6.4.B 6.4.C 6.4.D MA.6.AR.3.2 MA.6.AR.3.4 MA.6.AR.3.5

Ratios & Rates 6th Grade

Texas Essential Knowledge and Skills (TEKS): 6.4.B
apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates;
Texas Essential Knowledge and Skills (TEKS): 6.4.C
give examples of ratios as multiplicative comparisons of two quantities describing the same attribute;
Texas Essential Knowledge and Skills (TEKS): 6.4.D
give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients;
Florida - Benchmarks for Excellent Student Thinking: MA.6.AR.3.2
Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate.
Florida - Benchmarks for Excellent Student Thinking: MA.6.AR.3.4
Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities.
Florida - Benchmarks for Excellent Student Thinking: MA.6.AR.3.5
Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.

A ratio is a relationship between two values.

In the image below, there are 4 apples and 2 oranges.

The relationship between the number of apples and the number of oranges is a ratio.

What is the ratio of apples to oranges?

The ratio of apples to oranges can be written three ways.

4 to 2

4:2

\frac{4}{2}

What is the ratio of oranges to apples?

The answer is different from the answer above because order matters.

2 to 4

2:4

\frac{2}{4}

Ratios, like fractions, can be simplified.

So, the ratio of oranges to apples could also be written as follows.

1 to 2

1:2

\frac{1}{2}

What is the ratio of oranges to pieces of fruit?

Two of the 6 pieces of fruit are oranges.

So, one way to write the ratio of oranges to pieces of fruit is 2 to 6.

Ratios & Rates

Texas Essential Knowledge and Skills (TEKS): 6.4.B

apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates;

Texas Essential Knowledge and Skills (TEKS): 6.4.C

give examples of ratios as multiplicative comparisons of two quantities describing the same attribute;

Texas Essential Knowledge and Skills (TEKS): 6.4.D

give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients;

Florida - Benchmarks for Excellent Student Thinking: MA.6.AR.3.2

Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate.

Florida - Benchmarks for Excellent Student Thinking: MA.6.AR.3.4

Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities.

Florida - Benchmarks for Excellent Student Thinking: MA.6.AR.3.5

Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.

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