# Grade Five

__GRADE FIVE__

GCO A: Students will demonstrate number sense and apply number theory concepts. *Students will be expected to:*

A1 represent whole numbers to the millions

A2 interpret and model decimal tenths, hundredths, and thousandths

A3 interpret, model, and rename fractions

A4 demonstrate an understanding of the relationship between fractions and division

A5 explore the concepts of ratio and rate informally

A6 read and represent numbers to millions

A7 read and represent decimals to thousandths

A8 compare and order large numbers

A9 compare and order decimals

A10 compare and order fractions using conceptual methods

A11 recognize and find factors of numbers

• GCO B: Students will demonstrate operation sense and apply operation principles and procedures in both numeric and algebraic situations. *Students will be expected to:*

B1 find sums and differences involving decimals to thousandths

B2 multiply 2-, 3-, and 4-digit numbers by 1-digit numbers

B3 find the product of two, 2-digit numbers

B4 divided 2-, 3-, and 4-digit numbers by single-digit divisors and investigate division by 2-digit divisors

B5 find simple products of whole numbers and decimals

B6 divide decimal numbers by single-digit whole numbers

B7 determine whether an open sentence is always, sometimes, or never true

B8 solve and create addition and subtraction problems involving whole number and/or decimals

B9 solve and create multiplication and division problems involving whole numbers and/or decimals

B10 estimate sums and differences involving decimals to thousandths

B11 estimate products and quotients of two whole numbers

B12 estimate products and quotients of decimals by single-digit whole numbers

B13 perform appropriate mental multiplications with facility

B14 divide numbers mentally when appropriate

B15 multiply whole numbers mentally by 0.1, 0.01, 0.001

GCO C: Students will explore, recognize, represent, and apply patterns and relationships, both informally and formally.

*Students will be expected to:*

C1 use place value patterns to extend understanding of the representation of numbers to millions

C2 recognize and explain the patterns in dividing by 10, 100, and 1000 and/or in multiplying by 0.1, 0.01, 0.001

C3 solve problems using patterns

C4 rearrange factors to make multiplication simpler

C5 recognize how a change in one factor affects a product or quotient

C6 predict how a change in unit affects an SI measurement

C7 manipulate the dimensions of a rectangle so that the area remains the same

C8 demonstrate an understanding that the multiplicative relationship between numerators and denominators is constant for equivalent fractions

C9 represent measurement relationships using tables and two-dimensional graphs

GCO D: Students will demonstrate an understanding of and apply concepts and skills associated with measurement.

*Students will be expected to:*

D1 solve simple problems involving the perimeters of polygons

D2 calculate areas of irregular shapes

D3 determine the measures of right angles, acute angles and obtuse angles

D4 demonstrate an understanding of the relationships among particular SI units

D5 develop formulas for areas and perimeters of squares and other rectangles

D6 solve simple problems involving volume and capacity

D7 estimate angle size in degrees

D8 determine which unit is appropriate in a given situation and solve problems involving length and area

GCO E: Students will demonstrate spatial sense and apply geometric concepts, and relationships. *Students will be expected to:*

E1 draw a variety of nets for different prisms and pyramids

E2 identify, describe, and represent the various cross-sections of cubes and rectangular prisms

E3 make and interpret isometric drawings of shapes made from cubes

E4 explore relationships between area and perimeter of squares and rectangles

E5 predict and construct figures made by combining two triangles

E6 recognize, name, describe, and represent perpendicular lines/segments, bisectors of angles and segments, and perpendicular-bisectors of segments

E7 recognize, name, describe, and construct right, obtuse, and acute triangles

E8 make generalizations about the diagonal properties of squares and rectangles and apply these properties

E9 make generalizations about the properties of translations and reflections and apply these properties

E10 explore rotations of one-quarter, one-half, and three-quarter turns using a variety of centres

E11 make generalizations about the rotational symmetry property of squares and rectangles and apply them

E12 recognize, name, and represent figures that tessellate

E13 explore how figures can be dissected and transformed into other figures

• GCO F: Students will solve problems involving the collection, display, and analysis of data. *Students will be expected to:*

F1 use double bar graphs to display data

F2 use pictographs and bar graphs to display and interpret data

F3 use coordinate graphs to display data

F4 create and interpret line graphs

F5 group data appropriately and use stem-and-leaf plots to describe the data

F6 recognize and explain the effect of certain changes in data on the mean of that data

F7 explore relevant issues for which data collection assists in reaching conclusions

• GCO G: Students will represent and solve problems involving uncertainty. *Students will be expected to:*

G1 conduct simple experiments to determine experimental probabilities

G2 determine simple theoretical probabilities, and use fractions to describe them.

