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General Outcome
To Develop Number Sense
Demonstrate an understanding of place value, including numbers that are:
- greater than one million
- less than one thousandth.
Solve problems involving whole numbers and decimal numbers.
Demonstrate an understanding of factors and multiples by:
- determining multiples and factors of numbers less than 100
- identifying prime and composite numbers
- solving problems using multiples and factors.
Relate improper fractions to mixed numbers and mixed numbers to improper fractions.
Achievement Indicators
- Explain how the pattern of the place value system, i.e., the repetition of ones, tens and hundreds within each period, makes it possible to read and write numerals for numbers of any magnitude.
- Provide examples of where large and small numbers are used; e.g., media, science, medicine, technology.
- Identify which operation is necessary to solve a given problem, and solve it.
- Determine the reasonableness of an answer.
- Estimate the solution to, and solve, a given problem.
- Determine whether the use of technology is appropriate to solve a given problem, and explain why.
- Use technology when appropriate to solve a given problem.
- Identify multiples for a given number, and explain the strategy used to identify them.
- Determine all the whole number factors of a given number, using arrays.
- Identify the factors for a given number, and explain the strategy used; e.g., concrete or visual representations, repeated division by prime numbers, factor trees.
- Provide an example of a prime number, and explain why it is a prime number.
- Provide an example of a composite number, and explain why it is a composite number.
- Sort a given set of numbers as prime and composite.
- Solve a given problem involving factors or multiples.
- Explain why 0 and 1 are neither prime nor composite.
- Demonstrate, using models, that a given improper fraction represents a number greater than 1.
- Express improper fractions as mixed numbers.
- Express mixed numbers as improper fractions.
- Place a given set of fractions, including mixed numbers and improper fractions, on a number line, and explain strategies used to determine position.
- Translate a given improper fraction between concrete, pictorial and symbolic forms.
- Translate a given mixed number between concrete, pictorial and symbolic forms.
- Provide a concrete or pictorial representation for a given ratio.
- Write a ratio from a given concrete or pictorial representation.
Demonstrate an understanding of ratio, concretely, pictorially and symbolically.
Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolically.
Demonstrate an understanding of integers, concretely, pictorially and symbolically.
Demonstrate an understanding of multiplication and division of decimals (1-digit whole number multipliers and 1-digit natural number divisors).
Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers)
- Express a given ratio in multiple forms, such as 3:5, or 3 to 5.
- Identify and describe ratios from real-life contexts, and record them symbolically.
- Explain the part/whole and part/part ratios of a set; e.g., for a group of 3 girls and 5 boys, explain the ratios 3:5, 3:8 and 5:8.
- Solve a given problem involving ratio.
- Explain that "percent" means "out of 100."
- Explain that percent is a ratio out of 100.
- Use concrete materials and pictorial representations to illustrate a given percent.
- Record the percent displayed in a given concrete or pictorial representation.
- Express a given percent as a fraction and a decimal.
- Identify and describe percents from real-life contexts, and record them symbolically.
- Solve a given problem involving percents.
- Extend a given number line by adding numbers less than zero, and explain the pattern on each side of zero.
- Place given integers on a number line, and explain how integers are ordered.
- Describe contexts in which integers are used; e.g., on a thermometer.
- Compare two integers; represent their relationship using the symbols <, > and =; and verify the relationship, using a number line.
- Order given integers in ascending or descending order.
- Place the decimal point in a product, using front-end estimation; e.g., for 15.205 m x 4, think 15 m x 4, so the product is greater than 60 m.
- Place the decimal point in a quotient, using front-end estimation; e.g., for $26.83 ÷ 4, think $24 ÷ 4, so the quotient is greater than $6.
- Correct errors of decimal point placement in a given product or quotient without using paper and pencil.
- Predict products and quotients of decimals, using estimation strategies.
- Solve a given problem that involves multiplication and division of decimals using multipliers from 0 to 9 and divisors from 1 to 9.
- Explain, using examples, why there is a need to have a standardized order of operations.
- Apply the order of operations to solve multistep problems with and without technology; e.g., a computer, a calculator.
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