IM 6.5.6 Lesson: Methods for Multiplying Decimals

Write as many expressions as you can think of that are equal to 0.6. Do not use addition or subtraction. 
[size=150]Elena and Noah used different methods to compute [math]\left(0.23\right)\cdot\left(1.5\right)[/math]. Both calculations were correct.[/size][br][img]data:image/png;base64,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[/img][br][br]Analyze the two methods:
Then discuss the following questions with your partner:
Which method makes more sense to you? Why?
What might Elena do to compute [math]\left(0.16\right)\cdot\left(0.03\right)[/math]? [br]
What might Noah do to compute [math]\left(0.16\right)\cdot\left(0.03\right)[/math]? [br]
Will the two methods result in the same value?
[size=150]Compute the product using the equation [math]21\cdot47=987[/math] and what you know about fractions, decimals, and place value. Explain your reasoning.[/size][br]  [br][math]\left(2.1\right)\cdot\left(4.7\right)[/math]
[math]21\cdot\left(0.047\right)[/math]
[math]\left(0.021\right)\cdot\left(4.7\right)[/math]
In the diagram, the side length of each square is 0.1 unit.
Explain why the area of each square is [i]not[/i] 0.1 square unit.
How can you use the area of each square to find the area of the rectangle? Explain your reasoning.
Explain how the diagram shows that the equation [math]\left(0.4\right)\cdot\left(0.2\right)=0.08[/math] is true.
Label the squares with their side lengths so the area of this rectangle represents 40 · 20.
What is the area of each square in the picture above?
Use the squares to help you find [math]40\cdot20[/math]. Explain your reasoning or show it in the applet above.
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 [math]\left(0.04\right)\cdot\left(0.02\right)[/math]. Explain your reasoning or show it in the applet above.

IM 6.5.6 Practice: Methods for Multiplying Decimals

Find each product. Show your reasoning.
You can use a rectangle to represent (0.3)·(0.5).
What must the side length of each square represent for the rectangle to correctly represent [math]\left(0.3\right)\cdot\left(0.5\right)[/math]?
What area is represented by each square?
What is [math](0.3)\cdot(0.5)[/math]? Show your reasoning.[br]
[size=150]One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon. [br][br][size=100]How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.[/size][br][/size]
Is the cost of gas greater in Buffalo or in Toronto? How much greater?
Calculate each sum or difference:
[math]10.3+3.7[/math][br]
[math]20.99-4.97[/math][br]
[math]15.99+23.51[/math][br]
[math]1.893-0.353[/math][br]
Find the value of [math]\frac{49}{50}\div\frac{7}{6}[/math] using any method.
Find the area of the shaded region. All angles are right angles. Show your reasoning.
Priya finds [math]\left(1.05\right)\cdot\left(2.8\right)[/math] by calculating [math]105\cdot28[/math], then moving the decimal point three places to the left. Why does Priya’s method make sense?
Use Priya’s method to calculate [math]\left(1.05\right)\cdot\left(2.8\right)[/math]. You can use the fact that [math]105\cdot28=2,940[/math].
Use Priya’s method to calculate [math]\left(0.0015\right)\cdot\left(0.024\right)[/math].

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