Bell Work VOTE (SILENTLY) Turn the following into Decimals and state if they repeat or terminate. 13/999 15/75 7/9 Turn the following into fractions and state if they repeat or terminate. .749 2. .6324 3. .86 4. .333

Bell Work VOTE (SILENTLY) Turn the following into Decimals and state if they repeat or terminate. 13/999 = .013 7/75 = .093 7/9 = .7 Turn the following into fractions and state if they repeat or terminate. .749 2. .6324 3. .86 4. .333 749/1000 6324/9999 86/99 333/1000

Practice/Exit Ticket: Convert from fraction to decimal     .05 .44 1.85 1.24 .55 .875 1.38 .4

2.1.2 HOMEWORK ANSWERS

Modeling Addition with Number Lines and Integer Tiles Lesson 2.2.1 Modeling Addition with Number Lines and Integer Tiles Slides that contain animation… It is initiated with just one click. Don’t click again until the entire animation has completed. It will take a few moments for the entire animation to run its course.

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 addition problems and will learn how to justify our answers using a number line and integer tiles.

Why Learn? Before we start our lesson, let’s take a look at how storm chasing can lead to an understanding of modeling addition on a number line!

Storm Chasing… Storm chasing is broadly defined as the pursuit of any severe weather condition, regardless of motive, which can be curiosity, adventure, scientific investigation, or for news or media coverage. A person who chases storms is known as a storm chaser. The single most biggest objective for most storm chasers is to witness a tornado!

Meteorology major Reed Timmer and his team are by far some of the biggest storm chaser dare devils out there. They were a part of the hit show on the Discovery Channel called, “Storm Chasers”. They have documented hundreds of tornados!

Besides hurricanes, tornadoes are the most dangerous storms nature can throw at us. They can destroy entire buildings and cause thousands of injuries or deaths. Most people who live in areas susceptible to these storms keep a close eye on weather reports and take cover or evacuate when one is on the way. Storm chasers keep an even closer eye on weather data, but for a different reason. When a tornado happens, they want to be there to observe and record it! ­

There are some really good reasons for chasing storms – mainly, scientific research, though a few people make a living selling photographs or footage of storms.

There are also several reasons why amateurs shouldn't go storm chasing, no matter how fun it looks. For one thing, the eight to 12 hours spent driving around with no guarantee of actually seeing a tornado is anything but exciting. But also, storms are very dangerous. Professional storm chasers have meteorological training that allows them to understand the storms they're chasing. They know when conditions are safe and when it's time to back off. They also learn by chasing with other experienced storm chasers. Amateurs should never chase storms. Ever. Even experienced storm chasers like Reed Timmer can get hurt. or killed!

Most of us would be heading in the opposite direction…… Not true for storm chasers!

More images! Meteorologist and extreme storm chaser, Reed Timmer, captured this stunning tornado in Oklahoma in 2007 on a low-precipitation storm. Their vehicle is called “The Dominator” . It can withstand a direct hit from up to a level 3 tornado!

More images! Their website Reed’s fiancée, Maria Molina is a weather reporter and likes to chase in her spare time!

A rough 6 miles ahead! Real World Application Most storm chasers don’t like to chase in Mississippi because the trees make tornados hard to spot. However, Reed Timmer goes where the tornados are! Storm chaser Reed Timmer and his team are in the middle of a tornado outbreak near Tupelo, Mississippi. A weather radar has lead them down a country road. After stopping at a stop sign, they drive 2 miles down the road when they come across some debris in the road. They backup ¼ mile stop and begin to clear the debris. They then travel 3 more miles when they see a tornado straight in their path! They put their vehicle in reverse and travel ¾ of a mile to escape the tornado, yet still continue to film the event. When all is safe they drive another 2 miles to a local gas station where they stop and view their video footage. Use the number line to describe their adventure! A rough 6 miles ahead!

On to our lesson…

+ What mathematical symbol is this and what does it mean? When you add, are you always adding just positive numbers? It is the addition symbol. It means to “add”. No, for example any two integers (positive or negative) can be added together.

