6.5.a MA.6.3.1 MA.6.3.3

Ratio & Rate Representations 6th Grade

Texas Essential Knowledge and Skills (TEKS): 6.5.a
represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions;
Florida - Benchmarks for Excellent Student Thinking: MA.6.3.1
Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: ab, a to b, or a:b where b=/=0.
Florida - Benchmarks for Excellent Student Thinking: MA.6.3.3
Extend previous understanding of fractions and numerical patterns to generate or complete a two-or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios.

A proportion is an equation indicating two ratios are equal.

If a is to b as c is to d, then

\frac{a}{b} = \frac{c}{d}

\frac{a}{b} = \frac{c}{d}

, then, using cross multiplication,

a d = b c

Then, by rewriting the equation,

\frac{a}{c} = \frac{b}{d}

Similarly,

\frac{d}{b} = \frac{c}{a}

and

\frac{b}{a} = \frac{d}{c}

1 is to 2 can be written as

\frac{1}{2}

. 3 is to n can be written as

\frac{3}{n}

.
So,

\frac{1}{2} = \frac{3}{n}

Now, write all the possible variations of the proportion.

\frac{1}{3} = \frac{2}{n} \frac{n}{2} = \frac{3}{1} \frac{n}{3} = \frac{2}{1}

1 batch is to 2 eggs as 3 batches is to E can be written as follows.

\frac{1 batch}{2 eggs} = \frac{3 batches}{E}

Similar figures are the same shape, but not necessarily the same size.

Scale factor is the ratio of corresponding side lengths
(new image to old image) of similar figures.

So, any of the following proportions could be used to solve for x.

\frac{4 ft}{9 ft} = \frac{12.4 ft}{x} \frac{4 ft}{12.4 ft} = \frac{9 ft}{x} \frac{12.4 ft}{4 ft} = \frac{x}{9 ft} \frac{9 ft}{4 ft} = \frac{x}{12.4 ft}

A scale drawing (or scale model) is a proportional representation of an object.

A scale drawing's scale indicates the relationship between the
representation's measurements and the actual measurements.

The given scale is one of the ratios in the proportion,

\frac{1 in.}{14.4 ft}

The first ratio is written as the scale length to the actual length.
Write the second ratio the same way, scale length to actual length,

\frac{5 in.}{x}

So, a proportion which could be used to solve for x is

\frac{1 in.}{14.4 ft} = \frac{5 in.}{x}

Ratio & Rate Representations

Texas Essential Knowledge and Skills (TEKS): 6.5.a

represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions;

Florida - Benchmarks for Excellent Student Thinking: MA.6.3.1

Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: ab, a to b, or a:b where b=/=0.

Florida - Benchmarks for Excellent Student Thinking: MA.6.3.3

Extend previous understanding of fractions and numerical patterns to generate or complete a two-or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios.

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