Modeling SubtractionWith Number Lines and Counters

Course 27.NS.2a

Today’s Lesson

• When working math problems, it is important to understand the meaning behind the math. In other words… why does it work?

• Today, we will solve subtraction problems and will learn how to justify our answers using a number line and integer tiles.

Why Learn?• Well, let’s take a look at how a hike and a little

“butterfly watching” ties into today’s lesson!

Butterfly watching …(also called butterflying) is a hobby concerned with the observation and study of butterflies!

If you are in to butterflying, then you must add The Monarch Butterfly Biosphere Reserve to your bucket list of must-do’s.

Every year hundreds of millions of butterflies undertake a great journey of up to 3,000 miles in their annual migration from Canada and the United States to a protected reserve located just outside of Mexico City, Mexico.

The reserve is a 200 square mile protected area which serves as a winter home for up to 60 million to a billion butterflies!

Serious butterfly watchers should be prepared to hike anywhere from 20 minutes to over an hour (or to ride a donkey).

You can only reach the butterflies on paths laid by the reserve, and they congregate at extremely high altitudes — between 9,000 and 11,000 feet — so visitors should be in good enough physical condition to handle steep inclines.

Meet Henry the hiker!

Henry loves backpacking and has always wanted to hike the mountainous terrain of Mexico to see the annual migration of the monarch butterflies.

¡hola

Real World Application

Henry and his best friend start their hike at an elevation of 8,500 feet. They ascend 375 feet, then stop and take pictures of a cluster of butterflies on a tree. They hike another 1,000 feet on the same path where they next stumble upon a field of thousands of butterflies in flight. After enjoying the view for awhile, Henry and his friend decide they would like to tour the butterfly museum and gift shop. They turn the opposite direction, and descend 1,700 feet to the museum.

Write an expression that would determine the elevation of the butterfly museum.

8,500 + 375 + 1000 – 1700

Start Hike8,500 ft

Butterflies on tree

Butterflies in flight

MAP

What mathematical symbol is this?

Subtract

Take Away

Minus

Opposite

Negative

Well… the symbol can have several meanings.

Which meaning you use depends upon the given situation.

Modeling Subtraction

When modeling subtraction on a

number line we will use the term:

Opposite

1) Solve: 7 ─ 3 = ____

77 steps forward

─Turn the “opposite”direction

33 steps forward

4

Modeling Subtraction

When modeling subtraction with

counters we will use the term:

Take Away

7 7 positives

─ “take away”

33 positives

1) Solve: 7 ─ 3 = ____4

2) Solve: -7 ─ 3 = ____

-77 steps backward

─Turn the “opposite”direction

33 steps forward

-10

─7 7 negatives

─ “take away”

33 positives

2) Solve: ─7 ─ 3 = ____-10

There are not 3 positives to take away, so we must add enough zero pairs so that 3 positives can be taken away.

3) Solve: 2 ─ 5 = ____

22 steps forward

─Turn the “opposite”direction

55 steps forward

-3

2 2 positives

─ “take away”

55 positives

3) Solve: 2 ─ 5 = ____-3

There are not 5 positives to take away, so we must add enough zero pairs so that 5 positives can be taken away.

Your turn to practice…

• Take sixty seconds to try problem #4 on your own.

1 Minute

4) Solve: 8 ─ 1 = ____

88 steps forward

─Turn the “opposite”direction

11 step forward

7

Still having trouble?

Imagine your pencil is Henry the Hiker!

8 8 positives

─ “take away”

11 positive

4) Solve: 8 ─ 1 = ____7

You got this…

• Take sixty seconds to try problem #5 on your own.

1 Minute

Your Henry!

5) Solve: -3 ─ 6 = ____

-33 steps backward

─Turn the “opposite”direction

66 steps forward

-9

-3 3 negatives

─ “take away”

66 positives

5) Solve: -3 ─ 6 = ____-9

There are not 6 positives to take away, so we must add enough zero pairs so that 6 positives can be taken away.

Now let’s look at some tricky ones!• Try the problems on the next page. There

are five so I will give you 5 minutes. We will go over them together.

5 Minutes

6) Solve: -8 ─ (+2) = ____

8 steps backward

Turn the “opposite”direction

2 steps forward

-10

-8 ─ (+2)

-8 8 negatives

─ “take away”

(+2)2 positives

6) Solve: -8 ─ (+2) = ____-10

There are not 2 positives to take away, so we must add enough zero pairs so that 2 positives can be taken away.

7) Solve: 5 ─ (-2) = ____

55 steps forward

─Turn the “opposite”direction

(-2)2 steps backward

7

5 5 positives

─ “take away”

(-2)2 negatives

7) Solve: 5 ─ (-2) = ____7

There are not 2 negatives to take away, so we must add enough zero pairs so that 2 negatives can be taken away.

8) Solve: -3 ─ (+6) = ____

-33 steps backward

─Turn the “opposite”direction

(+6)6 steps forward

-9

-3 3 negatives

─ “take away”

(+6)6 positives

8) Solve: -3 ─ (+6) = ____-9

There are not 6 positives to take away, so we must add enough zero pairs so that 6 positives can be taken away.

9) Solve: -5 ─ (-3) = ____

-55 steps backward

─Turn the “opposite”direction

(-3)3 steps backward

-2

-5 5 negatives

─ “take away”

(-3)3 negatives

9) Solve: -5 ─ (-3) = ____-2

10) Solve: -7 ─ (-8) = ____

-77 steps backward

─Turn the “opposite”direction

(-8)8 steps backward

1

-7 7 negatives

─ “take away”

(-8)8 negatives

10) Solve: -7 ─ (-8) = ____1

There are not 8 positives to take away, so we must add enough zero pairs so that 8 negatives can be taken away.

End of Presentation