Math 7 Unit 2 Name: _____________________________________ Add & Subtract Integers Unit 2.1 Introduction to Integers What You’ll Learn... • To look at integers as whole numbers (there are no decimals or fractions with integers) • to add integers using integer chips • to add integers using a number line • to subtract integers using integer chips. Why is it important? • Integers help us “find the exact change” when we are purchasing something. • Integers allow us to think about numbers in both positive and negative terms, which is useful when thinking about banking, gaming, shopping, travelling over time zones, or even when you talk about your mood. • Careers as a veterinarian, business owner, CEO, architect,
Transcript
Math 7 Unit 2 Name: _____________________________________
Add & Subtract Integers
1.1 Square Numbers and Area Models
Unit 2.1 Introduction to Integers
Investigate: (Text pg. 310) How can you use integer chips to add two integers?
What You’ll Learn...• To look at integers as whole numbers
(there are no decimals or fractions with integers)
• to add integers using integer chips
• to add integers using a number line
• to subtract integers using integer chips.
• When to add or subtract integers when solving problems.
• to connect integer operations to the real world.
Why is it important?• Integers help us “find the exact change” when we are purchasing
something.
• Integers allow us to think about numbers in both positive and negative terms, which is useful when thinking about banking, gaming, shopping, travelling over time zones, or even when you talk about your mood.
• Careers as a veterinarian, business owner, CEO, architect, electrician, marine biologist, athlete, or engineers would all require these mathematical skills.
Grade 7 Math
Integer chips are ______________________________ that represent integers. The happy face (yellow) represents _______ or ________________________ and the sad face (blue) represents _______ or ________________________. A ZERO PAIR includes one positive and one negative chip.
Discuss: “What are all the ways do we see numbers represented in the real world…
Using the template provided, create your own set of integer chips.
Grade 7 Math
Before we Begin- Tricks & Tips about Integers
1. Examples of Integers are the following (circle): 2, 4, -3, 0, 1, ½, 30%, 112, -20, 1.56, 0.5
2. List 7 integers between -10 and 10 in the box below. At least two must be negative integers:
3. Graph the numbers
from question #2 on the number line below. You may add hash marks as needed.
4. Each number has a ________ and ________ on each side of the zero.
5. Which set of integers is in order from least to greatest?a. -4, -6, -7, -8, -9b. 0, 1, -1, 9, -8
c. -15, -12, -10, 0, 9d. 10, 8, -1, -3, -6
6. Evaluate the expression when x= 2a. 12-x = _______ b. x +3 = _______
8. When adding:1. a negative + a negative is always a ____________2. a positive + a positive is always a _____________3. an integer + a 0 always has the ___________
Explore:1. Use your integer chips to pair OPPOSITE INTEGERS:
a. Use two positive chip to represent +2.b. Use two negative chip to represent -2.
FYI
Brackets help keep integer problems tidy. Imagine the chaos without them!
- 2 + + 3 =
Grade 7 Mathc. What is the sum of +2 and -2? _______
How do you know?d. Complete the following operation: (+2) + (-2) = _______
2. Repeat question one with +5 and -3a. How many chips do you have altogether: __________b. Line up the negatives. Place the positives next to them (from left to
right). c. Fill in the circles below to represent the problem:
d. For every
positive a negative is cancelled out. Cross out each “pair” to see what is leftover. (If you are using chips, put the chips you take away in a separate pile, off to the side)
e. Write out the equations and solve: (________) + (________) = _____
Example #1: Using integer chips, complete the following addition statements:
a) (+1) + (+2) =b) (-3) + (-2) =
c) (+5) + (-4) =d) (-6) + (+2) =
Tip: if it helps, draw smiley face examples to find the solutions:
a) + 1+ 2The sum of the chips = _______
Discuss: “Where do we use integers in the real world?”
Example #2: Break down this word problem by drawing integer chips (smiley faces):
Grade 7 MathLucy spent $5 on bus fare to visit her aunt. During the visit, she gave Lucy $12 for doing some yard work. What a nice aunt! How much shopping money did Lucy have at the end of the day?
What do you think?1. Do the integer chips in this diagram represent a sum +3 or -3. How do you
Reflection: Talk to the person next to you about what you have noticed about integers so far. What seems pretty straightforward? What is way too complicated? Is there anything you find easy/ difficult? Write down some of your ideas.
