Math is more than just numbers. It includes sorting things into categories such as ‘big’, ‘bigger’ and ‘biggest’; solving problems using patterns; understanding quantity and applying spatial thinking. Working memory and a good command of language are key.

This page describes the typical math achievements for a child at different grade levels from kindergarten to Grade 5.

The "milestones" below are a general guide.

## Kindergarten

By the end of kindergarten, many children are able to:

### Number sense

- Sort and classify objects into sets according to specific attributes (e.g., size, colour, shape, quantity)
- Match objects using one-to-one correspondence
- Understand estimation terms such as ‘more’, ‘fewer’ or ‘the same’
- Understand location/position terms such as ‘inside’ and ‘outside’, ‘behind’ and ‘next to’, ‘top’, ‘middle’, and ‘bottom’
- Recognize and write the numbers 1 to 10

### Measurement

- Understand measurement terms such as ‘tall’/’short’; ‘big’/’small’ ‘long’/’narrow’, ‘light’/’heavy’, and ‘more’/’less’
- Arrange two or more objects according to size

### Spatial sense and geometry

- Understand and use spatial terms such as ‘in’/’out’, ‘bottom’/’top’, and ‘above’/’below’
- Identify and sort two-dimensional shapes (e.g., circle, square, triangle, rectangle)

### Patterning

- Arrange sequences based on changing colours, sizes, or shapes

### Data management and probability

- Compare objects using two features such as ‘rough’/’smooth’ or ‘big’/’small’
- Understand and use probability terms such as ‘more likely’ or ‘less likely’ based on personal experiences (e.g., chance of participating in a particular activity)
- Sequence numbers in order

## Grade 1

By the end of Grade 1, many children are able to:

### Number sense and numeration

- Read and print numbers from 0 to 100
- Read and print number words from 0 to 10
- Count by ones, twos, fives and 10s up to 100 (e.g., skip count)
- Count backward from 10
- Add and subtract to and from 20 using real-life objects

### Measurement

- Record measurements using real-life objects to gain a relative understanding of dimensions
- Sequence events in order (e.g., first, second, third)
- Read digital clocks
- Understand coin values and compare money amounts (e.g., a nickel is worth less than a dime)

### Geometry and spatial sense

- Name two-dimensional shapes such as oval, hexagon, octagon, etc.
- Move objects in relation to others based on terms such as ‘over’, ‘under’, ‘to the left’, etc.

### Patterning and algebra

- Make and extend patterns using objects, diagrams, and actions
- Recognize similarities and differences in various patterns

### Data management and probability

- Sort shapes into a Venn Diagram
- Place objects on grids, graphs and pictographs
- Understand that an event may or may not occur
- Use terms to describe the chance of something happening such as ‘certain’, ‘probable’, ‘unlikely’ and ‘impossible’ in everyday life

## Grade 2

By the end of Grade 2, many children are able to:

### Number sense and numeration

- Compare and order whole numbers to 1000 or beyond
- Understand pie charts of fractions such as halves, quarters, and thirds
- Understand and count money equivalents up to $5.00 and above
- Determine if they have enough money to buy something (e.g., “ A ball costs two dollars and 25 cents. Do you have enough money to buy it?“)
- Add and subtract using two- and three-digit numbers, using a variety of strategies (e.g., carrying and regrouping)
- Know the multiplication tables up to 5 or above

### Measurement

- Understand and choose different methods for measuring (e.g., “Which is better to measure the length of a pencil: millimetres or litres?”; “What would you used to find out how many days it is until school holiday: a thermometer, a measuring cup, a tape measure, a calendar?”)
- Read analog clocks and time using words such as ‘o’clock’,’ half-past’, and ‘quarter to’, and understand the difference between a.m. and p.m.
- Read a calendar and understand days of the week and months of the year

### Geometry and spatial sense

- Describe locations of objects
- Understand shape concepts and terms such as ‘flip’, ‘turn’, ‘rotate’, ‘congruent’
- Identify the shapes of everyday objects when drawn (e.g., balloon, flashlight, a bell)

