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Methods for Multiplying Decimals

Grade 6 Unit 5: Arithmetic in Base Ten Methods for Multiplying Decimals

Warmup

Activity #1

Multiply Decimals by Whole Numbers.

When using the applet, always remember to deselect a tool when its action is complete, by clicking on the pointer .

Use the text tool , or the pen tool to complete the table below. You may want to enter your answers leaving sufficient room.
Now, verify your answers by checking the box.
Click for a new set of numbers.

Activity #2

Compare Multiplication Methods.

There is no unique method to multiply. it is up to the learner to choose the one that is more convenient. Of course, you’d like to choose a method that is easy to remember, and less likely to lead you into errors.

Follow the different methods used below by two students to multiply decimals and answer the questions.

Elena and Noah used different methods to compute (0.23)·(1.5). Both calculations were correct.

(1.) Analyze the two methods.

(2.) Which method makes more sense to you? Why?

(3.) What might Elena do to compute (0.16)·(0.03)?

(4.) What might Noah do to compute (0.16)·(0.03)?

(5.) Will the two methods result in the same value?

Activity #3

Find Area by Adding Square Units.

Study the diagram below and answer the questions.

In the diagram below, the side length of each square is 0.1 unit.

(1.) Explain why the area of each square is not 0.1 square unit.

(2.) How can you use the area of each square to find the area of the rectangle? Explain your reasoning.

(3.) Explain how the diagram shows that the equation (0.4) · (0.2) = 0.08 is true.

Label the squares in the applet below with their side lengths so the area of the rectangle represents 40 · 20.

(1.) What is the area of each square in the picture above?

(2.) Use the squares to help you find 40 · 20 . Explain your reasoning or show it in the applet above.

(3.) Now, label the squares with their side lengths so the area of this rectangle represents (0.04) times (0.02).

Next, use the diagram to help you find (0.04) · (0.02).
Explain your reasoning or show it in the applet above.

Challenge #1

Compute the product using the equation 21 · 47 = 987 and what you know about fractions, decimals, and place value. Explain your reasoning to each answer.

(a.) (2.1) · (4.7)

(b.) (2.1) · (0.047)

(c.) (0.021) · (4.7)

Challenge #2

(1.) Priya finds (1.05) · (2.8) by calculating 105 · 28, then moving the decimal point 3 places to the left. Why does Priya’s method make sense?

(2.) Use Priya’s method to calculate (1.05) · (2.8). you can use the fact that 105 · 28 = 2,940.

(3.) Use Priya’s method to calculate (0.005) · (0.024).

Challenge #3

You can use a rectangle to represent (0.3)·(0.5).

(1.) What must the side length of each square represent for the rectangle to correctly represent (0.3)·(0.5)?

(2.) What area is represented by each square?

(3.) What is (0.3)·(0.5)? Explain you reasoning.