Mr. Huang Foundations of Math and Pre-Calculus 10: Skills Development
Unit 1: Basic Operations and Algebra
1. Basic Arithmetic 2. BEDMAS 3. Integers 4. BEDMAS II 5. Fractions 6. Fractions II 7. Algebra *Funsheets This note package belongs to ____________________
Table of Contents
Day Date Agenda Homework 1
1. Course Outline / Calculators 2. Set-up folders 3. Lesson 1: Basic Arithmetic
-Bring binder 1.5 ring
2
1. Seat Change 3. Warm-up puzzle 4. Lesson 2: BEDMAS + Funsheet
-Finish Funsheet: BEDMAS for HW check next class -Bring Notebook
3
1. Set-up Notebooks 2. HW Check + Warm-up 3. Lesson 3: Integers 4. Lesson 4: BEDMAS II + Funsheet
-Finish Funsheet for HW Check
4
1. HW Check + Warm-up 2. Lesson 5: Fraction I + Funsheet 3. Board Questions
-Finish Funsheet
5
1. Warm-up puzzle 2. Lesson 6: Fraction II + Funsheet 3. Board Questions
-Finish Funsheet
6
1. Warm-up puzzle 2. Lesson 7: Algebra + Funsheet
-Finish Funsheet (Check on website) -Unit Assessment 1
7
Review Unit Assessment 1 (open notes)
Mr. Huang Math 10
Basic Arithmetic
Jeffrey Huang 1
Unit 1
Lesson
1 Before we get into the more complex units and topics in mathematics, we will spend some time reviewing basic operations and algebra. Our goal for the first few weeks of review is to get our brain back in the working mode and recall our prior knowledge and skills in mathematics. Addition
• Nothing too complicated. Let’s start easy and work our way to harder questions. As we are trying to exercise our brain, don’t use your calculators!
Subtraction
• We tend to remember the simple subtraction but not when we must do “carry overs”. Let’s practice that!
[Text Reference: Prior knowledge in Mathematics] Goal 1: Review our knowledge of basic mathematical operations
Example: Add
a) 17 + 9 = b) 85 + 28 = c) 79 + 43 =
d) 238 + 58 = e) 194 + 783 = f) 844 + 59 =
g) 183 + 743 = h) 1843 + 485 = i) 2384 + 984 =
Example: Subtract
a) 23 – 8 = b) 48 – 27 = c) 140 – 89 =
d) 1000 – 84 = e) 546 – 86 = f) 874 – 184 =
g) 784 – 379 = h) 533 – 289 = i) 2834 – 1833 =
Jeffrey Huang 2
Multiplication • Once again, we probably remember all the questions about “single digit multiplying by single
digit”, but it gets trickier when we have to deal with bigger numbers Division
• Don’t worry, we will just practice the easier division questions. We can worry about long division another year.
Example: Multiply
a) 6 x 9 = b) 7 x 11 = c) 12 x 8 =
d) 23 x 7 = e) 54 x 5 = f) 43 x 92 =
g) 62 x 81 = h) 321 x 43 = i) 354 x 74 =
Example: Divide
a) 22 / 2 = b) 63 / 9 = c) 36 / 3 =
d) 48 / 12 = e) 56 / 8 = f) 54 / 9 =
g) 72 / 9 = h) 36 / 6 = i) 42 / 7 =
Mr. Huang Math 10
BEDMAS
Jeffrey Huang 3
Unit 1
Lesson
2 BEDMAS
• Remember this? BEDMAS is a way for us to compute more complex looking questions correctly. Logic would tell us to solve a question from left to right. However, when we have a mixture of operations, there is a order to which we complete the operations.
• Just to review: B E D M A S
[Text Reference: Prior knowledge in Mathematics] Goal 2: Practice solving problems using BEDMAS
Example: Solve without a calculator
a) 5 + 5 x 8 – 7 = b) 21 + 24 ÷ 8 – 3 = c) 42 ÷ (3 x 2) + 4 = d) 5 + 18 – 6 x 2 ÷ 4 = e) 8 – 4 x 5 x (2 – 2) + 3 = f) 9 x (3 ÷ 3 ) + 4 x (5 x 2 ) ÷ 10 = g) 2(5 + 4) = h) 5(9 – 8 ) x 6 + 5 – 3 = i) 4 + 3(12 – 9) = j) 7 x 7 – 2(4 x 3 + 7) =
Mr. Huang Math 10
Integers
Jeffrey Huang 4
Unit 1
Lesson
3 Now that we have warmed-up our brain a little, let’s continue by exploring the topic of integers. If you remember from before integers are whole numbers on the number scale. This means that you could have positive integers (or positive numbers) or negative integers (or negative numbers).
