Untitled

Mathematics

Grade 3: Patterning and Algebra

Planning: Term #

Tracking: Ach. Level

Overall Expectations

1

2

3

4

• describe, extend, and create a variety of numeric patterns and geometric patterns;

 

 

 

 

• demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit numbers.

 

 

 

 

Specific Expectations

 

 

 

 

Patterns and Relationships

 

 

 

 

– identify, extend, and create a repeating pattern involving two attributes (e.g., size, colour, orientation, number), using a variety of tools (e.g., pattern blocks, attribute blocks, drawings) (Sample problem: Create a repeating pattern using three colours and two shapes.);

 

 

 

 

– identify and describe, through investigation, number patterns involving addition, subtraction, and multiplication, represented on a number line, on a calendar, and on a hundreds chart (e.g., the multiples of 9 appear diagonally in a hundreds chart);

 

 

 

 

– extend repeating, growing, and shrinking number patterns (Sample problem:Write the next three terms in the pattern 4, 8, 12, 16, ….);

 

 

 

 

– create a number pattern involving addition or subtraction, given a pattern represented on a number line or a pattern rule expressed in words (Sample problem: Make a number pattern that starts at 0 and grows by adding 7 each time.);

 

 

 

 

– represent simple geometric patterns using a number sequence, a number line, or a bar graph (e.g., the given growing pattern of toothpick squares can be represented numerically by the sequence 4, 7, 10, …, which represents the number of toothpicks used to make each figure);

 

 

 

 

– demonstrate, through investigation, an understanding that a pattern results from repeating an action (e.g., clapping, taking a step forward every second), repeating an operation (e.g., addition, subtraction), using a transformation (e.g., slide, flip, turn), or making some other repeated change to an attribute (e.g., colour, orientation).

 

 

 

 

Expressions and Equality

 

 

 

 

– determine, through investigation, the inverse relationship between addition and subtraction (e.g., since 4 + 5 = 9, then 9 – 5 = 4; since 16 – 9 = 7, then 7 + 9 = 16);

 

 

 

 

– determine, the missing number in equations involving addition and subtraction of one- and two-digit numbers, using a variety of tools and strategies (e.g., modelling with concrete materials, using guess and check with and without the aid of a calculator) (Sample problem: What is the missing number in the equation 25 – 4 = 15 + [1]?);

 

 

 

 

– identify, through investigation, the properties of zero and one in multiplication (i.e., any number multiplied by zero equals zero; any number multiplied by 1 equals the original number) (Sample problem: Use tiles to create arrays that represent 3 x 3, 3 x 2, 3 x 1, and 3 x 0. Explain what you think will happen when you multiply any number by 1, and when you multiply any number by 0.);

 

 

 

 

– identify, through investigation, and use the associative property of addition to facilitate computation with whole numbers (e.g., “I know that 17 + 16 equals 17 + 3 + 13. This is easier to add in my head because I get 20 + 13 = 33.”).

 

 

 

 

Student Name:

 

 

 

 

 Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.