Number Lines Integer Tiles Today, we will work ten guided practice problems together. Each of the ten problems will be solved in two ways using modeling… Number Lines Integer Tiles

Modeling Addition Number Line

7 + 3 1) Solve: 7 + 3 = ____ 10 ADD 3 moves forward 7 moves forward - Always start at zero facing the positives. The first number is positive 7, so the car moves up to the 7. The second number is positive, so the car moves up another 3 units forward. Answer: 10 ADD 3 moves forward 7 moves forward

Modeling Addition Integer Tiles We will now work the same problem, but this time we will use integer tiles to represent our numbers. Something to remember: Opposite quantities combine to make 0. Let’s take a look!

7 + 3 1) Solve: 7 + 3 = ____ 10 7 positives ADD 3 positives The first number is positive 7, so start with 7 “+” tiles. The second number is positive, so add 3 more “+” tiles. Answer: 10 7 positives ADD 3 positives

─ 7 + 3 2) Solve: ─7 + 3 = ____ ─ 4 ADD 3 moves forward 7 moves - Always start at zero facing the positives. The first number is negative 7, so the car moves backward 7 units. The second number is positive, so the car moves forward 3 units. Answer: -4 ADD 3 moves forward 7 moves backward

─ 4 Opposite quantities combine to make zero! 2) Solve: ─7 + 3 = ____ ─7 + 3 The first number is negative 7, so start with 7 “-” tiles. - The second number is positive, so add 3 more “+” tiles. Opposite quantities cancel to make zero. Answer: -4 7 negatives “ADD” 3 positives

─ 4 + 9 3) Solve: ─ 4 + 9 = ____ 5 ADD 4 moves backward - Always start at zero facing the positives. The first number is negative 4, so the car moves backward 4 units. The second number is positive, so the car moves forward 9 units. Answer: 5 ADD 4 moves backward 9 moves forward

5 Opposite quantities combine to make zero! 3) Solve: ─ 4 + 9 = ____ ─ 4 + 9 The first number is negative 4, so start with 4 “-” tiles. The second number is positive, so add 9 “+” tiles. - Opposite quantities cancel to make zero. Answer: 5 4 negatives ADD 9 positives

Your turn to practice… Take sixty seconds to try problem #4 on your own. 1 Minute

─ 1 + 8 4) Solve: ─ 1 + 8 = ____ 7 Still having trouble? Imagine your pencil is the car! ─ 1 + 8 - Always start at zero, the student’s pencil will face towards the positives. The first number is negative, so with the pencil still facing the positives move the pencil backward by 1. The second number is positive. With the pencil still facing the positives move forward 8 places. Answer: 7 ADD 8 moves forward 1 move backward

7 Opposite quantities combine to make zero! 4) Solve: ─ 1 + 8 = ____ + 8 ─ 1 The first number is negative 1, so start with 1 “-” tile. - The second number is positive, so add 8 “+” tiles. Opposite quantities cancel to make zero. Answer: 7 1 negative ADD 8 positives

You got this… Take sixty seconds to try problem #5 on your own. Face your pencil towards the positives! Don’t forget… Everyone hold up your pencil! Put your pencil on zero and face the point towards the positives…. Now GO! 1 Minute

8 + (─ 5) 5) Solve: 8 + (─ 5) = ____ 3 “ADD” 5 moves backward 8 moves - Always start at zero with your pencil facing the positives. The first number is positive 8, so move forward 8 spaces. The second number is negative 5, so keep your pencil still facing the positives, but move it back 5 spaces. Answer: 3 “ADD” 5 moves backward 8 moves forward

+ (─ 5) 8 5) Solve: 8 + (─ 5) = ____ 3 Opposite quantities combine to make zero! + 8 (─ 5) The first number is positive 8, so start with 8 “+” tile. - The second number is negative 5, so add 5 “-” tiles. Opposite quantities cancel to make zero. Answer: 3 8 positives “ADD” 5 negatives

