Math Unit 3 Mrs. ClementTeachers Signature _____________________________

Connect Decimals, Percents & Fractions

1.1 Square Numbers and Area

Unit 3.1 What are decimals and

Investigate: (Text pg. 124-131) How can we relate decimals and percents?

What You’ll Learn...• To estimate percents as fractions or as

decimals• To compare and order fractions,

decimals and percents• To estimate and solve problems using

simple and complex conversions• To add, subtract, divide and multiply

using fractions• To estimate percent values• To solve problems with percents,

decimals and fractions• to connect integer operations to the

real world.Why is it important?• We use fractions everyday of our lives for cooking, shopping, telling time,

measuring and even sports

• Fractions allow us to look at the numbers that exist between whole numbers. This allows us to look at the world in more detail.

• Careers as a athletes, business owners, teachers, artists, publishers, veterinarians, architects, or engineers would all require these mathematical skills.

Decimals are ____________________ that represent _________ of a whole. Percents are _______________ that represent _________ of a whole. We most often use percents when _______ is the whole number.

Before we Begin: Types of Decimals:

Decimals, such as 0.1 and 0.25 are ____________________________

Each _________ decimal has a definite number of decimal places.

Decimals, such as .333 333 333… and 0.454 545 454… are ______________________. Some digits in each repeating decimal repeat forever. We draw a bar over the top of the digits that repeat:

For example: 4/33 = 4 ÷ 33 = 0.121 212 121… = .12

Some decimals do not terminate or repeat. Example:3.14159…

Repeating Decimals Magic Tricks

Use a Calculator:

Write each fraction as a decimal: 111, 211,

311

, 411

What pattern do you see?

Discussion Point: Where have you seen decimals or percents used in the real world?

Use your pattern to predict the decimal forms of these fractions: 511

, 611

, 711

, 811

, 911

,

Use your calculator to check your predictions.

Calculator Magic Tricks:In this trick you will guess the end result of a series of mathematical operationsThe steps involved are:

1. Give the calculator to a friend and ask him/her to do the following:Write a number of less than 8 digits, as usually this is the limit of most calculators. Tell them to remember the number they originally wrote.

2. Multiply the number by 33. Add 15 to the result4. Multiply the resulting number by 25. Now divide by 66. From the total, subtract the original number entered in step 17. Finally, tell your friend that you will guess the number that is in the display of the

calculator. It does not matter what the original number was, the answer will always be 5!!!

Awesome! Right?

Let’s Explore:

Example #1. Write each decimal to the eight decimal place.

a) 0.3 ≈ 0. __ __ __ __ __ __ __ __b) 0.03 ≈ 0.__ __ __ __ __ __ __ __c) 0.52 ≈ 0. __ __ __ __ __ __ __ __d) 7.23 ≈ 7. __ __ __ __ __ __ __ __e) 8.2539 ≈ 8.__ __ __ __ __ __ __ __f) 0.2537 ≈ 0. __ __ __ __ __ __ __ __

Reflect & Share: Compare your pattern, decimals and fractions with those of another classmate. How did you use patterns to make predictions?

Example #2. Circle the repeating decimals.

0.123412312 0.77 0.22222222 …0.512512512… 0.123238…

Example #3. Write each repeating decimal using bar notation.

a) 0.55555… = ___________

b) 2.343434 = ___________

c) 5.237237 = ___________

d) 57.12121 = ___________

Example #4. If 1/9 = 0.1 and 1/99 = 0.01, what is 1/999 = _______

Example #5. The denominators of 3/6, 3/12, 6/12, 3/15, 9/15 and 12/15 all have 3 as a factor. But they are all terminating decimals. Why?

Example #6. Compare the decimals

Example #7 Write each group of numbers in order from least to greatest.

How to Compare Decimals

Step 1: Write out the few digits of each decimal.

(Add zeros at the end of terminating decimals)

Step 2: Circle the first digits where the decimals differ.

Step 3: The decimal with the greater circled digit is differ.

Place Value and DecimalsRound the repeating decimals to the nearest tenth, hundreds, and thousandths.

