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 b0. (They can be written as ______or ______.)
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.
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.
Examples
1. 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 ?
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 1
Day 3 (Lesson 2.2) Rational Numbers in Decminal Form
LESSON 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. ______
Estimate, then calculate (to the neareast thousandth, if necessary).
1. Adding and Subtracting Rational Numbers in Decimal Form
Estimate Calculate
a) 0.56 + (–3.14) = ______
b) –6.92 + (–8.02) = ______
c) –2.75 – (–4.13) = ______
2. Multiplying and Dividing Rational Numbers in Decimal Form
Estimate Calculate
a) –5.1 × (–9.3)= ______
b) –1.68 ÷ (–1.4)= ______
c) (2.7)(–4.2)= ______
3. Calculate: Remember to apply order of operations
a) –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 multiplying
2. Find ______pairs of two negatives
1. 2.
3.
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 negatives
3. 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. One January day in Prince George, British Columbia, the temperature read -10.6ْ 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:
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? à 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 ______
Try
1. 3.
2. 4.
Part II – Evaluating Square Roots
Evaluate the following equations:
1. 2.
3. 4.
5.
Evaluate the following if a = 5 and b = -4
1. 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
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 1
· 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.
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 1
Example 3
A square garden has a side length of 5.2 m. Calculate the area of the garden.
Example 4
The 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. Mara¢s solution is shown below.
A = s2
2A = s2
2(2.25) = s2
4.5 = s2
= s
2.12 = s
Example 5
Sean’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 6
Sarah 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
~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)