Kindergarten Program: Kindergarten
Skills available for Ontario kindergarten math objectives
Strand
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Numbers
15 demonstrate an understanding of numbers, using concrete materials to explore and investigate counting, quantity, and number relationships
15.1 investigate (e.g., using a number line, a hundreds carpet, a board game with numbered squares) the idea that a number's position in the counting sequence determines its magnitude (e.g., the quantity is greater when counting forward and less when counting backward)
Numbers on a number line
Hundreds chart
Complete the number sequence
Count forward and backward: up to 10
Count forward and backward: up to 20
Count one more or less - up to 5
Count one more or less - up to 10
Count up and down - up to 10
15.1 investigate (e.g., using a number line, a hundreds carpet, a board game with numbered squares) the idea that a number's position in the counting sequence determines its magnitude (e.g., the quantity is greater when counting forward and less when counting backward)
Numbers on a number line
Hundreds chart
Complete the number sequence
Count forward and backward: up to 10
Count forward and backward: up to 20
Count one more or less - up to 5
Count one more or less - up to 10
Count up and down - up to 10
15.2 investigate some concepts of quantity and equality through identifying and comparing sets with more, fewer, or the same number of objects (e.g., find out which of two cups contains more or fewer beans [i.e., the concept of one-to-one correspondence]; investigate the ideas of more, less, or the same, using concrete materials such as counters or five and ten frames; recognize that the last number counted represents the number of objects in the set [i.e., the concept of cardinality])
Compare numbers
Compare sets
15.2 investigate some concepts of quantity and equality through identifying and comparing sets with more, fewer, or the same number of objects (e.g., find out which of two cups contains more or fewer beans [i.e., the concept of one-to-one correspondence]; investigate the ideas of more, less, or the same, using concrete materials such as counters or five and ten frames; recognize that the last number counted represents the number of objects in the set [i.e., the concept of cardinality])
Compare numbers
Compare sets
15.3 make use of one-to-one correspondence in counting objects and matching groups of objects
Count up to 3
Count up to 5
Count up to 10
15.3 make use of one-to-one correspondence in counting objects and matching groups of objects
Count up to 3
Count up to 5
Count up to 10
15.4 demonstrate an understanding of the counting concepts of stable order (i.e., the concept that the counting sequence is always the same – 1 is followed by 2, 2 by 3, and so on) and of order irrelevance (i.e., the concept that the number of objects in a set will be the same regardless of which object is used to begin the counting)
Count up to 3
Count up to 5
Count up to 10
Order numbers up to 30
15.4 demonstrate an understanding of the counting concepts of stable order (i.e., the concept that the counting sequence is always the same – 1 is followed by 2, 2 by 3, and so on) and of order irrelevance (i.e., the concept that the number of objects in a set will be the same regardless of which object is used to begin the counting)
Count up to 3
Count up to 5
Count up to 10
Order numbers up to 30
15.5 subitize quantities to 5 without having to count, using a variety of materials (e.g., dominoes, dot plates, dice, number of fingers) and strategies (e.g., composing or decomposing numbers)
15.5 subitize quantities to 5 without having to count, using a variety of materials (e.g., dominoes, dot plates, dice, number of fingers) and strategies (e.g., composing or decomposing numbers)
15.6 use information to estimate the number in a small set (e.g., apply knowledge of quantity; use a common reference such as a five frame; subitize)
15.6 use information to estimate the number in a small set (e.g., apply knowledge of quantity; use a common reference such as a five frame; subitize)
15.7 explore and communicate the function/purpose of numbers in a variety of contexts (e.g., use magnetic and sandpaper numerals to represent the number of objects in a set [to indicate quantity]; line up toys and manipulatives, and identify the first, second, and so on [to indicate ordinality]; use footsteps to discover the distance between the door and the sink [to measure]; identify a favourite sports player: "My favourite player is number twenty-four"[to label or name])
15.7 explore and communicate the function/purpose of numbers in a variety of contexts (e.g., use magnetic and sandpaper numerals to represent the number of objects in a set [to indicate quantity]; line up toys and manipulatives, and identify the first, second, and so on [to indicate ordinality]; use footsteps to discover the distance between the door and the sink [to measure]; identify a favourite sports player: "My favourite player is number twenty-four"[to label or name])
