LES ADJECTIFS - oneillmath9 - home B.doc... · Web view... Today, we will learn to compare rational numbers using a number line and identify rational numbers between two given rational

Day 1 (Lesson 2.1 Part I) Comparing and Ordering Rational Numbers

INTRODUCTION: Rational Numbers are numbers that can be expressed in the form

____ where a & b are integers and b 0. (They can be written as ________ or ________.)

NAME: _________________________________

DATE: __________________________

MATHEMATICS 9CHAPTER 2

RATIONAL NUMBERS

http://images.google.com/imgres?imgurl=http://mathmomblog.files.wordpress.com/2008/01/math02.gif&imgrefurl=http://mathmomblog.wordpress.com/2008/01/27/multiplication/&usg=__R9il6_Sa_CoSuonQksMfS1-h3w8=&h=319&w=487&sz=18&hl=EN&start=5&tbnid=x0ufG5BsKCDhHM:&tbnh=84&tbnw=129&prev=/images%3Fq%3Dmath%26gbv%3D2%26hl%3DEN%26safe%3Dactive%00%E5%A1%B9%EF%92%81%E1%B4%BB%E4%A1%BF%E2%B2%AF%E5%B6%82%E8%97%84%E6%8C%A7%00%00%EA%AE%A5

Examples:

LESSON FOCUS: In this lesson, we will learn to reduce, compare and order rational numbers, and express them in fractional form with a common denominator or decimal form.

Reducing Fractions: We begin by learning to reduce fractions. To reduce fractions, find the ______________________________ for the numerator and denominator.

1. 2. 3.

Compare & Order Fractions: We can compare rational numbers by expressing them all as ______________ with a common denominator or by expressing them as_____________.

A) To compare fractions, express each pair of fractions with the common denominator. To find a common denominator, determine the ________________________________ (LCM) of the given denominators.

Ex: Which is greater → or ?

Step 1: The LCM of 6 and 9 is ________.

Step 2: Re-write and as:

Step 3: Compare the numerators.

Practice: Replace with > or <.

1. 2. 3.

4. List from least to greatest using a common denominator: Note: Careful with negative numbers.

Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 1

B) To convert fractions to decimals, divide the ______________ by the _____________. Note: A fraction is essentially a _______________ operation.

Example: means = 0.75

1. 2.

C) To convert decimals to fractions, write the number as you would read it.ex. 0.05 is read as 5 ____________. Therefore, put 5 over ________, and reduce to lowest term.

1. 0.3 = 2. 3. 0.024 =

Day 2 (Lesson 2.1 Part II) Comparing & Ordering Rational Numbers

REVIEW: We begin our lesson by reviewing what we learned yesterday.

A. Comparing Fractions

A fraction can represent __________ of a whole.

The shaded part of the diagram shows or or 0.5.

Ex. Compare and . Use denominators that are the same.

Examples1. Give the fraction and decimal value 2. What is the opposite of the following l


for the shaded part of the diagram. rational numbers? a) a)

b)

B. Compare the Following Fractions. Which is greater? Replace with > or <.

1. 2.

C. Arrange from least to greatest (by finding the LCM)

1. 2.

NEW LESSON FOCUS: Today, we will learn to compare rational numbers using a number line and identify rational numbers between two given rational numbers.

A. Match each fraction below with a letter on the number line.

____ ____ ____ ____

a) Which letter is closest to zero? ____

b) Which fraction is closest to zero? ____

c) Which fraction is smallest? ____

d) Is or closer to 0? Explain. _____________________________

___________________________________________________________

B. Match each letter on the number line to one of the rational numbers below.


____ –0.3 ____ ____

____ –2.1 ____ ____

C. Identify the rational number (in decimal and fractional form) between two given rational numbers.

To do this, we need to find express the rationals as fractions and find ________________________.

1. and 2. and

D. Find as many integers as you can between and ?


E. Compare and order the following rational numbers. , , , , To solve:

a) Express your numbers in the same form (decimal or fractional)

b) Place the numbers on a number line

c) Arrange the numbers in ascending order.

