Algebraic Expressions & Equations

Algebraic Expressions & Equations

Ideal Weight

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Ideal Weight

This man, Sultan Kösen, is one of the tallest men on Earth. He is 251 cm tall, and his brother Hasan, who is standing next to him, is 178 cm tall.

A rule of thumb is an easy-to-remember guide for making an estimate.

One rule of thumb is that an adult’s ideal weight in kilograms is 100 less than his or her height in centimeters.

  • Use this rule of thumb to estimate the weights in kilograms of Sultan Kösen and his brother.

Math Mission

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Evaluate expressions and solve equations to find measurements of height and weight.

Adult Ideal Weight

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Adult Ideal Weight

Use this rule of thumb: an adult’s ideal weight in kilograms is 100 less than his or her height in centimeters.

  • Let h = an adult’s height in centimeters. Write an algebraic expression for the person’s ideal weight in kilograms. Evaluate your expression to find the ideal weight, in kilograms, for an adult who is 150 cm tall.
  • Write and solve an equation to find the height, in centimeters, of an adult who has an ideal weight of 30 kg.

Hint:

  • An algebraic expression can combine arithmetic operations, numbers, and letters. Letters are used to represent variables. These are examples of algebraic expressions that contain variables: a , 3b , and 4x + 5. The variables in the expressions area ,b , andx .
  • To evaluate an algebraic expression, replace each variable in the expression with a number and find the value of the expression. For example, to evaluate the expression 4 x + 5 whenx = 7, replacex with 7 and find the value of 4 • 7 + 5, which is 28 + 5, or 33
  • An equation is a statement where two expressions are equal. It is formed by placing an equals sign between the two equivalent expressions
  • To solve an equation, find the value of the variable that makes the equation true.

Weight in Pounds

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Weight in Pounds

Many people in the United States know their weight only in pounds. There is a rule of thumb that can help you use your weight in pounds to estimate your weight in kilograms: divide your weight in pounds by 2, and then subtract 10% of that number from the result.

  • Let p = a person’s weight in pounds. Write an expression for the person’s weight in kilograms.
  • Can you write an equivalent expression for the person’s weight in kilograms?
  • Use the rule of thumb to find the weight, in kilograms, of a person who weighs 115 lb.
  • Use the rule of thumb to find the weight, in pounds, of a person who weighs 49.5 kg.

Hint:

  • Equivalent expressions are expressions that have the same value when a given value is substituted for the variable. For example, 3(x + 6) and 3x + 18 are equivalent expressions. Whenx = 2, both expressions have the value 24.
  • If you have 80 pounds, how do you take 10% of it?
  • How might you use the distributive property to write equivalent expressions?
  • Now think back to the difference between an expression and an equation. To find a person’s weight in kilograms, do you need to evaluate an expression or solve an equation?
  • To find a person’s weight in pounds, do you need to evaluate an expression or solve an equation?

Prepare a Presentation

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Prepare a Presentation

Explain your solutions for the weight in kilograms and in pounds. Use your work to support your explanation.

Challenge Problem

To estimate your weight in kilograms, divide your weight in pounds by 2 and then subtract 10% of that number from the result.

Let p = weight in pounds. Let k = weight in kilograms.

  • Write an equation for the relationship between k and p.
  • Now draw a graph to show the relationship between k and p. Let p be the independent variable.
  • Use the graph to find the weight in kilograms of a person who weighs 115 lb and the weight in pounds of a person who weighs 49.5 kg.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ strategies for writing and evaluating expressions and for writing and solving equations.

Hint:

As your classmates present, ask questions such as:

  • How did you know whether to use an expression or an equation?
  • How did you find the expression (or equation)?
  • How can you check the solution to your equation?
  • How do you know whether two expressions are equivalent?

Expressions and Equations

Formative Assessment

Summary of the Math: Expressions and Equations

Read and Discuss

An expression can combine arithmetic operations with numbers, letters, or both. Letters are used to represent variables.

  • To evaluate an expression, find the value of the expression by replacing each variable in the expression with a given number.
  • Two expressions are equivalent if they represent the same amount. When a given value is substituted for each variable (such as x), equivalent expressions have the same value.
  • An equation is a statement that two expressions are equal. Every equation is composed of two expressions linked by an equal sign.
  • To solve an equation, find the value of the variable that makes the two sides of the equation equal.

Hint:

Can you:

  • Describe the differences between an expression and an equation?
  • Explain what it means to evaluate an expression?
  • Explain what it means to solve an equation?
  • Explain what it means for expressions to be equivalent?

Reflect On Your Work

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Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

I think an expression is different from an equation because …