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•

To....... 

.

SENATE 

?

SENATE UNDERGRADUATE ADMISSIONS 

FOR INFORMA.T ION 

BOARD 

Subj.d

ALGEBRA 11 AND 12: ? 

D&. ? 

15TH DECEMBER, 1976 

INFORMATION

........

44p• 

or

The Senate Undergraduate Admissions Board wishes to 

lnfonn Senate of the Department of Education revisions 

to the Mathematics Curriculum, such that Algebra 11 

and Algebra 12 will replace Mathematics 11 and Mathe- 

matics 12. 

As a result of this revision, and the fact that we 

currently require Math 11 for admission purposes, it 

will be necessary to accept either Algebra 11 OR 

Math 11, until the new curriculum is fully Impl—emented 

by all secondary schools. 

Appendix B contains extracts from the Department of 

Education Mathematics Curriculum Guide (1976). 

)44) 

Attach. 

ACM: bc 

Registrar's Note: The intent is to accept 

either of Math 11 or Aig 11, and to 

accept either of Math 12 or Aig 12 as 

a recognized "12 level" subject for ad mission 

purposes. 

•

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to the programs is

the dealing with those

prohloic through

the following

sequence of ctivitie:

) ?

ipuJLtive, 

exploratory activitiso 

with

real objects; 

b)

oloti'(2 

activities

with 

non-reproonttionl 3-D 

C) MiMOlativG activities

with 

pictorial reprebentationaL 

d)

UuILtive activities with 

pictorial nonropreeentition&il 

til8;

e)

graphical representation or model buildingactivities; 

-

1 -

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in the

-2-

SEQUENCE OF ACTIVITIES 

The

following is a 

simple

illustration of a sequence of 

activities. 

Two people are in a room. 

?

A problem is perceived. 

One person comes into the room. 

How many people are now in the 

room? 

4, ? 

.r

Act out using real peo Le. 

()

Deni11trate using bi 

Illustrate using pictures of 

peo le. 

0

,

CE:

Illustrate using pictures of 

blocks. 

L ?

I ?

w

Construct a graphical model.? 

2+ I 

Write the number sentence. 

2

+1

3,

Solve by addition. 

a+D= 

a + b= n 

Write a generalized statement. 

Real objects are manipulated 

to arrive at solutions. 

Nonreprentational concrete 

objects are manipulated to 

arrive at solutions. 

Pictures of real objects 

are used in arriving at 

solutions. 

Drawings of nonrepresentational 

objects are used in arriving 

at solutions. 

A

graphical model is constructed. 

A mathematical model is 

constructed to represent the 

structure of the relationship. 

Algorithms and mathematical 

processes are 

applied. 

A generalized mathematical 

model is developed for 

future use. 

- 3 - 

II. NOTES RE IMPLEMENTATION (Prescribed and Permissive Courses) 

1.

Prescribed Courses: As of September. 1976, courses 

outlined in this document from years 1 - 8 inclusive 

are prescribed courses. 

2.

Permissive Courses: 

Junior Secondar 

y

School Mathematics 

To enable a smooth transition to the new courses at the 

Senior Secondary School level, the Department would 

encourage schools which have not yet implemented the 

revised Mathematics 9 and 10 courses to do so in the 

L976-77 school year. 

Senior Secondary School Mathelnat ics 

At the present time (April, 1976) the proposed new 

courses at the Senior Secondary School level have been 

finalized, except for selection of a supporting text 

for computing Science 11. 

For the 1976-77 school year, schools will have the 

option of introducing the new courses Algebra It, (and 

Algebra 12 in the second semester), Consumer Mathema- 

tics 11, and Trades Mathematics 11 or continuing to 

offer the prescribed courses Mathematics 11, Mathematics 

12, and General Mathematics 11. 

.

?

The additional mathematics courses outlined for the 11, 

12 level are planned for implementation when textbook 

references are available in the near future. These 

include Computing Science 11, Probability and Statistics 

12 (Finite Mathematics), and Geometry 12. 

* See Instructional Services Circular (23.2.76 - 843) 

for additional 

information

regarding implementation of 

thf Senior Secondary Mathematics programme. 

3.