Hint: when you spend money, you lose it. When you earn money, you gain it.
Homework Assignment TIPS & TRICKS: Visualize the problem (*sketch it out/ picture it in your head before you do the
work) Use the Guess & Check method (make a guess about the answer; do the work;
use the check back “mental math” to eliminate mistakes. Show your work. Use the Internet, YouTube, your teacher, your friends, your parents as
resources when you get stuck. Use the textbook to T.I.F. (take it further).
Grade 7 Math
FREEZE- time for a story about a story….
Once upon a time there was this quite an intelligent civilization called Mesopotamia. One day, some pretty smart guys were sitting around the watering hole when one of them said, “I wonder how deep this well is?” The others said, “Hark! Tie some rope around Bobby here and lower him in to find out!” One problem- these guys were not knot experts… Frankly Bobby did not make it back up to live to tell the tale and reveal the great mystery. BUT, the rather smart men developed a theory nonetheless: “Let’s call the top of the well zero and every meter the bucket descends a negative.” Thus integers were born.
Pretty soon the Greeks got their hands on this newfangled theory. And doing what Greeks did best back then, they gave it a fancy name: “I shall call him… ALGEBRA” One difference: the Greeks saw integers in sets (Good and Evil! Night and Day! Black and White… you get the picture): “for every positive, there is a negative.”
It took a while for people to fiddle with integers again, but sure enough it happened. In 1795 Fredrick Gauss- neither Greek NOR Babylonian- wrote a pretty heavy book (literally) called “Arithmetical Disquisitions.” Cool title, huh? His theory
was so popular is basically paved the way for Albert Einstein to develop his Theory of Relativity.
So… interested in reviving the tradition of integer take-it-further-than-the-last-guy?
Yes!
I thought you would say that…
Complete the following questions: (p.314-315)
1. Use the sum of two integers to answer the following questions:
Grade 7 Matha. Kyra found $10 and then lost $4. How much did she have left?
b. Derby the horse walked 7cm forward to eat hay out of Emily’s hand, but backed up 5cm when became scared by Madi. How far from his original spot was Derby the horse?
c. In one game, the QMS Lightening Bolt girls’ soccer team scored 4 goals and had 1 goal scored against them. How many goals did the team win by?
2. On Saturday morning, Alexis wanted to go shopping so she borrowed some money from her Mom. She spent $6 at the first store and $9 at the next store. How much money did she owe her mom at the end of the day?
3. At Camp Thunderbird, the temperature was +6°C when the girls went to bed. The temperature increased by 10°C during the night. What was the overnight low temperature?
4. Complete the table below:
(+2) + (+3) = (+3) + (+2) =
Grade 7 Math(-1) + (-4) = (-4) + (-1) =
(+2) + (-2) = (-2) + (+2) =
(+4) + (-7) = (-7) + (+4) =
* Notice the similarities between some of the questions in the table above. What can you conclude about the order in which you add two integers?
5. What is the opposite of -3?What is the opposite of the opposite of -3? What integer doesn’t have an opposite?
Unit 2.2 Adding IntegersInvestigate: (Text pg. 316) How can you use a number line to add two integers?
A number line is a __________________________________________________. The number on the left of zero are _____ _______________ and the numbers on the right of zero are _____ _______________.
Using the problems above, name 4 examples of places where you would use integers in the real world:
Create your own integer lines for the questions below using the blank line below each question. Place zero at the centre. Negatives go on the left and
positives on the right.
Grade 7 Math1. Model (+2) + (+3) using the number line.
How can you use a number line show the sum?
_________________________________________________
2. Model (-4) + (-2) using the number line.How can you use a number line show the sum?
_________________________________________________
3. Model (-2) + (+3) using the number line.How can you use a number line show the sum?
_________________________________________________
Example #1: Find the sum using a number line. Complete the addition statement in each example:
a) (+4) + (+2) = b) (-5) + (-3) =
a)
b)
Example #2: Temperature is shown vertically on a number line. Complete the addition statement in each example:
a) (+2) + (-4) = b) (-6) + (+6) =
Grade 7 Math
What do you think?
1. You can use an arrow on a horizontal or vertical line to represent integer addition. What integer does this diagram represent? Explain:__________________________________________________________________________________________________________________________________________
2. In this problem there are two arrows, one red and one blue. Explain the directions of the two arrows. What do the lengths of the arrows mean?
