Unit 1 Grade 8
Integers and Algebraic Expressions
; review adding and subtracting of integers in context;
; develop estimation skills for solving everyday problems;-
; develop an understanding of multiplication and division by and of integers (making use of both manipulatives and
; solve problems requiring an understanding of integers and their arithmetic manipulation;
; evaluate arithmetic and algebraic expressions involving integers and including brackets and exponents, emphasizing
the need for knowing and following the order of operations.
Day Lesson Title Math Learning Goals Expectations
1 A Positive Attitude 8m18, 8m22 ; Re-establish necessary conceptual understanding and skills Toward Negative required for this unit. Numbers CGE 2b, 7b ; Mastery of adding and subtracting integers and contextualizing these operations in real life. ; Show that addition and subtraction are inverse operations.
2 Living with Negatives 8m18, 8m22 ; Solve a variety of application questions requiring the choosing of operations and the applying of skills (adding/subtracting) with CGE 3c integers.
3 Unfamiliar Territory 8m18, 8m22 ; Explore and investigate multiplication of integers with opposite signs using a variety of approaches, e.g., patterns in a CGE 3c, 7b multiplication table; multiplication as repeated addition of sets.
; Investigate multiplication of integers within everyday contexts to
4 Getting Used to the 8m21, 8m22 ; Solve simple problems requiring the multiplication of integers Territory with opposite signs. CGE 5b ; Explore multiplication of integers with the same sign, utilizing the approaches from the previous day.
5 Writing Letters in 8m59, 8m62 ; Review the use of algebra in real life and evaluate algebraic Math Class expressions with integers. CGE 3c, 7b
6 It‟s the Inverse 8m21 ; Investigate division of integers. ; Connect the operation of division as the inverse of the operation CGE 4b, 4f, 5a of multiplication. Provide examples where division is either
partitive or quotative, i.e., How big is one share? How many equal
7 Dividing It Up 8m21, 8m22 ; Solve simple problems requiring the division of integers.
CGE 5b, 7b
8 But Is It Useful? 8m18, 8m21, 8m22 ; Solve problems requiring multiplication and division of integers, utilizing estimation as well as calculation. CGE 3c, 5b
9 Now, What Did 8m20, 8m23 ; Operate with integers by evaluating arithmetic expressions BEDMAS Stand For? requiring the application of Order of Operations. CGE 3c, 5b
Day Lesson Title Math Learning Goals Expectations 10 Putting It Together 8m62 ; Evaluate algebraic expressions requiring the multiplication and division of integers. CGE 4b, 4f 11 Life‟s Full of Numbers 8m18, 8m21, ; Solve problems requiring operating with integers and explaining 8m22, 8m23 the thinking behind the solutions.
CGE 2b, 2c 12 Summative
Unit 1: Day 1: A Positive Attitude to Negative Numbers Grade 8
Materials Math Learning Goals ; BLM 1.1.1 ; Students will re-establish necessary conceptual understanding and skills required for ; BLM 1.1.2 this unit. ; BLM 1.1.3 ; Students will gain mastery of adding and subtracting integers and contextualizing ; Decks of cards these operations in real life. for pairs of students ; Students will show that addition and subtraction are inverse operations ; Paper and pencil
; Wall Anchor
Teacher Tip: Whole Class ; Investigation Look for students Minds On… Students play Integer Football: who find patterns in Have the classroom or large area (gymnasium or outdoor area) marked out as a football the game.
field. The centre line is 0, while one end is the +50 goal line and the other end is the -50
goal line. You will need to mark off 5 unit increments on each side. Any position on the field is determined by a signed number between +50 and -50.
Break students into two teams: positive and negative. The positive team moves towards the positive goal line and the negative team moves towards the negative goal line.
If the negative team starts on the -20 yard line and has a loss of 20 yards, it will be on
the +5 yard line.
Use the changes on BLM 1.1.1 to move the teams around the field; have a QB come and pick a change for their team. Have a designated student from each team be the “ball” for that turn, allowing every student a turn, and have three downs. After three
downs, the other team takes the field. Have the team members tell the student where to go on the field.
Play continues until a team scores a touchdown or teacher feels enough time has passed for students to have grasped the concept.
Whole Class ; Connecting Action! Lead the class into a discussion about the most important ideas/rules/patterns
discovered during the game.
- What happened when the negative team GAINED (added) yards?
- What happened when the positive team GAINED (added) yards?
- What happened when the negative team LOST (subtracted) yards?
- What happened when the positive team LOST (subtracted) yards?
In groups, have the class come up with rules or patterns for adding and subtracting
integers. Go over each groups‟ conclusions.
As a class, create class rules for adding and subtracting integers and put them, along with illustrations, on a pre-made Wall Anchor poster. Give students BLM 1.1.2 to make
Content Expectations/Observation/Mental Note: Circulate to assess whether or not
students can make connections to the patterns in the football game. The recognition and understanding of these patterns is key to success in this unit.
Small Group ; Integer game Consolidate Students work in groups of two and play the Integer WAR game. Debrief Students are given a deck of cards: red cards are positive integers from 1-13 and black cards are negative integers from 1-13. Decks are shuffled and two cards are turned over
at the same time. Students write down an addition or subtraction expression using the numbers shown. The person to make the largest number by adding or subtracting wins a point.
