Multiplying & Dividing Integers Real World Connection and Lesson Multiplying & Dividing Integers Note from Amy and Amanda… The images for this PowerPoint came from the public domain and from government websites. Thank-you for viewing! Balto Nome, Alaska 1925

Section 1: Introduction and Real-World Connection Multiplying and Dividing Integers

What are Integers? …-3, -2, -1, 0, 1, 2, 3… Integers are the whole numbers and their opposites. …-3, -2, -1, 0, 1, 2, 3…

Today… We are going to learn the rules for multiplying and dividing integers. We are also going to apply the rules to real life situations.

Why learn this skill? Integers are a part of everyday life... They’re used at sporting events. Think of football with net gains and losses. They’re used to determine checking account balances. It’s based on what we call debits and credits. They are also used to describe temperatures and calculate changes in temperature.

Let’s look at an example based on a Real-Life Historical Event… Date: January 21, 1925

Nome, Alaska Can anyone tell me what this town is know for?

Iditarod Sled Dog Race Finish line - Nome, Alaska

Iditarod Sled Dog Race The annual race is in honor of the 20 sled dog teams who in 1925 raced to deliver a life saving diphtheria vaccine to Nome, Alaska. Sled dog racer Leonhard Seppala was part of the relay team that delivered diphtheria vaccine to Nome, Alaska in January 1925. Seppala's team, led by his dog Togo, traveled hundreds of miles through some of the most treacherous parts of Alaska's wilderness.

Story of Balto. On January 21, 1925, several children in Nome, Alaska were diagnosed with diphtheria. Diphtheria is a bacteria that invades the nose, mouth, and throat and can make it hard to swallow and even cause a patient to suffocate. Without the vaccine, the highly contagious disease would quickly spread to all of the children in Nome. Balto, a Siberian Husky sled dog, became a hero after completing the final leg of a journey to deliver the desperately needed serum from Anchorage to Nome, Alaska.

Story of Balto. The only serum in Alaska was found to be at a hospital in Anchorage, nearly 1000 miles away. A train would be able to transport the medicine from Anchorage to Nenana, Alaska. After that, transportation methods were almost non-existent. Packed ice prevented delivery to Nome by ship and blizzard conditions prevented transport by air. It was finally decided that the only way to get the medicine over the remaining distance was by using a relay of dog sled teams.

Story of Balto. More than 20 mushers and their dog sled teams eventually took part in a Pony Express type relay. They battled against temperatures that rarely rose above ‒40° and winds that were sometimes strong enough to knock over both the dogs and the sleds. On February 1, 1925, the package was handed off for the last time to a musher named Gunnar Kassen. Gunnar’s sled dog team, led by Balto, set off to cover the final leg to Nome.

Blizzard Soon after Balto’s team left, a blinding blizzard began, dropping temperatures to ‒50° and producing wind gusts over 50 mph. Gunnar found himself unable to navigate , but Balto knew the trail well, and, following his instincts, led the team through the blinding blizzard. Over the next 20 hours, Balto slowly led his sled dog team over the final 53 miles. On February 2 at 5.30 AM, the team finally arrived in Nome, successfully delivering the vaccine .

– Real World Connection – Integer Reading Problem In the small town of Nome, Alaska in 1925, it was recorded that the temperature dropped 4° every hour for 5 straight hours during a blizzard. Describe, as an integer, the change in temperature. If the temperature started at -30°, what was the temperature after 5 hours? 1) 4 x 5 = 20… Since the temperature dropped, the integer that would describe the situation would be -20. 2) -30 – 20 = -50. Nome, Alaska 1925

Section 2: Lesson Multiplying and Dividing Integers

Rules for Multiplying Integers The product of two integers with the same signs is positive. For example -2 x -2 = 4. The product of two integers with different signs is negative. For example 3 x -2 = -6.

The same applies for Dividing Integers The quotient of two integers with the same signs is positive. The quotient of two integers with different signs is negative.