3. Justin Bieber came to the conclusion that the sum of +3 and +5 is -2. Was he right? Explain using a number line:
Reflection: Talk to the person next to you about what you have noticed about number lines so far. What seems pretty straightforward? What is way too complicated? Is there anything you find easy/ difficult? Write down some of your ideas.
Grade 7 Math
Complete the following questions: (p.320-321)
1. Turn this number line into an addition problem:
2. Write the following question using a negative integer and positive integer. Kyra`s dad gave her $20. She spent $12 at Claire’s. How much did she have leftover?
3. On one of her amazing deep-sea adventures, Mrs. Clement was cruising a submarine at 50m looking for four-eyed octopus. She decided to bring the sub up by 34m. What is her new depth?
Later that day she realized she had made a mistake. She needed to be at 74m. How much distance does she need to travel? Draw your answer.
4. What is the sum of +1987AD and -1987AD:
Homework Assignment TIPS & TRICKS: Visualize the problem (*sketch it out/ picture it in your head before you do the
work) Use the Guess & Check method (make a guess about the answer; do the work;
use the check back “mental math” to eliminate mistakes. Show your work. Use the Internet, YouTube, your teacher, your friends, your parents as
resources when you get stuck. Use the textbook to T.I.F. (take it further).
Grade 7 Math5. The integers from +1 to +6 are marked on the faces of a number cube. The
integers from -1 to -6 are marked on another. Roll the dice in your imagination and create an equation for the pairs that you came up with:
6. Are the following statements TRUE, SOMETIMES TRUE or NEVER TRUE? Provide an example problem for each statement (for never true, provide the correct answer)
Grade 7 Matha. The sum of two negative is a positive integer: _________________
b. The sum of a positive and a negative is zero: _________________
c. The sum of a positive and zero is a positive integer: _________________
d. The sum of a positive and a negative is a negative: _________________
7. If you had choose a way to solve the following problems, would you choose integer chips or number line? Explain?
a. (-6) + (+4) b. (+90) + (-140)
Unit 2.3 Explore & Practice Integer Subtraction
Investigate: (Text pg. 323) How can you use integer chips to subtract integers?
To add chips, we combine opposite pairs.To subtract chips, we do the reverse: we remove chips from a group.
1. Use chips to model (+7) – (+4). a. Complete the subtraction statement (+7) – (+4) = _______
2. Use chips to solve the following problemsa) Use happy chips to model +5.
Grade 7 Mathb) Take 5 chips away. How many chips do you have?
3. Complete the following problemsa. (+2) – (+5) = _____b. (-1) – (-3) = _____c. Check your understanding: what is (-1) + (-3) ___________
Reflect & Share: Compare your results with another classmates. When you subtracted, how many tiles did you use to model the integer?
Check your understanding:
1. What is the opposite of +6 __________2. What does difference mean: ___________________3. To subtract an integer, you must add the _________________4. Write a subtraction question that would give each of the following numbers
Example #1: Use tiles to subtract. Draw your answers.
a. (-2) – (-6)b. (-6) – (+2)c. (+2) – (-6)
Example #2. Work in a group of 4 to come up with a short skit that explains a situation in which you would subtract integers. Write your group’s ideas here:
Subtracting on a Number LineWhere will I use this? Subtraction is used in when talking about temperature and time zones, for example- when taking numbers away from other numbers
Step 1: Use a number line to subtractWrite down two integers on the line.
Step 2: Model each subtraction on the number lineStep 3: To subtract two whole numbers, such as 5 and -2, think “What do we
add to -2 to get 5?”Step 4: Remember- the result of subtracting an integer is the same as adding
2. What is the difference in temperatures?How can you subtract to find out?a. A temperature 7°C above zero and a temperature of 5°C
below.
b. A temperature of 15°C below and a 8°C below
c. A temperature 4°C and a temperature 9°C above
3. Look at each integer pattern. Write the next 4 terms. What is the pattern rule?a. +6, +2, -2…b. -3, -1, 1…c. +5, +12, +19…d. +1, 0, -1…
Reflection: Talk to the person next to you about what you have noticed about number lines so far. What seems pretty straightforward? What is way too complicated? Is there anything you find easy/ difficult? Write down some of your ideas.
