Mathematics
Kindergarten: Mathematics 
Planning: Term # Tracking: Ach. Level 

Overall Expectations 
1 
2 
3 
4 
A.
demonstrate an understanding of number, using concrete materials to explore and
investigate counting, quantity, and number relationships; 




B.
measure and compare length, mass, capacity, area, temperature of
objects/materials, and the passage of time, using nonstandard units, through
free exploration, focused exploration, and guided activity; 




C.
describe, sort, classify, and compare twodimensional shapes and
threedimensional figures, and describe the location and movement of objects
through investigation; 




D.
explore, recognize, describe, and create patterns, using a variety of
materials in different contexts; 




E.
sort, classify, and display a variety of concrete objects, collect data, begin
to read and describe displays of data, and begin to explore the concept of
probability in everyday contexts. 




Specific Expectations 




Number Sense and
Numeration (Quantity Relationships; Counting; Operational Sense) 




1.
investigate the idea that quantity is greater when counting forwards and less
when counting backwards (e.g., use manipulatives to create a quantity number
line; move along a number line; move around on a hundreds carpet; play simple
games on numberline game boards; build a structure using blocks, and
describe what happens as blocks are added or removed) [A] Student Talk:
Initially “This is getting bigger.” “Every time I add a block, my building
gets taller.” Eventually “We need three more blocks to finish the base.” 




2.
investigate some concepts of quantity 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, using counters; investigate the ideas of more,
less, and the same, using five and ten frames; compare two sets of objects
that have the same number of items, one set having the items spread out, and
recognize that both sets have the same quantity [concept of conservation];
recognize that the last count represents the actual number of objects in the
set [concept of cardinality]; compare five beans with five blocks, and
recognize that the number 5 represents the same quantity regardless of the
different materials [concept of abstraction]) [A] Student
Talk: “Let’s count the cars. I have six and you have five. That means I have
one more. Let’s get another one so we can have the same.” “You counted 35
buttons. I go even higher. I can count 40 buttons.” Sample
Problems: “Let’s find out how many marbles I can hold in my hand. How many do
you think? Let’s count and see. How many marbles can you hold in your hand?
Let’s count. Do you have more or less than me?” 




3.
recognize some quantities without having to count, using a variety of tools
(e.g., dominoes, dot plates, dice, number of fingers) or strategies (e.g.,
composing and decomposing numbers, subitizing) [A] Teacher
Prompts: “How did you know it was five? How did you figure out how many?”
Student Responses: “I know it’s five because it looks like the dice in my
game.” “It’s five. I saw four red and one blue.” 




4.
begin to use information to estimate the number in a small set (e.g., apply
knowledge of quantity, use a common referent such as a five frame) [A]
Student Talk: Initially “I think it will take three scoops to fill up the
pail. …It took six.” Eventually “I know that is not 100. A hundred is a lot
and this is only a little bit.” “I think there are more than five buttons
because they wouldn’t all fit on a five frame.” 




5.
use, read, and represent whole numbers to 10 in a variety of meaningful
contexts (e.g., use a hundreds chart; use magnetic and sandpaper numerals; put
the house number on a house built at the block centre; find and recognize
numbers in the environment; use magnetic numerals to represent the number of
objects in a set; write numerals on imaginary bills at the restaurant at the
dramatic play centre) [A] Student Talk: Initially “I’m five years old. ”
Eventually (pointing to numbers in a book and reading them aloud to a
classmate) “Five. There are five frogs on the log.” 




6.
use ordinal numbers in a variety of everyday contexts (e.g., line up toys and
manipulatives, and identify the first, second, and so on; after reading a
book, respond to the teacher’s questions about who was the first or third
person to come in the door; identify the first, seventh, or tenth person to
arrive at school or in the group) [A] 




7.
demonstrate an understanding of number relationships for numbers from 0 to
10, through investigation (e.g., initially: show smaller quantities using anchors
of five and ten, such as their fingers or manipulatives; eventually: show
quantities to 10, using such tools as five and ten frames and manipulatives)
[A] Student Talk: “I know there are seven counters because all of the ten
frame is full except for three spaces.” “I know there are seven counters
because all of the five frame is full and there are two left over.” Teacher
Prompts: “Show me 3 on a five frame.” “How do you know that it is 3?” “What
comes in 5’s [e.g., fingers, toes]?” 




