6th Gr. Ratios

Additive reasoning

focuses on the use of addition and subtraction for comparisons.

Multiplicative reasoning

focuses on the use of multiplication and division for comparisons.

Ratio

is a comparison of two quantities using division. Ratios may be written in 3 ways. (ex. The ratio of boys (12) to girls (14) in Mr. Levine's class maybe written as 12:14, 12 to 14, or 12/14 (fraction form))

Terms of a ratio

Are the quantities x and y in the ratio. The terms of the ratio 12:14 are 12 and 14.

Equivalent ratios

are ratios that represent the same part-to-part or part-to-whole relationship. (ex. 2:3 and 4:6 are equivalent ratios.)

Percent

is a part-to-whole ratio where the whole is equal to 100.

Part-to-part ratio

compares parts.

Part-to-whole ratio

compares a part of a whole to the total number of parts.

Qualitative reasoning

comparing ratios without measuring or counting quantities. Use qualities (describing with adjectives).

Quantitative reasoning

comparing ratios by measuring or counting quantities.

Tape diagram

illustrates number relationships by using rectangles to represent ratio parts.

Rate

is a ratio that compares two quantities measured in different units.

Proportion

is an equation that states that two ratios are equal. In a proportion, the quantities composing each part of the ratio have the same multiplicative relationship between them.

Scaling up

means you multiply both parts of the ratio by the same factor greater than 1.

Scaling down

means you divide both parts of the ratio by the same factor greater than 1 or multiply both parts of the ratio by same factor less than 1.

Double number line

e is a model made up of two number lines used together to represent the ratio between two quantities. The intervals on each number line maintain the same ratio.

Linear relationship

When a set of points graphed on a coordinate plane forms a straight line.