First Year of the First Cycle
Secondary
Mathematics End of Year Learning
Outcomes
Numeration:
Understanding and Writing Natural Numbers
0-999,999
 Reading, writing, grouping and regrouping
numbers,
 Base Ten System
 Place Value, concept of zero, equivalent
expressions, expanded form, patterns, comparing,
ordering
 Properties: even, odd, prime, composite, square,
triangular, ordinal numbers
 Exponential form: should also be familiar with the
following terms: kilo 103, mega 106, giga 109,
tera 1012
 Approximation: estimating and rounding off
Understanding and writing Fractions
 Fractions based on a whole or collection
 Reading ,writing
 Placing on a number line
 Equivalent fractions
 Comparing, ordering
 Concept of a mixed number and an improper
fraction
Understanding and Writing Decimals
 Reading, writing up to 3 decimal places (tenths,
hundredths, thousands)
 Placing on a number line
 Place Value
 Comparing, ordering
 Expanded form
 Equivalent expressions
 Approximation: estimation, rounding off
Understanding and Writing Percent
 Reading ,writing
 Equivalent percents
 Comparing, ordering
Integers
 Concept of positive and negative numbers
 Integers on a number line
Number Operations
Natural Numbers
 Reviewing adding and subtracting of a series of
numbers involving carrying and borrowing (4 digits)
 Multiplying a three digit number by a 3 digit
number
 Dividing a three digit number by a two digit
number
 Divisibility rules (2,3,4,5,6,9,10)
 Multiples (LCM)
 Factors (GCF)
 Prime Factors
 Order of operations
 Integers: Basic adding and subtracting using a
number line.
 Commutative, Associative, and Distributive Laws
 Mental Math (Making tens, breaking apart and
putting together, grouping in column addition, etc)
 Problems involving addition, subtraction,
multiplication, and division
 Unknown variable (precursor to algebra)
 Approximation
Fractions
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Reducing fractions
Mixed numbers
Improper fractions
Changing a whole number to a fraction
Adding and subtracting fractions with like
denominators or when the denominator of one is a
multiple of the other
 Equivalent fractions
 Position on a number line
Decimals
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Adding and subtracting decimals
Multiplying and dividing decimals by 10,100,1000
Comparing, ordering
Position on a number line
Percent
 Calculate percent
 See the relationship between percent, decimals,
fractions (simple: 1/2,1/4, 1/10,0.50,0.25,
0.10,50%, 25%, 10%
Problem Solving
 Able to solve problems using the appropriate
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strategies
Finding the needed information
Finding missing information
Being able to ignore unneeded information
Being able to record your findings in a logical
manner
Being able to explain your answer
Comparing your answer to others and reevaluating your answer
Geometry
Space
 Review spatial vocabulary (on, under, at , to the
right, North, South, East, West, etc)
 Locating points on an axis
 Degrees and cardinal points
 Plane, point ,rays ,lines segment, horizontal lines,
vertical lines, diagonal lines, perpendicular lines,
parallel lines, intersecting lines, angles: right,
obtuse, acute
Plane Figures
 Triangles: equilateral, isosceles, right, scalene
 Quadrilaterals: trapezoid, parallelogram,
rectangle, rhombus, square, pentagon, hexagon,
octagon
 Circle: diameter, radius, circumference
 Measuring angles and constructing angles with a
protractor
 Terms similar and congruent
Transformations
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Translations
Rotations
Point symmetry
Reflections
Line Symmetry
Tessellations
Solid Figures
 Terms: face, edge, vertices
 Skeletons
 Nets of Prisms : cube, rectangular prism,
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triangular prism
Pyramids: triangular pyramid ,square pyramid
,rectangular pyramid
Nets of the above pyramids
Cylinders: nets
Cones: nets
Spheres
Measurement
Length
 Estimating and measuring using conventional units
(km, m, dm, cm, mm)
 Relationship between units of measure
 Perimeter
Angle
 Estimating and measuring angles
 Use of a protractor
 Concept of Degree
Area
 Estimating and measuring area using conventional
units (m2,cm2) geoboard
Volume
 Estimating and measuring volume using
conventional units (m3,cm3)
Capacity
 Estimating and measuring using conventional units
(L, mL)
 Relationship between units
Mass
 Estimating and measuring using conventional units
(g, kg)
 Relationship between units
Time
 Conventional units: day, hour, minute, second,
week, month, year
 Metric Time :twenty four hour clock
 Relationship between units
Temperature
 Being able to read the temperature on a
thermometer
 Relating below zero to integers
Statistics
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Formulating questions for a survey
Collecting data
Organizing data onto a simple graph
Interpreting data on a bar graph, pictograph,
circle graph
Probability
 Experimenting with activities involving chance
 Predicting the likelihood of an event
(Certainty, possible, impossible)
 Probability that a simple event will occur (more
likely, just as likely, less likely, not likely)
 Enumerating the possible outcome of a random
experiment using a table or simple tree diagram
First Year of the First Cycle
Secondary
Numeration:
Reading and writing:
Standard form: 27 568
Word form: twenty- seven thousand five hundred sixty - eight
Grouping and regrouping: being able to see that twenty five hundred
is the same as two thousand five hundred (can be done with images)
Base Ten: Make sure that you emphasise that in our everyday number
system is based on the ten symbols. Comparing it to another base system
might help (base 4, 2, etc.)