• Rules with integers: 1) A negative “-“ sign in front of integer means that this is a negative number 2) A positive “+” sign in front of the integer means that this is a positive number 3) If there are no signs in front of the integer, it also means that it is a positive number
Addition
• When we add positive and negative numbers, just remember that you are moving through the number line. Or that you are filling holes or digging holes…
• We don’t’ like putting two signs directly side by side. To get away from this, we like to put brackets around the second number, just to make it easier for us to see
Subtraction
• Same idea as addition. The only tricky part is what happens when we subtract a negative number? Well, because it can get confusing to read, when we subtract a negative number, we tend to put brackets round the negative number.
• Rules: 4) When subtracting a negative number, just add them together.
[Text Reference: Prior knowledge in Mathematics] Goal 3: Perform math operations with Integers
Example: Add
a) 16 + 7 = b) 85 + (-28) = c) -18 + 3 =
d) -441 + 57 = e) 821 + (-33) = f) 452 + (-81) =
Example: Subtract
a) 23 – (-8) = b) -48 – 27 = c) -140 – 89 =
d) 1000 – (-84) = e) 546 – (-86) = f) -874 – 184 =
Jeffrey Huang 5
Multiplication • With multiplications, these are the rules: • Rules:
5) positive number x positive number = positive number 6) positive number x negative number = negative number 7) negative number x negative number = positive number
Division
• Same set of rules as multiplication, except this time you are subtracting
Example: Multiply
a) 6 x -7 = b) -7 x 4 = c) -12 x -6 =
d) 21 x -5 = e) 54 x -3 = f) -41 x -72 =
Example: Divide
a) 24 / -2 = b) -63 / 7 = c) -30 / -3 =
d) -48 / 12 = e) 56 / -7 = f) -54 / -9 =
Mr. Huang Math 10
BEDMAS II
Jeffrey Huang 6
Unit 1
Lesson
4 BEDMAS
• Using BEDMAS with integers is the same idea as before. You prioritize your operations according to BEDMAS. Keep in mind whether the number is positive or negative
• Now try these harder ones! This is one of those moments where you are encouraged to use your calculator! Make sure you use the “-“ button for negative numbers!
[Text Reference: Prior knowledge in Mathematics] Goal 4: Learn to use a scientific calculator to solve questions
Example: Solve
a) -9 x (3 ÷ -3 ) + 4 x (-5 x 2 ) ÷ 10 =
b) -2(5 + 4) =
c) -5(9 – 8 ) x 6 + (-5) – 3 =
d) -4 + 3(-12 – 9) =
Example: Solve
a) 5 + 5 x (-8) – (-7)
b) 21 – (-24) ÷ (-8) – (3)
c) -42 ÷ (-3 x 2) + 4
Mr. Huang Math 10
Fractions
Jeffrey Huang 7
Unit 1
Lesson
5 Fractions, fractions, fractions. Fractions is usually one of the most disliked topics as it involves quite a few steps when included in calculations. We will review the concepts involving performing calculations with fractions. Hopefully with enough practice, doing math with fractions become clockwork.
• Rules with fractions: 1) The number “on top” is called the numerator 2) The number “on the bottom” is called the denominator 3) Fractions can be written as 1/2 or 12. We say “one over two”. It is also correct to say, “one divided by two”
Addition/Subtraction
• Rules: 5) You can only add/subtract fractions if the denominator is the same and they are in improper fraction format. When you add, you only add the top numbers. The denominator stays the same
• If the denominators are not the same, then we must make the denominators the same through multiplication. Observe the example below:
[Text Reference: Prior knowledge in Mathematics] Goal 5: Perform math operations with fractions
Example: Add or Subtract without a calculator. Try these with Mr. Huang
a) 54+ 2
3= b) 7
9− 1
3= c) 2
5+ 1
2=
d) 32− 4
7= e) 27
8− 1
2= f) 5
6+ 6
7=
Jeffrey Huang 8
Example: Add or Subtract without a calculator. Try these on your own.
