Math Games

Grade 8 - Number

Standard 8.N.3 - Compare and understand ratios in a word problem.

Included Skills:

Demonstrate understanding of rates, ratios, and proportional reasoning concretely, pictorially, and symbolically.
• Identify and explain ratios and rates in familiar situations (e.g., cost per music download, traditional mixtures for bleaching, time for a hand-sized piece of fungus to burn, mixing of colours, number of boys to girls at a school dance, rates of traveling such as car, skidoo, motor boat or canoe, fishing nets and expected catches, or number of animals hunted and number of people to feed).
• Identify situations (such as providing for the family or community through hunting) in which a given quantity of represents a:
- fraction
- rate
- quotient
- percent
- probability
- ratio.
• Demonstrate (orally, through arts, concretely, pictorially, symbolically, and/or physically) the difference between ratios and rates.
• Verify or contradict proposed relationships between the different roles for quantities that can be expressed in the form a/b. For example:
- a rate cannot be represented by a percent because a rate compares two different types of measurements while a percent compares two measurements of the same type
- probabilities cannot be used to represent ratios because probabilities describe a part to whole relationship but ratios describe a part to part relationship
- a fraction is not a ratio because a fraction represents part to whole
- a ratio cannot be written as a fraction, unless the quantity of the whole is first determined (e.g., 2 parts white and 5 parts red paint is 2/7 white)
- a ratio cannot be written as percent unless the quantity of the whole is first determined (e.g., a ratio of 4 parts blue and 6 parts red paint can be described as having 40% blue).
• Write the symbolic form (e.g., 3:5 or 3 to 5 as a ratio, $3/min or $3 per one minute as a rate) for a concrete, physical, or pictorial representation of a ratio or rate.
• Explain how to recognize whether a comparison requires the use of proportional reasoning (ratios or rates) or subtraction.
• Create and solve problems involving rates, ratios, and/or probabilities.