Unit 3 Week 1 – 6th grade Math – Lesson Plan Morning Work
Problem solving: Divide fractions of a whole number Breakfast of Champions: Convert improper fractions to mixed numbers Can You Hang: Order of operations
Monday
Objective and Key Points
Tuesday Solve proportions.
A ratio compares two or more values. “For every __, there is ____.”
A proportion says that two ratios are equal.
Identify and simplify/reduce proportions.
A proportion is true if the conversion (what you multiply or divide by” on the numerator and denominator is the same.
A proportion is true if the conversion (what you multiply or divide by” on the numerator and denominator is the same.
Set up the known ratio, then match the terms, and multiply and divide to find the unknown term.
To simplify/reduce proportions, you must divide the top and the bottom by the same number.
1. Do Now: First Five and Whole Class Review (0:10) 2. Direct Instruction: Matching terms and applying the conversion (0:10) 3. GP: Matching terms and applying the conversion (0:10) 4. IP: Matching terms and applying the conversion (0:45) a. MW & LW check at back table and with Ms. Taylor: row by row
1. Do Now: First Five and Whole Class Review (0:10) 2. Direct Instruction: Identify proportions (0:05) 3. GP: Identify proportions (0:10) 4. Direct Instruction: Simplify/reduce proportions (0:05) 5. GP: Simplify/reduce proportions (0:10) 6. IP: (above) (0:30) • MW & LW check at back table and with Ms. Taylor: row by row
Ratios can compare: parts to parts or parts of whole.
1. Do Now: First Five and Whole Class Review (0:10) 2. NWEA goals (percentiles), Benchmark scores, Learning Teams, and Class Structure (0:15)
(times listed are elapsed time)
3. Direct Instruction: Writing ratios in five different ways (0:10) 4. GP: Writing Ratios in five different ways (0:10) 5. IP: Writing ratios (0:30) a. MW & LW check at back table and with Ms. Taylor: row by row
5.
6. Review LW expectations, Top Ten (0:05)
Wednesday
Read and write ratios.
Ratios can be written in three main ways. “to” “:” “as a fraction”. You can also write it as a decimal and a percent.
Core Learning Experiences
Daily Do Now
1. Function Tables: Write algebraic expressions 2. Function Tables: Find the Rule 3. Multiply and divide fractions 4. Properties of Operations 5. Mad Minute: Division Fluency
Review LW expectations, Top Ten (0:05)
7. Review LW expectations, Top Ten (0:05)
Homew ork
1. Day’s Objective 2. Multiply and divide fractions 3. Multiply and divide decimals 4. Add and subtract fractions 5. Add and subtract decimals 6. Use the rubric
Thursday Find unit rates. Unit rates are ratios that have a term of 1 at the bottom. You can use proportions to find rates. To find a rate, divide the bottom (and the top) by the value of the bottom term to make the bottom term a value of one.
1. Do Now: First Five and Whole Class Review (0:10) 2. Direct Instruction: Setting up unit rates (0:10) 3. GP: Setting up unit rates (0:10) 4. GP: Solving unit rates (0:10) 5. IP: Setting up and solving unit rates (0:30) • MW & LW check at back table and with Ms. Taylor: row by row 6. Review LW expectations, Top Ten (0:05)
Friday Solve proportions in context. Use your new math knowledge to prove your answers. Without work shown, your answer is just a guess. If you are guessing, you are not an expert and not hire-able!
1. Do Now: First Five and Whole Class Review (0:10) 2. GP: Showing your work in ratios, proportions, and unit rates (0:10) 3. IP: Assessment (0:30) 4. Review LW expectations, Top Ten (0:05)
Name: ___________________________________ Class: ____________
Keep me at least until the Unit 3 Benchmark on Wednesday, December 21!
UNIT 3: WEEK 1 RATIOS, RATES, AND PROPORTIONS “Every moment is your chance to be better.” – Ms. Taylor Homework
Mon
Key Takeaways:
Anchor Problem:
Ratios can be written in five ways 1. Using number names and the word “to” 2. Using number names and a colon “:” 3. As a fraction 4. As a decimal 5. As a percent
2 weekend days to 5 weekdays 2 weekend days : 5 weekdays 2 weekend days 5 weekdays 5÷2 = 0.4 of the ratio is weekend days 0.4 = 40% of the ratio is weekend days 2 weekend days x3 6 weekend days = 5 weekdays x3 15 weekdays 2 weekend days x5 10 weekend days = 5 weekdays x5 25 weekdays
Tues
Wed
Solving proportions means using the same conversion on the top and the bottom.
A proportion is true if the same conversion is used on the top and the bottom. Reducing/simplifying proportions means dividing by the same conversion on the top and the bottom.
NOT TRUE 2 weekend days x 2 4 weekend days = 5 weekdays x5 25 weekdays TRUE 2 weekend days x3 6 weekend days = 5 weekdays x3 15 weekdays 2 weekend days x5 10 weekend days = 5 weekdays x5 25 weekdays 2 weekend days ÷5 0.4 weekend days = 5 weekdays ÷5 1weekday
Thurs
A unit rate has a term of 1 at the bottom. Divide the top and the bottom by the original bottom to get a unit rate.