a) 56+ 2
3= b) 7
8− 1
4= c) 2
3+ 1
12=
d) 310+ 3
5= e) 5
16+ 7
8= f) 5
6− 1
3=
g) 54− 5
6= h) 1
5+ 3
4= i) 2
3− 2
3=
j) 2225− 4
5= k) 25
4+ 1
2= l) 11
6+ 6
7=
Mr. Huang Math 10
Fractions II
Jeffrey Huang 9
Unit 1
Lesson
6 Multiplication
• Rules: 6) The top number multiplies by the top number. The denominator multiplies the denominator. Must be in improper fraction form
Division
• We will not be using division with our fractions work in Math 10. Let’s just practice inputting fractions into our calculators
[Text Reference: Prior knowledge in Mathematics] Goal 5: Perform math operations with fractions
Example: Multiply without a calculator!
a) 54
× 23
= b) 79
× 14
= c) 25
× 23
=
d) 254
× 127
= e) 279
× 12
= f) 56
× 67
=
Example: Now you can use your calculator!
a) 79
× 25
= b) 72
× 34
= c) 37
× 32
=
d) 2549
× 27
= e) 720
× 13
= f) 507
× 611
=
Jeffrey Huang 10
Mixed Fractions vs Improper Fractions
• It’s confusing when you try to figure out if the fraction is written as an improper fraction or mixed fraction:
• Improper fractions:
• Mixed fractions:
• Rules: 4) Use improper fractions
• We will only use improper fractions. If you see mixed fractions, we will use our calculator:
Example: Now you can use your calculator!
a) 72
÷ 25
= b) 65
÷ 34
= c) 15
÷ 92
=
d) 1454
÷ 2725
= e) 17200
÷ 817
= f) 543
÷ 611
=
Example: Convert to Improper Fractions
a) 3 23 b) 2 4
5 c) 1 2
7
d) 3 89 e) 10 1
3 f) 5 2
3
Mr. Huang Math 10
Algebra
Jeffrey Huang 10
Unit 1
Lesson
7 When we are asked to solve an algebraic equation, we are really looking to solve the value of an unknown variable, usually defined as “x”. What this means is that we need to find the missing number. Of course, one way to do this is by guessing different numbers and hopefully find a number that fits the equation. What we will do instead, however, is solve for x algebraically.
𝑥 + 5 = 7
2𝑥 = 14
3𝑥 + 5 = 11
3𝑥 + 5𝑥 = 16
• Rules for solving x: 1) Isolate x by undoing all the operations surrounding x. We want one side of the quation to only have “x” 2) We do this by reverse BEDMAS 3) What you do to one side of the equation, must be done to the other side of the equation or 3) To “move” an operation to the other side
[Text Reference: Prior knowledge in Mathematics] Goal 6: Solve for the unknown variable x when given an algebraic equation
Example: Solve for x (use of calculator is permitted)
a) 4𝑥 − 7 = 5 b) 𝑥2
+ 3 = 5 c) 7 − 𝑥 = 4
d) 2𝑥 = 12 − 𝑥 e) 8𝑥 − 20 = 4𝑥 f) 3𝑥 + 8 = 2𝑥 + 13
Jeffrey Huang 11
Example: Try these harder ones! Make sure you are comfortable solving these equations!
