Grade 7 / Grade 8 / Grade 9
Outcomes / A7Apply patterning in renaming numbers from fractions and mixed numbers to decimal numbers
A8Rename single-digit and double-digit repeating decimals to fractions through the use of patterns, and use these patterns to make predictions
A9Compare and order proper and improper fractions, mixed numbers and decimal numbers
A10Illustrate, explain and express ratios, fractions, decimals and percents in alternative forms
B6Estimate the sum or difference of fractions when appropriate
B7Multiply mentally a fraction by a whole number and vice versa
B8Estimate and determine percent when given the part and the whole
B9 Estimate and determine the percent of a number
G1 Identify situations for which the probability would be near 0, ¼, ½, ¾ and 1
G4Create and solve problems, using the numerical definition of probability
G5Compare experimental results with theoretical results
G6Use fractions, decimals and percents as numerical expressions to describe probability / A7Compare and order integers and positive and negative rational numbers (in decimal and fractional forms)
A8Represent and apply fractional percents, and percents greater than 100, in fraction or decimal form, and vice versa
A9Solve proportion problems that involve equivalent ratios and rates
B1Demonstrate an understanding of the properties of operations with integers and positive and negative rational numbers (in decimal and fractional forms)
B2Solve problems involving proportions, using a variety of methods
B3Create and solve problems which involve finding a, b, or c in the relationship a% of b=c, using estimation and calculation
B5Add and subtract fractions concretely, pictorially and symbolically
B6Add and subtract fractions mentally, when appropriate
B7Multiply fractions concretely, pictorially and symbolically
B8Divide fractions concretely, pictorially and symbolically
B9Estimate and mentally compute products and quotients involving fractions
B10Apply the order of operations to fraction computations, using both pencil and paper and the calculator
B11Model, solve and create problems involving fractions in meaningful contexts
G1Conduct experiments and simulations to find probabilities of single and complementary events
G2 Determine theoretical probabilities of singles and complementary events
G3 Compare experimental and theoretical probabilities / A3Demonstrate an understanding of the meaning and uses of irrational numbers
A4Demonstrate an understanding of the interrelationships of subsets of real numbers
B1Model, solve and create problems involving real numbers
B2Add, subtract, multiply and divide rational numbers in fractional and decimal forms, using the most appropriate method
B3Apply the order of operations in rational number computations
D5Demonstrate an understanding of and apply proportions within similar triangles
G1Make predictions of probabilities involving dependent and independent events by designing and conducting experiments and simulations
G2Determine theoretical probabilities of independent ad dependent events
G3Demonstrate an understanding of how experimental and theoretical probabilities are related
G4Recognize and explain why decisions based on probabilities may be combinations of theoretical calculations, experimental results and subjective judgments
Concepts / Main Ideas
Meaning / Grade 7 / Grade 8 / Grade 9
- understanding of simple fractions with denominators equal to or less than 10
- fractions used in context
- part of a whole
- part of a set
- fair sharing
- fraction families are introduced
- delay use of symbols until concept is fully explored
- develop understanding of negative fractions
- understand the meaning of percent increase, percent decrease and percent greater than 100
Comparing and Ordering /
- compare and order fractions, mixed numbers and decimals through benchmarks, common denominators and/or numerators, or conversion models
- develop strategies to order numbers of size and various forms in the same problem
- compare and order positive and negative fractions and decimals
Equivalent Fractions /
- equivalence of mixed numbers and improper fractions
- convert fractions to decimals using a calculator
Operations /
- estimate sums and differences of fractions
- mentally multiply fractions by whole numbers and whole numbers by fractions
- add, subtract, multiply and divide fractions concretely, pictorially and symbolically
- estimate sums and differences
- add and subtract fractions mentally
- estimate products and quotients
- work on order of operations with fractions using both pen and paper and calculator
- assess competence with fraction operations through problem situations
- develop comfort in working with real numbers and order of operations to solve problem situations
- apply order of operations
Fractions/ Decimals and/or Percents /
- use patterns in single and double-digit repeating decimals to name fractions
- continue work on changing fractions and mixed numbers to decimals and vice-versa
- introduce terminating and repeating decimals, their symbols and explore patterns
- work on mentally being able to change from fractions to percents
- use models to help equate an improper fraction with its corresponding mix number
- continue to work on the alternate ways to express fractions, decimals, percents and ratios using illustrations, models and symbols
- work on intuitive understand and context for percent
- use fractions, decimals and percents to numerically describe probabilities
- represent and apply fractional percents in fraction or decimal form
- be able to create and solve a% of b = c problems for each variable
- use fractions to determine theoretical probabilities in dependent and independent events
Ratio and Proportion /
- express ratios and fractions in alternative forms
- solve proportion problems using equivalent ratios and rates
- provide a number of strategies for solving problems involving proportionality
- use proportions with similar triangles