10 2- 1 -2

Day 3 (Lesson 2.2) Rational Numbers in Decminal FormLESSON FOCUS: Today, we will expand our understanding of decimal numbers. We will learn to estimate and calculate decimals and apply operations with rational numbers in decimal form.

Why estimate?

Estimation can help you work with decimal numbers. For example, you can use estimation to place the decimal point in the correct _____________ in the answer.

16.94 + 3.41 + 81.07

Estimate: Calculation:

1. Without calculating the answer, place the decimal point in the correct position to make a true statement for each.

a) 149.8 ÷ 0.98 = 15285714

b) 2.7 × 100.9 = 272430

c) 40.6 × 9.61 = 39016600

d) 317 ÷ 99 = 32020202

2. a) Is 349 × 0.9 greater than, less than, or equal to 349? ______________

b) How do you know? ________________________________________

3. a) You know that 48 ÷ 16 = 3. Without finding the exact answer, tell whether the answer to 48 ÷ 15 is greater than, less than, or equal to 3. __________

b) Explain how you know. ______________________________________


Place the decimal so that the answer is

close to 100.

Estimate, then calculate (to the neareast thousandth, if necessary).

1. Adding and Subtracting Rational Numbers in Decimal Form

Estimate Calculatea) 0.56 + (–3.14) = __________________ ____________

b) –6.92 + (–8.02) = __________________ ____________

c) –2.75 – (–4.13) = __________________ ____________

2. Multiplying and Dividing Rational Numbers in Decimal Form

Estimate Calculatea) –5.1 × (–9.3)= __________________ ____________

b) –1.68 ÷ (–1.4)= __________________ ____________

c) (2.7)(–4.2)= __________________ ____________

3. Calculate: Remember to apply order of operationsa) –6.2 + (–0.72) ÷ (–1.3 + 0.4) b) –2.2 × (–3.2) + (–0.88) × 2.3

Applying Operations with Rational Numbers in Decimal Form

For Questions 4 and 5, a) write an expression using rational numbers to represent the problem, then calculate. b) write a sentence to answer the problem.

4. Camille’s chequing account balance is$135.25. She writes a cheque for the amount of $159.15. What is the balance in her account now?


5. The hottest day in Canada on record was on July 5, 1937, in Midale and Yellowgrass, Saskatchewan, when the temperature peaked at 45 °C. The coldest day in Canada was in Snag, Yukon, at –63 °C. What is the difference in temperature between the hottest day and coldest day in Canada?

Day 4 (Lesson 2.3 Part I) Multiplying & Dividing Rational #s.

LESSON FOCUS: Today, we will learn to multiply and divide rational numbers.

Recall: Multiplying Integers: Dividing Integers: Rules: Rules:

1. + + = _____ 1) + + = _____2. – + = _____ 2) – + = _____3. + – = _____ 3) + – = _____4. – – = _____ 4) – – = _____

Recall as well:

Muliplying Fractions: Simply the following expressions. Ensure your answer is in lowest term.

When simplifying rationals, it is best to 1. ___________ the fractions first before multiplying2. Find _____________ pairs of two negatives

1. 2.

3.


1) 2) 3) 4) 5)

Dividing Fractions: Simply the following expressions. Ensure your answer is in lowest term.

When dividing fractions, we 1. Multiply the _______________ of the divisor. 2. Ensure that our fractions are in the _____________ form before simplifying.

1. 2.

3. 4.

Word Problem:NOTE: In solving problems with fractions, the word ________ means to multiply.

1. Mark has 24 newspapers to deliver. In one apartment building, he delivers of

them. In the next apartment building, he delivers of the remaining amount. How many papers does he have left to deliver?


2. John created a painting on a large piece of paper with a length of m and a

width of m. Write an expression in the form that represents the area

of the painting in lowest terms.

Day 5 (Lesson 2.3 Part II) Adding & Subtracting Rational #s.

LESSON FOCUS: Today, we will learn to add and subtract fractions.

To add and subtract fractions, we need to 1. Find the _______________ Common Denominator (LCD) 2. Find _____________ pairs of two negatives3. When subtracting, add the positives (or _________, _________)

Note: When adding or subtracting: 1. you can only tick, tick two negatives that are _________ each other.2. always move the negatives to the top. 3. always convert mixed fraction to the _____________ form first.