Example #1 Write the number shown in the place value chart as a decimal. Use one as a placeholder.

a.

b. 0 .0 9

c. __. __ __

d. __. __ __ __

e. __. __ __ __

Example #2 Write the number as a decimal in expanded form.

a. 0.407 = __ tenths + __ hundredths + __ thousandthsb. 0.163 = __ tenths + __ hundredths + __ thousandthsc. 0.08 = __ tenths + __ hundredths + __ thousandthsd. 0.76 = __ tenths + __ hundredths + __ thousandths

Is the decimal to the right or the left of the ones place? RIGHT LEFT

Example #3 Put a decimal point in the number so the digit 3 as a value of 3100 .Add zeros if you need to.

a. 3 2

b. 1 3 5

c. 9 8 7 3

d. 3

Tenths Hundredths Thousandths

2/7 = 0. 2857142857134…

5/13 =

Show You Know1. Complete the table below. Place each number in the correct place value space and add the total.

2. Add zeros to rewrite the whole numbers as decimal tenths, hundreds, and

thousandths. For example 2 = 2.0 = 2.00 = 2.000

a) 7 =____________ b) 15 =____________ c) 230 = ____________

____________ ____________ ____________

____________ ____________ ____________

Reflection: Talk to the person next to you about what you have noticed about decimals so far. What seems pretty straightforward? What is way too complicated? Is there anything you find easy/ difficult? Write down some of your ideas.

We convert percents to decimals often in the real world. For instance, when you see a sale for 50% off an item, you convert the discount into a decimal to subtract from the price of the item. When you add taxes to an item, you do the reverse; you add the amount as a decimal onto the prices. What are some other places you convert back and forth between decimals and percents?

FREEZE- time for a story about a story….

Once upon a time, in Ancient Egypt, Pete the Slave was sitting by the river eating some bread and contemplating the meaning of life. “Have you ever noticed,” said Pete to his friend Ramses, “That the day seems to be divided up more and more lately? Like, just yesterday the head slave driver… what’s his name-“

“Looming Larry?”

“Yah, that guy… He says to me ‘You there, hemu, after you eat breakfast I want you to make another thousand cinder blocks. And then after lunch you better finishing the nose on that sphinx!’”

“You think that’s weird,” said Ramses. “Sometimes I feel like they are dividing up the SEASONS that way too: Akhet, Peret, Shemu! All of a sudden we have three seasons? It is just too obvious to deny.”

Reflection: Talk to the person next to you about what you have noticed about decimals so far. What seems pretty straightforward? What is way too complicated? Is there anything you find easy/ difficult? Write down some of your ideas.

Tricks & Tips for percents and decimals

Rule for % to . __________________________________Rule for . to % __________________________________

“You think THAT’S weird,” said Pete, now standing up he was so angry. “Even the MONTHS are divided up these days. Why just this past First of Akhet, I was thinking to myself, soon it will be the Second of Akhet! And then

a third, and then a fourth. And then a first Peret, like some never ending project the pharaoh comes up with.”

Ramses nodded sadly and turned back to his bread, “Would you like ½ ?”

“Sure,” said Pete, and sat back down.

Percents

Example #1: 30 out of 100 squares are shaded. The ratio of shaded squares to all squares is ___ : 100.

So, ____ % of the grid is shaded.

Example #2: Pretend that 47 out of 100 letters are B’s in a scrabble box. The ratio of B’s to all the letters is

____ : 100 So the _____ % of the letters are B’s.

Example #3: Which percent of the figure is shaded.

_________ _________ _________ _________

The word per cent mean “out of 100.” A percent is a ratio that compares a number of an amount to 100. The symbol is %. For example 45% = 5 : 100 =45/100

Example #4: Shade 50% of each circle.

Recap:50% of something is the same as saying ________________

25% of something is __________ of ___________ or a quarter of the original.

10% of something is 1/100.

Let’s Explore:1. Find the percent of a number

Four students in Mrs. Clement’s class were late coming back from lunch. Mrs. Clement explained that they owed 20 clement bucks in total. What percent of the total cost does each person owe?

Solution:

a) Find 50% of $20.00.50% of 20 is _________ This is how much TWO people would owe Mrs. Clement.

b) Now find 25% of $20.00.25% of 20 is _________ = one quarter is ___________. This is how much FOUR people would owe Mrs. Clement.

c) Check:

__________ x 4 = ____________.

Each student owes ______ or ____ % of the total to Mrs. Clement = $ 20.00

2. Find the percentage of each price. Show the steps.

a) Find 50% of $45.80Step 1: 50% = ___________Step 2: 50 x 2 = ___________

Tip: use the check back method in step 2 to double check your answer.

