## Where Does the Decimal Point Go?

## Opening

# Where Does the Decimal Point Go?

The decimal points are missing from these products and quotients.

- Work with your partner to place the decimal points in the correct locations.

The decimal points are missing from these products and quotients.

- Work with your partner to place the decimal points in the correct locations.

Watch the video that shows Jan and Carlos using a general rule that they developed after seeing something happen over and over again.

- What do you think Jan noticed over and over again as she solved decimal multiplication problems?
- How did this repetition help her come up with her general rule?
- How did Jan justify that her rule works?
- Do you think Jan’s rule works?

VIDEO: Mathematical Practice 8

Solve mathematical and real-world problems involving multidigit decimals.

Solve each problem and show your steps.

- 26.19 + 378.5
- 56.4 – 5.22
- 7.5 × 0.57
- 19.76 ÷ 5.2

Ask yourself:

- How can you use estimation to help you determine where to place the decimal point?

Explain how you found the solution to each problem. What was similar about the processes? What was different?

Take notes on your classmates’ methods for performing operations with multidigit decimals.

As your classmates present, ask questions such as:

- How are operations with whole numbers similar to operations with decimals?
- How can you use estimation to check whether your solution is reasonable?
- Why do you need to align the decimal points when adding and subtracting with decimals?
- In a multiplication problem with decimals, how do you know where to place the decimal point in the product?
- In a division problem with decimals, why do you move the decimal point the same number of places in both the dividend and divisor?
- Why does your solution method make sense?

Choose one problem to solve. Use the table to solve the problem. Clearly show each step in your solution.

- Mia bought 1 pair of flip-flops and 3 beach balls. If she paid with a $20 bill, how much change did she get?
- Carlos spent $24.35 on a pair of sunglasses for himself and ice pops for his nieces and nephews. How many ice pops did he buy?
- Martin bought a towel and a bottle of water. He paid for the items using quarters. How many quarters did he use? How much change did he get?

- Write your own problem about the items in the table. Your problem should require using at least two operations to solve.
- Show the solution to your problem.

Ask yourself:

- What is the price of the flip-flops that Mia bought?
- What is the price of a beach ball? How much do 3 beach balls cost?
- How much money did Carlos spend on the sunglasses? How much money altogether did Carlos spend on ice pops? How can you find how many ice pops Carlos bought?
- What is the price of the towel that Martin bought? What is the price of the bottled water? How much money did Martin spend altogether? How can you find how many quarters Martin used?

Take notes about your classmates' approaches to writing and solving real-world problems involving operations with decimals.

As your classmates present, ask questions such as:

- What information from the table did you use to solve the problem?
- What do you need to find?
- What operations do you need to use to solve the problem? Why?
- How does this expression, equation, or model match the problem situation?
- Why does your solution method make sense? Do you show all the steps?
- Is your answer reasonable?

**Read and Discuss**

- Adding or Subtracting Decimals
- Line up the digits according to place value.
- Line up the decimal points.
- “Carry” regrouped numbers from one column to the next, just as you do when adding or subtracting whole numbers.

- Multiplying Decimals
- Multiply decimals using the same method that you use to multiply whole numbers. Ignore the decimal points (do not line up the decimal points).
- After multiplying, use estimation to place the decimal point. Or, count the total number of decimal places in the numbers you multiplied. In your product, start from the right and move one place to the left for each of the decimal places you counted. Place the decimal point at the resulting location.

- Dividing Decimals
- Multiply the divisor and the dividend by the same power of 10. The power of 10 should be large enough so that the resulting numbers are whole numbers. Then divide using the long division method. Use estimation to make sure your answer makes sense.

Can you:

- Explain how to add and subtract decimals?
- Explain how to multiply and divide decimals?
- Explain how estimating can help when you are performing operations with decimals?

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

**Something that confuses me about operations with decimals is …**