8.
investigate and develop strategies for composing and decomposing quantities
to 10 (e.g., use manipulatives or “shake and spill” activities; initially: to
represent the quantity of 8, the child may first count from 1 through to 8
using his or her fingers; later, the child may put up one hand, count from 1
to 5 using each finger, pause, and then continue to count to 8 using three
more fingers; eventually: the child may put up all five fingers of one hand
at once and simply say “Five”, then count on, using three more fingers and
saying “Six, seven, eight. There are eight.”) [A] Student Talk: “I only have
three wheels for my car. I need one more to make four.” “There are five
people at the snow table but we only have three shovels. We need two more
shovels.” 




9.
explore different Canadian coins, using coin manipulatives (e.g., roleplay
the purchasing of items at the store at the dramatic play centre; determine
which coin will purchase more – a loonie or a quarter) [A] 




10.
demonstrate understanding of the counting concepts of stable order (that is,
the concept that the counting sequence is always the same – 1 is always
followed by 2, 2 by 3, and so on) and of order irrelevance (that is, the
concept that the number of objects in a set will be the same regardless of
which object is used to begin the counting) [A] 




11.
begin to make use of onetoone correspondence in counting objects and
matching groups of objects (e.g., one napkin for each of the people at the table)
[A] Sample Problems: “I am meeting with three children. I wonder how many
chairs I will need.” “Show me how you know you need six cages for your
lions.” Student Talk: “I counted five children. I need five pieces of apple,
one for each child.” 




12.
investigate addition and subtraction in everyday activities through the use
of manipulatives (e.g., interlocking cubes), visual models (e.g., a number
line, tally marks, a hundreds carpet), or oral exploration (e.g., dramatizing
of songs) [A] Sample Problems: “How can you use the five bear counters to
tell a story about them going to the woods?” “In our story, one more duck
went into the pond. How many ducks are in the pond now? How do you know?” 




Measurement
(Attributes, Units, and Measurement Sense; Measurement Relationships) 




13.
compare and order two or more objects according to an appropriate measure
(e.g., length, mass, area, temperature, capacity), and use measurement terms
(e.g., hot/cold for temperature, small/ medium/large for capacity, longer/
shorter or thicker/thinner for length) [B] Student Talk: “I lined the teddy
bears up from shortest to tallest.” “This book is heavier than 10 cubes.” “We
used 5 papers to cover the small table. It took us 15 papers to cover the big
table.” 




14.
demonstrate, through investigation, an awareness of the use of different
measurement tools for measuring different things (e.g., a balance is used for
measuring mass, a tape measure for measuring length, a sandglass for
measuring time) [B] 




15.
demonstrate awareness of nonstandard measuring devices (e.g., feet, hand
spans, string, or cubes to measure length; hand claps to measure time; scoops
of water or sand to measure capacity) and strategies for using them (e.g.,
place common objects end to end; use cubes to plan the length of a road at
the sand table or the block centre; measure the distance between the
classroom and the water fountain in number of footsteps) [B,A] 




16.
demonstrate, through investigation, a beginning understanding of the use of
nonstandard units of the same size (e.g., straws, paper clips) [B,A] Sample
Problems: “How many blocks make up the length of your foot?” “How many hand
spans will it take to measure the table?” “We need to see if the block
trolley will fit in this space. How could we measure it?” “Jason says the
train track is 6 building blocks long but Chris says the track is 10 building
blocks long. How can we find out how long the track is?” 




Geometry
and Spatial Sense (Geometric Properties; Geometric Relationships; Location
and Movement) 




17.
explore, sort, and compare traditional and nontraditional twodimensional
shapes and threedimensional figures (e.g., compare equilateral triangles
with triangles that are not equilateral; sort different sizes of boxes,
attribute blocks,5 pattern blocks, a variety of triangles, shapes with three
curved sides, objects that create an open shape with three lines) [C] Sample
Problems: “Look at the objects in the sorting circle. Can you guess the rule
I was using to sort them? What other objects could we put in the circle?”
“Use three strips of paper to show me a triangle. Use your strips to show me
something that is not a triangle.” Student Talk: “We sorted our shapes into
ones that are round and ones that have points.” “It is a weird, long triangle
but it has three sides. It looks like a triangle that is all stretched out.” 