Write a problem for 50% for your friend. Switch papers and try to solve each others equation:

b) Find 25% of $50.00Step 1: 50% = ____________

Step 2: 25% = ______________

Step 3: 25 x 4 = ____________

c) Find 10% of $72.40Step 1: 10% = move the decimal over one to the right = ___ . ___

Step 2: 10 x __ . __ = _____ . ______

3. Use mental math to convert the percent to a decimal.

What is 50% of 100 _____________

What is 50% of 200 _____________

What is 25% of 80 _____________

What is 25% of 100 _____________

What is 10% of 200 _____________

What is 10% of 80 _____________

BonusWhat is 75% of 100 _____________

What is 75% of 200 _____________

Write a problem for 25% for your friend. Switch papers and try to solve each others equation:

Write a problem for 10% for your friend. Switch papers and try to solve each others equation:

What is 75% of 80 _____________

Check Your understanding:

75% of 100 = 25% + 25% + 25% of 100 75% of 200 = 75% x2 of 100 75% of 80 = 50% (40) + 25% (20)

4. What percent is being represented in this picture? Explain your reasoning:

5. Convert the following statements to decimal or percent.

a. 50% = ______________ b. 75% = ______________

c. .60 = ______________ d. .32 = ______________

6. What is 50% of each of the following:

a. 34 students

b. $45.22

c. 12 banana cream pies

d. 4 slices of apples

7. What is 25% of each of the following:

a. 68 daffodils

Solution:

________ of 80 is __________. 50% of 80 is __________ of 80. 25% is half of 50% 75% is 3x 25%

b. 42 birds

c. 7.2 meters d. $0.56

8. What is 10% of each of the following:

1. 15 minutes

2. 50 cats

3. 34 horses

4. $89.50

9. Describe how you could find 35 percent of 68 using only the ability to divide in half and to then use addition. Show each step:

10. In British Columbia, HST (PST + GST) is 12%. When you buy a bag of Halloween candy (it’s on sale now) for $5.47, how much are you paying in tax? Show each step:

11. Shade the continent of Asia. Asia covers 30% of the world’s land mass.

Using this map, estimate the % of land mass Canada covers: ____________British Columbia: ________________Vancouver Island: ________________

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Unit 3.3 Connecting Percents and Decimals to Fractions

Investigate: (Text pg. 132-139) How can you convert decimals and percents to fractions?

What are Ratios?

Question # 1: Write the number of girls (g), boys (b) and children (c) in each a) There are 8 boys and 5 girls in a class b: ____ g: ____ c:____

b) There are 4 boys and 7 girls in a class b: ____ g: ____ c:____

c) There are 12 boys and 15 girls in a class b: ____ g: ____ c:____

d) There are 7 boys and 10 children in the classb: ____ g: ____ c:____Question #2: Write the number of boys, girls and children in each class.

Then write the fraction of children who are boys and the fraction who are girls in the boxes provided.

a) 5 boys and 6 girls b:___ g:____ c: ____

b) 15 children. 8 are boys. b:___ g:____ c: ____

Question #3: Write a fraction of the children in the class who are boys or girls:

a) 5 boys, 12 children b) 9 girls and 20 children

The word ratio means “relationship.” A percent is a ratio that compares a number of an amount to 100. A ratio shows how many times one number shows up out of a whole number. Ratios are shown with a colon (:) separating the part from the whole.

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c) ratio of girls to boys is 7:8 d) ratios of boys and children is 10:11

Take it Further:Question #4: From the information given, determine the number of cats and dogs in each class.

a) 20 pets. 2/5 are dogs.

b) 42 pets. 3/7 are girls.

c) 15 flowers. The ratio of daises to violets is 3:2.

d) There are 24 pieces of candy. The ratio of chocolates to fuzzy peaches is

3:5.

Question #5: Find the number of boys and girls in each classroom. Show the steps.

a) In classroom A, there are 25 children: 60% are girls. ______________________b) In classroom B, there are 28 children. The ratio of boys to girls is 3:4.

