# Grade Four

__GRADE FOUR__

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

A1 identify and model fractions and mixed numbers

A2 interpret and model decimal tenths and hundredths

A3 model and record numbers to 99 999

A4 compare and order whole numbers

A5 compare and order fractions

A6 rename fractions with and without the use of models

A7 compare and order decimals with and without models

• 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 add and subtract decimals involving tenths and hundredths, and whole numbers to five digits

B2 demonstrate an understanding of multiplication meanings and applications

B3 demonstrate an understanding of the various meanings of division

B4 multiply 2- and 3-digit numbers by single-digit numbers concretely, pictorially, and symbolically

B5 divide 2- and 3-digit whole numbers by a single-digit divisor

B6 use models informally to add simple fractions with common denominators

B7 demonstrate an understanding of use of the open frame as a place holder for a digit on some occasions and for a number on other occasions

B8 relate multiplication and division facts, using principles of these operations

B9 demonstrate a knowledge of multiplication facts to 9 x 9

B10 demonstrate an understanding of various treatments of remainders in division situations

B11 solve and create word problems involving whole number computations

B12 solve and create word problems involving adding and subtracting decimals (to hundredths)

B13 estimate sums and differences of whole numbers and decimals

B14 estimate the product or quotient of 2- or 3-digit numbers and single-digit numbers

B15 mentally solve appropriate addition and subtraction computations

B16 mentally multiply 2-digit numbers by 10 or 100

B17 use technology for computations involving many decimal places or large whole numbers

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

*Students will be expected to:*

C1 demonstrate an understanding of the relationship between adding decimals and adding whole numbers

C2 apply the pattern identified when multiplying by increasing powers of ten

C3 use patterns to solve computation problems

C4 understand how a change in either *a* or *b*, in * a + b, a - b, a *x* b,* or *a ÷ b* will affect the result of the computation

C5 represent multiplication facts either in a table or graphically

C6 complete open sentences of the form *a *x* b *= G, *a *x* *G = *c, a ÷ b = *G, and *a ÷ *G = *c*

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

*Students will be expected to:*

D1 recognize and demonstrate that objects of various shapes can have the same area

D2 recognize and demonstrate that objects of the same area can have different perimeters

D3 measure volume, using non-standard units

D4 estimate and determine the volume of rectangular prisms, using centimetre cubes

D5 recognize that the measure of an angle indicates an amount of turn

D6 estimate and measure angles, using non-standard units

D7 use a thermometer to read temperatures

D8 estimate and measure in millimetres, centimetres, decimetres, metres, and kilometres

D9 estimate and measure area in square centimetres

D10 solve relevant problems involving millilitres and litres, grams and kilograms

D11 relate dimensions and areas of rectangles to factors and products

• GCO E: Students will demonstrate spatial sense and apply geometric concepts, properties, and relationships.

*Students will be expected to*:

E1 draw various nets for rectangular prisms and cubes

E2 construct models for various cylinders, cones, prisms, and pyramids

E3 construct shapes given isometric drawings

E4 explore relationships among 3-D shapes

E5 find all possible composite figures that can be made from a given set of figures

E6 recognize, name, describe, and construct acute and obtuse angles

E7 recognize, name, describe, and construct equilateral, isosceles, and scalene triangles

E8 make generalizations about the angle, side length, and parallel side properties of the various quadrilaterals

E9 sort quadrilaterals under property headings

E10 make generalizations about the number of vertices, edges, and faces of various prisms, pyramids, cones, and cylinders

E11 predict and confirm the results of various 2-D figures under slides, reflections, and quarter/half turns

E12 make generalizations about the reflective symmetry property of the various quadrilaterals

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

F1 recognize and use a variety of methods for the collection and organization of data

F2 describe data maxima, minima, range, and frequency

F3 read and interpret bar graphs, line graphs, pictographs, and stem-and-leaf plots

F4 display position, using ordered pairs on a grid

F5 construct bar graphs, pictographs, and stem-and-leaf plots

F6 interpolate data from a display

F7 describe data, using the mean

F8 explore real-world issues of interest to students and for which data collection is necessary to determine an answer

• GCO G: Students will represent and solve problems involving uncertainty.

