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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.

# Grade 1

## 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

### Whole numbers

- read and represent whole numbers up to and including 50 and describe various ways they are used in everyday life.
- compose and decompose whole numbers up to and including 50, using a variety of tools and strategies, in various contexts.
- compare and order whole numbers up to and including 50, in various contexts.
- estimatethe number of objects in collections of up to 50 and verify their estimates by counting.

### Fractions

- use drawingsto represent and solve fair-share problems that involve 2 and 4 sharers, respectively, and have remainders of 1 or 2.
- recognize that one half and two fourths of the same whole are equal, in fair-sharing contexts.
- use drawings to compare and order unit fractions representing the individual portions that result when a whole is shared by different numbers of sharers, up to a maximum of 10.

**Operations:**

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

### Properties and Relationships

use the properties of addition and subtraction, and the relationship between addition and subtraction, to solve problems and check calculations.

### Addition and Subtraction

- use objects, diagrams, and equationsto represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 50.

### Math Facts

- recall and demonstrate addition facts for numbers up to 10, and related subtraction facts.

### Multiplication and Division

- represent and solve equal-group problemswhere the total number of items is no more than 10, including problems in which each group is a half, using tools and drawings.

### Mental Math

- recall and demonstrate addition facts for numbers up to 10, and related subtraction facts.

## 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 ### Patterns

- identify and describe the regularities in a variety of patterns, including patterns found in real-life contexts.
- create and translate patterns using movements, sounds, objects, shapes, letters, and numbers.
- determine pattern rulesand use them to extend patterns, make and justify predictions, and identify missing elements in patterns.
- create and describe patterns to illustrate relationshipsamong whole numbers up to 50.

**Equations and Inequalities:**

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

- identify quantities that can change and quantities that always remain the same in real-life contexts.

###
Equalities

and Inequalities

- determine whether given pairs of addition and subtraction expressions are equivalent or not.
- identify and use equivalent relationships for whole numbers up to 50, in various contexts.

**Coding:**

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

- solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves sequential events.
- read and alter existing code, including code that involves sequential events, and describe how changes to the code affect the outcomes.

###
Equalities

and Inequalities

- determine whether given pairs of addition and subtraction expressions are equivalent or not.
- identify and use equivalent relationships for whole numbers up to 50, in various contexts.

**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 ### Data Collection and Organization

- sort sets of data about people or things according to one attribute, and describe rules used for sorting.
- collect data through observations, experiments, and interviews to answer questions of interestthat focus on a single piece of information; record the data using methods of their choice; and organize the data in tally tables.

### Data Visualization

- display sets of data, using one-to-one correspondence, in concrete graphs and pictographs with proper sources, titles, and labels.

### Data Analysis

- order categories of data from greatest to least frequency for various data sets displayed in tally tables, concrete graphs, and pictographs.
- analyse different sets of data presented in various ways, including in tally tables, concrete graphs, and pictographs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions.

**Probability:**

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

- use mathematical language, including the terms “impossible”, “possible”, and “certain”, to describe the likelihood of events happening, and use that likelihood to make predictions and informed decisions.
- make and test predictions about the likelihood that the categories in a data set from one population will have the same frequencies in data collected from a different population of the same size.

## 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 ### Geometric Reasoning

- sort three-dimensional objects and two-dimensional shapes according to one attribute at a time and identify the sorting rule being used.
- construct three-dimensional objects, and identify two-dimensional shapes contained within structures and objects.
- construct and describe two-dimensional shapes and three-dimensional objects that have matching halves.

### Location and Movement

- describe the relative locations of objects or people, using positional language.
- give and follow directions for moving from one location to another.

**Measurement:**

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

- identify measurable attributes of two-dimensional shapes and three-dimensional objects, including length, area, mass, capacity, and angle.
- compare several everyday objects and order them according to length, area, mass, and capacity.

### Time

- read the date on a calendar, and use a calendar to identify days, weeks, months, holidays, and seasons.

## 5. Financial Literacy

**Money and Finances:**

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

- identify the various Canadian coins up to 50¢ and coins and bills up to $50 and compare their values.

### Student assessment methods

## 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.

### Free Quiz

**Problem 1.** What is the missing number in the following subtraction?

· · · − 2 = 7

(a) 3

(b) 4

(c) 7

(d) 5

(e) 9

**Problem 2.** What is the fourth element of the following patterns:

CCD, CCCDD, CCCCDDD, …….

(a) CCCCDDDD

(b) CCCDDDD

(c) CCCCCDDDD

(d) CCCCCDDD

(e) CCCCCDDDDD

**Problem 3.** Consider numbers **18, 10, 3, 4, 9, 8**

Which option puts these numbers in the order from the least to greatest?

(a) 18, 10, 9, 8, 4, 3

(b) 9, 8, 4, 3, 18, 10

(c) 3, 4, 8, 9, 10, 18

(d) 3, 4, 8, 10, 9, 18

(e) 4, 3, 8, 9, 10, 18

### 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:

- Mixed operations
- Patterns
- Data analysis
- Symmetry
- Measurement
- 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:

- To review and practice their class notes and handouts
- To be helped with their homework, quizzes, and tests
- To improve their math skills in general
- To level up (e.g., moving from B- to B+)
- To get A+
- To learn topics beyond curriculum
- To prepare for math competitions

Mixed operation, measurements, and data and graphs are the most challenging topics in first grade.

## Counting and number patterns

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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

## Addition

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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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Related addition facts

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Addition sentences: true or false?

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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

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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

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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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Add and subtract tens

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Addition and subtraction terms

## Comparing

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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

## Fractions

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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

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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

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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

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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

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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

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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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Read a thermometer

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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

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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

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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

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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

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Certain, probable, unlikely and impossible

## Sorting, ordering, and classifying

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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

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Match digital clocks and times

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Match analogue and digital clocks

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Read clocks and write times

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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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Read a calendar