Exploration Home Activity or Further Classroom Consolidation Reflection Students complete BLM 1.1.3
1.1.1: Possible Football Moves Grade 8
Gain of Loss of Gain of Loss of Gain of 10 10 2 yards 2 yards 20
yards yards yards Loss of Gain of Loss of Gain of Loss of 20 1 yard 1 yard 19 19
Yards yards yards Gain of Loss of Gain of Loss of Gain of 15 15 5 yards 5 yards 30
yards yards yards Loss of Gain of Loss of Gain of Loss of 30 35 35 12 12
yards yards yards yards yards Gain of Loss of Gain of Loss of Gain of 50 50 80 80 100 yards yards yards yards yards
1.1.2: Integer Wall Anchor Poster Grade 8
1.1.3: Inverse Operations Take Home Activity Grade 8
How could the ball get from the +40 yard line to the -10 yard line if the negative team had the ball? What if the positive team had the ball?
If the positive team had a gain of 20 yards and a loss of 30 yards and ended up at the -20 yard line, where did they start?
10 – 20 = 10 + -20 =
-30 + 40 = -30 - -40 =
-40 – 10 = -40 + -10 =
Unit 1: Day 2: Living with Negatives Grade 8
Materials Math Learning Goals ; BLM 1.2.1, ; Students will solve a variety of application questions requiring the choosing of 1.2.2, 1.2.3 operations and the applying of skills (adding/subtracting) with integers. ; Algebra tiles
; Number line
; Thermometer ; Calculator
Whole Class ; Problem Solving Minds On… Have a big problem on the board for when students enter the classroom. The problem
should address concerns with notation (e.g. Owed money is represented using a
negative sign) and allow for incorrect notations to be discussed (representing owing
money with a positive amount).
Example Problem: Emmanuelle owes her brother $20 for a CD he bought for her and is
getting $10 from her grandmother for mowing the lawn. If she started out with $25,
how much money will she have now? Have students share solutions and discuss any
Small Group ; Connecting Action! Set up five stations around the classroom and break students into groups around each
station. See BLM 1.2.1 for activities for each station.
Station A: algebra tiles, Station B: coloured counters/ two-colour discs, Station C:
number line, Station D: thermometer, Station E: calculator.
Give students BLM 1.2.2. Allow students sufficient time at each station to discuss the
problem and record their work.
Content Expectations/Observation/Mental Note: Circulate to assess whether or not
students are understanding and using the rules discussed on Day 1. The recognition and
understanding of these rules is key to success in this unit.
Whole Class ; Discuss Consolidate As a class, summarize and discuss their results from the „Action!‟ section. Have
Debrief students put samples of their answers to each station on the board and discuss other possible representations. Discuss which manipulatives worked best for what situations.
Exploration Home Activity or Further Classroom Consolidation Reflection Students complete BLM 1.2.3
1.2.1: Activity Centers Grade 8
Jim is on the golf course. He has the following results for the first three holes: +3, par and -2. What is his total score at this point? Is the answer positive or negative? How do you know this? Model your work using the manipulative provided and then record your work on your record sheet.
You are buying a barrel of 35 apples. As you pick up the barrel you notice there are some bad apples in the barrel. You remove the bad apples and have 20 apples left. How many bad apples were there? Is the answer positive or negative? How do you know this? Model your work using the manipulative provided and then record your work on your record sheet.
You and your friends live on the same street. One friend lives to the East of you and the other lives to the West. You walk the three blocks West to pick up your first friend and then walk five blocks East to visit your other friend. How far does the second friend live from you? Is the answer positive or negative? How do you know this? Model your work using the manipulative provided and then record your work on your record sheet.
A temperature gauge in an airplane measures the following changes in temperature 0 0 0 after takeoff: + 2C, - 30 C and +20C. If the plane landed in Montreal and the 0 temperature there was 26C, what was the temperature when the plane took off? Is the
answer positive or negative? How do you know this? Model your work using the manipulative provided and then record your work on your record sheet.
Benny gets paid $500 every two weeks. After his paycheck is deposited, he has to pay his cell phone bill of $30 and buy a birthday gift for his girlfriend. If Benny has $390 left in his account, how much did he spend on the gift? Is the answer positive or negative? How do you know this? Model your work using the manipulative provided and then record your work on your record sheet.
1.2.2: Student Work Sheet for Activity Centers Grade 8
1.2.3: Living with Negatives Grade 8
For each problem below, please indicate
i. what operation(s) you will use to solve the problem and
ii. whether the result will be positive or negative
Choose TWO problems to solve completely.
Brent scores a -2 on Hole 1, +4 on Hole 2 and par on Hole 3. He forgets to write his and then choose TWO problems to solve score for Hole 4 but his friend has his total score as par for the course so far. What did
Brent score on Hole four?
Marie is buying light bulbs for her Christmas decorations. She buys 12 but when she
gets to the cash, she has to put back four because they are broken. How many light
bulbs does Marie buy?
You are tracking the movements of an ant as he searches for food for a science
project. You notice that he travels 10 m north of the colony and then moves 60 m
south. How far away from the colony is the ant when he finally finds food?
Annie monitors the temperature in her swimming pool on a daily basis. On Monday it 0was 25C and then it dropped two degrees before climbing five degrees by Friday. What was the temperature of the pool on Friday?
Phil gets paid $500 every two weeks. After getting paid he had to pay $30 for repairs to his skateboard, but then received a check from his grandparents for his birthday. If his balance is $520, how much did he receive from his grandparents?