Mathematics

Grade 7: Number Sense and Numeration	Planning: Term # Tracking: Ach. Level
Overall Expectations	1	2	3	4
• represent, compare, and order numbers, including integers;
• demonstrate an understanding of addition and subtraction of fractions and integers, and apply a variety of computational strategies to solve problems involving whole numbers and decimal numbers;
• demonstrate an understanding of proportional relationships using percent, ratio, and rate.
Specific Expectations
Quantity Relationships
– represent, compare, and order decimals to hundredths and fractions, using a variety of tools (e.g., number lines, Cuisenaire rods, base ten materials, calculators);
– generate multiples and factors, using a variety of tools and strategies (e.g., identify multiples on a hundreds chart; create rectangles on a geoboard) (Sample problem: List all the rectangles that have an area of 36 cm2 and have whole-number dimensions.);
– identify and compare integers found in real-life contexts (e.g., –10°C is much colder than +5°C);
– represent and order integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines);
– select and justify the most appropriate representation of a quantity (i.e., fraction, decimal, percent) for a given context (e.g., “I would use a decimal for recording the length or mass of an object, and a fraction for part of an hour.”);
– represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper);
– explain the relationship between exponential notation and the measurement of area and volume (Sample problem: Explain why area is expressed in square units [units2] and volume is expressed in cubic units [units3].).
Operational Sense
– divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials (e.g., divide 3 by ½ using fraction strips; divide 4 by 0.8 using base ten materials and estimation);
– use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals (e.g., use the commutative property: 3 x 2/5 x 1/3 = 3 x 1/3 x 2/5, which gives 1 x 2/5 = 2/5 ; use the distributive property: 16.8 ÷ 0.2 can be thought of as (16 + 0.8) ÷ 0.2 = 16 ÷ 0.2 + 0.8 ÷ 0.2, which gives 80 + 4 = 84);
– solve problems involving the multiplication and division of decimal numbers to thousandths by one-digit whole numbers, using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);
– solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);
– use estimation when solving problems involving operations with whole numbers, decimals, and percents, to help judge the reasonableness of a solution (Sample problem: A book costs $18.49. The salesperson tells you that the total price, including taxes, is $22.37. How can you tell if the total price is reasonable without using a calculator?);
– evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations;
– add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms;
– demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number (e.g., 1/2 + 1/2 + 1/2 = 3 x 1/2);
– add and subtract integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines).
Proportional Relationships
– determine, through investigation, the relationships among fractions, decimals, percents, and ratios;
– solve problems that involve determining whole number percents, using a variety of tools (e.g., base ten materials, paper and pencil, calculators) (Sample problem: If there are 5 blue marbles in a bag of 20 marbles, what percent of the marbles are not blue?);
– demonstrate an understanding of rate as a comparison, or ratio, of two measurements with different units (e.g., speed is a rate that compares distance to time and that can be expressed as kilometres per hour);
– solve problems involving the calculation of unit rates (Sample problem: You go shopping and notice that 25 kg of Ryan’s Famous Potatoes cost $12.95, and 10 kg of Gillian’s Potatoes cost $5.78. Which is the better deal? Justify your answer.).
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Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.