Numeracy 8.3

N8.3 I can demonstrate an understanding of ratio and rate.
(a)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).

(b) Identify situations (such as providing for the family or community through hunting) in which a given quantity of a/b represents a:

(c)Demonstrate (orally, through arts, concretely, pictorially, symbolically, and/or physically) the difference between ratios and rates.

(d)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).

(e)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.

(f)Explain how to recognize whether a comparison requires the use of proportional reasoning (ratios or rates) or subtraction.

(g)Create and solve problems involving rates, ratios, and/or probabilities.

Questions to consider:

How might you compare the size of the images mathematically? What measurements would you need to make?

How would it change things if the larger photo was the original and the smaller was a reduction?

What information would you need to know to determine the scale of the photos?

Using graph paper, draw an irregular shape using the graph paper. Then draw an enlargement or a reduction of the shape on the graph paper.

How does the size of your second image compare to the first?
Is the size comparison between the two drawings the same for all parts of the drawing? Why or why not?
What is the best way to express this comparison mathematically? Why?
How can you use ratios to express size comparison of enlarged and reduced images?