Number

N01: Students will be expected to represent, partition, and compare whole numbers to 1,000,000.

N02: Students will be expected to use estimation strategies, including front-end, front-end adjusted, rounding, and compatible numbers, in problem-solving contexts.

N03: Students will be expected to describe and apply mental mathematics strategies and number properties to recall, with fluency, answers for basic multiplication facts to 81 and related division facts.

N04: Students will be expected to apply mental mathematics strategies for multiplication, including

- multiplying by multiples of 10, 100, and 1000

- halving and doubling

- using the distributive property

N05: Students will be expected to demonstrate, with and without concrete materials, an understanding of multiplication (two-digit by two-digit) to solve problems.

N06: Students will be expected to demonstrate, with and without concrete materials, an understanding of division (three-digit by one-digit), and interpret remainders to solve problems.

N07: Students will be expected to demonstrate an understanding of fractions by using concrete, pictorial, and symbolic representations to

- create sets of equivalent fractions

- compare and order fractions with like and unlike denominators

N08: Students will be expected to describe and represent decimals (tenths, hundredths, and thousandths) concretely, pictorially, and symbolically.

N09: Students will be expected to relate decimals to fractions and fractions to decimals (to thousandths).

N10: Students will be expected to compare and order decimals (to thousandths) by using benchmarks, place value, and equivalent decimals.

N11: Students will be expected to demonstrate an understanding of addition and subtraction of decimals (limited to thousandths).

Patterns and Relations

PR01: Students will be expected to determine the pattern rule to make predictions about subsequent terms.

PR02: Students will be expected to solve problems involving single-variable, one-step equations with whole number coefficients and whole number solutions.

Measurement

M01: Students will be expected to design and construct different rectangles, given a perimeter or an area or both (whole numbers), and make generalizations.

M02: Students will be expected to demonstrate an understanding of measuring length (mm) by

- selecting and justifying referents for the unit millimetre (mm)

- modelling and describing the relationship between millimetre (mm) and centimetre (cm) units, and between millimetre (mm) and metre (m) units

M03: Students will be expected to demonstrate an understanding of volume by

- selecting and justifying referents for cubic centimetre (cm^{3}) or cubic metre (m^{3}) units

- estimating volume using referents for cubic centimetre (cm^{3}) or cubic metre (m^{3})

- measuring and recording volume (cm^{3} or m^{3})

- constructing rectangular prisms for a given volume

M04: Students will be expected to demonstrate an understanding of capacity by

- describing the relationship between millilitre (mL) and litre (L) units

- selecting and justifying referents for millilitre (mL) and litre (L) units

- estimating capacity using referents for millilitre (mL) and litre (L)

- measuring and recording capacity (mL or L)

Geometry

G01: Students will be expected to describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes that are parallel, intersecting, perpendicular, vertical, and horizontal.

G02: Students will be expected to name, identify, and sort quadrilaterals, including rectangles, squares, trapezoids, parallelograms, and rhombi, according to their attributes.

G03: Students will be expected to perform a single transformation (translation, rotation, or reflection) of a 2-D shape (with and without technology) and draw and describe the image.

G04: Students will be expected to identify and describe a single transformation, including a translation, rotation, and reflection of 2-D shapes.

G05: Students will be expected to identify right angles.

Statistics and Probability

SP01: Students will be expected to differentiate between first-hand and second-hand data.

SP02: Students will be expected to construct and interpret double bar graphs to draw conclusions.

SP03: Students will be expected to describe the likelihood of a single outcome occurring, using words such as **impossible**, **possible**, and **certain**.

SP04: Students will be expected to compare the likelihood of two possible outcomes occurring, using words such as **less likely**, **equally likely**, or **more likely**.** **

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**See also**