Number Sense and Numeration

Measurement

Kindergarten

/ Grade 1 /

Grade 2

/ Grade 3 / Grade 4

use simple measurement terms correctly

(e.g., tall/short, big/small, empty/full,heavy/light, tomorrow/yesterday);

order two or more objects according to size

or mass (e.g., the Three Bears);

use non-standard measuring device

appropriately (e.g., string, scoops, sugarcubes, sand timer);

use some standard measuring device

appropriately (e.g., tape measure,balance scale, thermometer, clock);

identify the values of some coins.

UNITS OF MEASURE

compare two objects and identify similarities and

differences (e.g., compare the length and width of
two pencils);

represent the results ofmeasurement activities using

concrete materials and drawings;

demonstrate that a non-standardunit is used

repeatedly to measure (e.g., count the number of floor tiles to measure the length of the classroom);

use mathematical language todescribe dimensions

(e.g., height, length);

select an appropriate non-standard unit to measure

length;

estimate, measure, and record thelinear dimensions

(e.g., length, height) of objects using non-standard units, and compare and order objects by their linear dimensions;

order sequences of events orallyand with pictures;

demonstrate an understanding of the passage of time by comparing the duration of various activities (e.g., walking home will take as long as watching one television show);

name the days of the week in order,and the seasons;

estimate and measure the passage of time using non-standard units;

read analog clocks, and tell and write time to the

hour and half-hour;

relate temperature to their dailyactivities;

demonstrate an understanding of the value of some

coins (1¢, 5¢, 10¢);

represent a given value of coins up to 10¢ using

concrete materials ordrawings;

name coins up to $2 and state the value of pennies,

nickels, and dimes;

use appropriate language to describe relative times,

sizes, temperatures, amounts of money, areas, masses, and capacities (e.g., tallest, warmer);

use non-standard units to solve oralmeasurement

problems related to everyday issues;

PERIMETER AND AREA

demonstrate an understanding ofthe relationship

between the tiling of a surface and the number of units
needed to cover the surface;

estimate and count the number of uniform and non

uniform shapes that will cover a surface;

CAPACITY, VOLUME, AND MASS

estimate, measure, and record thecapacity of

containers using non-standard units, and compare
the measures;

estimate, measure, and record the mass of objects

using non-standard units, and compare the measures. /

UNITS OF MEASURE

demonstrate an understanding that the measure of

one object can be used to describe a similar attribute of another object (e.g., the mass of a box can be used to measure the mass of a larger box);

record the results of measurementactivities in a

variety of ways (e.g., in graphs, stories);

demonstrate an understanding that a standard unit of

measure is used to describe the measure of an object (e.g., a metre length is used repeatedly to describe the length of a room);

demonstrate an understanding of some standard

units of measure: for length and distance (centimetre,
metre) and time (second, minute, hour, day);

use the terms centimetre and metrein measurement

and describe the relationship between the two linear
measures;

select an appropriate non-standardunit and an

appropriate standard unit to measure length;

demonstrate an understanding of the relationship

between days and weeks, months and years, minutes
and hours, hours and days;

name the months of the year inorder and read the

date on a calendar;

estimate and measure the passage of time using

minutes and hours;

read digital and analog clocks, and tell and write

time to the quarter-hour;

relate changes in temperature totheir own

experiences (e.g., how changes in temperature during the day affect their activities);

use a thermometer to determinewhether

temperature is rising or falling;

name and state the value of all coins and

demonstrate an understanding of their value;

estimate and count money amounts to $1 and record

money amounts using the cent symbol;

create equivalent sets of coins up to$1 in value;

use mathematical language to describe relative

times, sizes, temperatures, amounts of money, areas, masses, and capacities (e.g., higher tower, fewer cups);

use non-standard and standardunits to solve

measurement problems relating to themselves
and their environment;

PERIMETER AND AREA

estimate, measure, and record the linear dimensions

of objects using non-standard and standard units
(centimetre, metre), and compare and order objects by their linear dimensions;

measure and record the distancearound objects

using non-standard units, and compare the distances;

estimate and measure specified areas using uniform

non-standard units, and record the measures (e.g., the area of the page is four pencil cases);

CAPACITY, VOLUME, AND MASS

estimate, measure, and record thecapacity of

containers using non-standard units, compare the
measures, and order a collection of containers by capacity;

estimate, measure, and record the mass of objects

using non-standard units, compare the measures, and
order a collection of objects bymass. /

