IM 6.5.7 Lesson: Using Diagrams to Represent Multiplication
For each of the following products, choose the best estimate of its value. Be prepared to explain your reasoning.
[math]\left(6.8\right)\cdot\left(2.3\right)[/math]
[math]74\cdot\left(8.1\right)[/math]
[math]166\cdot\left(0.09\right)[/math]
[math]\left(3.4\right)\cdot\left(1.9\right)[/math]
Here are three ways of finding the area of a rectangle that is 24 units by 13 units.
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[/img][br][br]Discuss with your partner:[br]What do the diagrams have in common? How are they alike?
Discuss with your partner:[br]How are they different?
Discuss with your partner:[br]If you were to find the area of a rectangle that is 37 units by 19 units, which of the three ways of decomposing the rectangle would you use? Why?
You may be familiar with different ways to write multiplication calculations. Here are two ways to calculate 24 times 13.
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[/img][br][br]Discuss with your partner:[br]In Calculation A, how are each of the partial products obtained? For instance, where does the 12 come from?
Discuss with your partner:[br]In Calculation B, how are the 72 and 240 obtained?
Discuss with your partner:[br]Look at the diagrams in the first question. Which diagram corresponds to Calculation A? Which one corresponds to Calculation B?
Discuss with your partner:[br]How are the partial products in Calculation A and the 72 and 240 in Calculation B related to the numbers in the diagrams?
Use the two following methods to find the product of 18 and 14, then compare the values obtained. (a) Calculate numerically.
(b) Here is a rectangle that is 18 units by 14 units. Find its area, in square units by decomposing it. Show your reasoning.
Compare the values of [math]18\cdot14[/math] that you obtained using the two methods. If they are not the same, check your work.
Use the applet to verify your answers and explore your own scenarios. To adjust the values, move the dots on the ends of the segments.
You can use area diagrams to represent products of decimals. Here is an area diagram that represents (2.4) · (1.3). Find the region that represents (0.4) · (0.3)? Label that region with its area of 0.12.
In the applet above, label each of the other regions with their respective areas. Then, find the value of [math]\left(2.4\right)\cdot\left(1.3\right)[/math]. Show your reasoning.
Here are two ways of calculating 2.4 times 1.3.
[img]data:image/png;base64,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[/img][br][size=150]Analyze the calculations and discuss with a partner:[br][/size][br]In Calculation A, where does the 0.12 and other partial products come from? In Calculation B, where do the 0.72 and 2.4 come from? How are the other numbers in blue calculated?
In each calculation, why are the numbers in blue lined up vertically the way they are?
Find the product of (3.1) · (1.5) by drawing and labeling an area diagram. Show your reasoning.
Show how to calculate [math]\left(3.1\right)\cdot\left(1.5\right)[/math] using numbers without a diagram. Be prepared to explain your reasoning. If you are stuck, use the examples in a previous question to help you.
Use the applet to verify your answers and explore your own scenarios. To adjust the values, move the dots on the ends of the segments.
How many hectares is the property of your school? How many morgens is that?
Label the area diagram to represent (2.5) · (1.2) and to find that product. Decompose each number into its base-ten units (ones, tenths, etc.) and write them in the boxes on each side of the rectangle.
Label regions A, B, C, and D with their areas. Show your reasoning.[br][br]Then, find the product that the area diagram represents. Show your reasoning.[br]
Here are two ways to calculate (2.5) · (1.2). Each number with a box gives the area of one or more regions in the area diagram.
In the boxes next to each number, write the letter(s) of the corresponding region(s).[br][br]In Calculation B, which two numbers are being multiplied to obtain 0.5?[br]Which numbers are being multiplied to obtain 2.5?
IM 6.5.7 Practice: Using Diagrams to Represent Multiplication
Here is a rectangle that has been partitioned into four smaller rectangles. For each expression, choose the sub-rectangle whose area, in square units, matches the expression.
Expression: [math]3\cdot\left(0.6\right)[/math][br]
Expression: [math]\left(0.4\right)\cdot2[/math][br]
Expression: [math]\left(0.4\right)\cdot\left(0.6\right)[/math][br]
Expression: [math]3\cdot2[/math][br]
Here is an area diagram that represents (3.1) · (1.4). Find the areas of sub-rectangles A and B.
What is the area of the 3.1 by 1.4 rectangle?
Draw an area diagram to find (0.36) · (0.53). Label and organize your work so that it can be followed by others.
Find the product: (2.5) · (1.4). Show your reasoning.
Find the product: (0.64) · (0.81). Show your reasoning.
Complete the calculations so that each shows the correct sum.
Diego bought 12 mini muffins for $4.20. At this rate, how much would Diego pay for 4 mini muffins? Add this to the table.
How many mini muffins could Diego buy with $3.00? Explain or show your reasoning. If you get stuck, consider using the table.