2020 LEVELS OF ATTAINMENT IN MATHEMATICS
FOR GRADE FIVE
NUMBER CONCEPTS
1.
Count in a variety of ways: counting on (forward),
counting backwards, skip counting. (G4) and complete sequences of
numbers.
2.
Read and write numbers up to
99 999 written in words and numerals (999 for G3, 9999 for G4))
3.
Identify
the place value and total value of any digit in a number
with up to five digits. (G4 – 4
digits)
4.
Write numbers with up to five digits in expanded
notation. (G4 – 4 digits)
5.
Classify
numbers using several number concepts: e.g. prime, odd, prime and even, prime
and odd, composite and odd and explain how the various types of numbers (prime,
composite, odd, etc.) are related.
6.
Create
and solve problems involving factors
and multiples of whole numbers.
7.
List: (a)
multiples of a given number. (G4) (b) factors of a given number
8.
Identify real life situations that involve the
use of Roman Numerals (e.g. the
numbers on clocks and watches, numbering of chapters in a book).
9.
Identify,
read and write Roman Numerals for numbers 1 to 12 (G3) and explain how the
Roman Numerals for 1, 5, and 10 should be used to form other Roman Numerals
between 2 and 12 inclusive.
10. Explain the concept of ‘highest common factor’ and find the highest common factor of two or three numbers by listing factors (G4)
or prime factorisation.
11. Use diagrams/pictures to represent unit,
proper, and improper fractions and mixed numbers.
12. Convert an improper fraction to a mixed number
and a mixed number to an improper fraction.
13. Express fractions in their lowest terms and
explain the concept of ‘lowest terms’
and its relationship to equivalent
fractions.
14. Generate fractions that are equivalent to a
given fraction.
15. Calculate the least common denominator (LCM) for fractions with unlike but
related denominators.
16. Arrange in order
of magnitude: (a) a set of
fractions.
(b) a set of decimal numbers with up to two
decimal places.
17. Explain how decimal numbers and whole numbers are related.
18. Identify
the place value and total value of the digits in a decimal number with up to
two decimal places.
19. Represent
simple decimal numbers with up to two decimal places (e.g. 1.5 2.21) using
diagrams.
20. Read and write decimal numbers with up to two
decimal places.
21. Explain:
(a) the concept of percent.
(b)the meaning of a given percent (e.g. 10% or 10 percent)
(c) the relationship between fractions,
decimals, and percents (how fractions and decimals, fractions and percentage,
decimal and percentage are related).
22. Represent a given percent using
pictures/diagrams and symbols.
23. Express: (a) a percent as a decimal or fraction
(b) simple proper fractions and decimals as percents (c) a decimal number as a
fraction (d) a fraction as a decimal number.
24. Create, solve, and analyse problems involving
fractions, decimals, and percents.
25. Round
off three-digit or four-digit numbers to the nearest 10 or 100. G4 Term 1
COMPUTATION
1. Use computation vocabulary (e.g. sum, product,
total, etc.) to describe situations that involve any of the four basic
operations. (G4)
2. Explain: (a) the likely effects of an operation
(b) the relationships that exist among the four basic operations. (G4)
3. Estimate the answer to a computation.
4. Determine the reasonableness of an estimated or
exact answer to a computation, (G3) and justify their conclusion. (G4)
5. Explain:
(a)mental computation strategies that may be
used in calculations involving addition, subtraction, multiplication or
division. (G4)
(b) pencil and paper computation procedures
that may be used in calculations involving addition, subtraction,
multiplication and division. (G4)
(c) how to use a calculator to carry out
addition, subtraction, multiplication and division. (G4)
6. Select an appropriate computation strategy
(mental computation, use of pencil and paper, or use of a calculator) to carry
out any of the four basic operations. (G4)
7. Recall the basic facts for addition,
subtraction, (G3) multiplication and division of whole numbers.