*Students will be expected to:*

G1 predict probabilities as either close to 0, near 1, or near ½

G2 cite examples of everyday events with very high or very low probabilities

G3 predict whether one simple outcome is more or less likely than another

G4 use fractions to describe experimental probabilities

Number

N01: Students will be expected to represent and partition whole numbers to 10,000.

N02: Students will be expected to compare and order numbers to 10,000.

N03: Students will be expected to demonstrate an understanding of addition and subtraction of numbers with answers to 10,000 (limited to three- and four-digit numerals) by

- using personal strategies for adding and subtracting

- estimating sums and differences

- solving problems involving addition and subtraction

N04: Students will be expected to apply and explain the properties of 0 and 1 for multiplication and the property of 1 for division.

N05: Students will be expected to describe and apply mental mathematics strategies, to recall basic multiplication facts to 9x9, and to determine related division facts.

N06: Students will be expected to demonstrate an understanding of multiplication (one-, two-, or three-digit by one-digit numerals) to solve problems by

- using personal strategies for multiplication, with and without concrete materials

- using arrays to represent multiplication

- connecting concrete representations to symbolic representations

- estimating products

- applying the distributive property

N07: Students will be expected to demonstrate an understanding of division (one-digit divisor and up to two-digit dividend) to solve problems by

- using personal strategies for dividing, with and without concrete materials

- estimating quotients

- relating division to multiplication

N08: Students will be expected to demonstrate an understanding of fractions less than or equal to 1 by using concrete, pictorial, and symbolic representations to

- name and record fractions for the parts of one whole or a set

- compare and order fractions

- model and explain that for different wholes, two identical fractions may not represent the same quantity

- provide examples of where fractions are used

N09: Students will be expected to describe and represent decimals (tenths and hundredths) concretely, pictorially, and symbolically.

N10: Students will be expected to relate decimals to fractions and fractions to decimals (to hundredths).

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

- estimating sums and differences

- using mental mathematics strategies to solve problems

- using personal strategies to determine sums and differences

Patterns and Relations

PR01: Students will be expected to identify and describe patterns found in tables and charts, including a multiplication chart.

PR02: Students will be expected to translate among different representations of a pattern (a table, a chart, or concrete materials).

PR03: Students will be expected to represent, describe, and extend patterns and relationships, using charts and tables, to solve problems.

PR04: Students will be expected to identify and explain mathematical relationships, using charts and diagrams, to solve problems.

PR05: Students will be expected to express a given problem as an equation in which a symbol is used to represent an unknown number.

PR06: Students will be expected to solve one-step equations involving a symbol to represent an unknown number.

Measurement

M01: Students will be expected to read and record time using digital and analog clocks, including 24-hour clocks.

M02: Students will be expected to read and record calendar dates in a variety of formats.

M03: Students will be expected to demonstrate an understanding of area of regular and irregular 2-D shapes by

-recognizing that area is measured in square units

- selecting and justifying referents for the units square centimetre(cm^{2}) or square metre (m^{2})

- estimating area using referents for cm^{2} or m^{2}

- determining and recording area (cm^{2} or m^{2})

- constructing different rectangles for a given area (cm^{2} or m^{2}) in order to demonstrate that many different rectangles may have the same area

Geometry

G01: Students will be expected to describe and construct rectangular and triangular prisms.

G02: Students will be expected to demonstrate an understanding of congruency, concretely and pictorially.

G03: Students will be expected to demonstrate an understanding of line symmetry by

- identifying symmetrical 2-D shapes

- creating symmetrical 2-D shapes

- drawing one or more lines of symmetry in a 2-D shape

Statistics and Probability

SP01: Students will be expected to demonstrate an understanding of many-to-one correspondence.

SP02: Students will be expected to construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions.

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**See also**