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Chapter 6
Pages: 262 323
Assignments:
Due DateSectionPagesHomework Assignments6-1267 268#16 42 (evens), #51, #52, #56 70 (evens)6-2273 274#10 26 (evens), #30 or #31, #32, #34, #38, #42, #45*, #46, #47, #48, #52, #546-3279 280#8 17 (all), #18, #19, #20, #23 25 (all), #26 44 (evens)
You will need graph paper and a ruler for this assignment6-4284 285#16 48 (evens), #54, #55, #56, #58, #66 70 (evens)6-5291 292#10 16 (evens), #21, #22, #28, #30 40 (evens)6-6296 297#14 24 (evens), #28 34 (evens), #36, #41, #42, #45, #46, #48, #49, #50 56 (evens), #62 66 (evens)6-8307 308#10 20 (evens), #27, #28, #29 31 (pick 1), #32, #34, #38 42 (pick 2)6-9313 314#12 28 (evens), #31 34 (pick 3), #40, #41, #42 46 (evens)321Practice Test
Prerequisite Knowledge:
Basic operations with whole numbers, decimals, and fractions
Estimating and rounding
Evaluating, simplifying, and solving numeric and algebraic expressions and equations
Use Distributive Property
Prerequisite Skills:
Using a calculator to convert between decimals and percents
Study Guide:
Getting Started (pg. 263, before 6-1)
Reading Mathematics (pg. 269, after 6-1)
Technology Notes (fractions((decimals, before 6-4)
Algebra Activity (pg. 286 287, after 6-4)
Practice Quiz #1 (pg. 292, after 6-5)
Percents/Fractions/Decimals Study Cards (before 6-6)
Spreadsheet Investigation (pg. 303, after 6-7)
Practice Quiz #2 (pg. 308, after 6-8)
Algebra Activity (pg. 309, before 6-9)
Graphing Calculator Investigation (pg. 315, after 6-9)
Section 6-1
Objectives:
Write ratios as fractions in simplest form
Determine unit rates
Vocabulary:
Ratio a comparison of numbers using division (i.e. a fraction)
Rate ratio of two measurements having different units (e.g. 90 miles in 2 hours or $16 for 4 pounds)
Unit Rate a rate that is simplified so that the denominator is 1 (e.g. 45 miles per hour or $4 per pound)
Concepts:
Ratios can be written several ways:
2 to 4
2:4
EMBED Equation.3
To simplify a ratio, write it as a fraction and reduce.
To simplify ratios with similar units, write as a fraction and include the units. If the units are the same on the top and bottom of the fraction, cancel them out. If they arent the same, convert the bigger unit into terms of the smaller unit.
To simplify ratios with different units, reduce the numeric parts only. Keep the original units.
When converting between different unit rates, multiply the amount by the conversion factor when going from big units to small units, and divide the amount by the conversion factor when going from small units to big units.
Examples:
A class consists of 12 girls and 16 boys. Express this as a ratio of boys to girls, girls to boys, boys to total students, and girls to total students.
Express 10 roses out of 12 flowers as a fraction in simplest form.
Express 21 inches to 2 yards as a fraction in simplest form.
A 12-oz bottle of cleaner costs $4.50. A 16-oz bottle of cleaner costs $6.56. Which bottle costs less per ounce?
A snail moved 30 feet in 2 hours. How many inches per minute did it move?
A cheetah can run up to 50 mi/hr. How many feet/sec is this?
Classwork:
Check for Understanding (pg 266) #1, #4 #12 (evens), #14, #15
Section 6-2
Objectives:
Solve proportions
Use proportions to solve real-world problems
Vocabulary:
Proportion an equation that says two ratios are equal
Concepts:
To solve a proportion, multiply the diagonal values together and then set the products equal to each other. Solve for the missing value.
EMBED Equation.3 ( EMBED Equation.3
Another way to solve a proportion missing only one value is to multiply the diagonal values then divide by the remaining value.
Two ratios are equal if they form a true proportion. To check this, divide the top number by the bottom number on the calculator. If the answers are equal, then the ratios form a proportion (in other words, the ratios are equal).
Examples:
Determine whether each pair of ratios below forms a proportion:
EMBED Equation.3
EMBED Equation.3
Solve each proportion below:
EMBED Equation.3
EMBED Equation.3
An architect builds a model of a building before the actual building is built. The model is 8 inches tall and the actual building will be 22 feet tall. The model is 20 inches wide. Find the width of the actual building.
The Circleville Pumpkin Show in Circleville, Ohio, boasts the worlds largest pumpkin pie. The pie weighs 350 pounds and is 5 feet in diameter. Find the diameter of the pie in centimeters if 1 ft = 30.48 cm.
Classwork:
Check for Understanding (pg 272) #3 #8 (all)
Section 6-3
Objectives:
Use scale drawings
Construct scale drawings
Vocabulary:
Scale Drawing (or Scale Model) a drawing or model used to represent an object that is too big or too small to be built in actual size (e.g. model cars, blueprints, and maps)
Scale the relationship between the model or drawing size and the actual size (usually written as 1:24 or 1 inch = 3 feet)
Scale Factor the ratio of the model/drawing length to the actual length (usually written as a fraction). Note that the numerator and denominator of the scale factor fraction must be in the same units.
Concepts:
To find a missing length, set up a proportion with one fraction being the scale factor. The other fraction should be set up the same way as the scale factor fraction. Put the given length in its proper place, then solve the proportion accordingly.
Examples:
A map has a scale of 1 inch = 8 miles. Two towns are 3.25 inches apart on the map. What is the actual distance between the towns? What is the scale factor?
