Adding with Tiles
If I have 11 yellow tiles and 6 red tiles what addition problem is being shown?
11 + (-6)
When we are subtracting integers, subtraction means "take away". What do we do if we don't start with the right amount of tiles to take away?
Add zero pairs
How would we show (+3) + (+9) on a number line? What is the sum?
Draw an arrow from 0 to (+3) and then another arrow from (+3) to (+12)
How would we show this subtraction on a number line: (+4) - (+7)?
Start at zero, draw an arrow to +4, draw an arrow from +4 to -3.
What is Ms. Helen's favorite dessert?
Chocolate Chip cookies
What sum does this set of tiles model: 2 red tiles and 2 yellow tiles
0
How would we subtract 10 - 4 with the tiles?
Draw 10 yellow tiles, circle four of them to take away. Left with 6 yellow tiles
How could we represent (-4) + (-6) on a number line?
start at zero, draw an arrow down to -4, then an arrow from -4 to -10.
How would we show this subtraction on a number line? (-2) - (+9)
Start at zero, draw an arrow to -2, then from -2 draw an arrow to -11.
What are opposite integers (explain in terms of number line and tiles) and what is special about their sums?
integers that are the same distance from 0 but in opposite direction on the number line
integers that are made from the same number of red and yellow tiles
their sums are always equal to 0
You have 9 yellow tiles and 7 red tiles. What additional tiles do you need to model (-2)?
4 red tiles
Explain how you would represent this subtraction equation with tiles and the steps you would take to solve it: 8 - 10
Start with 8 yellow tiles, add 2 zero pairs, take away the 10 yellow tiles, you are left with 2 red tiles (that is the answer: -2)
How can we represent (+5) + (-2) on a number line?
Start at 0, draw arrow to (+5) and then an arrow from (+5) to (+3).
How do we show (-6) - (-6) on a number line? What is the difference?
draw a line going from 0 to -6, then circle it and draw it being taken away. The difference is 0.
What is a zero pair? Explain and give an example of how you could represent this with tiles.
opposite integers, ie: two red tiles and two yellow tiles
Describe how you would represent this sentence with tiles and how you would use them to find the sum. Then find the sum: Jeremy moved his game piece 3 squares backward, then 8 squares forward.
three red tiles add 8 yellow tiles, 3 zero pairs leaves us with 5 yellow tiles. Sum = 5
How would you subtract (-4) - 13 with the tiles? List the steps. What is the difference?
Start with 4 red tiles. Add 13 zero pairs. Take away 13 yellow tiles. You are left with 17 red tiles. Difference: -17
What are the two methods we decided we could use to show an addition equation on a number line? (for example, what are two ways to show 3 + 2?)
start at 0, draw arrow to three, then draw arrow from 3 to 5
OR start at 3, draw one arrow to 5
What is subtracting a positive the same thing as? What other operation could we use to represent the same thing?
We can use addition and add a negative.
What are the three sports Ms. Helen did in high school?
Swimming, diving, and gymnastics
Suppose we have three yellow tiles and then add seven red tiles.
Now suppose we have three red tiles and seven yellow tiles.
How does the number of zero pairs change? How does the sum change? What are the sums?
Number of zero pairs doesn't change.
Sums are opposite integers. (-4) and (+4)
How would you subtract (-4) - (-13) with the tiles? What is the difference?
Start with 4 red tiles. Add 9 zero pairs. Take away 13 red tiles. You are left with 9 yellow tiles. The difference is +9.
Sandra and Joe buy and sell CDs at a flea market. One day they bought 3 CDs for $5 each. They sold 2 CDs for $9 each. Model the expenses and income on a number line. Did they make money or lose money that day?
Draw an arrow from 0 to -5, then from there to -10, then from there to -15, then an arrow from -15 to +3. They made $3.
What is subtracting a negative the same thing as? What other operation could we use to represent this? How?
Subtracting a negative = adding a positive
A whale dived down 200 feet and then realized it went too deep, so it came back up 23 feet. Write an equation to represent this situation with integers and solve. (pay attention to direction --negative or positive)
-200 + 23 = -177