15.8 explore different Canadian coins, using coin manipulatives (e.g., role-play the purchasing of items at the store in the dramatic play area; determine which coin will purchase more – a loonie or a quarter)
Identify coin values
Count money
Equivalent amounts
15.8 explore different Canadian coins, using coin manipulatives (e.g., role-play the purchasing of items at the store in the dramatic play area; determine which coin will purchase more – a loonie or a quarter)
Identify coin values
Count money
Equivalent amounts
15.9 compose and decompose quantities to 10 (e.g., make multiple representations of numbers using two or more colours of linking cubes, blocks, dot strips, and other manipulatives; play "shake and spill" games)
15.9 compose and decompose quantities to 10 (e.g., make multiple representations of numbers using two or more colours of linking cubes, blocks, dot strips, and other manipulatives; play "shake and spill" games)
15.10 investigate addition and subtraction in everyday experiences and routines through the use of modelling strategies and manipulatives (e.g., join two sets of objects, one containing a greater number than the other, and count all the objects; separate out the smaller number of objects and determine how many remain) and counting strategies (e.g., use a counting sequence to determine how many objects there are altogether; count backward from the largest number to determine how many objects remain)
Add with pictures
Addition sentences
Addition
Addition word problems
Subtract with pictures
Subtraction sentences
Subtraction
Subtraction word problems
Sum and difference
Skip-count by twos
Skip-count by fives
Skip-count by tens
Skip-counting mixed review
15.10 investigate addition and subtraction in everyday experiences and routines through the use of modelling strategies and manipulatives (e.g., join two sets of objects, one containing a greater number than the other, and count all the objects; separate out the smaller number of objects and determine how many remain) and counting strategies (e.g., use a counting sequence to determine how many objects there are altogether; count backward from the largest number to determine how many objects remain)
Add with pictures
Addition sentences
Addition
Addition word problems
Subtract with pictures
Subtraction sentences
Subtraction
Subtraction word problems
Sum and difference
Skip-count by twos
Skip-count by fives
Skip-count by tens
Skip-counting mixed review
Measurements
16 measure, using non-standard units of the same size, and compare objects, materials, and spaces in terms of their length, mass, capacity, area, and temperature, and explore ways of measuring the passage of time, through inquiry and play-based learning
16.1 select an attribute to measure (e.g., capacity), determine an appropriate non-standard unit of measure (e.g., a small margarine container), and measure and compare two or more objects (e.g., determine which of two other containers holds the most water)
Length and width
Weight
Capacity
16.1 select an attribute to measure (e.g., capacity), determine an appropriate non-standard unit of measure (e.g., a small margarine container), and measure and compare two or more objects (e.g., determine which of two other containers holds the most water)
Length and width
Weight
Capacity
16.2 investigate strategies and materials used when measuring with non-standard units of measure (e.g., why feet used to measure length must be placed end to end with no gaps and not overlapping, and must all be the same size; why scoops used to measure water must be the same size and be filled to the top)
16.2 investigate strategies and materials used when measuring with non-standard units of measure (e.g., why feet used to measure length must be placed end to end with no gaps and not overlapping, and must all be the same size; why scoops used to measure water must be the same size and be filled to the top)
Shapes and Spatial Relationships
17 describe, sort, classify, build, and compare two-dimensional shapes and three-dimensional figures, and describe the location and movement of objects through investigation
17.1 explore, sort, and compare the attributes (e.g., reflective symmetry) and the properties (e.g., number of faces) of traditional and non-traditional two-dimensional shapes and three-dimensional figures (e.g., when sorting and comparing a variety of triangles: notice similarities in number of sides, differences in side lengths, sizes of angles, sizes of the triangles themselves; see smaller triangles in a larger triangle)
Two-dimensional shapes
Attributes of two-dimensional shapes
Compare two-dimensional shapes
Three-dimensional figures
Two-dimensional and three-dimensional shapes
Shapes in the real world
Symmetry
