Setting up an Interactive Notebook: Date Lesson #Math Interactive Notebook
Interactive Notebook: Table of Contents:A note about Interactive Notebooks…1.0 Interactive Notebooks (Left side of two-page spread)1.0 Interactive Notebooks (Right side)1.1 Left (write down your group and Qs)1.2 Factors and Multiples (Left)1.2 Factors and Multiples (Right)1.3 Factors (Left)1.3 Prime Factors (Right)1.4 Factors & GCF (Greatest Common Factor) [Left]1.4 (7) Factors & GCF (Right)1.4 (8)Prime Factorization GCF (Left)1.4 Prime Factorization GCF: (Right)1.5 Lowest Common Multiple (Left side)1.5 Lowest Common Multiple (Right side)1.6 problem solving (Left side)1.6 HotDog Archetype (Right side)1.7 problem solving (Left side)1.7 Garden Archetype (Right)1.8 Left side:Write a ‘needs factors’ question and a ‘needsmultiples’ question -- and get a buddy totry them both:Decimals (definition in own words)1.8 Reading Decimals (Right side) - a fraction whose denominatoris a power of ten and whose numerator is expressed by figures placed tothe Right of a decimal point.1.10 (Left) Learning goal in own words:1.10 Right:1.11 [Left]
1.11Equivalents (Right)1.12 Problem solving with mixed representations: (two page practice)1.13(Left)1.13 (Right)1.14 Integers (Left)1.14 (Right) Integers⚈⚈⚈⚈⚈⚈ ⚈⚈⚈⚈⚈⚈⚈⚈⚈ = 0 ⚈⚈⚈ = 01.15 (Left) Practice:1.15 Combining Positives and Negatives (Right side)1.16 [Left side]1.16 Integers take 2 (combining Integers) ⚈⚈1.17 (Left side:)1.17 (Right Side ) Multiplying Integers1.18 (Left)1.18 (Right) ‘Givens’ in NumeracyCheck in Assessment:
A note about Interactive Notebooks… Students write notes, or do the ‘learning’ of new content on the Right-hand page.Then, to work with that new content, students reflect or complete practice tasks on the Left-handpage.This allows students to see the ‘how-to’ at the same time as working on the task.Left Right Practice, Class notes reflection & foldables, questions, model and critical questions, & thinking vocabularyThese Right-hand notes should be: 1. Neatly labeled at the top with the lesson number and date 2. Carefully written to ensure accuracy and neatness 3. Complete!The in-class notes are not optional. If you find it hard to get them down accurately within the100-minute math-block, you can: 1. Start in class, and finish copying the notes from the web site later in the day, 2. Start in class, and finish copying the notes from the web site later at home as homework 3. Print the notes-page and paste it into your bookYour interactive notebook is your take-home textbook. You will be allowed to use it as a tool duringtests. It is in your best interest to have it as complete as possible.
1.0 Interactive Notebooks (Left side of two-page spread) Learning Goal: (put the curriculum objectives in your own words)What I know: (What do you know at the start of the question) - invent one Q of each type with parts labelledWhat I learned: (what was new? AFTER doing Right side)- what is my take-away? what is the important ‘thing’ about all this vocabulary?
1.0 Interactive Notebooks (Right side) Learning Goal:- add and subtract integers, using a variety of tools- evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations- solve problems involving the multiplication and division of decimalnumbers to thousandths by one-digit whole numbersVocabulary:Product – the answer to a multiplication QuestionTwo factors multiply to result in a product 2 x 5 = 10Sum – the Answer to an addition QuestionAn Augend and an addend add to result in a sum 3 + 4 = 7Difference – the answer to a subtraction QuestionA Minuend and a Subtrahend subtract to result in a difference 9 – 6 = 3Quotient – the answer to a division QuestionA Dividend is divided by a divisor to result in a quotient 12/4 = 3