8. Create and solve problems involving addition,
subtraction, multiplication (G3) and division of whole numbers. (G4)
9. Add sets of numbers with totals up to 99 999,
without and with regrouping. (G4 numbers with up to 4 digits)
10. Carry out subtraction involving whole numbers
with up to five digits, without and
with regrouping. (G4 -4 digits)
11. Multiply two- and three-digit numbers by one-
and two-digit numbers.
12. Divide whole numbers with up to five digits by
one- and two-digit numbers, without and with remainders.
13. Create and solve problems involving addition,
(G3) subtraction, or multiplication of fractions.
14. Add: (a)
proper fractions with like (G3) or unlike but related denominators.
(b) a whole number to a proper
fraction.
(c) a proper fraction
and a mixed number with like denominators.
(d)a proper fraction
and a mixed number with unlike bur related denominators.
15. Subtract: (a) proper fractions with like (G3)
or unlike but related denominators.
(b) a proper fraction from a mixed number with like denominator,
without regrouping.
(c) a proper fraction
from a mixed number with unlike but related denominator, without regrouping.
(d) a proper fraction
from a whole number.
16. Multiply: (a)
a proper fraction (and a mixed fraction)
by a whole number.
(b) a whole number by a proper fraction.
(c) two proper fractions.
17. Divide a proper fraction by a whole number.
18. Create and solve problems involving addition,
subtraction, and multiplication of decimal
numbers.
19. Explain how computation procedures for whole
numbers can be applied to decimal numbers.
20. Add and subtract decimal numbers with up to two
decimal places without and with regrouping.
21. Multiply a decimal number with up to two
decimal places by a one-digit number.
22. Create and solve problems involving percent.
23. Calculate a percent of a number.
24. Express one number as a percent of another.
25. Calculate: (a)
profit or loss, given the cost price and selling price of an article.
(b) profit or loss as a percent of the cost
price of an article
MEASUREMENT
1.
Tell and
write time using the 12-hour (G3) and 24-hour clock.
2.
Represent
time on the analogue or digital clock. (G4)
3.
Create
and solve problems involving duration of an event, time between events (G4),
starting time, finishing time, and relationships between units of time.
4.
Select:
(a) the most appropriate instrument to estimate and measure length, the mass, or the
capacity of a given object.
(b) the most appropriate unit to estimate and measure a length, the mass, or the capacity of
a given object.
5.
Read and
record estimates and measurements using appropriate notation.
6.
Estimate
and measure:
(a) distances, lengths and heights using the metre, centimetre, (G3, G4) and/or millimetre as the units of
measure.
(b) the capacity of containers using litres, centilitres, (G4) and/or millilitres or “milligrams” as the units of measure.
7.
Identify
and interpret the scale that was used in a scale drawing.
8.
Use scale
drawings (e.g. maps) to determine actual measurements in metres or kilometres
(G4).
9.
Make
simple scale drawings.
10. Create and solve problems involving linear
measurement and mass
11. Estimate and measure temperatures using the
Celsius scale.
12. Measure and estimate the length, mass, or
capacity of objects using common Imperial units, e.g. the yard, pound, quart,
pint.
13. Explain why metric and Imperial units are used
in real life.
14. Explain the relationships that exist among
metric units of measure of the same attribute. (e.g. 100cm = 1m; 1 litre = 1000
ml, 1kg =1000g etc.)
15. Use the relationships among the metric units to
record measurements. (E.g. a measurement of 2m 85cm could be written as 2.85m).
16. Use the relationships among the metric units to
carry out simple conversions involving measurements of the same attributes.
17. Read and write amounts of money up to $99 999.
(G3 up to $999, G4 up to $9, 999.99)
18. Describe situations that involve the use of
large amounts (thousands) of money.
19. Describe the role of cheques in transactions
involving money.
20. Represent amounts of money in a variety of ways
(G4 using various combination of notes and coins).
21. Create and solve problems involving money (G3)
- Make up bills, calculate change and Calculate the total cost of a set of items,
given the cost of one item and/or the cost of multiples of items (G4)
22. Explain the concepts of cost price, selling
price, profit, loss, and discount.