Simplify:

1) 2)

3. 4.

Word Problem:


1) 2) 3) 4)

1. One January day in Prince George, British Columbia, the temperature read -10.6 ْ C at 9:00 a.m. and 2.4 ْC at 4:00 p.m.

a) What was the change in temperature?b) What was the average rate of change in temperature?

2. The Rodriquez family has a monthly income of $6000. They budget for food,

for rent, for clothing, and for savings. How much money is left for other

expenses?

Day 6 (Lesson 2.3 Part III) Order of Operations with Rationals

LESSON FOCUS: Today, we will learn to simplify rationals using order of operations.

Recall:When solving equations, the following order must be taken:

1) B____________________

2) E____________________

3) D____________________

M____________________

4) A____________________

S____________________

Do the following examples:Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 10

In addition, follow these simple keep these orders in mind:

1. Start inside and work outward.

2. Go Left to Right

1) 2)

3) = 4.

Working backward: Complete each statement. Show your work.

1) ____ = 2) ____

3. ____ = 4. ____ =


Day 7 Part I - Perfect Squares and Square Roots

What is a square of a number? A number times ____________ (ex. the product )

Examples:

1. 2.

3. 4.

What is a square root of number? The square root of a number x is the number that when multiplied by itself gives the number x (ex. ).

Examples: Find the square root of:

1. 2. 3.

The radical sign, _______, is used to represent the _______________ square root of a number. The positive square root is also called the principal square root. Examples:

1. 2. 3. 4.

Note: _________ and _______________ _________ and _______________

How do we find square roots of large numbers?

We use ____________________________ Examples:

1. = 2. =

3. = 4. =

What about decimal roots?If = _______Then _______What about _______ And _______


Note: does ______ = .4. Therefore, perfect roots in decimal must have an _________ number of digits following the decimal point.

ex 1. _______ 2. _______

Note also that each pair of numbers results in one decimal point.

ex1. _______ 2. _______

Try 1. 3.

2. 4.

Part II – Evaluating Square RootsEvaluate the following equations:

1. 2.

3. 4.

5.

Evaluate the following if a = 5 and b = -41. 2.

3.

Day 8 (Lesson 2.4) Determining Square Roots of Rational #s

LESSON FOCUS: Today, we will learn to find square roots of rational numbers.


Key Ideas


If the side length of a square models a number, the area of the square models the ___________ of the number.

If the area of a square models a number, the side length of the square models the ____________ of the number.


A perfect square can be expressed as the product of ________ equal rational factors.

ex. The square root of a perfect square can be determined _____________.

ex. The square root of a non-perfect square determined using a calculator is an __________________.

ex.

Example 1Determine whether each of the following numbers is a perfect square. Show your work.a) b) 1.2

c) 0.9 d) 0.09

Example 2Evaluate (round to the nearest thousandth where necessary). Show your worka) b) c)

d) e) f)

Example 3A square garden has a side length of 5.2 m. Calculate the area of the garden.

Example 4The area of Mara’s square pumpkin patch is 2.25 m2. She has a square tomato garden with the same area. She wants to determine the dimensions of each garden. Maras solution is shown below.

A = s2

2A = s2

2(2.25) = s2

4.5 = s2

= s2.12 = s

Example 5Sean’s kitchen measures 4.3 m by 3.2 m. He wants to cover the floor with square tiles. The side dimension of each square tile is 10.5 cm. How many tiles will he need to cover the floor?

Example 6Sarah wants to put a string across her paper with the dimensions of 30 cm by 45 cm. What is the length of the string she needs. (Round to the nearest cm).

STUDENT PRACTICE SECTION


What error did Mara make in her solution? Correct her solution and determine the dimensions of each garden.