17.1 explore, sort, and compare the attributes (e.g., reflective symmetry) and the properties (e.g., number of faces) of traditional and non-traditional two-dimensional shapes and three-dimensional figures (e.g., when sorting and comparing a variety of triangles: notice similarities in number of sides, differences in side lengths, sizes of angles, sizes of the triangles themselves; see smaller triangles in a larger triangle)
Two-dimensional shapes
Attributes of two-dimensional shapes
Compare two-dimensional shapes
Three-dimensional figures
Two-dimensional and three-dimensional shapes
Shapes in the real world
Symmetry
17.2 communicate an understanding of basic spatial relationships (e.g., use terms such as "above/below", "in/out", "forward/backward"; use visualization, perspective, and movements [flips/reflections, slides/translations, and turns/rotations]) in their conversations and play, in their predictions and visualizations, and during transitions and routines
Inside or outside
Above or below
Beside or next to
Left, middle or right
Top, middle or bottom
Determine location
In front of or behind
17.2 communicate an understanding of basic spatial relationships (e.g., use terms such as "above/below", "in/out", "forward/backward"; use visualization, perspective, and movements [flips/reflections, slides/translations, and turns/rotations]) in their conversations and play, in their predictions and visualizations, and during transitions and routines
Inside or outside
Above or below
Beside or next to
Left, middle or right
Top, middle or bottom
Determine location
In front of or behind
17.3 investigate and explain the relationship between two-dimensional shapes and three-dimensional figures in objects they have made (e.g., explain that the flat surface of a cube is a square)
17.3 investigate and explain the relationship between two-dimensional shapes and three-dimensional figures in objects they have made (e.g., explain that the flat surface of a cube is a square)
Patterns
18 recognize, explore, describe, and compare patterns, and extend, translate, and create them, using the core of a pattern and predicting what comes next
18.1 identify and describe informally the repeating nature of patterns in everyday contexts (e.g., patterns in nature such as morning-noon-night, the four seasons, or the arrangement of leaves on the stem of a plant; the pattern on a piece of clothing; the pattern made by floor tiles; the pattern of words in a book or poem; the pattern on a calendar or in a schedule; the pattern of the beat or rhythm in songs), using appropriate terminology (e.g., "goes before", "goes after", "repeats") and gestures (e.g., pointing, nodding, using slap/claps)
18.1 identify and describe informally the repeating nature of patterns in everyday contexts (e.g., patterns in nature such as morning-noon-night, the four seasons, or the arrangement of leaves on the stem of a plant; the pattern on a piece of clothing; the pattern made by floor tiles; the pattern of words in a book or poem; the pattern on a calendar or in a schedule; the pattern of the beat or rhythm in songs), using appropriate terminology (e.g., "goes before", "goes after", "repeats") and gestures (e.g., pointing, nodding, using slap/claps)
18.2 explore and extend patterns (e.g., fill in missing elements of a repeating pattern) using a variety of materials (e.g., beads, shapes, words in a poem, beat and rhythm in music, objects from the natural world)
Copy the pattern
Complete the pattern
18.2 explore and extend patterns (e.g., fill in missing elements of a repeating pattern) using a variety of materials (e.g., beads, shapes, words in a poem, beat and rhythm in music, objects from the natural world)
Copy the pattern
Complete the pattern
18.3 identify the smallest unit (the core) of a pattern (e.g., ABBABBABB – the core is ABB) and describe why it is important (e.g., it helps us to know what comes next; it helps us make generalizations)
18.3 identify the smallest unit (the core) of a pattern (e.g., ABBABBABB – the core is ABB) and describe why it is important (e.g., it helps us to know what comes next; it helps us make generalizations)
18.4 create and translate patterns (e.g., re-represent "red-blue-blue, red-blue-blue, red-blue-blue" as "circle-square-square, circle-square-square, circle-square-square")
18.4 create and translate patterns (e.g., re-represent "red-blue-blue, red-blue-blue, red-blue-blue" as "circle-square-square, circle-square-square, circle-square-square")
Data Analysis and Probability
19 collect, organize, display, and interpret data to solve problems and to communicate information, and explore the concept of probability in everyday contexts
19.1 ask questions that can be answered through data collection (e.g., "What is your favourite …?"; "How many pets do our classmates have?"; "Which month had the most snowy days – January or February?"), collect data, and make representations of their observations, using graphs (e.g., concrete graphs such as people graphs or graphs using representational objects; picture graphs)