A model car is 4 inches long. The actual car is 12 feet long. What is the scale of the car?
Sheila is designing a patio that is 16 feet long and 14 feet wide. Make a scale drawing of the patio. Use a scale of 6 inches = 4 feet.
Classwork:
Check for Understanding (pg 278 279) #1 #6 (all)
Section 6-4
Objectives:
Convert between percents and fractions
Convert between percents and decimals
Vocabulary:
Percent a ratio that compares a number to 100
Concepts:
To write a percent as a fraction, put the given percent over 100 and then reduce.
To write a fraction as a percent, set up a proportion with one side as the given fraction and the other side as a fraction with a denominator of 100. The numerator is the percent.
To write a percent as a decimal, divide by 100 and remove the percent symbol OR slide the decimal point two places to the left.
To write a decimal as a percent, multiply by 100 and add the percent symbol OR slide the decimal point two places to the right.
Examples:
Express each percent as a fraction in simplest form
60%
104%
.3%
56 EMBED Equation.3 %
Express each fraction as a percent
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
Express each percent as a decimal
60%
2%
658%
.4%
Express each decimal as a percent
.4
.05
.0008
7.3
A baker says that 25% of his customers buy only bread and EMBED Equation.3 of his customers buy only cookies. Which group is larger?
Classwork:
Check for Understanding (pg 283) #3 #15 (odds)
Section 6-5
Objectives:
Use percent proportions to solve problems
Vocabulary:
Percent Proportion a proportion in which one ratio is a ratio of percents
Concepts:
The basic setup of a percent proportion:
EMBED Equation.3
The part is called the part and the whole is called the base.
Types of Percent ProblemsTypeExampleProportionFind the percent3 is what percent of 4? EMBED Equation.3 Find the partWhat number is 75% of 4? EMBED Equation.3 Find the whole3 is 75% of what number? EMBED Equation.3
Examples:
20 is what percent of 25?
What percent of 8 is 12?
What number is 8.8% of 20?
70 is 28% of what number?
At Kington Middle School, 600 students were asked if their families recycle cans and/or newspapers. 32% said they recycle both. 25% said they recycle cans. 19% said they recycle newspapers. 24% said they do not recycle. How many families recycle both cans and newspapers?
Classwork:
Check for Understanding (pg 291) #2, #3 #6 (all), #7
Section 6-6
Objectives:
Compute mentally with percents
Estimate with percents
Concepts:
There are several percents that you should be able to estimate in your head. I expect you to know and memorize multiples of 10%, 25%, and 33 EMBED Equation.3 % and their decimal/fractional equivalents. We will make flash cards to help you. I will also give you a pop quiz on these at some point, so be prepared. This will be done without calculators.
To estimate with percents, round the percent and the number to easy numbers and then figure out the amount mentally.
Examples:
Find the percent of each number mentally:
50% of 46
25% of 88
70% of 110
Estimate the following
22% of 494
63% of 788
EMBED Equation.3 of 1219
155% of 38
A restaurant bill totals $21.35. you want to leave a 15% tip. What is a reasonable amount for the tip?
Classwork:
Check for Understanding (pg 295) #2 #12 (evens)
Section 6-8
Objectives:
Find percent of increase and decrease
Vocabulary:
Percent of Change the percent of increase or decrease compared to the original amount
Percent of Increase when an amount increases, the percent of change is an increase
Percent of Decrease when an amount decreases, the percent of change is a decrease
Concepts:
To find the percent of change, subtract the original and the new amounts (subtract the smaller from the bigger). If the original is bigger than the new, the percent of change is a decrease. If the original is smaller than the new, the percent of change is an increase. Use that difference as the part in the percent proportion. Use the original as the whole in the percent proportion. Solve for the percent.
Examples:
Find the percent of change from 325 to 390.
Find the percent of change from 56 to 63.
Find the percent of change from 49 to 35.
In 2001, when I entered college, tuition was around $2400 per semester. When I graduated four years later, tuition was around $2800 per semester. What was the percent change?
A shirt went on clearance for 20% off. Find the sale price. Find the cost if the store marked up the shirt 20% from its sale price. Would the new cost be less than, equal to, or greater than the original cost?
Classwork:
Check for Understanding (pg 306) #1, #3, #4 #8 (all)
Section 6-9
Objectives:
Find the probability of simple events
Use a sample to predict the actions of a larger group
Vocabulary:
Outcomes the results of an event or experiment
Simple Event one specific outcome
Probability the chances that an event occurs
Sample Space the set of all possible outcomes
Theoretical Probability what should occur
Experimental Probability what actually does occur
Concepts:
To calculate the probability of an event, put the number of favorable outcomes on the top of a fraction and the total number of possible outcomes on the bottom of the fraction
To calculate the probability that two events will occur in a row, multiply the probability of the first event by the probability by the second event.
Examples:
A die is rolled. What is the probability of rolling a 5? Of rolling a 4 or 5?
Suppose two dice are rolled. Find the probability of rolling 2 matching numbers.]
A blue die and a red die are rolled. What is the probability of rolling a 2 on the blue die and an odd number on the red die.
If a coin is flipped 10 times, how many times do you expect it to come up heads (what is its theoretical probability)? If a coin is flipped 10 times, and it comes up heads 8 times, what is the experimental probability of getting heads?
What is your favorite sport? If these probabilities hold up, how many people in this school likes _____ best? Assume there are 350 students in the school.
Classwork:
Check for Understanding (pg 312) #1, #2, #4 #7 (all), #11
Technology Notes
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