a) −4𝑥 − 6 = −6𝑥 b) −2𝑥 − 7 = 5𝑥 c) 3𝑥 = −9 + 2𝑥 d) −8 + 5𝑥 = 4𝑥 e) −10𝑥 + 7 = −9 − 6𝑥 f) 6𝑥 = 8𝑥 + 8
g) 10 − 5𝑥 = −4𝑥 h) 8𝑥 − 2 = 5𝑥 − 5 i) 7𝑥 − 10 = 10𝑥 + 7 + 1
j) 2(𝑥 + 3) = 20 k) 32
(𝑥 + 2) = 15 l) 7 − 25
(𝑥 − 1) = 9
Mr. Huang Math 10
BEDMAS
Jeffrey Huang 1
Unit 1
Funsheet
Level A Solve without a calculator
a) 3 + 8 ÷ 2 – 1 =
b) 8 + 2 ÷ 2 + 10 = c) 2 × 2 + 3 × 3 =
d) 4 – 2 × 2 + 8 =
e) 3 × 2 × 4 + 1 = f) 3 × 2 + 1 × 4 =
Level B Solve without a calculator
a) 3(4 + 2) =
b) 2(1 + 3) − 5 = c) 3 − 2(8 − 7) =
d) 7 − (3 + 2)(4 − 3) =
e) 8 ÷ 2(5 − 3) + 2 = f) 9 + (4 + 3) − (3 − 1)(3) =
Level C Solve without a calculator
a) 3+4(5−2)
5=
b) 62
+ 8(7 − 3) = c) 4(3+1)
8 + 8
4=
Mr. Huang Math 10
BEDMAS II
Jeffrey Huang 1
Unit 1
Funsheet
Level A Solve without a calculator
a) −3 + 8 ÷ (−2) – 1 =
b) 6 + (−2) ÷ 2 + 10 = c) −2 × (−4) + (−3) × 3 =
d) −9 – 2 × (−3) + 3 =
e) −3 × (−3) × 4 − 3 = f) 3 × (−6) + 1 × (−9) =
Level B Solve without a calculator
a) −3(−9 + 2) =
b) 12(1 − 3) − 5 = c) −3 − 4(−8 − 9) =
d) 3 − 2(3 + 2)(4 − 7) =
e) −8 ÷ 2(2 − 7) + 2 = f) 9 + (3 − 8) − (1 − 8)(3) =
Level C Solve without a calculator
a) −3+4(2−6)
−5=
b) −62
+ 8(9 − 12) = c) −4(2−10)
8 + 8
4=
Mr. Huang Math 10
Fractions I
Jeffrey Huang 1
Unit 1
Funsheet
Level A Solve without a calculator
a) 56
+ 68
=
b) 112
+ 1924
= c) 15
+ 1420
= d) 2080
+ 58
=
e) 78
− 34
=
f) 1112
− 14
= g) 143
− 116
= f) 1725
− 35
=
Level B Solve without a calculator
a) 311
+ 1044
=
b) 1213
+ 34
= c) 27
+ 1798
= d) 14
+ 1126
=
e) 1316
− 312
=
f) 1213
− 4052
= g) 100144
− 712
= h) 520
− 18
=
Level C Solve without a calculator
a) 56
+ 78
+ 412
=
b) 10064
− 316
− 14
= c) 17
+ 849
− 514
=
Mr. Huang Math 10
Fractions I
Jeffrey Huang 1
Unit 1
Funsheet
Level A Solve without a calculator. Don’t forget to reduce your fractions!
a) 56
× 68
=
b) 112
× 93
= c) 15
× 147
= d) 2010
× 58
=
e) 78
× 34
=
f) 1112
× 14
= g) 143
× 116
= f) 1725
× 35
=
Level B Use your calculator to solve
a) 311
÷ 1044
=
b) 1213
÷ 34
= c) 27
÷ 1720
= d) 14
÷ 1120
=
Level C Solve without a calculator
a) 56
× 78
× 52
=
b) 10010
× 35
× 14
= c) 17
× 85
× 52
=
d) 32
× 75
+ 710
= e) 82
× 13
+ 16
× 92
=
Mr. Huang Math 10
Algebra
Jeffrey Huang 1
Unit 1
Funsheet
Level A Solve:
a) 5𝑥 + 2 = 12
b) 40 − 𝑥 = 10 c) 8𝑥 + 2 𝑥 = 10
d) 13𝑥 + 20 = 3𝑥
e) −3𝑥 = 21 − 2𝑥 f) 2𝑥 = 12 − 2𝑥
g) 15𝑥 = 45
h) 13𝑥 − 3 = 49 i) 11𝑥 + 7 − 6𝑥 = 32
j) 8𝑥 − 16 = 4𝑥
k) 3𝑥 + 50 = 47 l) 18 = 4𝑥 + 2
Level C Solve:
a) 5(𝑥 − 1) = 20
b) 43
(𝑥 − 3) = 8 c) −8𝑥 − 2 = 4𝑥 − 14
