Task Sets: Recognize and represent proportional relationships between quantities - Common Core Math - Grade 7

Recall / Warm-Up

Which table shows a proportional relationship between $x$ and $y$ ?

$(x, y)$ pairs: $(2, 6)$ , $(4, 12)$ , $(6, 18)$ — ratios $y/x$ : $3, 3, 3$

$(x, y)$ pairs: $(1, 5)$ , $(3, 9)$ , $(5, 15)$ — ratios $y/x$ : $5, 3, 3$

$(x, y)$ pairs: $(2, 7)$ , $(4, 10)$ , $(6, 13)$ — ratios $y/x$ : $3.5, 2.5, 2.17$

$(x, y)$ pairs: $(0, 4)$ , $(2, 6)$ , $(4, 8)$ — ratios $y/x$ : undefined, $3$ , $2$

A map scale is 1 inch = 25 miles. How many miles does 3 inches represent?

$28$

$75$

$8\frac{1}{3}$

$225$

In a proportional relationship, $y = 9$ when $x = 3$ . What is $y$ when $x = 7$ ? Express as a whole number or fraction.

Fluency Practice

A table shows the relationship between $x$ and $y$ with these $(x, y)$ pairs: $(3, 15)$ , $(6, 30)$ , $(9, 45)$ , $(12, 60)$ .

Which conclusion is correct?

The relationship is proportional because $y/x = 5$ for the first row, so $k = 5$ .

The relationship is proportional because $y/x = 5$ for every row, confirming a constant ratio.

The relationship is not proportional because the $y$ -values are multiples of 15.

The relationship is proportional because all $y$ -values are larger than $x$ -values.

A proportional relationship between pounds of apples ( $x$ ) and total cost in dollars ( $y$ ) has these $(x, y)$ pairs: $(2, 5)$ , $(5, 12.5)$ , $(8, 20)$ .

What is the constant of proportionality $k$ ? Express as a decimal.

A baker uses flour and sugar in a proportional relationship with constant of proportionality $k = \frac{2}{3}$ (cups of sugar per cup of flour). How many cups of sugar does the baker need for 12 cups of flour?

A factory produces widgets at a constant rate: 240 widgets in 4 hours. Find the constant of proportionality, then find $w$ when $h = 7$ .

Gas costs $3.50$ per gallon. Let $c$ be the total cost in dollars and $g$ be the number of gallons. Which equation correctly represents this proportional relationship?

$c = \dfrac{g}{3.50}$

$c = g + 3.50$

$c = 3.50g$

$c = 3.50 + g$

Proportional Relationships — Tables, Graphs, Equations, and Verbal Descriptions

Recall / Warm-Up

Fluency Practice