Course Outlines Years 9-10, 11-12: In each of the 

levels indicated preliminary drafts of the Course Out].in 

were included in the curriculum Guide for one year prior 

to: preparing the final draft. Many comments and constrw 

tive criticisms were received from individual teachers 

and/or groups of teachers from throughout the Province. 

These comments and criticisms were given careful consi- 

deration in the preparation of the fianl drafts. 

4.

Prescribed Materials: Materials prescribed to support 

mathematic courses are listed in the 

p rescribed Textbook 

List, published annually by the Curriculum Development 

Branch and available from the 

p ublication Services 

Branch. 

-4-

The revised programme 

recognizes that there is 

a

body of 

mathematical knowledge and skills 

that must 

be provided for all 

pupils. In addition, provision must be made for pupils with 

specific requirements. As a consequences a two part mathematics 

programme has been planned. The first part, essentially the 

same for 

all. pupils, includes 

the elementary 

programme and ex- 

tends into the secondary. The second part consists of elective. 

courses 

selected by the pupil because of 

(a)

post-secondary goals 

(b)

secondary school programme requirements 

and

?

(c)

pupil i4tereat and ability 

Provision has also been made through a 

multiple-text 

authorization for alternative sub-programmes for groups of 

pupils. These alternatives allow for differences 

in

approach, 

depth and rate of Learning. The extent to which the inherent 

benefits are achieved, however, depends in large measure on the 

resourcefulness of the teacher and the 

organization of the 

school. 

It cannot be too strongly emphasized that no single text 

should be 

regarded as the sole instrument for meeting the 

objectives of the programme 

as outlined in this curriculum guide. 

If the 

programme is 

to be relevant to present needs of 

.

pupils while also 

providing 

the foundations for future learning, 

then mathematics should be integrated with the other subjects. 

A meaningful 

.

intigratiort will 

go far towards achieving a deep 

and continuing interest in mathematics and an appreciation for 

its power and usefulness. The nature and the means of integra- 

tion will be determined at the school level by the specific 

programmes being offered to the pupils. 

III. STATEMENT OF METRICATION 

The Federal 

Go,ernment 

has committed Canada to the change 

to the Metric System. This change will take place over a ten 

year period and is to be completed by 1981. Commencing in 

September, 1973, all primary pupils began to use the metric 

system as a standard of measurement. It has been agreed by the 

Council of Ministers, Canada, that all instruction in elementary 

and secondary schools be predominently metric by 1978. 

Mathematics for years K-12 will be completely metric by that date. 

It is the intent of 

practice of using spaces 

larger numbers (e.g. 746 

However, you will find b 

the prescribed texts. S 

the Metric Commission to establish the 

rather than commas in the writing of 

321 988 rather than 746, 321, 988). 

oth forms used in present editions of 

paces are not used in computation. 

- 5 - 

IV. OBJECTIVEL

A. General 

stated on the pages following are the cognitive objectives 

generally thought desirable at this time. The specific 

objectives listed for each year are meant to be more than merely 

1

illustrative but are not exhaustive. Teachers are encouraged 

to formulate specific objedtiVes for their own situation consis- 

?

I

tent with those in 

?

this guide. 

No mention is made here of objectives in the affective 

domain, not because they are less important, but because there 

is no consensus among educators of what they should be or how 

they might be achieved. Again, teachers are encouraged to 

develop their own specific objectives in this area. 

In identifying the major objectives of a mathematics pro- 

gramme. one must consider that the broad goals of mathematics 

are derived from the needs of individuals and of society. The 

practical usefulness of mathematics in our scientific and 

technological society is increasingly apparent. 

With few exceptionS, the content of the revised courses in 

years 1-10 does not differ significantly from the content of 

previous courses. The emphasis in years 1-10 remains on the 

operations with natural, whole and rational numbers and the 

study of their properties. One major exception is an expanded 

study of geometry. The treatment is largely intuitive though 

somewhat more formal at the secondary Level.. Two other excep- 

tions are an introduction to the concept of function and the 

employment of flow charting. 

The courses are organized around 9 "themes" or strands: 

I sets and set operation 

ii number and number operations 

iii geometry 

IV measurement 

V problem solving 

vi graphs and functions 

?

VII

?

applications of mathematics 

?

VIII ? 

logical thinking 

?

IX ? 

probability and statistics 

The development of a course, however, does not follow a 

single strand exclusively but must draw on several strands at 

once. 

- 6 - 