Mathematics

Grade 6: Number Sense and Numeration	Planning: Term # Tracking: Ach. Level
Overall Expectations	1	2	3	4
• read, represent, compare, and order whole numbers to 1 000 000, decimal numbers to thousandths, proper and improper fractions, and mixed numbers;
• solve problems involving the multiplication and division of whole numbers, and the addition and subtraction of decimal numbers to thousandths, using a variety of strategies;
• demonstrate an understanding of relationships involving percent, ratio, and unit rate.
Specific Expectations
Quantity Relationships
– represent, compare, and order whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals);
– demonstrate an understanding of place value in whole numbers and decimal numbers from 0.001 to 1 000 000, using a variety of tools and strategies (e.g. use base ten materials to represent the relationship between 1, 0.1, 0.01, and 0.001) (Sample problem: How many thousands cubes would be needed to make a base ten block for 1 000 000?);
– read and print in words whole numbers to one hundred thousand, using meaningful contexts (e.g., the Internet, reference books);
– represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, number lines, calculators) and using standard fractional notation (Sample problem: Use fraction strips to show that 1 1/2 is greater than 5/4);
– estimate quantities using benchmarks of 10%, 25%, 50%, 75%, and 100% (e.g., the container is about 75% full; approximately 50% of our students walk to school);
– solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1 000 000 (Sample problem: How would you determine if a person could live to be 1 000 000 hours old? Show your work.);
– identify composite numbers and prime numbers, and explain the relationship between them (i.e., any composite number can be factored into prime factors) (e.g., 42 = 2 x 3 x 7).
Operational Sense
– use a variety of mental strategies to solve addition, subtraction, multiplication, and division problems involving whole numbers (e.g., use the commutative property: 4 x 16 x 5 = 4 x 5 x 16, which gives 20 x 16 = 320; use the distributive property: (500 + 15) ÷ 5 = 500 ÷ 5 + 15 ÷ 5, which gives 100 + 3 = 103);
– multiply whole numbers by 0.1, 0.01, and 0.001 using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule);
– multiply and divide decimal numbers by 10, 100, 1000, and 10 000 using mental strategies (e.g., “To convert 0.6 m2 to square centimetres, I calculated in my head 0.6 x 10 000 and got 6000 cm2.”) (Sample problem: Use a calculator to help you generalize a rule for multiplying numbers by 10 000.);
– solve problems involving the multiplication and division of whole numbers (four digit by two-digit), using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);
– add and subtract decimal numbers to thousandths, using concrete materials, estimation, algorithms, and calculators;
– multiply and divide decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms, and calculators (e.g., calculate 4 x 1.4 using base ten materials; calculate 5.6 ÷ 4 using base ten materials);
– use estimation when solving problems involving the addition and subtraction of whole numbers and decimals, to help judge the reasonableness of a solution;
– explain the need for a standard order for performing operations, by investigating the impact that changing the order has when performing a series of operations (Sample problem: Calculate and compare the answers to 3 + 2 x 5 using a basic four function calculator and using a scientific calculator.).
Proportional Relationships
– represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation (Sample problem: In a classroom of 28 students, 12 are female. What is the ratio of male students to female students?);
– determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100), decimal numbers, and percents (e.g., use a 10 x 10 grid to show that 1/4 = 0.25 or 25%);
– represent relationships using unit rates (Sample problem: If 5 batteries cost $4.75, what is the cost of 1 battery?).
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Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.