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Interpreting linear expressions
Description
Exercise Name: Interpreting linear expressions
Math Missions: 7th grade (U.S.) Math Mission, Algebra I Math Mission, Mathematics II Math Mission
Types of Problems: 1

The Interpreting linear expressions exercise appears under the 7th grade (U.S.) Math Mission, Algebra I Math Mission and Mathematics II Math Mission. This exercise provides examples of some of subtleties in linear expressions and word problems.

## Types of Problems

There is one type of problem in this exercise:

1. Tell which of these expressions model which statement: This problem provides a chart, several expressions and some statements. The user is asked to select which mathematical expressions represent the corresponding English statements.

## Strategies

Confidence with translation between mathematics and English can help to perform this exercise.

1. Some of the problems use markup equations. The amount of a markup is ${\frac{p}{100}}$ times the amount and the price after markup is ${\frac{(1+p)}{100}}$times the amount.
2. Some of the problems use discount equations. The amount of a discount is ${\frac{p}{100}}$ times the amount and the price after discount is ${\frac{(1+p)}{100}}$ times the amount.
3. The commutative property is used on some problem to rewrite equivalent expressions. Remember that ${a+b=b+a}$.
4. The "not represented" category is used often so expect it.

## Real-life Applications

1. Melting Snow: Suppose a water district wants to know how much snowmelt runoff it can expect this year. The melt comes from a big valley, and every year the district measures the snowpack and the water supply. It gets 60 acre-feet from every 6 inches of snowpack. This year surveyors measure 6 feet and 4 inches of snow. The district put that in the linear expression (${\frac{60 \text{ acre-feet}}{6 \text{ inches}})\times 76 \text{ inches}}$. Water officials can expect 760 acre-feet of snowmelt from the water.
2. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.