1.1 Left (write down your group and Qs) Solve collaboratively as a group, using new vocab when thinking aloudModified kids: 2 digit multiplication with friendly numbers 71 82 21 12 41 32 15 12 82 967s: 2 digit multiplication with nasty numbers 27 47 56 19 49 388s: 2 digit multiplication with decimals42.5 x 26 51.6 x 8395.27 x 1.66 8.345 x 25.7Long Division Model: (for everyone) 3 | 972 5 | 862 71 4 | 284 - 2 8 04 -4 0
1.1 Review of Processes (Right) Goal: add, subtract, multiply, divide 3 digits, 4 digits, and decimals by hand 1 1 11Adding: 213 200 + 10 + 3 765 45.60 + 145 100 + 40 + 5 578 74.52 358 300 + 50 + 8 =358 1343 120.12 11Subtraction: 987 900 + 80 + 7 232 - 453 -400 + 50 + 3 -376 534 500 + 30 + 4 = 534 -166Multiplication: 23 x 21 = 10 10 3 65 10 100 100 30 23 89 21 76 10 100 100 30 23 534 460 6 230 1 10 10 3 483 6764 =483Division: 84/4 = _ 21_ _041.33___ 9 | 372.00 4 | 84 36 8 12 9 04 30 4 27 0 30
1.2 Factors and Multiples (Left) What is the Learning Goal: (own words)What is the Difference between Factors and Multiples: (how will I remember)What is the Application: (when will I use this)Use Factor Rainbows/Lists to find the factors of the following:36:40:56:90: Challenge: Farmer Jeff has a yard that has an area of 60m2 What are the possible lengths of the yard if it is a r ectangle? Remember: A = bh (where ‘b’ and ‘h’ are f actors of ‘A’)
1.2 Factors and Multiples (Right) Learning goal: Find Factors and Multiples using Factor Rainbows/Lists Factors: Numbers that go evenly into bigger numbers GCF: the biggest factor that will go into 2 different numbers evenly Prime: divisible only by itself and '1' Composite: divisible by several numbers (ie. not prime)Finding Factors: The Rainbow or List method:36: 1, 2, 3, 4 , 6 , 9, 12, 18, 36 (notice: ascending order, commas)72: 1, 2, 3 , 4 ,6 , 8,9, 12, 1 8, 2 4, 36,721 goes into 36….36 times2 goes into 36… 18 times3 goes into 36… 12 times4 goes into 36… 9 times5 goes into 36…… Nope6 goes into 36… 6 times7 goes into 36….. Nope8 goes into 36…… Nope9 goes into 36.... 4 times, which we already have, so we’re done36: prime factors. 36Divisible by 2? 2 182 is prime, 18 isn'tIs 18 divisible by 2? 2 92 is prime, 9 isn'tIs 9 divisible by 2? NoIs 9 divisible by 3? 3 3 (2, 2, 3, 3) 3 is prime, we’re done
1.3 Factors (Left) Definition: Prime Factorization (own words)Application: Using Prime Factors, make prime factor-trees of the following: 72 45 84 Challenge: The prime factors of two numbers are: 24: 2 , 2, 2, 3 30: 2, 3, 5GCF is: 6 how do you get '6' from these lists of prime factors? What is the short-cutfor finding Greatest Common Factor using Prime Factorization?
1.3 Prime Factors (Right) 40 40 40 /\ /\ /\ 2 x 20 4 x 10 5x 8 /\ /\ /\ 2x2 2x5 /\ 2 x 10 2x4 40: 2, 2, 2, 5 /\ /\ 2x5 2x240: 2, 2, 2, 5 40: 2, 2, 2, 5 6 8 96: /\ /\ 2 34 /\ 2 48 /\ 17 2 2 2468: 2, 2, 17 /\ 2 1 2 /\ 3 4 /\ 2 2 96: 2, 2, 2, 2, 2, 31. Choose two numbers that, when multiplied, equal your start number.2. Write both down.3. Keep breaking down numbers until you reach a prime, then circle the prime.4. When the whole tree is done, write all the prime factors in ascending order, separated by commas.
1.4 Factors & GCF (Greatest Common Factor) (Left) Steps (in own words):Find the GCF of the following pairs of numbers using Factor Rainbows/lists:1. 14: ____________________________________________ 70: ____________________________________________ GCF = _______2. 18: ___________________________________________ 81: ___________________________________________ GCF = ______3. 121: ___________________________________________ 77: ____________________________________________ GCF = ______
1.4 (7) Factors & GCF (Right) This is the Traditional, comparative GCF method:1. Find the factors of 2 large numbers2. Compare the lists of factors, underline those ‘in common’ or ‘found in both lists’3. Find the G reatest of the Common Factors → that is your GCFex 1.6: 1, 2, 3 , 6 1, 2, 3, and 6 are common18: 1 , 2, 3 , 6, 9, 18 6 is the biggest, so the GCF is 6ex 2.24: 1 , 2, 3, 4, 6, 8, 1 2, 2460: 1 , 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 601, 2, 3, 4, 6, 12 are common, so the GCF = 12