UNITS OF MEASURE

explain the use of standard units of measurement and

the relationships between linear measures (e.g., millimetres are smaller than metres);

select the most appropriate unit of measure to

measure length (centimetre, metre, kilometre);

estimate, measure, and recordlinear dimensions of

objects (using centimetre, metre, kilometre);

compare and order objects by their linear

dimensions;

demonstrate an understanding ofthe relationship

between days and years, weeks and years;

estimate and measure the passage of time in five

minute intervals, and in days, weeks, months, and years;

tell and write time to the nearestminute in 12-hour

notation using digital clocks;

read and write time to the nearest five minutes using

analog clocks;

estimate, read, and recordtemperature to the nearest

degree Celsius;

demonstrate the relationship between all coins and

bills up to $100;

make purchases and change for money amounts up

to $10, and estimate, count, and record the value up to $10 of a collection of coins and bills;

read and write money amounts using two forms of

notation (89¢ and $0.89);

PERIMETER AND AREA

measure the perimeter oftwo-dimensional shapes

using standard units (centimetre and metre), and compare the perimeters;

estimate and measure the area ofshapes using

uniform non-standard units, and compare and order the shapes by area;

CAPACITY, VOLUME, AND MASS

estimate, measure, and record thecapacity of

containers using standard units (millilitre, litre), and
compare the measures;

estimate, measure, and record the mass of familiar

objects using standard units (gram, kilogram). /

UNITS OF MEASURE

describe the relationship between millimetres,

centimetres, decimetres, metres, and kilometres;

draw items given specific lengths (e.g., a pencil 5

cm long);

select the most appropriate standard unit

(millimetre, centimetre, decimetre, metre, or kilometre) to measure linear dimensions and the perimeter of
regular polygons;

estimate lengths in millimetres,centimetres, metres,

and kilometres;

distinguish between estimatedand precise

measurements and know when each kind is required;

relate years to decades, decadesto centuries,

centuries to millenniums;

estimate and measure time intervals to the nearest

minute;

make purchases of and changefor items up to $50;

read and write money values to $50;

estimate the amount of money incollections of

coins and bills to $50 and count to determine the total value;

PERIMETER AND AREA

select the most appropriate standard unit (square

centimetre or square metre) to measure the area of polygons of different sizes;

use linear dimensions and perimeterand area

measures with precision to measure length, perimeter, and area;

estimate the area of regular polygonsand measure

the area in square centimetres using grid paper;

understand that differenttwo-dimensional shapes

can have the same perimeter or the same area;

explain the meaning of lineardimension, perimeter,

and area;

relate measures of area and perimeter to the linear

dimensions of parts of rectangles or squares;

explain the difference between perimeter and area

and indicatewhen each measure should be used;

CAPACITY, VOLUME, AND MASS

select the most appropriate standard unit (e.g.,

millilitre, litre) to measure the capacity of containers;
model three-dimensional figures of specific volumes using blocks;

estimate, measure, and record themass of objects

using standard units (gram, kilogram), compare the
measures, and order objects by mass;

select the most appropriate standard unit to measure

mass (e.g., milligram or gram);

describe the relationship betweengrams and

kilograms and millilitres and litres.

Measurement

Grade 5

/ Grade 6 /

Grade 7

/ Grade 8
UNITS OF MEASURE

use prefixes in the metric systemcorrectly;

draw items using a wide variety ofSI units of length (e.g., a

trianglewith 9-dm sides);

select the most appropriate standard unit (millimetre,

centimetre, decimetre, metre, or kilometre) to measure linear dimensions and the perimeter of irregular polygons;

determine the relationshipbetween linear units (e.g.,

centimetre to metre);

estimate long lengths usingnon-standard units (e.g., a tall

building is about 15 car lengths);

investigate measures of circumference using concretematerials

(e.g., use string to measure the circumference of cans or bottles);

estimate and measure timeintervals to the nearest second;

read and write dates and timesusing SI notation (e.g., June 30,

1998, is written 1998 06 30);

read an analog clock to the nearest second and write the time

to the nearest minute;

estimate the amount of money incollections of coins and bills

to $1000 and count to determine the total value;

read and write money values to$1000;

make purchases of and changefor items up to $100;

identify the relationship betweenthe movement of objects and

speed (e.g., how long will it take a bowling ball to travel the length of a bowling lane?);

PERIMETER AND AREA

develop rules for calculating theperimeter and area of

rectangles,generalize rules, and develop formulas;

estimate and calculate the perimeter and area of rectangles and

squares;

explain the rules used in calculatingthe perimeter and area of

rectangles and squares;

estimate the area of irregularpolygons and measure the area by

dividing the polygons into parts, using grid paper;

develop methods of using grid paper to track and measure the

perimeter and area of polygons and irregular two-dimensional shapes;

