IM 7.5.5 Lesson: Representing Subtraction

Consider the equation [math]2+3=5[/math]. Here are some more equations, using the same numbers, that express the same relationship in a different way:[br][table][tr][td][math]3+2=5[/math][/td][td][/td][td][math]5-3=2[/math][/td][td][/td][td][math]5-2=3[/math][/td][/tr][/table][br]For the following equation, write two more equations, using the same numbers, that express the same relationship in a different way.[br][math]9+\left(-1\right)=8[/math]
For the following equation, write two more equations, using the same numbers, that express the same relationship in a different way.[br][math]-11+x=7[/math]
Here is an unfinished number line diagram that represents a sum of 8. How long should the other arrow be? Draw it.
For an equation that goes with the diagram above, Mai writes [math]3+?=8[/math].[br]Tyler writes [math]8-3=?[/math]. Do you agree with either of them?
What is the unknown number? How do you know?[br][br]
Here is another unfinished diagram that represent sums:
[br][br][img]data:image/png;base64,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[/img][br][br]What equation would Mai write if she used the same reasoning as before?[br][br]
What equation would Tyler write if he used the same reasoning as before?
How long should the other arrow be?[br]
What number would complete [b][i]each [/i][/b]equation? Explain your reasoning. [br]
Here is another unfinished diagram that represents a sum.
[img]data:image/png;base64,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[/img][br][br]What equation would Mai write if she used the same reasoning as before?[br][br]
What equation would Tyler write if he used the same reasoning as before?
How long should the other arrow be?[br]
What number would complete [b][i]each [/i][/b]equation? Explain your reasoning. [br]
Draw a number line diagram for -(-8)-(3)=?
What is the unknown number? How do you know?
Match each diagram to one of these expressions:
[img]data:image/png;base64,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[/img]
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[/img]
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[/img]
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[/img]
Which expressions in the first question have the same value? What do you notice?
Complete the table.
Complete the table.
Look at the values in both tables. What do you notice?
It is possible to make a new number system using [i]only[/i] the numbers 0, 1, 2, and 3. We will write the symbols for adding and subtracting in this system like this: [math]2\oplus1=3[/math] and [math]2\ominus1=1[/math]. The table shows some of the sums.[br][img]data:image/png;base64,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[/img][br]In this system, [math]1\oplus2=3[/math] and [math]2\oplus3=1[/math]. How can you see that in the table?
What do you think [math]3\oplus1[/math] should be?
What about [math]3\oplus3[/math] ?
What do you think [math]3\ominus1[/math] should be?
What about [math]2\ominus3[/math] ?
Can you think of any uses for this number system?

IM 7.5.5 Practice: Representing Subtraction

Write each subtraction equation as an addition equation.
[math]a-9=6[/math]
[math]p-20=-30[/math]
[math]z-\left(-12\right)=15[/math]
[math]x-\left(-7\right)=-10[/math]
Find each difference. If you get stuck, consider drawing a number line diagram below.
[math]9-4[/math][br]
[math]4-9[/math][br]
[math]9-\left(-4\right)[/math]
[math]-9-\left(-4\right)[/math]
[math]-9-4[/math]
[math]4-\left(-9\right)[/math][br]
[math]-4-\left(-9\right)[/math]
[math]-4-9[/math]
If you get stuck, consider drawing a number line diagram.
[size=150]A restaurant bill is $59 and you pay $72. What percentage gratuity did you pay?[/size]
Find the solution to each equation mentally.
[math]30+a=40[/math]
[math]500+b=200[/math]
[math]-1+c=-2[/math]
[math]d+3567=0[/math]
One kilogram is 2.2 pounds. Complete the table.
What is the interpretation of the constant of proportionality in this case?[br][br]______ kilogram per pound[br]
One kilogram is 2.2 pounds. Complete the table.
What is the interpretation of the constant of proportionality in this case?[br][br]______ pounds per kilogram

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