Regina Public Schools
Grade 3 Essential and Extended Mathematics Outcomes (2010)
Grade 3 – Number (Number Sense)Outcomes / Big Ideas / Teaching Information
Counting, Quantity and Place Value
N3.1 Demonstrate understanding of whole numbers to 1000 (concretely, pictorially, physically, orally, in writing, and symbolically) including:
· representing (including place value)
· describing
· estimating with referents
· comparing two numbers
· ordering three or more numbers.
Fractions
N3.4 Demonstrate understanding of fractions concretely, pictorially, physically, and orally including:
· representing
· observing and describing situations
· comparing
· relating to quantity. / Number sense requires understanding the many relationships within a single quantity (175) or between two or more quantities (175 and 185). These relationships are developed through:
· seeing patterns in counting,
· grouping hundreds (tens of tens) in place value,
· seeing a variety of groupings in a quantity (65=50 +15).
These are ways of representing larger quantities that can no longer be managed at-a-glance.
A fraction is a number that describes the relationship between a part (represented by the numerator) and a whole (represented by the denominator).
· A fraction is not meaningful without knowing what the whole is
· Fractions can represent parts of regions, parts of sets, or parts of a measure. / Fractions are introduced for the first time in Grade 3. To begin students’ understanding of fractions as representing a quantity, it is important to explore fractions concretely, pictorially, physically and orally.
Grade 3 – Number (Operations) and Patterns and Relations (Equality)
Outcomes / Big Ideas / Teaching Information
Addition, Subtraction, Multiplication, and Division
N3.2 Demonstrate understanding of addition of whole numbers with answers to 1000 and their corresponding subtractions (limited to 1, 2, and 3-digit numerals) including:
· representing strategies for adding and subtracting concretely, pictorially, and symbolically
· solving situational questions involving addition and subtraction
· estimating using personal strategies for adding and subtracting.
N3.3 Demonstrate understanding of multiplication to 5 x 5 and the corresponding division statements including:
· representing and explaining using repeated addition or subtraction, equal grouping, and arrays
· creating and solving situational questions
· modeling processes using concrete, physical and visual representations, and recording the process symbolically
· relating multiplication and division.
Equality
P3.2 Demonstrate understanding of equality by solving one-step addition and subtraction equations involving symbols representing an unknown quantity. / Addition, subtraction, multiplication, and division are related operations that involve taking apart and combining numbers.
There are many different strategies to add, subtract, multiply and divide. It is important to choose a strategy that best fits the numbers.
The relationship between two quantities can be written as an equation.
· Equations represent a balance between two quantities
· A quantity may be a single number (8) or an expression (5+3) or (o+6)
· A symbol such as o, can represent a missing part that will bring the quantities back into balance. / The focus of this outcome is for students to become familiar with multiplication and division and strategies for mentally determining products and quotients. It is not intended that students “memorize” the basic facts. But they still have to learn them.
The equal sign means “is the same as”, it does not mean “do”.
Grade 3 - Patterns and Relations (Patterns)
Outcome / Big Idea / Teaching Information
Patterns
P3.1 Demonstrate understanding of increasing and decreasing patterns including:
· observing and describing
· extending
· comparing
· creating patterns using manipulatives, pictures, sounds, and actions. / The structure of a pattern can be represented in a variety of ways including words, manipulatives, pictures, numbers, sounds and actions.
· Patterns have a rule. The rule tells you what repeats or changes. / Students have worked on repeating patterns in K, Grade 1 and Grade 2. They explored increasing patterns in Grade 2 and decreasing patterns for the first time in Grade 3.
Grade 3 - Shape and Space
Outcomes / Big Ideas / Teaching Information
Measurement
SS3.1 Demonstrate understanding of the passage of time including:
· relating common activities to standard and non-standard units
· describing relationships between units
· solving situational questions.
SS3.2 Demonstrate understanding of measuring mass in g and kg by:
· selecting and justifying referents for g and kg
· modeling and describing the relationship between the g and kg
· estimating mass using referents
· measuring and recording mass.
SS3.3 Demonstrate an understanding of linear measurement (cm and m) including:
· selecting and justifying referents
· generalizing the relationship between cm and m
· estimating length and perimeter using referents
· measuring and recording length, width, height, and perimeter.
3-D Objects and 2-D Shapes
SS3.4 Demonstrate understanding of 3-D objects by analyzing characteristics including faces, edges, and vertices.
SS3.5 Demonstrate understanding of 2-D shapes (regular and irregular) including triangles, quadrilaterals, pentagons, hexagons, and octagons including:
· describing
· comparing
· sorting. / Measurement involves the comparison of an attribute of an object or event with a unit that has the same attribute. This involves:
· understanding attributes of things being measured,
· familiarity with the units for a particular attribute,
· understanding the process of using units to measure
· using measurement tools.
There are many ways to see and describe similarities and differences within and among 2-D shapes and 3-D objects.
· Many of the properties and attributes that apply to 2-D shapes also apply to 3-D objects. / The VAA team felt SS3.1 was an extended outcome since it could be taught throughout the year in situational contexts.
Measurement of time is a comparison of the duration of an event using units that measure the passage of time. We measure duration of an event with:
· non-standard units such as pendulum swings, movement of the sun, or steady taps
· standard units such as minutes, hours, weeks, years.
The use of standard measurement units simplifies communication about the size of an object or shape.
The VAA team felt SS3.4 and SS3.5 were extended outcomes since they could be taught in the context of other subjects such as Art or Science.
2-D shapes include all regular and irregular polygons.
3-D objects include cubes, spheres, cones, cylinders, pyramids, and prisms.
Grade 3 - Statistics and Probability
Outcomes / Big Ideas / Teaching Information
Statistics
SP3.1 Demonstrate understanding of first-hand data, using tally marks, charts, lists, bar graphs, and line plots (abstract pictographs), through:
· collecting, organizing and representing
· solving situational questions. / Data can be collected, organized and displayed in different ways to see the “at-a-glance” answer to our question.
· There are different strategies for organizing and displaying data. / The VAA team felt SP3.1 was an extended outcome since it could be taught in the context of other subjects such as Science, Social, or Health.
There are four steps in working with data:
1. Formulating a good question
2. Collecting and organizing data
3. Displaying data visually (a graph)
4. Analyzing data to answer our question.
1