23. Use the concepts of cost price, selling price,
profit, loss, and discount in descriptions of situations involving buying and
selling.
24. Calculate the perimeter of 2D shapes (G4)
25. Find the area of 2D shapes by counting
squares(G4) and of rectangles by using the formula, Area = Length x width
STATISTICS
1.
Identify and
describe situations where data collection, representation, and interpretation
could be used to solve problems. (everyday life G3)
2.
Create and solve
problems whose solutions require data collection, representation, and/or
interpretation.
3.
Describe procedures
for collecting data using observation, interview, (G2) or simple questionnaire.
(G3) (G4)
4.
Identify
similarities and differences between interviews and questionnaires.
5.
Explain when it is
appropriate to use observation, interviews (G3) and questionnaires to collect
data.
6.
Select the data collection
method that is appropriate for a particular problem situation, and give reasons
for selection.
7.
Plan data collection
activities (G3) and Collect data using observation, interviews, (G3) or simple
questionnaires. (G4)
8.
Select appropriate: (a) methods
to represent data and give reason for selection (G4)
(b) scales
to represent data graphically and explain why selection is appropriate (G4 scales for
constructing pictograph and bar graphs)
9. Use tally
charts and tables to organise
collected data. (G3)
10. Represent/display data using pictographs
or bar graphs. G3 (G2 – complete)
11. Describe the characteristics of line
graphs. (G3 - describe
the characteristics of pictographs in which one picture represents one unit of
data and more than one unit of data.)
12. Identify similarities and differences
between bar graphs and line graphs.
13. Explain when it is appropriate to use bar
graphs and line graphs to represent data.
14. Read and interpret data presented in
tables, pictographs, bar graphs (G2&3) and line graphs.
15. Calculate the mean/average of a set of
data.
GEOMETRY
1.
Identify three-dimensional shapes (cubes,
cuboids, cylinders, cones and spheres) and describe
them in terms of the number and type of faces and the number of edges and
vertices. (Gr 3)
2.
Generate and test hypotheses for the purposes
of identifying three-dimensional shapes that are appropriate for particular
functions in real life.
3.
Use the attributes of a three-dimensional shape
to formulate reasons for its uses in everyday life.
4.
Identify nets that will form a cube, cuboid, or
cylinder
5.
Make nets of cubes, cuboids, (G4) and
cylinders.
6.
Construct cubes, cuboids (G4) and cylinders.
7.
Identify angles in three-dimensional and plane
shapes. (G4 – right angles)
8. Draw and label angles
(e.g. angle A) (G4)
9. Classify angles according to size, as equal to, larger than, or smaller than a right
angle.
10.
Identify and Describe angles - right angles, acute angles and
obtuse angles.
11.
Draw and label line segments (e.g. line segment
AB). (G4)
12.
Explain the concepts of horizontal, vertical,
parallel, and perpendicular lines.
13.
Identify and draw: (a) horizontal and vertical line segments. (G4)
(b) parallel and perpendicular lines.
14.
Identify two-dimensional shapes that have the
same size and shape.
15. Create and solve problems involving
plane shapes.
16.
Describe two-dimensional shapes in terms of the number and type of
sides (G3) and measure of angles.
(G4)
17.
Explain the concept of: (a) ‘circumference of a
circle’; (b) ‘congruent figures’.
18.
State the relationship between radii and
diameters of circles.
19.
Draw circles
and identify the following parts:
circumference, radius, diameter, centre. (G4)
20.
Classify two-dimensional shapes using a variety
of attributes: e.g. open (G4), closed (G4), symmetrical, congruent, the number
and type of angles and sides, etc.
21.
Explain how various groups of persons (e.g.
artists, craft persons, and builders) use geometric concepts such as angles,
symmetry, congruency, etc.
22.
Describe a simple co-ordinate system with only
positive numbers.
23.
Plot points on a simple co-ordinate system with
only positive numbers.
24.
Identify points on a simple co-ordinate system.
25.
Identify and draw lines of symmetry and
complete drawings of diagrams that are symmetrical (G4)
