Addition: Putting Things Together

Name______We will be using virtual integer chips for this activity Open File from the Algebra Calendar

Addition: Putting things together Subtraction: Old way to think about: Taking things away New way with integers is ADDING a negative. WE NO LONGER NEED SUBTRACTION!!!

The Additive Identity is zero adding 0 to a number does not change the value therefore when adding or subtracting don’t count zeros they go away

Terms: The terms in an expression are separated by the + and – signs the sign(s) in front of the term belong to it Example (5 terms) 16 – 24 + 3 – (-10) – 18

16 – 24 + 3 – (-10) – 18 Integer chips Blue +1 Yellow -1

Blue + Yellow = Green +1 -1 = 0

When a blue is placed with a yellow it becomes green: Green means GO it goes away because +1-1=0

Exploration 1: Subtracting a positive the same as adding the negative?

Subtraction 8 – 2 = is the same as Addition 8 + (–2) =_____ Place 8 blue chips down Place 2 yellow chips down Pair up yellow and blue to make green Count the non green chips

So we can think of the problem 8 – 2 two ways You have 8 and you take away 2 or You have 8 and you add a negative 2

Exploration 2: Subtracting a negative turn into a +? Model Subtraction –19 – (–3) =______Place down 19 yellow chips Remove 3 yellow chips is the same as Addition –19 + 3=_____ Place down 19 yellow chips Place down 3 blue chips Pair up yellow and blue to make green Count the non green chips Name______

Exploration 3: Addition with negatives is easier than subtracting. As we have mentioned addition is putting things together and subtraction is taking things away. While you can always put more things down you cannot take away something you do not have

Model Subtraction –12 – 5=_____ Place down 12 yellow chips You have to take away 5 blue chips but there are no blue chips on the table To get the blue chips on the table you must put 5 zero pairs (a blue and yellow chip) on the table You can then separate the pairs giving you the 5 blue chips to take away Count the remaining yellow chips to get your answer. Instead think of the problem as TWO terms -12 and -5 being added Addition –12 – 5 is the same as –12 + –5=_____ Place 12 yellow chips down Place 5 yellow chips down No chips pair up so count how many yellow chips there are to get your answer.

Exploration 4 In algebra we use the + and – signs to break problems into terms and then combine those terms using addition. The sign(s) in front of the term belongs to it.

How many terms are in the following problem?______Circle them. 15 – 8 + 25 – 6 – 10 + 2

Model: Place 15 blue chips Place 8 yellow chips Place 25 blue chips Place 6 yellow chips Place 10 yellow chips Place 2 blue chips Pair up yellow and blue to make green Count the non green chips

Exploration 5: A negative sign in front of () change the sign of everything inside the () Distribute the negative sign then combine like terms 7x + 7 – (3x + 5) becomes 7x + 7 – 3x –5 Place 7 blue x cards Place 7 blue chips Place 3 yellow x cards Place 5 yellow chips Pair up yellow and blue to make green Count the non green items Name______

Exploration 6: When there is more than one sign in front of the term rewrite the problem so that there is only one sign between each term remember + – becomes – – – becomes + –7 +(– 6) + 20 – (– 12) – –10 + –2 – 10

Can be rewritten as –7 - 6 + 20 + 12 + 10 - 2 – 10

How many terms are there???______

Model Place 7 yellow chips Place 6 yellow chips Place 20 blue chips Place 12 blue chips Place 10 blue chips Place 2 yellow chips Place 10 yellow chips Pair up yellow and blue to make green Count the non green chips

Model each of the problems below, following along with problems we modeled in class you must solve the problem and write/ draw a description of how to model the problem (Place 3 blue chips etc.) B B B Exploration 1: Why is subtracting a positive the same as adding the negative?

Model Subtraction think of as Addition Describe / draw model

10 – 5 is the same as 10 + (–5) =_____ Name______

Exploration 2: Why does subtracting a negative turn into a +? Model Subtraction think of as Addition Describe / draw how to model

–27 – (–8) is the same as –27 + 8=_____

Exploration 3: Why addition with negatives is easier than subtracting? As we have mentioned addition is putting things together and subtraction is taking things away. While you can always put more things on the table you cannot take away something you do not have

Model Subtraction think of as Addition Describe how to model

18 – (– 6) is the same as ______

Exploration 4

In algebra we use the + and – signs to break problems into terms and then combine those terms using addition. The sign in front of the term belongs to it.

How many terms are in the following problem?_____ Circle them. – 12 + 5 – 18 – 15 + 22 + 9 Describe how to model Name______

Exploration 5: A negative sign in front of () change the sign of everything inside the ()

Model Subtraction taking away

–5x – 9 – (–2x – 5) becomes ______

Describe / draw a model

Exploration 6: When there is more than one sign in front of the term rewrite the problem so that there is only one sign between each term remember + – becomes – – – becomes +

–12 – (– 8) + 15 + (– 12) –5 + –18 – 5 + 10

Rewrite

Describe how to model