Try the rest of the problems on your own! There are five so I will give you 5 minutes. We will go over them together. 5 Minutes

─ 1 6) Solve: ─ 6 + 5 = ____ ─ 6 + 5 5 moves forward 6 moves backward ─ 6 + 5 - Always start at zero with your pencil facing the positives. The first number is negative 6, so move backward 6 spaces. (Pencil still facing towards positives) The second number is positive 5, so keep your pencil still facing the positives, but move it back 5 spaces. Answer: -1 5 moves forward 6 moves backward ADD

-1 Opposite quantities combine to make zero! 6) Solve: ─ 6 + 5 = ____ ─ 6 + 5 The first number is negative 6, so start with 6 “-” tiles. - The second number is positive, so add 5 more “+” tiles. Opposite quantities cancel to make zero. Answer: -1 6 negatives ADD 5 positives

─ 6 + (─ 2) ─ 8 7) Solve: ─ 6 + (─ 2) = ____ ADD 2 moves - Always start at zero with your pencil facing the positives. The first number is negative 6, so move backward 6 spaces. (Pencil still facing towards positives) The second number is negative 2, so keep your pencil still facing the positives, but move it back 2 more spaces. Answer: -8 ADD 6 moves backward 2 moves backward

+ (─ 2) ─ 6 7) Solve: ─ 6 + (─ 2) = ____ ─ 8 6 negatives ADD The first number is negative 6, so start with 6 “-” tiles. - The second number is negative, so add 2 more “-” tiles. Answer: -8 6 negatives ADD 2 negatives

3 + (─ 7) 8) Solve: 3 + (─ 7) = ____ ─ 4 3 moves ADD 7 moves backward - Always start at zero with your pencil facing the positives. The first number is positive 3, so move forward 3 spaces. (Pencil still facing towards positives) The second number is negative 7, so keep your pencil still facing the positives, but move it back 7 spaces. Answer: -4 3 moves forward ADD 7 moves backward

3 + (─ 7) ─ 4 8) Solve: 3 + (─ 7) = ____ 3 positives ADD 7 negatives Opposite quantities combine to make zero! 8) Solve: 3 + (─ 7) = ____ 3 + (─ 7) The first number is positive 3, so start with 3 “+” tiles. - The second number is negative, so add 7 “-” tiles. Opposite quantities cancel to make zero. Answer: -4 3 positives ADD 7 negatives

─ 9 + (─ 1) ─ 10 9) Solve: ─ 9 + (─ 1) = ____ ADD 1 moves - Always start at zero with your pencil facing the positives. The first number is negative 9, so move backward 9 spaces. (Pencil still facing towards positives) The second number is negative 1, so keep your pencil still facing the positives, but move it back 1 more space. Answer: -10 ADD 9 moves backward 1 moves backward

+ (─ 1) ─ 9 9) Solve: ─ 9 + (─ 1) = ____ ─ 10 9 negatives ADD The first number is negative 9, so start with 9 “-” tiles. - The second number is negative, so add 1 more “-” tile. Answer: -10 9 negatives ADD 1 negatives

4 + (─ 2) 2 10) Solve: 4 + (─ 2) = ____ 4 moves ADD 2 moves backward - Always start at zero with your pencil facing the positives. The first number is positive 4, so move forward 4 spaces. (Pencil still facing towards positives) The second number is negative 2, so keep your pencil still facing the positives, but move it backward 2 spaces. Answer: 2 4 moves forward ADD 2 moves backward

4 + (─ 2) 2 10) Solve: 4 + (─ 2) = ____ 4 positives ADD 2 negatives Opposite quantities combine to make zero! 10) Solve: 4 + (─ 2) = ____ 4 + (─ 2) The first number is positive 4, so start with 4 “+” tiles. - The second number is negative, so add 2 “-” tiles. Opposite quantities cancel to make zero. Answer: 2 4 positives ADD 2 negatives

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