Understanding Fractions & Decimals

Understanding Fractions & Decimals

Temperature

Opening

Temperature

Work with your partner to write a word problem about temperature that can be represented by the following expression. You do not need to solve your word problem.

1.3 − (−2.7)

  • Share your problem with the class.

Hint:

To write a word problem for the expression, think about the different ways of looking at subtraction.

  • You can think of subtraction as “taking away from” or decreasing a starting amount.
  • You can think of subtraction as finding the distance between two numbers.

Math Mission

Opening

Use number lines to add and subtract positive and negative fractions and decimals.

Add and Subtract Decimals

Work Time

Add and Subtract Decimals

Use the Number Line Tool interactive to find each sum or difference. Write the answer as an equation.

  • 2.4 − 4.2
  • 1.3 − (−2.7)
  • −3.9 + 7.4

INTERACTIVE: Number Line Tool

Add and Subtract Fractions

Work Time

Add and Subtract Fractions

Use the Number Line Tool to find each sum or difference. Write the answer as an equation.

  • 34+(212)
  • 313523
  • 415(325)

INTERACTIVE: Number Line Tool

Hint:

What is the method for adding numbers with different signs?

  • Apply this method to the addition problem with different signs from this task or from the previous task.
  • Do you get the same answer that you got using the number line?

Add and Subtract Money

Work Time

Add and Subtract Money

Kevin writes a check for $52.75, but he has only $32.45 in his checking account.

Because Kevin’s balance is now less than $0, his bank charges him a penalty fee of $20.

  • What is the balance in Kevin’s account now?

Hint:

Start with $32.45.

  • Do you need to add or subtract $52.75 to represent the check that Kevin wrote?
  • Do you need to add or subtract the penalty fee?

Add and Subtract Distance

Work Time

Add and Subtract Distance

Sophie and Jack are hiking on the same trail.

Sophie is at an elevation of 1712 ft.

Jack is at an elevation of 1923 ft.

  • How much greater is Jack’s elevation than Sophie’s?

Hint:

Try sketching a number line and showing the two elevations. How can you find the difference between the elevations?

Prepare a Presentation

Work Time

Prepare a Presentation

Explain how the methods you used in previous lessons to add and subtract integers also work to add and subtract rational numbers (fractions and decimals). Support your thinking with examples of your work.

Challenge Problem

Each equation has two solutions. Find both of them.

  • |x − 1.7| = 2.8
  • |x38|=14

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ methods for adding and subtracting positive and negative fractions and decimals.

Hint:

As other students present, ask questions such as:

  • Are you sure you moved the correct number of units for the second number?
  • Are you sure you moved in the correct direction for the second number?
  • Can you explain again how you found your answer?
  • How did you decide which operations you needed to perform in order to solve the problem?
  • Shouldn’t the answer to that problem be negative?
  • How does your explanation compare with that of other students?

Add and Subtract Positive and Negative Numbers

Formative Assessment

Summary of the Math: Add and Subtract Positive and Negative Numbers

Write a summary about adding and subtracting positive and negative numbers.

Hint:

Check your summary.

  • Do you explain how you can use the methods for adding and subtracting positive and negative integers to add and subtract positive and negative fractions and decimals?

Reflect On Your Work

Work Time

Reflection

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

The most important thing I learned in this lesson is …