Target Numbers (Investigation)

Objectives

• To understand how to fluently add, subtract, multiply and divide decimals.
• To practice with order of operations for decimals and negative decimals.
• To visualize the operations for positive and negative decimals.

Materials

• Construction Paper
• Marker or Pen
• Internet

Procedure

Work on your own or in pairs. 

1. On your construction paper draw a number line going from -10 to 10.
2. Mark each halfway point between the numbers with a slightly smaller mark.
   
3. Indicate where you think each of the numbers given in the table lay on the number line.
   
4. Represent the recurring decimals as fractions.
5. Use the numbers in the table to find as many ways as possible to reach 10. You can combine as many numbers as you would like using either addition, subtraction, multiplication or division. For example I could use the combination -2(-2.5)+(-0.5)(-10). Use your number line to help you do this.
6. Make sure you write down each expression you come up with.
7. When you are finished count the number of ways to reach 10 you came up with.

Questions

1. How many ways did you find to create 10 from the numbers given?
2. From using your number line, what do you notice of the addition and subtraction of negative decimals? How is it similar to addition and subtraction with positive decimals? How is it different?
3. Can you think of a way to rewrite an addition problem involving a negative decimal? Explain your reasoning.
4. From using your number line, what do you notice of the multiplication and division of negative decimals? How is it similar to multiplication and division with positive decimals? How is it different?
5. Compare with a friend! Who was able to find more ways to make 10? Did you have any expressions in common? What expressions did you come up with that were different?
6. How could you use the addition of negative decimals to represent money you spend? Work with a friend to come up with a scenario that involves spending money and use negative decimals to represent it. This may involve some research.