Operational Sense, Multiples, Factors, Decimal Numbers and Fractions / Percent
Our first unit in Math will focus on Multiples, Factors, Decimal Numbers (Multiplication / Division), Proportional Reasoning (rate / ratio), and Operational Sense. Students can begin to review multiplication and division at home. Students should have a strong understanding of place value (including whole numbers and decimal numbers to hundredths). You may need to spend some time reviewing this with your child.
You can also help at home by reviewing with your child percent and fractions so they can switch back and forth easily between the two. (E.g. 2 / 5 = 40%) They also need to be able to reason this out and show how they arrived at the answer.
We will spend some time working with Math manipulatives to help students have a strong understanding of fractions, percent and decimal numbers.
Below you will find a list of the Ontario Curriculum Expectations that we will be covering the first 5 weeks of school.
Please encourage your child to check their UG Cloud Calendar for homework, assignments, projects, quizzes and tests.
In this unit, students will:
– 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.);
– 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.”);
– use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals
– 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?);
– 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;
– 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?).
– represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper);
– divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials (e.g., divide 3 by 1/2; divide 4 by 0.8);
– 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);
– evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations;
- demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number
– 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.).
You can also help at home by reviewing with your child percent and fractions so they can switch back and forth easily between the two. (E.g. 2 / 5 = 40%) They also need to be able to reason this out and show how they arrived at the answer.
We will spend some time working with Math manipulatives to help students have a strong understanding of fractions, percent and decimal numbers.
Below you will find a list of the Ontario Curriculum Expectations that we will be covering the first 5 weeks of school.
Please encourage your child to check their UG Cloud Calendar for homework, assignments, projects, quizzes and tests.
In this unit, students will:
– 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.);
– 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.”);
– use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals
– 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?);
– 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;
– 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?).
– represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper);
– divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials (e.g., divide 3 by 1/2; divide 4 by 0.8);
– 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);
– evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations;
- demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number
– 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.).