___________________________________________________

~Chapter 2 Day 1 Lesson 2.1~Comparing and Ordering Rational Numbers

1. Reduce to the lowest terms.

a) b) c) d) e) f)

2. Compare each pair of fractions. Replace the comma with > or <.

a) b) c) d)

3. Reduce each set of fractions to lowest terms. Then list them from greatest to least.

a) b)

4. In each set, express the fractions with a common denominator. Then list them from least to greatest.

a) b)

5. List these fractions from least to greatest.

6. List these fractions from greatest to least.

7. Write in decimal form.

a) b) c) d) e) f)

8. Express in fractional form. a) 0.75 b) -0.625 c) -2.75 d) 16.4

9. Compare each pair of fractions. Replace the comma with > or <.

a) b) c) d)

10. Arrange these fractions from greatest to least.

~Chapter 2 Day 4 Lesson 2.3~Multiplying and Dividing Fractions

1. a) b) c) d)

e) f) g) h)


2. a) b) c) d)

e) f) g) h)

i)

3. a) b) c)

d) e) f)

g) h) i)

4. a) b) c)

d)

e) f)

g) h)

i)

~Chapter 2 Day 5 Lesson 2.3~Adding and Subtracting Fractions

1. a) b) c) d)

e) f) g) h)

2. a) b) c) d) e) f) g) h) i)

3. a) b) c) d)

e) f) g) h)

4. a) b) c) d)

e) f) g) h)

5. a) -2.387 + 4.923 b) 33.78 – (-64.35) c) 204.9 – 256.1 d) -0.405 – 18.924 e) -12.37 + 8.88 f) -45.8 – (-327.6) g) 4.29 + 563.08 h) 84.91 – 37.08 i) -0.046 + (-0.104)


6. a) b) c)

d) e) f)

g) h) i)

~Chapter 2 Day 6 Lesson 2.3~Order of Operations with Fractions

1. a) b) c)

d)

e) f)

g) h) i)

2. a) b)

c) d)

e) f)

g) h)

i) j)

3. a) b) c) d)

4. a) b) c) d) e) f)

5. a) b) c)

d)

e) f)

6. a) b)

c)


d)

e) f)

~Chapter 2 Day 7 Lesson 2.4~Part I – Perfect Squares and Square Roots

Evaluate : indicate the imperfect roots with “IR”

1. a) b) c) d) e) f) g) h) i) j) k) l) m) n) o)

p) q) r) s) t) u) v) w) x)

2. a) b) c)

d) e) f)

g) h) i)

Part II – Evaluating Square Roots

1. Evaluate. a) b) c) d) e) f) g) h) i) j)

2. Simplify. a) b) c) d) e) f) g) h) i)

3.) Evaluate each expression for a = 5 and b = -3.

a) b) c)

d) e) f) g) h) i) j) k) l)

4.) Evaluate each expression for x = 3, y = -4, and z = -7. a) b) c) d) e) f)


g) h) i) j) k) l)

~Chapter 2 Day 9 Review~Fractions (Days 1, 4, 5, 6)

1. a) b) c) d)

2. a) b) c)

3. a) b) c) d)

4. a) b) c) d)

5. a) b)

6. a) b)

7. a) b)

Chapter 2 Answer Key

Chapter 2 Day 1 Lesson 2.1 (Equivalent Fractions)

1. a) b) c) d) e) f)

2. a) b) c) d)

3. a) b)

4. a) b)


5.

6.

7. a) 0.6 b) c) d) e)0.3125 f)

8. a) b) c) d)

9. a) b) c) d)

10.

Chapter 2 Day 4 Lesson 2.3 (Multiplying and Dividing Fractions)

1. a) b) c) d) e)

f) g) h)

2. a) b) c) d) e)

f) g) h) i)

3. a) b) c) d) e)

f) g) h) i)

4. a) b) c) d) e)

f) g) h) i)

Chapter 2 Day 5 Lesson 2.3 (Adding and Subtracting Fractions)

1. a) b) c) - d) - e)

f) - g) - h)

2. a) b) c) d) e) f) 5.4 g) 1.1 h) 8.3 i)

3. a) b) c) d) e)

f) g) h) 1

4. a) b) c) d) e)

f) g) h)

5. a) 2.536 b) 98.13 c) d) e) f) g) 567.37 h) 47.83 i)

6. a) b) c) d) e)


f) 9

86 g) h) i)

Chapter 2 Day 6 Lesson 2.3 (Order of Operations with Fractions)

1. a) b) c) 245

d) 4017

e) 1237

f) g) h) i)