1.4 (8)Prime Factorization GCF (Left) Steps (in own words)Practice: FInd the GCF of each pair using the Prime Factors:1. 18: 48:2. 24: 49:3. 81: 54
1.4(8) Prime Factorization GCF: (Right) step 1. do factor trees for each number step 2. write the prime factors in ascending order step 3. circle the common prime factors step 4. find the product of the common prime factors = GCFEx. 1: 100: 68: /\ /\ 2 50 2 34 /\ /\ 2 25 2 17 /\ 2 is common and 2 is common 55 2 x 2 = 4 GCF = 4 100: 2 , 2, 5, 5 68: 2 , 2, 17Ex. 2: 24: 36: /\ /\ 2 12 2 18 /\ /\ 26 29 /\ /\ 23 33 24: 2, 2 , 2, 3 2, 2 , and 3 are common 36: 2, 2, 3 3 2 x 2 x 3 = 12 GCF = 12Ex. 3: 56: 87: /\ /\ 2 28 3 29 /\ 56: 2, 2, 2, 7 2 14 87: 3, 29 → GCF: 1 (because nothing else is common) /\ 27
1.5 Lowest Common Multiple (Left side) Definition (in own words)Traditional (7s):ex 1. 10: __________________________________ 15: __________________________________Prime Factors (8s):ex 2. 10: 15: __ __ __ __ 10: ___, ___ 15: ___, ___ LCM: ____FInd the LCM of each using your choice of method:1) 24 & 42 4) 36 & 402) 9 & 12 5) 15 and 183) 11 and 25 6) 8 and 50
1.5 Lowest Common Multiple (Right side) Multiples: 'counting by'LCM: the smallest number common on two 'counting by' listsTraditional (7): step 1 ‘count by’ each number step 2 starting with the largest number, look for common multiples step 3 the lowest multiple common to both lists is LCM12: 24, 3 6, 48, 60, 72 → LCM = 36 9: 18, 27, 3 6, 45 5:10 15 20 25 3010: 20 30 40 50 60 → LCM 107: 14 21 28 35 42 49 56 63 70 779: 18 27 36 45 54 63 72 81 → LCM: 63Prime Factor: step 1: build prime factor trees:12: 9:/\ /\3 4 3 3/\22 Step 2: stack the prime factors 12: 2, 2, 3 9: 3, 3 Step 3: bring down ONE of each common pair 12: 2 , 2 , 3 9: 3, 3 ↓ 3 Step 4 : multiply by all remaining factors 3 x 2 x 2 x 3 LCM = 36
1.6 problem solving (Left side) What mathematical facts are needed to solve this problem?What words help you choose a mathematical process?What information do you really need to use?What problem solving strategy did you use?Task :Make up and solve 2 similar questions using the same math concepts:
1.6 HotDog Archetype (Right side) Suzie is hosting a BBQ. She wants enough hotdogs to feed 65 people one each. Buns come inpackages of 8, and hotdogs come in packages of 12. How many packages of each product doesSuzie need in order to make at least 65 hot dogs, with a few Left over.Additive Organized Lists dogs 12 1 pkg 12+12 = 24 buns 2 pkg 24 + 12 = 36 1 pkg 8 3 pkg 36 + 12 = 48 2 pkg 8+8 = 16 4 pkg 48 + 12 = 60 (not enough) 3 pkg 16 + 8 = 24 5 pkg 60 + 12 = 72 (enough) 4 pkg 24 + 8 = 32 6 pkg 5 pkg 32 + 8 = 40 7 pkg 6 pkg 40 + 8 = 48 8 pkg 7 pkg 48 + 8 = 56 9 pkg 8 pkg 56 + 8 = 64 (not enough) 9 pkg 64 + 8 = 72 (enough)Showing that you know to look for LCM: 8: 16, 24, 32, 40, 48, 56, 64, 72, 80 9 pkg 12: 24, 36, 48, 60, 7 2, ∴ 6 pkg hotdogsKyle wants to hand out mini chocolate bars to his class. The packages have 8 bars inthem. There are 30 kids in his class. How many packages does he need?Additive Organized List: Multiplicative Organized list:1→8 =8 8(1) = 82 → 8 = 8 + 8 = 16 8(2) = 163 → 8 = 8 + 8 + 8 = 24 → Still not enough 8(3) = 244 → 8 = 8 + 8 + 8 + 8 = 32 ∴ 4 pkg needed 8(4) = 32 → ∴ 4 pkg neededUsing/Recognizing Multiples: Algebraic:
8: 16, 24, 32, 40, ∴ 4 pkg needed 30 / n = 8 n = 3.75 pkg, so ∴ 4pkgs1.7 problem solving (Left side) What mathematical facts are needed to solve this problem?What words help you choose a mathematical process?What information do you really need to use?What problem solving strategy did you use?Task : Make up and answer a similar question using the same math concepts:Practice: find ALL of the possible dimensions of a rectangular playgroundwith an area of 96m2. (remember: A=bh, where ‘A’ is a product and ‘b’ and‘h’ are factors).