### Data management and probability

- Create and interpret line graphs, bar graphs, line plots, pictographs
- Sort shapes in a Venn diagram
- Describe probability in everyday situations (i.e., is something certain, probable, unlikely or impossible)

## Grade 3

By the end of Grade 3, many children are able to:

### Number sense and numeration

- Compare and order whole numbers to 1000 and beyond
- Use everyday objects to understand fractions (such as dividing a pizza or pie into slices)
- Understand money amounts (e.g., 10 dimes in a dollar)
- Count forward and backward from various starting points
- Solve basic multiplication and division questions

### Measurement

- Estimate, measure and record length, perimeter, area, mass, volume, weight, time, and temperature using standard units (e.g., centimeters, meters, kilometers, grams, millilitres, litres, etc.)
- Convert units of measurement from one to another (e.g., years into months, months into days)

### Geometry and spatial sense

- Compare and sort shapes by their properties (e.g., length of sides; angles greater, less than or equal to a right angle)
- Describe the movements of shapes and objects (e.g., reflections, rotations, translations)

### Patterning and algebra

- Understand how addition and subtraction are inverse operations (e.g., 3+5= 8 and 8-3=5)

### Data management and probability

- Collect, display, and interpret data on charts or graphs using titles and labels
- Calculate mean and mode on charts
- Play probability games (e.g., rolling dice, playing Rock, Paper, Scissors, etc.)

## Grade 4

By the end of Grade 4, many children are able to:

### Number sense and numeration

- Compare and order numbers to 10,000 or above
- Add and subtract decimal numbers
- Compare decimals and fractions
- Solve multi-step word problems

### Measurement

- Compare and change measurement units when using length, mass and volume
- Calculate durations of time (e.g., the length of time that has passed between arriving home from school and dinner time)
- Understand the difference between 12-hour and 24-hour time zones
- Measure the area and perimeter of rectangles

### Geometry and spatial sense

- Identify and compare angles of complex shapes (e.g., parallelograms, trapezoids, rhombuses)
- Describe the location of an object using a grid map

### Patterning and algebra

- Write and solve expressions to represent word problems
- Understand the inverse relationship between pairs of expressions, using addition, subtraction and multiplication

### Data management and probability

- Create and interpret a variety of graphs and plots (e.g., line, bar, plot, stem and leaf graphs)
- Interpret charts to find the mean and the mode
- Make predictions using available information

## Grade 5

By the end of Grade 5, many children are able to:

### Number sense and numeration

- Understand place values (e.g., what number is in the tens, hundredths, or thousandths column)
- Compare numbers to 100,000 or higher
- Estimate sums in word problems
- Add, subtract, multiply and divide money amounts
- Add, subtract and multiply fractions

### Measurement

- Choose the appropriate measurement for everyday items (e.g., “Which is best to estimate for the weight of a truck: kilograms or grams?”)
- Estimate and measure perimeter, area, temperature change, and elapsed time

### Geometry and spatial sense

- Calculate the area of a rectangle, as well as the volume of a cube or rectangular prism
- Name various types of triangles and quadrilaterals
- Recognize that three-dimensional figures can be drawn from different view points

### Patterning and algebra

- Identify patterns to complete a number sequence (e.g., 1, 2, 4, 8, 16, 32…)
- Understand the idea that variables in an equation represent an unknown number (e.g., 4x-7=5; x=3)

### Data management and probability

- Calculate probability (e.g., Finding the probability of landing on heads when flipping a coin)
- Use fractions to demonstrate the probability of something happening

## General tips

- Praise your child for engaging in math activities.
- Encourage your child to ask for help when they need it.
- Include math activities in daily life.

For more information on how to support your child at home, see Mathematics: How to help your child.

### What if I have questions about my child’s math development?

Early math skills provide the foundation for later math development. Practising math in a variety of contexts, both at school and at home, can support your child’s learning. Without mastering early skills, learning more advanced math can be difficult for your child. If you think your child may be falling behind in math, please speak to their teacher.