18.
identify and describe, using common geometric terms, twodimensional shapes
(e.g., triangle) and threedimensional figures (e.g., cone) through
investigations with concrete materials [C,A] Student Talk: “It has three
straight sides. It’s like the yield sign at the block centre.” “It’s like an
ice cream cone. It has a point.” 




19.
compose pictures and build designs, shapes, and patterns in twodimensional
shapes, and decompose twodimensional shapes into smaller shapes, using
various tools or strategies (e.g., sand at the sand table, stickers,
geoboards, pattern blocks, a computer program) [C,A] Sample Problem: After
reading a story in which tangrams are used, the teacher asks the children to
make one of the tangram designs in the story by first placing tangram pieces
on a premade outline of the design, and then recreating the design by placing
the tangram pieces beside the outline. The teacher could also ask what other
shapes the children could make by using two magnetic shapes on a cookie
sheet. Student Talk: “My house has a pointed roof.” “My picture has lots of
the same shapes – these ones are all round.” “This house shape has a triangle
on the top and a square on the bottom.” “I used two triangles to make a
rhombus.” 




20.
build threedimensional structures using a variety of materials, and begin to
recognize the threedimensional figures that the structure contains [C] Student
Talk: “I built a castle. I put three cubes on the bottom. I used a cone for
the tower.” 




21.investigate
the relationship between twodimensional shapes and threedimensional figures
in objects that they have made [C,A] Student Talk: “I built a rocket ship.
Look at the cone on the top. The front is a big rectangle.” “I painted and
stamped each side of the cube I made. I have six squares.” 




22.
demonstrate an understanding of basic spatial relationships and movements (e.g.,
use above/below, near/far, in/out; use these words while retelling a story)
[C] Student Talk: “I am sitting beside my friend.” “I have moved this block
on top of the tower.” 




Patterning 




23.
identify, extend, reproduce, and create repeating patterns through
investigation, using a variety of materials (e.g., attribute materials,
pattern blocks, a hundreds chart, toys, bottle tops, buttons, toothpicks) and
actions (e.g., physical actions such as clapping, jumping, tapping) [D] 




24.
identify and describe informally the repeating nature of patterns in everyday
contexts (e.g., patterns in nature, clothing, floor tiles, literature,
schedules), using oral expressions (e.g., “goes before”, “goes after”,
“morning, noon, and night”, “the four seasons”) and gestures (e.g., pointing,
nodding) [D] Student Talk: “The next word will rhyme with wall because there
is a pattern in the words.” “The pattern goes ’big button, small button, bead,
big button, small button, bead’ so a big button goes next.” 




Data Management and Probability 




25.
sort, classify, and compare objects and describe the attributes used (e.g., initially:
sort them into piles or collections on the basis of a common attribute;
eventually: state the rule they used to sort, classify, or compare) [E]
Student Talk: “I sorted my animals by size.” “I grouped these all together
because they are smooth.” “My shoes and your shoes all have zippers.” 




26.
collect objects or data and make representations of their observations, using
concrete graphs (e.g., conduct simple surveys and use graphs to represent the
data collected from questions posed; use a variety of graphs, such as graphs
using people to represent things, bar graphs, pictographs; use tally charts)
[E,A] Sample Problems: “How many
pockets are on our clothing today? How might we show how many pockets we
have?” Student Talk: “There are five people standing in the Tshirt row and
six people standing in the sweatshirt row.” “More people like to eat apples
than oranges.” “There is only one person left on the age chart that is 4
years old.” 




27.
respond to and pose questions about data collection and graphs [E] Teacher
Prompts: “How are these alike? Different? The same?” “Can you find another
one that would go in that group?” “Let’s look at our graph. What does it tell
you?” “How can we use the pictograph of helpers to find someone who knows how
to tie your shoe?” 




28.
use mathematical language in informal discussions to describe probability
(e.g., chance, never, sometimes, always) [E] 




Student Name: 




Expectations: Copyright The Queen's Printer for Ontario, 2006. Format: Copyright B.Phillips, 1998.