1.7 Garden Archetype (Right) John wants to dig a garden in his backyard. He has enough compost to cover 84m2 ofsurface area (think: A=bh, where ‘A’ is a product of those ‘factors’). What are thepossible dimensions of the garden?Step 1: find the factors of 84: 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84Step 2: if those are the factors, what would the ‘products’ be? bxh 1 x 84m 2 x 42m 7 x 12m 6 x 14m 3 x 24m 4 x 21m------ Billy has enough paint to cover 72ft2 of wall (he is only painting one wall). What are thepossible dimensions of his one wall.Step 1: find the factors of 72: 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72Step 2: each pair of factors are your new possible dimensions: 1 x 72 = 72 could work…. If you’re an ant. 2 x 36 = 72 could also work, for a smurf 3 x 24 = 72 could work for a Dachshund 4 x 18 = 72 ok for toddlers 6 x 12 = 72 ok for elves and juniors 8 x 9 = 72 perfect choice for room height.
1.8 Left side: Write a ‘needs factors’ question and a ‘needs multiples’ question -- and get a buddy totry them both:Decimals (definition in own words)Complete the following using long multiplication and long division:A. 14 x 0.01 = 0.01B. 14 ÷ 100 = ____ make sure you set it up correctly: 100|14.00000C 258 x 0.1 =D. 258 ÷ 10 = 258. 000/10E. 24.6 x 1000 =F. 24.6 ÷ 0.001 =G. 25 / 10 =H. 25 x 0.1 =Practice: Use decomposition strategies wherever possible 1. What is the sum of 45.2 and 7.287 2. What is the sum of 9.52 and 98.1 3. What is the sum of 134.0 and 21 4. subtract 45.8 from 86.2 5. find the difference between 92.93 and 4.3 6. find the product of 5.12 and 83.75 7. What is one tenth of 76 8. divide 223.2 by 7.2
1.8 Reading Decimals (Right side) - a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the Right of a decimal point. 53.3 = 53 3/10 “fifty-three AND three-tenths”53.36 = 53 36/100 “fifty-three AND thirty-six-hundredths”53.367 = 53 367/1000 “fifty-three AND three-hundred-sixty-seven thousandths” NB: AND means the “.” (Decimal)56 78 9.123“fifty-six thousand , seven hundred eighty-nine A ND one hundred twe nty threethousandths” 5= 50 000 = the value of the ‘5’ is 50 000 6= the value of the ‘6’ is 6 000 7= 700 8= 80 9= 9 0.1 = one tenth 1/10 = 0.10 0.02 = 2 hundredths 2/100 0.003 = 3 thousandths 3/1000add: 34.63 and 23.982 11 23.982 34.630 58 .612 1 1 11subtraction: subtract 23.982 from 22.410 2 3.982 9.538multiplying: 365.522 x 22.5
1 .9(Left) Learning goal in own words: practice:Add: 43 529.4 + 7 329.78 =Subtract: 85 734.89 - 72 396.5 =Multiply: 425.4 x 27.83 =Divide: 84.8 ÷ 12.2 =
1.9 Right: Alignment (or not) of decimals:When adding: Align and add zeros to fill in the gaps at the Right:so: 66.3 + 7.52 is NOT: 66.3 CORRECT: 66.30 7.52 7 .52When subtracting: Align and add zeros to fill in the gaps at the Right:so: 743.21 - 67.3 i s NOT: 743.21 CORRECT: 743.21 67.3 6 7.30When multiplying: Right-Justify and Align the digits, ignoring the decimals:so: 53.77 x 3.2 is NOT: 53.77 CORRECT: 5 3.7 7 3 .20 3.2Multiply by the lower ‘ones’ digit: 10754Add the zero so you can Multiply by the lower ‘tens’ digit: 161310Add the two lines of products: 1 7 2 0 6 4Count and mirror how many d ecimals w ere in the question answer = 172.064When Dividing: Copy and paste the decimal when you write out the frame, and add h elper zeroes: .726.5 ÷ 9 = 9 | 6.50 000 6 3↓ ↓ ↓ 20 - 18 _ 20 etc 6.5÷9 = 7.72
1.9b Practice for all: B. 12.3 x 4 C. 15.5 x 3.1 Modified kids: A. 55 x 6.21.10D. 1.51 x 5.02 E. 12 x 3.1 F. 90 x 5.2G. 120 divided by 15H. 86 divided by 12 I. 100 divided by 16 B. 55.6 x 72.51 C. 78.42 x 93.57s. A. 12.5 x 3.5 D. 40.2 x 14.62 E. 104.5 x 22.5 F. 74.32 x 52.7 G. 84 divided by 16 H. 1632 divided by 2.8 I. 94 divided by 138s:A. 52.6 x 34.15 B. 845.54 x 25.8 C. 52.4 x 71.842 D. 982.52 x 18.842 E. 78.92 x 802.54 F. 762.53 x 37.9 G. 742 divided by 67 H. 98.5 divided by 15 I. 963.12 divided by 143