CAPACITY, VOLUME, AND MASS

measure containers by volume using standard units: cubic

centimetres;

determine the relationship between capacity and volume (e.g.,

millilitre and cubic centimetre) by measuring the volume of various objects and by determining the displacement of liquid by each object;

relate the volume of an irregularthree-dimensional figure to its

capacity (e.g., through displacement of a liquid);

describe the relationship betweenmillilitres and cubic

centimetres;

determine the relationship betweenkilograms and metric

tonnes;

select the most appropriate standardunit to measure mass (e.g.,

kilogramor tonne). / UNITS OF MEASURE

use prefixes in the metric systemcorrectly;

select the most appropriatestandard unit (millimetre,centimetre,

decimetre, metre, or kilometre) to measure linear dimensions and the perimeter of irregular polygons;

determine the relationshipbetween linear, square, and cubic

units (e.g., compare cubic centimetres and cubic metres by constructing a cubic metre with rolled newspaper);

describe the relationship betweena 12-hour clock and a 24-hour

clock;

represent amounts of moneyunder $100 using the smallest

possible number of coins and bills;

read and write money values to $10 000;

estimate and count amounts of money to $10 000, using a

calculator for most calculations;

make simple conversionsbetween metric units (e.g., metres

to kilometres, grams to kilograms);

select among commonly used SIunits of length, mass, capacity,

area, and volume in solving problems;

relate time and distance andspeed: kilometres per hour;

PERIMETER AND AREA

relate dimensions of rectangles and area to factors and products

(e.g., in a rectangle 2 cm by 3 cm the side lengths are factors and the area, 6 cm2, is the product of the factors);

understand the relationship betweenthe area of a parallelogram

and the area of a rectangle, between the area of a triangle and the area of a rectangle, and between the area of a triangle and the area of a
parallelogram;

estimate and calculate the area of aparallelogram and the area of a

triangle, using a formula;

understand the relationship betweenarea and lengths of sides and

between perimeter and lengths of sides for squares, rectangles,
triangles, and parallelograms;

sketch a rectangle, square, triangle,or parallelogram given its area

and/or perimeter;

CAPACITY, VOLUME, AND MASS

estimate and calculate the volume ofrectangular prisms;

develop rules for calculating thevolume of rectangular prisms,

generalize rules, and develop formulas (e.g., Volume = surface
area of the base x height);

determine the relationship between milligrams, grams, and

kilograms. /

UNITS OF MEASURE

create definitions of measurementconcepts;

describe measurement concepts using appropriate measurement

vocabulary;

research and report on uses ofmeasurement instruments in

projects at home, in the workplace, and in the community;

make increasingly more informed and accurate measurement

estimations based on an understanding of formulas and the results of investigations;

PERIMETER AND AREA

understand that irregulartwo-dimensional shapes can be

decomposed into simple two-dimensional shapes to find the
area and perimeter;

estimate and calculate theperimeter and area of an irregular

two-dimensional shape (e.g., trapezoid, hexagon);

develop the formula for finding thearea of a trapezoid;

estimate and calculate the area ofa trapezoid, using a formula;

draw a trapezoid given its areaand/or perimeter;

develop the formulas for finding thearea of a parallelogram and

the area of a triangle;

develop the formula for finding the surface area of a rectangular

prism using nets;

CAPACITY, VOLUME, AND MASS

develop the formula for finding the volume of a rectangular prism

(area of base x height) using concrete materials;

understand the relationshipbetween the dimensions and the

volume of a rectangular prism;

calculate the surface area and thevolume of a rectangular prism in

aproblem-solving context;

sketch a rectangular prism given itsvolume.

UNITS OF MEASURE

use listening, reading, and viewingskills to interpret and

evaluate the use of measurement formulas;

explain the relationships betweenvarious units of

measurement;

research, describe, and report on uses of measurement in

projects athome, in the workplace, and in the community that require precise measurements;

make increasingly more informedand accurate measurement

estimations based on an understanding of formulas and the results of investigations;

ask questions to clarify and extendtheir knowledge of linear

measurement, area, volume, capacity, and mass, using appropriate measurement vocabulary;

PERIMETER, CIRCUMFERENCE, AND AREA

measure the radius, diameter, andcircumference of a circle

usingconcrete materials;

recognize that there is a constantrelationship between the

radius, diameter, and circumference of a circle, and approximate its value through investigation;

develop the formula for finding the circumference and the

formula for finding the area of a circle;

estimate and calculate the radius,diameter, circumference, and

areaof a circle, using a formula in a problem-solving context;

draw a circle given its area and/or circumference;
define radius, diameter, andcircumference and explain the

relationships between them;

develop the formula for finding thesurface area of a triangular

prism using nets;

CAPACITY, VOLUME, AND MASS

develop the formula for finding thevolume of a triangular

prism (area of base x height);

understand the relationship betweenthe dimensions and the

volume of a triangular prism;

calculate the surface area and thevolume of a triangular prism,

using aformula in a problem-solvingcontext;

sketch a triangular prism given its volume.