Grade 7 Math
Apply: (show your work)
1. Use subtraction for the following questions. Determine and explain the time difference between each pair of cities.
a. Perth, Australia (time zone +8) and Bermuda (time zone -4)
b. Lima, Peru (-5) and Calgary, Alberta (-7)
c. Honolulu, Hawaii (-10) and Lagoa, Nigeria (-7)
2. On a typical afternoon in Iqualuit, Nunavut, the temperature is -8C in the morning and -2C in the afternoon. Determine and explain the difference between these temperatures. Would you enjoy living there?
3. Use a subtraction of two integers to complete the following:a. Diara scored 20 points in a basketball game on Tuesday. She scored
16 points in a game on Wednesday. How many more points did she score on Tuesday than Wednesday?
Homework Assignment TIPS & TRICKS: Visualize the problem (*sketch it out/ picture it in your head before you do the
work) Use the Guess & Check method (make a guess about the answer; do the work;
use the check back “mental math” to eliminate mistakes. Show your work. Use the Internet, YouTube, your teacher, your friends, your parents as
resources when you get stuck. Use the textbook to T.I.F. (take it further).
Grade 7 Math4. Mrs. Clement owes $10 clement bucks to Allie and Olivia. But Allie owes Mrs.
Clement $4 clement bucks. How much will Allie and Olivia receive?
5. While she is waiting for her friends at the mall, Haleigh decides to ride the elevator for fun. She goes up to the 12th floor from the street, then she rides down to the parking level, three floors below street level. How many floors did she ride?
6. Complete the table:a.
Compare the differences on each row of the completed table. What do you notice about the order of the numbers? Are the results the same or different?
b. If you are asked to subtract (-4) – (+3), can you subtract integers in any order? Explain.
Unit 2.4 Apply Integer Operations
Investigate: (Text pg. 339) How do we know when to choose subtract or add?
What do you think?
Grade 7 Math
1. Find the sum of the following integers using a number line.
a. 3 - 4 =b. 1 + (-4) =
c. 3 + (+2) =d. (-3) – 2 =
a.
b.
c.
d.
2. Use the number line below for the following questions:
a. Draw an addition problem in red to represent the problem
b. Draw a subtraction problem in blue to represent the problem
Grade 7 MathMath Relay:9 questions $3
Find the sum or difference for each
question.
(-10) - (-5) = (-4) + (+1) = (-3) + (-1) =
(-4) + (-4) = (-6) - (-2) = (-2) + (+3) =
(+4) + (-2) = (5) + (+4) = (+5) + (-1) =
(0) + (+1) = (-5) + (-2) = (0) + (-1) =
(-5) + (-3) = (0) + (+2) = (-5) - (-3) =
(-1) - (-5) = (+3) + (+4) = (+2) - (+1) =
(+4) + (+1) = (+1) + (-3) = (+2) + (+4) =
(0) - (+2) = (-1) - (-4) = (-1) + (-4) =
(+4) - (+5) = (+2) - (-3) = (-4) + (-2) =
Bonus Activities ($10-30 Clement Bucks each):
“EduCreations” ($10)1. Open the App “Educreations”
Your Goal:
Grade 7 Math2. Use the whiteboard to create a lesson that explains your understanding of how to
add and subtract using a number line.3. Share your final presentation with the class or with Mrs. Clement.
Create a Board Game ($20)
You will be creating your own board game that will include everything you learn about integers in class. You may work in groups of 2-3 but no more than 3 people to a group. Your board game must meet the following guidelines:
1. You must include a set of rules that are clearly defined and easy to follow. How is the game played? How do you clarify a winner?
2. Your board game should be able to be played by 2-6 players3. Include a list of materials that are included in your board game. For example,
there must be game pieces included unless you identify what can be used as markers.
4. There should be at least 20 spaces on the game board. Depending on how the game is played, there may be a starting point and an end point.
5. Your game should include “cards” where players must solve integer problems. There should be a minimum of 20 different cards that include every operation and maybe other concepts we have learned. There should be about an even amount of each operation included.
6. On a separate piece of paper, you should have every integer problem (from the cards) written down with its correct solution.
7. Make sure the board game and directions are neat. 8. Be Creative.
Create a movie for Integers ($30)
1. Watch http://www.youtube.com/watch?v=-ydGOdl7iLc 2. Create your own awesome movie using stop motion OR a rough-cut video using
actorsa. Create a scriptb. Take a sequence of picturesc. Edit movie in movie maker or iMovied. Add a voice over
