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Mathematics

Grade 4: Patterning and Algebra

Planning: Term #

Tracking: Ach. Level

Overall Expectations

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• describe, extend, and create a variety of numeric and geometric patterns, make predictions related to the patterns, and investigate repeating patterns involving reflections;

 

 

 

 

• demonstrate an understanding of equality between pairs of expressions, using addition, subtraction, and multiplication.

 

 

 

 

Specific Expectations

 

 

 

 

Patterns and Relationships

 

 

 

 

– extend, describe, and create repeating, growing, and shrinking number patterns (e.g., “I created the pattern 1, 3, 4, 6, 7, 9, …. I started at 1, then added 2, then added 1, then added 2, then added 1, and I kept repeating this.”);

 

 

 

 

– connect each term in a growing or shrinking pattern with its term number (e.g., in the sequence 1, 4, 7, 10, …, the first term is 1, the second term is 4, the third term is 7, and so on), and record the patterns in a table of values that shows the term number and the term;

 

 

 

 

– create a number pattern involving addition, subtraction, or multiplication, given a pattern rule expressed in words (e.g., the pattern rule “start at 1 and multiply each term by 2 to get the next term” generates the sequence 1, 2, 4, 8, 16, 32, 64, …);

 

 

 

 

– make predictions related to repeating geometric and numeric patterns (Sample problem: Create a pattern block train by  alternating one green triangle with one red trapezoid. Predict which block will be in the 30th place.);

 

 

 

 

– extend and create repeating patterns that result from reflections, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper).

 

 

 

 

Expressions and Equality

 

 

 

 

– determine, through investigation, the inverse relationship between multiplication and division (e.g., since 4 x 5 = 20, then 20 5 = 4; since 35 5 = 7, then 7 x 5 = 35);

 

 

 

 

– determine the missing number in equations involving multiplication 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 [1] x 4 = 24?);

 

 

 

 

– identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the distributive property of multiplication over addition to facilitate computation with whole numbers (e.g., “I know that 9 x 52 equals 9 x 50 + 9 x 2. This is easier to calculate in my head because I get 450 + 18 = 468.”).

 

 

 

 

Student Name:

 

 

 

 

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