2. a) b) c) d) e)

f) g) h) 5 i) 3 j) 3

3. a) b) c) d) 62.64. a) 3598.608 b) 3.1 c) 169.36 d) e) f)

5. a) b) c) d) e) f)

6. a) b) c) d) e) f)

Chapter 2 Day 7 Part I Perfect Squares and Square Roots1.a) 8 b) 0.8 c) 15 d) 0.15 e) 10 f) IR g) 21 h) 25 i) IR j) 0.012 k) IR l) IR m) 45 n) 0.11 o) IR p) 0.0003 q) 0.009 r) 24 s) IR t) 17 u) 0.0017 v) IR w) 27 x) 482a) 11 b) 1.1 c) 9 d) 0.02 e) 5 f) 0.02 g) 12 h) 2 i) 70

Part II EvaluatingSquare Roots1. a) 7 b) -0.2 c) 40 d) 13 e) -60 f) 1.2 g) -15 h) i) 25 j) -42. a) 10 b) 7 c) 2 d) 28 e) 40 f) 5 g) -31 h) 32 i) 63. a) 10 b) 15 c) 5 d) 7 e) 6 f) -5 g) 4 h) 8 i) -32 j) -12 k) 4 l) 104. a) -6 b) 5 c) 20 d) 5 e) 35 f) -6 g) 10 h) -9 i) 42 j) 6 k) 8 l) -11

Chapter 2 Day 9 Fractions Review (Days 1, 4, 5, 6)

1. a) b) c) d)

2. a) b) c)

3. a) b) c) d)

4. a) b) c) d)

5. a) b)

6. a) b) 0


7. a) b)

Chapter 2 Assignments:

DAY SECTION ASSINMENT1 2.1 (Part I) Booklet Day 1 Pg. 16 #1-10 (all)

2 2.1 (Part II) Text Pg. 51 – 54 #4,5,7(all), 8,9,13 – 17 (o.l.), 21, 22 (o.l), 25, 26 – 30 (o.l) omit 27 3 2.2 Text Pg. 60 – 62 #4 – 9 (o.l.), 10, 13, 16, 17. 19, 22, 24 (o.l), 29 (o.l.) 4 2.3 (Part I) Booklet Day 4 Pg. 16-17 #1 – 4 (o.l.); Text Pg. 68 – 70 #7 & 8(all.), 9,10, 13, 16, 18, 5 2.3 (Part II) Booklet Day 5 Pg. 17-18 #1 – 6 (o.l.), Text Pg. 68 – 70 #5 & 6 (all), 12,14, 6 2.3 (Part III) Booklet Day 6 Pg. 18-19 #1 – 4 (o.l), 5 & 6 (all), Text Pg. 70 #15, 19, 21 (all), 26 7 2.4 (Part I) Booklet Day 7 Pg. 19-20 Part I #1-2 (o.l), Part II #1-4 (o.l) 8 2.4 (Part II) Text Pg. 78 – 81 # 1, 2, 7 – 14 (o.l), 15, 16, 18, 20, 22 – 30, 36 9 Review/ Quiz Booklet Day 9 Pg. 20#1- 7 (all), Text Pg. 84 & 85 # 1 – 20 (all)

Answer Key:

1. A 2. D 3. C 4. B 5. D 6. B 7. C 8. 4.8 9. Left10. Example: Any integer can be written as a quotient of two integers by making the integer the dividend and the number 1 the divisor

11. , 0.94 , 12.

13. a) b) -1.37 c) d) e) f)

14. 9.89 s 15. 0. Exmaple: [1.2 + (-1.2)] ÷ 2 = 016. Yes. Example: Both 3136 and 100 are perfect squares.17. a) 37.21 b) 0.37 c) 2.65 18. a) 62.5 cm² b) 43.8 cm19. $19.11 Assume that all shares are the same price20. a) 1. Example: The sum must be 1 because no other elements make up a quarter’s content. b) 1 c) 15.6 times as great d)2.816 g greater

10 Test Date: ________________________________


15

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LES ADJECTIFS - oneillmath9 - home B.doc... · Web view... Today, we will learn to compare rational numbers using a number line and identify rational numbers between two given rational