1.10 [Left] Convert to decimals: 7/12 0.583 (x100) -- 58%a 30% e 2/6b 7/10 f 13%c 92.4% g 6%d⅗ h 123/1000Convert to fractions:a 15% d 0.62b 0.2 e 3.5c 1% f 15.2%Convert to percents:a⅚ d 8/12b 0.56 e 7/9c 1.46 f 13/27
1.10 Equivalents (Right) Learning Goal: to be able to convert between fractions, percents,and decimals; to gain familiarity with benchmark fractions, To beable to use equivalent numbers to convert units when problemsolving½ = 5/10 = 0.50 = 50%Fraction numerator x 100 = % 8 = 0.80 x 100 = 80%Fraction denominator 10Percent = fraction 45% 4 5 *per cent = par cent = by 100100 100Numerator = decimal Decimal = fractiondenominator3 =0.75 depends on places4 0.1 /10 0.01 / 100 0.001 /10000.9 9/10 90% 0.41→ 41/100 → 41%64% → 64/100 → 0.64
1.11 Problem solving with mixed representations: (two page practice) 1. Jillian wonders if ⅘ is as good a mark as 90%. Jillian: “5 subtract 4 is one, and 10 subtract 9 is one, and 9/10 is 90%, so they are the same.” Is Jillian correct? is ⅘ = 90%? Why or Why not? Fractions: ⅘ 8/10 9/10 4 x2 8 5 x 2 10 ⅘ vs 90% 0.8 vs 0.9 ⅘ vs 90% 80% vs 90% ⅘ <90%, 0.8<0.92. Kim got ⅞ on a test. Her teacher writes down her percent mark as 87% Is she correct or not? Why or why not? is ⅞ = 87%?
3. Mark thinks that his math homework is done. They had to takefractions and convert them to percents. Here is his work: 16/23 = 0.69 x 100 = 69% Is his work correct? Why or why not?4. A broken scale is used to measure the height of the plant. Thelength of the broken scale is 12 cm. The height of the plant is 14.15times greater than the broken scale. What is the height of theplant? x= height of plant12cm scale ____ 14.15 = x x = ____5. Diego and Dora are close friends studying in the same school.Diego’s home is 6.87 miles away from school. Dora’s home is 7times as far as Diego’s home from school. Find the distancebetween Dora’s school and her home.let d = distance from Dora’s school to homed=6. E xplain how you can write an equivalent decimal in the hundredths orthousandths for any decimal in the tenths.7. Is a number with three digits to the Right of the decimal point alwaysgreater than a number with two digits to the Right of the decimal point?Explain your reasoning
8. Draw a model to describe and explain your thinking. The redkangaroo, the world’s largest marsupial, uses its tail for balance whenjumping. Its tail is about 0.53 times as long as its body. Its body is about2 meters long. How long is its tail?9. Matt ate ¼ of a pizza and Mike ate 2/5 of a pizza. Explain how tochange each fraction into an equivalent decimal to determine who atemore.
1.12(Left) Exponent - (in your own words)How to remember Expanded Exponential ScientificPractice:678 245.2 Expanded Exponential Scientific67 324 234.9851 Expanded Exponential ScientificModified Kids: 32 + 5 x 2 =Grade 7s: 5 2 + 3 x 103 + 14 =Grade 8s: 7(45 - 24 ) + (-4) x 10-3 + - (39 ) +73 =
1.12 (Right) Exponent: shorthand for repeated multiplicationeg. 62 = 6 x 6 = 36 93 = 3 ‘9s’ multiplied = 9 x 9 x 9 = 72910 5 = 5 ‘10s’ multiplied = 10 x 10 x 10 x 10 x 10 =100 000Expanded notation: shows what each digit represents13 567 = 10 000 + 3 000 + 500 + 60 + 7457 932.9 = 400 000 + 50 000 + 7 000 + 900 + 30 + 2 + 0.9 or 9/10Exponential notation:13 567 = 1 x 104 + 3 x 103 + 5 x 102 + 6 x 101 + 7 x 100372 947.67 =300 000 + 70 000 + 2000 + 900 +40 +7 + 0.6 + 0.073 x 105 + 7 x 104 + 2 x 103 + 9 x 102 +4x101+ 7 x 100 + 6 x 10- 1 + 7 x 10-2Scientific notation:13 567 = 1.3567 x 104583 472.98 = 5.8347298 x 1050.0000000000082 = 8.2 x 10-12
1.13 Integers (Left) practice: model and solve: 1. (+4) + (+7) 2. (-2)+(-5) 3. (+8)+(+2) 4. (+13)+(+12) 5. (+1)+(+25) 6. (-14)+(-3) 7. (-2)+(+9) 8. (-5)+(-9) 9. (-12)+(-4)10. (+5)+(-2) What does the model show? solve 1. +++++ +++ ----- (+8) + (-5) = +3 2. ---- ++++ -- 3. -- 4. +++ --- +++++ 5. +++++ +++++ ++++ ----- ----- -- 6. +++++ +++++ +++++ +++ ----- -- 7. (+3) + (-5) = 8. (-4 ) + (-6) = 9. (-6) + (+8) = 10. (-5) + (+3) = m ore practice and some m ore
