
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Tall and short
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Light and heavy
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Holds more or less
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Compare size, weight and capacity
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Measure using objects
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Measure length with cubes
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Measure height with cubes
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Measure using a centimetre ruler
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Which metric unit of length is appropriate?
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Metric units of length: word problems
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Which metric unit of mass is appropriate?

## Geometric measurement Geometric measurement is studying the properties of shapes by measuring them, like finding the Area or Perimeter of a shape.
Tile a rectangle with squares
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Area
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Select figures with a given area
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Create figures with a given area

## Money Teaching students about how to add and subtract money values and understanding the prices and rounding them up. It is an important practice for real life problems like understanding the prices and how money relates to real world.
Coin values
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Count nickels and dimes
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Count groups of coins
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Equivalent groups of coins
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Exchanging coins
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Compare money amounts
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Purchases: do you have enough money?

## Patterns A pattern is a series or sequence that repeats. Mathematics patterns are sequences that repeat according to a rule or rules. Numbers can have interesting patterns.
Colour patterns
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Size patterns
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Shape patterns
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Find the next shape in a pattern
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Complete a pattern
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Make a pattern
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Growing patterns
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Find the next shape in a growing pattern
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Find the next row in a growing pattern

## Probability and statistics Probability is a branch of mathematics which describes randomness of events happening around us. The more likely an event to happen, the higher its probability would be.
More, less and equally likely
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Certain, probable, unlikely and impossible

## Sorting, ordering, and classifying To arrange or group in a special way like by size or type or alphabetically.
Sort shapes into a Venn diagram
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Count shapes in a Venn diagram
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Put numbers in order – up to 20
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Put numbers in order – up to 100

## Time Time is the ongoing sequence of events taking place. The past, present and future. We can measure time using clocks. Time has different units like second, minutes, hours, days and so on.
Match analogue clocks and times
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Match digital clocks and times
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Match analogue and digital clocks
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A.M. or P.M.
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Times of everyday events
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Compare clocks
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Time and clocks: word problems
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Seasons of the year
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Days of the week
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Months of the year
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