IM 6.5.2 Practice: Using Diagrams to Represent Addition and Subtraction

Use the given key to answer the questions.[br][br][img]data:image/png;base64,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[/img][br][br]What number does this diagram represent?[br][img]data:image/png;base64,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[/img]
Draw a diagram that represents 0.216.
Draw a diagram that represents 0.304.
Here are diagrams that represent 0.137 and 0.284.
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[/img][br][br]Use the diagram to find the value of [math]0.137+0.284[/math]. Explain your reasoning.
Calculate the sum vertically.
How was your reasoning about [math]0.137+0.284[/math] the same with the two methods? How was it different?
Click the vertical calculation where digits of the same kind are lined up. Then, finish the calculation and find the sum.
Click the vertical calculation where digits of the same kind are lined up. Then, finish the calculation and find the sum.
Find the sum 10.6 + 1.7 using vertical calculation.
Find the sum 123 + 0.2 using vertical calculation.
Andre has been practicing his math facts. He can now complete 135 multiplication facts in 90 seconds.
If Andre is answering questions at a constant rate, how many facts can he answer per second?
Noah also works at a constant rate, and he can complete 75 facts in 1 minute. Who is working faster? Explain or show your reasoning.
Close

Information: IM 6.5.2 Practice: Using Diagrams to Represent Addition and Subtraction