Review and extend previous understanding of number including prime, whole numbers, integers and converting between fractions, decimals and percentages Review, develop and select appropriate algorithms and strategies for performing operations on the various number forms Develop an understanding of ratios and begin to develop understanding of direct proportionality Analyze proportional relationships and use them to solve problems in a variety of meaningful contexts
Conceptual Framework
relationships equivalence, quantity in the context of identities and relationships
Statements of Inquiry
Understanding properties of numbers and the relationships between them help us to make sense of the world, both real and abstract
Factual
How do we best use various important numerical forms to understand, describe and compare quantities that surround us?
Conceptual
How does understanding number properties help us solve problems?
Debatable
Are different forms of numbers really necessary in our daily lives?
Description
Proportional relationships can be used to solve problems in meaningful contexts. In this unit students will review and extend their understanding of the properties of numbers. Students will develop and select appropriate algorithms and strategies for performing operations on the various number forms. Students will explore the equivalent relationships between fractions, decimals and percentages. They will also compute the proportion of a quantity, and develop an understanding of ratio and how it relates to proportionality. In this context students will explore the identities of number forms and the relationship between them.
Learning Outcomes
Perform four operations on positive integers (including order of operations)
Develop and use strategies to make reasonable estimates when finding sums, differences, products and quotients of rational numbers
Understand and perform operations with directed (positive and negative) numbers
Develop fluency in converting between integers, fractions, decimals, and percentages
Express common fractions as decimals
Compare, order and perform operations with rational numbers
Represent rational numbers as percents, fractions & decimals and move comfortably between forms
Use a strategy to solve real life applications
Give examples of the following sets of numbers: odd, even, prime, composite, positive and negative
Apply ratio and proportionality to solve problems
Divide a quantity in a given ratio
Calculate a given percentage of a quantity and express one quantity as a percentage of another
Calculate the result of a percentage increase and decrease of a quantity
Apply percents to solve problems
Understand absolute value concepts such as ‘difference’ , ‘distance’