Multiplying & Dividing Integers (Guided Practice – Problem 1) Step 1 Determine the sign of your answer. + (+ )  + – ( + )  – – ( – )  + + (– )  – Step 2 Perform the calculation. (ignore the signs because we have already determined the sign of our answer) Step 1 ⊕ ⤫ ⊖ = ⊖ Step 2 3 ⤫ – 3 = – 9 Solve: 3 x –3 =

Multiplying & Dividing Integers (Guided Practice – Problem 2) Step 1 Determine the sign of your answer. + (+ )  + – ( + )  – – ( – )  + + (– )  – Step 2 Perform the calculation. (ignore the signs because we have already determined the sign of our answer) Step 1 ⊖ ⤫ ⊖ = ⊕ Step 2 –5 ⤫ –4 = 20 Solve: –5 x –4 =

Multiplying & Dividing Integers (Guided Practice – Problem 3) Step 1 Determine the sign of your answer. + (+ )  + – ( + )  – – ( – )  + + (– )  – Step 2 Perform the calculation. (ignore the signs because we have already determined the sign of our answer) Step 1 ⊖ ÷ ⊕ = ⊖ Step 2 –24 ÷ 6 = – 4 Solve: –24 ÷ 6 =

You Try! 8 · ‒9 = ______ ‒56 ÷ ‒7 = ________ 8 · ‒9 = ______ ‒56 ÷ ‒7 = ________ Step 1 ⊕ · ⊖ = ⊖ Step 2 8 · – 9 = – 72 Step 1 ⊖ ÷ ⊖ = ⊕ Step 2 –56 ÷ –7 = 8

Alternate Method (Guided Practice – Problem 1) Even Number Your answer will be positive ⊕. Determine the sign of your answer by counting the number of negative signs. Then perform the calculation. (ignore the signs because we have already determined the sign of our answer) Odd Number Your answer will be negative ⊖. Step 1 Count the negative signs. Step 2 2 (even) = ⊕ Step 3 –3 x 4 x –2 = 24 Solve: –3 x 4 x –2 =

Alternate Method (Guided Practice – Problem 2) Even Number Your answer will be positive ⊕. Determine the sign of your answer by counting the number of negative signs. Then perform the calculation. (ignore the signs because we have already determined the sign of our answer) Odd Number Your answer will be negative ⊖. Step 1 Count the negative signs. Step 2 3 (odd) = ⊖ Step 3 –5 · –4 · 2 · – 3 = – 120 Solve: –5 · –4 · 2 · – 3 =

You Try! ‒100 ÷ 10 = ________ ‒ 7 ∙ ‒ 3 ∙ ‒ 2 ∙ ‒ 1 = _____ ‒ 7 ∙ ‒ 3 ∙ ‒ 2 ∙ ‒ 1 = _____ ‒100 ÷ 10 = ________ Step 1 Count the negative signs. Step 2 4 (even) = ⊕ Step 3 ‒ 7 ∙ ‒ 3 ∙ ‒ 2 ∙ ‒ 1 = 42 Step 1 Count the negative signs. Step 2 1 (odd) = ⊖ Step 3 ‒100 ÷ 10 = ‒10

Reading Problem. Poyang Lake is China’s largest freshwater lake. China However, due to severe drought conditions, it was reported in 2011 that the water level is declining at a rate of about 15 centimeters per day leaving cracked and dry riverbeds. If the rate of decline remains the same, what would be the amount of decrease in the water level over a two week period (14 days)? -15 x 14 = -210 centimeters Satellite image

Reading Problem. Rainforests cover only about 7% of the Earth’s surface area, but is the home of 50% of the Earth’s plants and animals. The existence of rainforests is currently being threatened by logging companies, miners, ranchers and developers who react to the ever expanding human population. It is estimated that 9,000 acres of the Amazon Rainforest is lost every hour. Describe as an integer the average loss of the Amazon Rainforest per minute. -9000 ÷ 60 = -150 acres

Section 3: Closure Multiplying and Dividing Integers

Closure When multiplying and dividing two integers that have the same signs your answer will be ______? Positive or Negative? Who can give me an example of a problem that demonstrates this rule?

Closure When multiplying and dividing two integers that have different signs your answer will be ______? Positive or Negative? Who can give me an example of a problem that demonstrates this rule?

In honor of Balto… New York City, Central Park Yes… That’s really Balto. They stuffed him! Balto, at the Cleveland Museum of Natural History

Togo After the successful serum run, Balto became the most famous canine of the run. However, many mushers today consider Togo to be the true hero of the run, as Seppala's team led by Togo covered the longest and most hazardous leg. In the movie, Togo was portrayed as the villain. The real Togo as well. He was stuffed too  Togo, at the Iditarod Trail Museum

Northern Lights Just thought these were pretty. Nome, Alaska