19.1 ask questions that can be answered through data collection (e.g., "What is your favourite …?"; "How many pets do our classmates have?"; "Which month had the most snowy days – January or February?"), collect data, and make representations of their observations, using graphs (e.g., concrete graphs such as people graphs or graphs using representational objects; picture graphs)
19.2 interpret data presented in graphs (e.g., "There are more children in the pizza line than in the hot dog line – that means more children like pizza"; "The blue bar is twice as long as the yellow bar"; "There were twice as many snowy days in January as snowy days in February") and draw conclusions (e.g., "We need to order more pizza than hot dogs for play day"; "January was more snowy than February")
19.2 interpret data presented in graphs (e.g., "There are more children in the pizza line than in the hot dog line – that means more children like pizza"; "The blue bar is twice as long as the yellow bar"; "There were twice as many snowy days in January as snowy days in February") and draw conclusions (e.g., "We need to order more pizza than hot dogs for play day"; "January was more snowy than February")
19.3 respond to and pose questions about data collection and graphs
19.3 respond to and pose questions about data collection and graphs
Mathematical Processes
20 apply the mathematical processes to support the development of mathematical thinking, to demonstrate understanding, and to communicate thinking and learning in mathematics, while engaged in play-based learning and in other contexts*
20.1 demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation (e.g., show small quantities using fingers or manipulatives)
20.1 demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation (e.g., show small quantities using fingers or manipulatives)
20.2 use, read, and represent whole numbers to 10 in a variety of meaningful contexts (e.g., use a hundreds chart to read whole numbers; use magnetic and sandpaper numerals to represent the number of objects in a set; put the house number on a house built in the blocks area; find and recognize numbers in the environment; write numerals on imaginary bills at the restaurant in the dramatic play area)
20.2 use, read, and represent whole numbers to 10 in a variety of meaningful contexts (e.g., use a hundreds chart to read whole numbers; use magnetic and sandpaper numerals to represent the number of objects in a set; put the house number on a house built in the blocks area; find and recognize numbers in the environment; write numerals on imaginary bills at the restaurant in the dramatic play area)
20.3 compose pictures, designs, shapes, and patterns, using two-dimensional shapes; predict and explore reflective symmetry in two-dimensional shapes (e.g., visualize and predict what will happen when a square, a circle, or a rectangle is folded in half); and decompose two-dimensional shapes into smaller shapes and rearrange the pieces into other shapes, using various tools and materials (e.g., stickers, geoboards, pattern blocks, geometric puzzles, tangrams, a computer program)
Symmetry
Compose shapes
20.3 compose pictures, designs, shapes, and patterns, using two-dimensional shapes; predict and explore reflective symmetry in two-dimensional shapes (e.g., visualize and predict what will happen when a square, a circle, or a rectangle is folded in half); and decompose two-dimensional shapes into smaller shapes and rearrange the pieces into other shapes, using various tools and materials (e.g., stickers, geoboards, pattern blocks, geometric puzzles, tangrams, a computer program)
Symmetry
Compose shapes
20.4 build three-dimensional structures using a variety of materials and identify the three-dimensional figures their structure contains
20.4 build three-dimensional structures using a variety of materials and identify the three-dimensional figures their structure contains
20.5 investigate and describe how objects can be collected, grouped, and organized according to similarities and differences (e.g., attributes like size, colour)
Same or different
Classify and sort
Venn diagrams
20.5 investigate and describe how objects can be collected, grouped, and organized according to similarities and differences (e.g., attributes like size, colour)
Same or different
Classify and sort
Venn diagrams
20.6 use mathematical language (e.g., "always/sometimes/never"; "likely/unlikely") in informal discussions to describe probability in familiar, everyday situations (e.g., "Sometimes Kindergarten children like pizza more than hot dogs"; "It is likely that January will be a snowy month")
20.6 use mathematical language (e.g., "always/sometimes/never"; "likely/unlikely") in informal discussions to describe probability in familiar, everyday situations (e.g., "Sometimes Kindergarten children like pizza more than hot dogs"; "It is likely that January will be a snowy month")