Place Value:
a) Concept of zero : It is used to mark a place not
occupied by any other numeral e.g. when writing
three hundred eight, zero is used to indicate that there
are no tens:308
b) When zero is added to or subtracted from any number,
that number is unchanged: n + 0 = n; n – 0 = n.
c) When a number is multiplied by zero, the result is
zero: n x 0 = 0
d) Division by zero is not allowed.
e) Zero on a number line separates the negative and the
positive numbers
f) Equivalent expressions: equal in value (568 = 2 x
284)
g) Expanded form: 3489 = 3000+400+80+9 and
3x1000+4x100+8x10+9x1
h) Patterns: Number patterns; 1, 3, 6, 10, 15, 21…., size
pattern, colour pattern, block pattern, etc.
i) Comparing : 578 367 < 578 376
j) Ordering: Put the following numbers in order:
5697,5890,54327, etc.
Properties:
a. Even: every even number has 0,2,4,6,or 8 in its
ones place
b. Odd: every odd number has 1,3,5,7,9 in its one
place.
c. Prime : a prime number has exactly two
different factors,1 and itself
d. Composite: a composite number has more than
two factors
e. Square: a whole number that is the square of a
whole number, e.g. the number of dots in a
square array, 1,4,9 16,…..
f. Triangular number: the number of dots in a
triangular array: 3,6,10, 15,…
g. Ordinal Numbers: a whole number that names
the position of an object in sequence: first,
second, third, forth etc. Date: June 24th
Exponential Form: 2x2x2 = 23
Approximation:
a. Estimation: find a number close to an exact amount ; there
were about 540 people at the arena
b. Rounding off: round the following number to the nearest
tens : 512-510; 5328 rounded to the nearest 100 =
5300;5830 rounded to the nearest 1000 = 6000
Understanding and Writing Fractions
a) Fraction based on a whole: stress that the parts are equal: ⅔ of a
pizza
b) Fraction as part of a collection: ⅜ of the students are boys
c) Denominator and Numerator
d) Reading: reading a fraction is different than reading a whole
number. The numerator is easy, just say the number. To read the
denominator, use words to describe the total number of equal parts
(thirds, fourths, etc.
e) Writing: Standard form:⅓,⅔,⅛,⅜,⅝,⅞
Word form: one third, two thirds, one eighth, etc.
f) Placing a fraction on a number line:
g) Equivalent fractions:
h) Comparing fractions: ½ > ¼
i) Place the following fractions in increasing order:
3/5,4/8,2/3/etc.
j) Concept of an improper fraction: a fraction where the
numerator is bigger that the denominator: 4/3
k) Concept of a mixed number: a number expressed as a
whole number and a fraction: 5 ½
Understanding and Writing Decimals
Reading a decimal: You must make sure that the students read the
decimal as follows: 3.5 is to be read as three and five tenths, 3.56 is to be
read as, three and fifty six hundredths, and 3.456 is read as three and four
hundred fifty six thousandths
Writing a decimal: they should be able to write a decimal in standard form
as follows: 4.6, 4.56, and 4.765
Placing on a number line
Place value:
Comparing Decimals:
Ordering Decimals: write the following decimals in increasing order: 3.567, 3.432,
3.123,etc.
Expanded form:
Equivalent expressions:
Approximation:
Estimation: I ran about 3.1 kilometres
Rounding:
Example 1: Round 0.1284 to 2 decimal places.
Solution: The 3rd decimal number, 8, is bigger than 4, so we add 1 to the 2nd decimal
number 2, and drop the rest of the decimal numbers. Our answer is 0.13.
Example 2: Round 0.1284 to 1 decimal place.
Solution: The 2nd decimal number, 2, is less than 4, so we do nothing to the 1 and drop
the rest of the decimal numbers. Our answer is 0.1.
Example 3: Round 0.895 to 2 decimal places.
Solution: The third decimal number, 5, is bigger than 4, so we add 1 to 9 to get 10, and
drop the rest of the decimal numbers. But, we have to carry the 1 to the 8 to get 9. So our
answer is 0.90 or just 0.9.
Understanding and Writing Percent
Make sure that the students understand that percent means per 100.
Reading: being able to read 25% as twenty- five percent
Writing: being able to write twenty-five percent as 25%
Equivalent percents:
¼=.25=25%
Comparing and ordering percents:
25% > 20%
Place the following percents in decreasing order: 75%, 17%, 45%,
Integers
Understanding that integers are positive and negative numbers
Integers on a number line: