Comparing and Scaling Develop students ability to make intelligent comparisons of quantitative information using ratios, fractions, decimals, rates, unit rates and percents . Students will learn different ways to reason in proportional situations. Students will use various proportional reasoning strategies they developed and apply these strategies in different context. We will also review solving 1 step equations, cross multiplying and multiplying and dividing fractions

Comparing and Scaling Rates Investigation 2 Comparing and Scaling Rates

Homework page 51 A 4, 5, 8, 11, 12, 13 B 5, 10, 11, 12, 27

Vocab Rate: a comparison of two quantities measured in different units Unit Rate: second quantity in a rate is 1 Rate table: table that shows the comparison of two quantities, find the 10 and 1 you can find all Constant of Proportionality: the constant multiplier in an equation or line

Investigation 2.1: Comparing Strategies How can you determine whether two ratios are equivalent or find which of two ratios is more favorable?

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What you should know Ratios Rates Equivalent rates Unit rates Does order of rate matter – no but you need to understand what the order means How can you determine whether two ratios are equivalent or find which of two ratios is more favorable? Get a common denominator then compare Put on a number line Convert to a decimal – unit rate

Investigation 2.2: Scaling Rates How can you use rate tables to find missing values? How are rate tables similar to scaling quantities and solving proportions? Students will be able to use rate tables to help compare amounts.

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What you should know Know how to make a rate table and what it is used for Rate is what you constantly add to get next value Use combinations in table to find the values that are not there, such as 6 is 5 and 1 How can you use rate tables to find missing values? Set up table to get needed values and then combine to get non listed values How are rate tables similar to scaling quantities and solving proportions? Gives you the unit rate or scale factor to then add to get next value or multiply to get larger values

Investigation 2.3: Unit Rates and Constant of Proportionality How can you find a unit rate in a description, an equation, a table, or a graph? Students will be able to identify the unit rates and determine if relationships have a constant of proportionality.

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Examples What is the constant of proportionality from this table and what is the equation that would represent this information

Examples What is the constant of proportionality and what is the equation that would represent this graph.

What you should know How to calculate a unit rate, which value needs to be zero, the denominator Set up a proportion with denom = 1 Divide the rate and this will give the unit rate How to determine the constant of proportionality from a graph or table, or word problem Table look to see if all ordered pairs give the same rate, constant of proportionality Rate (CP) is y to x, if they do not state which is which either way would work Equation is always y=kx, y is the top value of the rate (CP) Graph does it start at (0,0) then look at rise over run this is your rate (CP) Word problem do they give you an ordered pair, this should give you the rate, y over x How can you find a unit rate in a description, an equation, a table, or a graph? Similar to what we stated above