1.13 (Right) Integers integers: an integer is commonly known as a ‘whole number’ a numberthat can be written without a fractional component (21, -2, 8 are all integers,while 4.73, and ½ are not.)Positive: a whole number greater than zero - represents a gain, what you have ⚈ Negative: a whole number less than zero - represents a loss or a debt, what you take away, “in the red’ ⚈ Zero principle: inverse additives cancel to zero: -x and +x = 0⚈⚈⚈⚈⚈⚈ ⚈⚈⚈ ⚈⚈⚈⚈⚈⚈ = 0 ⚈⚈⚈ = 0 Addition of positives: (+4) + (+3) = ⚈ ⚈⚈⚈+ ⚈⚈⚈ = (+7)Addition of negatives: (-2) + (-5)=⚈⚈ + ⚈⚈⚈⚈⚈= (-7)Addition of mixed integers: (-4) + (+2) = ⚈ ⚈⚈⚈ = (-2) ⚈ ⚈ (-3) + (+7) = ⚈⚈⚈ =(+4) ⚈ ⚈⚈⚈⚈⚈⚈
1.14 (Left) Practice: Addition (combining) of Positives and Negatives: 1. (+3) + (-1) = 2. (+6) + (-2) = 3. (-2) + (-6) = 4. (-12) + (+3) = 5. (-10) + (+3) + (-1)= 6. (+5) + (-4)+(+6) = 7. (+20) + (-12) = 8. (-11) + (-6) + (+5) = 9. (+5) + (-2) + (+7) + (-6) =10. (+25) + (-15) + (+32) = more practiceRepresent the following in math-language: 1. John owes Tim four dollars 2. Kyle found 20$ on the road 3. Marcy lost her cat 4. Bob got 50$ for his birthday. He gave 20$ to the humane society. 5. Kim wants to buy a new coat, but she doesn’t have the money. She uses her brand new credit card to buy it.And…. watch the signs…. 1. (+5) - (-3) 2. (-3) + (-2) 3. (+6) - (-4) 4. (-3) + (-5) 5. (+7) - (-3) 6. (+7) - (-6) 7. (+5) - (-7) 8. (+8) - (-4) 9. (-3) + (-6)10. (-5) - (-8)
1.14 Combining Positives and Negatives (Right side) Given that the zero principle states that every + is cancelled by a -Given that (+12) = + + + + + + + + + + + +and (-7) = ----- --Then…. (+12) + (-7) = (+5) + + + + + + + + + + + + ----- --Given that the zero principle states that every + is cancelled by a -This is a model of (-5): -----So is this: +++++ +++++ ----- ----- -----And this +++++ ----- -----And this: +++++ ++ ----- ----- --You can add as many cancelled pairs (+ - ) as you need to model a questionSo try: (+12) - (-4) = + + + + + + + + + + + + + + + + + _____ (+5) - (-7) = + + + + + + + + + + + +
1.15 [Left side] Reflection: How do you think of negative and positive numbers? What are some examples now?How does having a real-world model for integers help you solve world problems?1. Katherine is very interested in cryogenics (the science of very low temperatures). With thehelp of her science teacher she is doing an experiment on the effect of low temperatures onbacteria. She cools one sample of bacteria to a temperature of -51°C and another to -76°C.What was the temperature difference in the two experiments? 2. On Tuesday the mailman delivers 3 checks for $5 each and 2 bills for $2 each. If you had a starting balance of $25, what is the ending balance? 3. You owe $225. on your credit card. You make a $55 payment a nd then purchase $87 worth of clothes at Dillards. What is the integer that represents the balance owed (-) on the credit card? 4. If it is -25F in Rantoul and it is +75F in Honolulu, what is the temperature difference between the two cities? 5. on Monday morning when you wake up at 8 am, it is +2 degrees C. The temperature rises steadily 2 degrees per hour. At 1 pm the temperature holds steady. At 5 pm the temperature begins to drop a steady 2 degrees per hour. at 10 o’clock it reaches it’s lowest point. What temperature is it at 11 pm? 6. A seagull flies over the ocean 14 ft above the water. It spies a yummy fish and dives, ending up under 1ft of water, then zooms back up 4 ft. what elevation does it end up at after catching the fish? 7. each morning you drive to work, and go down two floors to the underground parking lot. Then you ride the elevator up 6 floors to the office. you go down 2 floors to the mailroom, then back up 5 floors to finance. What floor do you end up on?