______________________c) In classroom C, there are 30 children. The ratio of boys to girls is 1:2.

______________________

Tips and Tricks for Converting:Method #1: Think of a percent as a Number

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$0.05 $0.10 $0.25

5/100 10/100 25/100

5% of a dollar 10% of a dollar 25% of a dollar

Method #2: Use the fractions you know

Method #2: Think of a model

Divide the blocks into

4 equal parts…

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Let’s Explore:1. Compare Fractions, Decimals and Percents:

How do we convert a percentage to a decimal to a fraction? Use one of the models from page 8 to show you know.

Example: 100% 1.00 100100

Example: 75% 0.75 34

2. Look at the circle graph. Estimate the fraction of pets owned according to the chart.

bird cat dog other

3. Write each set of numbers in ascending order (smallest to greatest):

a) 56%, 0.45, ½

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PetsType Fraction

out of 100Percent

Dog

Cat

Bird

Other

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b) 35%, 39/100, 0.36

c) 1.25, 123% ¾

4. Complete the following chart:

Drawing

Fraction 23/100 45/100

Percent 23% 63%

Decimal .23 .33

Show You Know1. Change these fractions to decimals. Estimate your answer. Use a calculator to check your answer.

a. 1/10 0.10

b. 1/3

c. 1/2

d. 4/10

Homework Assignment TIPS & TRICKS: Visualize the problem (*sketch it out/ picture it in your head before you do the

work) Use the Guess & Check method (make a guess about the answer; do the work;

use the check back “mental math” to eliminate mistakes. Show your work. Use the Internet, YouTube, your teacher, your friends, your parents as

resources when you get stuck. Use the textbook to T.I.F. (take it further).

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Unit 3 Booklet

e. 2/10

f. 23/50

g. 2/3

h. 8/10

i. 9/6

j. 5/10

2. Change these percents into decimals.

a. 10% 0.10

b. 25%

c. 75%

d. 100%

e. 73%

f. 3%

g. 45%

h. 123%

i. 150%

j. 25%

2. Change these decimals into fractions. Reduce if possible.

a. .10 10100 = 110

b. .25

c. .75

d. 1.00

e. .34

f. .45

g. 1.23

h. 1.002

i. 3.56

j. .054

3. Use a calculator to convert these fractions into decimals numbers. Round to the place value indicated.

Take it Further:

Conduct a survey with at least 5 people (for example: which of the napoleon ice cream flavour do you prefer?) Write your question and the results here. Calculate the percentage of each result (for example: 3/5 people prefer chocolate, 1/5 vanilla and 1/5 strawberry) and write the equation and results on a separate piece of paper.

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a. 13/25 (tenths)b. 107/215 (hundreds)c. 43/50 (tenths)d. 197/289 (thousandths)

4. The QMS Rocket Rangers field hockey team has an outstanding goal average. The following data reflects the numbers from their last season.

a. What is the average goal per game? Round to the nearest tenth.

b. Which player produced the better average for the season? Explain your answer.

______________________________________________________________________________________________________________________________________________________

5. Change each fraction to a repeating decimal. Then use bar notation to show the repeating part.

a. 5/6

b. 2/3

c. 45/99

d. 7/11

6. Estimate (i.e. don’t use a calculator) the following as a percent:

a. . 50 out of 100

b. .78 out of 100

c. .35 out of 70

d. 150 out of 300

Goal average = Number of goals

Number of games

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Player Number of Goals Number of Games

A 8 5

B 5 8

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7. Change each decimal to a fraction

a. 0.95

b. 0.3

c. 0.243

d. 0.08

8. Express the value of each coin as a fraction of a dollar.

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Unit 3.3 Review

Investigate: (Text pg. 130--146) How can we use percents in the real world?

Example #1: Write each of the following statements as a percent or decimal:

a. Ana ate all of her Halloween candy.

b. Madi shared half of her Halloween candy with her brother.

c. Hannah’s brother stole 4/5 of her Halloween candy.

d. Olivia gave away all of her candy because the dentist said she wasn’t allowed to eat it.

