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Interpreting linear expressions
Interpreting-expressions 256
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.
    Ile1

    Tell which of these expressions model which statement

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.

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