1.15 Integers take 2 (combining Integers) ⚈⚈ A. model and solve:1. (-4) + (+3) = -1 - - - - + + + = 2. (+2) + (-4) = ⚈⚈ ⚈⚈ ⚈⚈ 3. (-6) + (+5) = 4. (+2) + (+5) = 5. (-4) + (-5) =6. 6. (+6) - (-3) =Show all work (in math language and symbols) to communicate HOW you solved thesequestions:Eg: The temperature when you wake up is 10C. THe temperature goes up 8 more degrees bynoon. Then the temperature drops again by 17 degrees. What is the temperature at the endof the day? “+10C” + “(+ 8)”+10C + (+8) + (-17) = ⚈ ⚈⚈⚈⚈⚈⚈⚈⚈⚈ ⚈⚈⚈⚈⚈⚈⚈( ⚈ ) ⚈⚈⚈⚈⚈⚈⚈⚈⚈⚈ ⚈⚈⚈⚈⚈⚈⚈ = (+1) “+ (-17)”1. Snuffy leaves his penthouse and hops on the elevator in his building on the 13th floor.The elevator goes down two floors, then goes back to the 13th floor. The Bird familygets on, and they all journey 7 floors down. The manager, Luis, gets on and takeseveryone back up one floor. Then, finally, Elmo gets on, and they all travel down threefloors together, at which point they all get off to go to a birthday party for Oscar. Whichfloor is the party on?2. A submarine dives 836 ft. It rises at a rate of 22 ft per minute. What was the depth of the submarine after 12 minutes?
1.16 (Left side:) (+) x (+) = (+) (-) x (-) = (+)adding groups of positives removing groups of negatives(+) x (-) = (-) (-) x (+) = (-)adding groups of negatives removing groups of positives.....all from the field of 'zeroes'try modelling them: 4. (+6) x (-2) =1. (+2) x (-5) = 5. (-7) x (-3) =2. (-3) x (-4)= 6. (-4) x (-5) =3. (-4) x (+2) =Modified 7s 8s 1. (+2) + (-2) 1. (-4) x (-5) = 1. (-21) x (+3) = 2. (-10) + (-3) = 2. (-10) + (-3) = 2. (+6) x (-15) = 3. (+3) x (+2) = 3. (+9) x (+3) = 3. (-12) x (-6) = 4. (+3) x (-2) = 4. (+3) x (-12) = 4. (-15) x (+7) = 5. (+2) x (-4) = 5. (+2) x (-12) = 5. (-35) x (-2)
1.16 (Right Side ) Multiplying Integers Multiplying is...- repeated addition ( (5 x 4) = (5 + 5 + 5 + 5) - adding or subtracting 'groups' of stuff(+++++) (+++++) (+++++) (+++++) = +20(+5) x (-4) = ??? (----) (----) (----) (----) (----) = -20You ‘have’ 5 groups of ‘4 negatives’(-3) x (-2) =+6 (start with a field of zeroes)++++++++++++++++__________(-4) x (+2) = -8++__________(+2) x (-4)= -8---- ---- = -8 + x+=+ + x-=- - x+=- - x-=+
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1.18 (Left) Practice :) 7s 8s(friendly) 8sModified (+4) - (+3) = (+8) • (+3) = (+4) • (+3) =(+4) - (+3) = 5 x (2 + 6)= 5 x (2 + 6) - (+2) = 5(12 + 6) - (+2) =3 x (2 + 6) 15 - (3 x 6) = 52 - (3x6)= 52 - 2(3x6) =10 - (2 x 4) 24 + (-2 • +7) = 20 + (-2 • +7) = 20 + (-2)(+7) =10 + (-2 • 4)= (-4) + (-2) • 9= (-4) + (-12) • (-2)= (-2)2 + (-12) • (-5)=(-4 + -7)= 15 • 3 - (3)(4) = 15 • 3 - (-3)(4) = 15 • 3 - (-3)(-4) =15 • 3 - 12 = 50 - 2 • (+18) = 40 - 2 • (+12) = 40 - 9 • (+12) =50 - 2 • (+3) = +2(+3 • +8) = +2(+3)(-8) = +12(+6)(-4) =+2(+3 • +5) =turn into mathematical sentences and solve:1. Joe babysits for $5 an hour, plus a flat tip of 4$ per child.2. A certain small factory employs 98 workers. Of these, 10 receive a wage of $150 per day and the rest receive $85.50 per day. To the management, a week is equal to 6 working days. How much does the factory pay out for each week?3. A certain Math Club makes 35 bars of laundry soap a week and sells these at $20 each. Before the soap can all be sold, the pupils found out that 6 bars were destroyed by mice. How much will be the total sale at the end of a four-week month?4. Lilia scores 15 points fewer than Bob, who scores 35 points. Carol scores half as many points as Lilia. How many points does Carol score?Modified: only underline what to do FIRST (do not solve)Everyone else: SOLVE1. 32 + (5 ● 3)2 - 12 + 4(2 - 1) =2. 40 - 5 ● 2 + 7 x 3 + (-3) =3. 142 - 5 ● 3 - 20 x 4 =4. 7 ● (6 - 2) + (8 - 3) + 9 - 8 =& then make up and solve one of your own:
1.18 (Right) ‘Givens’ in Numeracy 1. Order of Operations ALWAYS needs to be followed: Brackets (Parentheses) Exponents (squares, square roots, etc) Division and Multiplication in the order they appear from Left to Right Addition and Subtraction in the order they appear from Left to Right 2. a number with no sign is ‘understood’ to be ‘positive: 5 = (+5) 3. a number immediately in front of a bracket implies multiplication 3(6) = 18 4. brackets can be placed around a digit and it’s sign to clarify ‘quality’ from ‘process’ (+6) + (-3) = vs +6 + -3= 5. because ‘x’ will soon represent a variable, we can use • for multiplication Xxx x•x 6. rewrite the entire equation as you substitute solutions for operationsex. 1 15 + 2(6 -1) - 5(+22 ) = BEDMAS 15 + 2(5) - 5(4) = 15 + 10 - 20 = 25 -20 = +5Ex. 2. 45 - (5x 32 ) + ( 4(6-2) x 42 ) -6 = BEDMAS 45 - (5x32 ) + (4 (4) x 42 ) - 6= 45- (5 x 9) + ( 4 ( 4) x 16) - 6 = 45 - 45 + 256 -6= 0 + 256 - 6 = 250 = 250 :)ex. 3 (-7) + (-4) • (+3) + (+2)4 - 52 = BEDMAS (-7) + (-4) • (+3) + 16 - 25 = (-7) + (-12) + 16 - 25 = -19 -9 = -28 :)Tim babysits for a flat rate of 10$ per hour, plus 3$ per kid tip. What would he make sitting 4 kidsfor 2 hours?
1.19 - order of operations Left practice: BEDMASGoal - in own wordsReflect: Solve the following in order Left to Right, and again using bedmas.9 + (- 5) • 2 + 7 • (-3) =Now direct input on a calculator: does your calculator use BEDMAS logic?I’m not feeling confident: I’m the king of MATH! :1. 3 • (-7) - 3 = 3 • (-17) - 3(4-1) =2. 15 ÷ 3 • 22 -3 = 15 ÷ 3 • 26 -7 =3. 3(7-4) • (5 x 2)3 + √49 - 3 = 3(4-7) • (5 x 2)3 + √49 - 13 =4. √(36) - (-5) • (+5) = √(64) - (-5) • (+15) =5. 32 • 7-3 = 82 • 7-3 =6. 15 - 2 • 10 + 52 = 15 - ( - 2) • 10 + 52 =7. (-3)(4 - 1)2 = ((-3)(5 - 1))2 =8. 5(102 - 8) = 5(102 - 8)2 =9. 100 - (4)(7) = 100 - (-4)(-7) =10. (3)(-7) • +6 = 9 - (3)(-7) • +6 + (-9)=11. 5 times the product of negative 3 and five is…12. The difference of 7, and 3 squared is…13. The sum of 15, and the product of 3 and negative 8, is…14. The product of eight, and the sum of nine and negative two, subtract 7, is…15. The square root of the product of eight and two is...
1.19 Bedmas Investigation (Right)Goal: communicate mathematical thinking orally, visually, and in writing, usingmathematical vocabulary and a variety of appropriate representations, and observingmathematical conventions.Investigate how BEDMAS effects answers:Solve from Left to Right: 7 + 3 • (-6) + 2 • 10 = (-580)Solve using Bedmas: 7 + 3 • (-6) + 2 • 10 = 7 + (-18) + 2 • 10 = 7 + (-18) + 20 = (-11) + 20= (+9)
Hand in Assessment:Modified kiddoes: 1. 5 x 3 + 9 = 2. 6 - 3x5= 3. (42 +7) x (3)=Grade 7s: 1. (+7) + (-3) + 32 = 2. (-5) + 42 = 3. (+4 - 1)2 + (-5)(-3) =Grade 8s: 1. (+72) + (-3) x 32= 2. 3(-5) + 42= 3. (+4 - 1)2 + (-5)(-3)2 =
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