Unit 1 - Up in the Air - 7th - Math - GA - 23

Activate
Knowledge

Multiple Choice

If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he?

• 3

• 4

• 5

Multiple Choice

If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he?

• -3

• -2

• 2

• 3

Multiple Choice

If the flea starts at 0 and jumps 5 units away, where might he have landed?

• -5

• 5

• 5 or -5

• 4

Multiple Choice

If the flea jumps 2 units and lands at zero, where might he have started?

• -2

• 2

• 2 or -2

• 0

Multiple Choice

The absolute value of a number is the distance it is from zero. The absolute value of the flea’s location is 4 and he is to the left of zero. Where is he on the number line?

• -4

• 4

• 4 or -4

• 0

Balloon Challenge

Learning Intention - We are
learning to use concrete objects
and visuals to understand
adding and subtracting positive
and negative numbers.

Balloon Challenge

Success Criteria -

●I can show that a number and its opposite have a sum of 0 (are additive inverses) and can
describe situations in which opposite quantities combine to make 0.

●I can show and explain p + q (p and q are rational numbers) as the number located a distance
|q| from p, in the positive or negative direction, depending on whether q is positive or negative,
and can interpret sums of rational numbers by describing applicable situations.

●I can represent addition and subtraction with rational numbers on a horizontal or a vertical number
line diagram to solve authentic problems.

●I can show and explain subtraction of rational numbers by adding the additive inverse, p – q = p +
(–q).

●I can show that the distance between two rational numbers on the number line is the absolute
value of their difference and apply this in contextual situations.

●I can apply properties of operations, including part-whole reasoning, as strategies to add and
subtract rational numbers.

●I can solve multi-step, contextual problems involving rational numbers, converting between forms
as appropriate, and assessing the reasonableness of answers using mental computation and
estimation strategies.

Let’s Look, Listen, and Learn

Click to watch

The Balloon Challenge Model

Make Sure YOU have the following materials ready:

Worksheet

Balloon model (1 index card per student)

Vertical number lines drawn on graph paper

3 colors per student (colored pencils, pens, or markers)

Rulers

The Balloon Challenge Model - How to set it up
I. Make a balloon model and vertical number
line.

When using hot air balloons to add
or subtract integers, there are
several important things to
remember:

● The first number indicates where the
balloon starts.

● The sign tells you if you will be adding or
subtracting something from the balloon. An
addition sign tells you that you will be adding
something to the balloon and a subtraction
sign tells you that you will be subtracting
something from the balloon

● The second number tells you what you will
add or subtract from the balloon

Elevation

2000 Ft.

1500 FT.

500 FT.

1000 FT.

USE TWO COLORS FOR
POSITIVE AND NEGATIVE

Next… Make a hot air balloon on your index card

Did you know that hot air inside the balloon is what

Makes the hot air balloon rise?

In our experiment,

Helium gas makes the balloon rise (positive)

Washers weights makes the balloon lower

(negative)

Example how this works

We are going to write helium gas as positive numbers, for example 3 pumps of
helium will be expressed as +3 and 10 pumps of helium will be expressed as +10.
Washers will be expressed as negative numbers, for example 5 washers will be
expressed as (-5) and 7 washers will be expressed as (-7). One pump of helium is
equivalent to one washer.

Balloon Challenge

Learning Intention - We are
learning to use concrete objects
and visuals to understand
adding and subtracting positive
and negative numbers.

Balloon Challenge

Success Criteria -

●I can show that a number and its opposite have a sum of 0 (are additive inverses) and can
describe situations in which opposite quantities combine to make 0.

●I can show and explain p + q (p and q are rational numbers) as the number located a distance
|q| from p, in the positive or negative direction, depending on whether q is positive or negative,
and can interpret sums of rational numbers by describing applicable situations.

●I can represent addition and subtraction with rational numbers on a horizontal or a vertical number
line diagram to solve authentic problems.

●I can show and explain subtraction of rational numbers by adding the additive inverse, p – q = p +
(–q).

●I can show that the distance between two rational numbers on the number line is the absolute
value of their difference and apply this in contextual situations.

●I can apply properties of operations, including part-whole reasoning, as strategies to add and
subtract rational numbers.

●I can solve multi-step, contextual problems involving rational numbers, converting between forms
as appropriate, and assessing the reasonableness of answers using mental computation and
estimation strategies.

Let’s Explore What Happens When

Please Complete the Graph

Explore

Draw

Follow the chart to fill in the blanks.

Let’s Use the
Models to
Determine…

Fill in the Blank

-4 + 4

Where does the balloon start on the number line? ________

-

Fill in the Blank

-4 + 4

Do you add or subtract something from the balloon? ____

Fill in the Blank

-4 + 4

What do you add or subtract from the balloon?

Fill in the Blank

-4 + 4

What is the final location of the balloon?

Fill in the Blank

2 + (-2)

Where does the balloon start on the number line?________

Fill in the Blank

2 + (-2)

Do you add or subtract something from the balloon?

Fill in the Blank

2 + (-2)

What do you add or subtract from the balloon?

Fill in the Blank

2 + (-2)

What is the final location of the balloon?

Fill in the Blank

-3 + 6

Where does the balloon start on the number line?

Fill in the Blank

-3 + 6

Do you add or subtract something from the balloon?

-

Fill in the Blank

-3 + 6

What do you add or subtract from the balloon?

-

Fill in the Blank

-3 + 6

What is the final location of the balloon?

Who wins the race?

Fill in the Blank

4 + (-7)

What is the final location of the balloon?

Fill in the Blank

-3 + -5

What is the final location of the balloon?

Open Ended

-3 + -5

Fill in the Blank

-3 - (-9)

Where does the balloon start?

Fill in the Blank

-3 - (-9)

Do you add or subtract something from the balloon?

Fill in the Blank

-3 - (-9)

What do you add or subtract from the balloon?

Multiple Choice

6 - 9

What is the final location of the balloon?

• -3

• 3

• where it stops

• 15

Multiple Choice

-6 - 2

What is the final location of the balloon?

• -8

• -4

• where it stops

• -2

​Please go to Google Classroom if time permits.

Let’s Start Again and Look at “Winning the Challenge”

Open Ended

Explain the final location of the balloon (-a) + (-b).

Open Ended

.Explain the final location of the balloon a + (-b).

Open Ended

Explain the final location of the balloon a - (-b).

Open Ended

Explain the final location of the balloon a - b; describe this situation two ways: use the idea of the subtraction of pumps of helium and the addition of washers in your explanation.

Open Ended

Explain the final location of the balloon (-a) - (-b).

Open Ended

Explain the final location of the balloon (-a) + b.

Open Ended

If a, b, and c are all positive numbers, explain the final location of the balloon

a + b + (-c).

Open Ended

What happened when you were adding integers that had the same signs; (-a) + (- b) and a + b?

Open Ended

What rule can you make by your discovery? Explain.

Open Ended

What happened when you were adding integers that have different signs (a positive integer and a negative integer: (-a) + b and a + (-b))?

Open Ended

What rule can you make by your discovery? Explain.