Example #2: There is an average of 15 students in each class at QMS, which means there are about 210 students in the school (k-12)? What percentage of the school is Jr. School? Show me the steps you took to get your answer

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Example #3: QMS has a population of about 210. Out of these people, 85 are over the age of 10.

a. Estimate the percentage of the school’s population are older than 10:

b. Show the number of people over 10 as a fraction. Express your fraction as a decimal (to 3 decimal places)

Show You Know1. Draw a number line. Place each of the following numbers on your number

line:

65% .60 .089 ½ 1.23 198%

2. Show each fraction as a repeating decimal. Use a calculator to find your answer.

a. 4/9 b. 3/11 c. 2/9

3. Taylor Swift releases three hit new singles. Use the data to answer the following questions:

Reflect & Share: Share your answers for question 2-3 with the person next to you. Explain to them how you came to the answer.

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a. Which percentage of people heard the song the most?

b. Which audience provides the greatest percentage of profit to Taylor Swift, assuming iTunes costs 99 per song, concert tickets are $100.98 and listening to the radio is free. Which is the most affordable listening option for people listening to the song?

4. Show each terminating decimal as a fraction. Can you reduce the fraction.

a. 0.35 b. 0.2 c. 0.025

5. Alexis sold 220 out of 250 raffle tickets. Lauren sold 85% of her 260 raffle tickets.

a. Who sold the most raffle tickets? Show the steps.

b. How many did each girl sell? Show the steps.

6. At a fairground game, Olivia can throw a dart at the square target to win a prize. Emily bets her she can guess which colour she will hit. If she is correct, she gets Olivia’s prize. If she is wrong, she has to buy her ice cream.

a. Which do you think is easier to hit: The black, the grey or the white (center)?

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Number of times played

Number of people listening

Radio 5 500

iTunes download 23 1

Concert 1 2000

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b. Every dart that lands on one of the coloured regions is a winner. Which colour will get the biggest prize?

c. Rank the colours from least to greatest.

d. There are 28 small squares represented in this target. Write each as a fraction.

Math Relay:9 questions $3

Which is greater or less than or equal to?

1% ____ .01 1/3 ____ 25% 4/5 ____ 98%

Your Goal:

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50% ____ 1/3 1/2 ____ .50 1/2 ____ 51%

1.25 ____ 1.75 .093 ____ 93% $4 ____ 4/4

3.25 ____ 3.25% 14% ____ .14 2% ____ .2

22% ____ 2/6 2/3 ____ 75% 3/4 ____ 75%

41% ____ 50% 0.08 ____ 80% 76 ½ ____ .765

2 ½ ____ 2 ¼ 95% ____ 100% 75% ____ 200%

2.54 ____ 200% 8% ____ .09 24 ½ ____ 24.6%

63% ____ .36 342% ____ $4 703% ____ 7/8

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A

B

C

D

E

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Unit Review: Pirate’s Cove

Pirate’s CovePrecincts, Decimals and Fractions

Opponents Lives:

1 2 3 4 5

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Three Lives

Unit 3 Booklet

Bonus ActivitiesNewspaper Hunt: ($10 ClementBucks)

Look in the newspaper. Find at least 5 examples of fractions, percents or decimals. Clip the examples and create a poster. Describe the conversion to fraction, decimal or percent.

Create a Game: ($20 ClementBucks)Create a game that teaches people to convert fractions, decimals and percents. Your board game must meet the following guidelines:  

1. You must include a set of rules that are clearly defined and easy to follow. How is the game played? How do you clarify a winner?

2. Your board game should be able to be played by 2-6 players3. Include a list of materials that are included in your board game. For

example, there must be game pieces included unless you identify what can be used as markers.

4. There should be at least 20 spaces on the game board. Depending on how the game is played, there may be a starting point and an end point.

5. Your game should include “cards” where players must solve problems. There should be a minimum of 20 different cards that include every operation and maybe other concepts we have learned. There should be about an even amount of each operation included.

6. On a separate piece of paper, you should have every problem (from the cards) written down with its correct solution.

7. Make sure the board game and directions are neat. 8. Be Creative.

Create a movie for converting percent to decimal: ($30 ClementBucks)

1. Watch a few videos on YouTube to get an idea of what is out there. 2. Create your own awesome movie using stop motion OR a rough-cut video using

actorsa. Create a scriptb. Take a sequence of picturesc. Edit movie in movie maker or iMovied. Add a voice over.

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