There are 0.4 weekend days for every weekday. 0.4 weekend days/weekday (read: “0.4 weekend days per weekday”)
Fri Questions: Call or text Ms. Taylor at 314-‐632-‐6201
If you do not leave a clear voicemail with your name, question, and phone number, I will not return your call.
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READ AND WRITE RATIOS NOTES: A ratio compares two (or more) different values. The number of yellow squares compared to the number of blue squares
blue blue blue yellow It can be written in five different ways. Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
1 yellow square to 3 blue squares
1 yellow square : 3 blue squares 1:3
1 yellow square 1 = 3 blue squares 3
1 divided by 3 = 0.333…
0.333… = 33%
__________ vowels to ________ consonants
_________ boys in this room to __________ girls in this room
Ratios can show two different kinds of comparisons: part to part or part to whole
Part to part
Part to whole
Shaded to unshaded 5 shaded boxes to 11 unshaded boxes
Shaded to total 5 shaded boxes to 16 total boxes
circles to triangles
triangles to total shapes
★★★★★★ stars to apples
★★★★★★ stars to total
✔✔✔✔✖✖✖✖✖✖✖✖✖✖✖✖ x’s to check marks
✔✔✔✔✖✖✖✖✖✖✖✖✖✖✖✖ total to x’s
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PRACTICE: 1. The ratio of hours in a day to minutes in an hour Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
Circle the correct kind of comparison: part to a part or part to a whole ? 2. The ratio of student tables to student chairs Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
Circle the correct kind of comparison: part to a part or part to a whole ? 3.
The ratio of students with long sleeves to total students
Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
Circle the correct kind of comparison: part to a part or part to a whole ? 4. The ratio of teachers to students in this classroom
Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
Circle the correct kind of comparison: part to a part or part to a whole ?
3
As a percent
5. The ratio of students wearing glasses to total students Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
Circle the correct kind of comparison: part to a part or part to a whole ? 6. The ratio of students wearing glasses to students not wearing glasses
Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
Circle the correct kind of comparison: part to a part or part to a whole ? 7. The ratio of consonants to letter in the word SLANT Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
Circle the correct kind of comparison: part to a part or part to a whole ? 8. The ratio of number of eyes in this room to people in this room
Using number names and the word “to”
Using number names and a colon “:”
As a fraction
As a decimal
As a percent
Circle the correct kind of comparison: part to a part or part to a whole ?
4
SOLVE PROPORTIONS NOTES: A proportion is two equivalent ratios separated by an equal sign.
2 hands x 4 8 hands = 1person x 4 4 people Proportions are best shown when they have two ratios and two (of the same) conversions, including number names. EXAMPLE: Elm City Elementary wants to open a petting zoo for their scholars. In the zoo the ratio of goats to ponies is 3:2. If the zoo has a total of 21 goats, how many ponies does it have?
Step One: Set up the proportion
Step Two: Find the conversion
Step Three: Apply the conversion
3 goats 21goats = 2 ponies p ponies 3 goats x7 21goats = 2 ponies p ponies 3 goats x7 21goats = 2 ponies x7 14 ponies
You can complete a proportion using either multiplication or division in your conversion. Bosco is driving at 75 miles per hour. If he continues to drive at this rate, how many hours will it take him to drive 300 miles?
x
75 miles 300 miles = x 1hour hour
5
Hubert earned $97 in three hours. How much does he earn every hour?
$96 ÷ miles = ÷ 3 hours 1 hour
PRACTICE: 1. Pedro can eat 15 grapes in 2 minutes. If he continues to eat at this rate, how many grapes can he eat in 18 minutes?
2. Shelly knows that there are 16 cups in every gallon. If she has punch bowl that holds 2 ½ gallons of punch, how many cups of punch does she need to fill the bowl?
3. When making chocolate chip cookies Jonny knows that the ratio of batches of cookies to eggs is 1:2. What is the amount of eggs in 8 batches of chocolate chip cookies?
4. In country Z, there are 4 goobers for every 3 doodads. How many goobers are in country Z if there are 729 doodads?
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5. Carla has 5 teddy bears for every 2 dolls. If Carla has 4 dolls, how many teddy bears does she have?
6. Emilio has 10 bugs for every 2 glass jars. How many bugs does Emilio have if he owns 16 glass jars?
7. Jaunita puts 3 scoops of juice mix for every 11 glasses of water. How many scoops of mix does Jaunita need to place in the water if she needs to make 55 glasses of juice?
8. In the cafeteria, the ratio of tables to chairs is 1:9. There are 189 chairs in the cafeteria. How many tables are there?
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 9. Sheila earns $15 in 3 hours. How much will she earn in 15 hours?
10. Rochelle buys 4 tops for every 3 pants she purchases. If she bought 21 pairs of pants, how many tops did Rochelle purchase?
11. There are 3 adults for every child in the school auditorium. If there are 321 adults, how many children are there?
12. Mr. Torokio has 7 math students for every 9 history students. If he has 112 students in his math classes, how many students does he have in his history classes?
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13. The ratio of nails to screws is 5:3. If there are 375 screws, how many nails are there?
14. Leslie drew 7 butterflies for every 2 flowers in her picture. If there are 12 flowers in her picture, how many butterflies are there?
15. Keeley earns $500 for every 3 days. How many days will it take here to earn $2500?
16. For every 5 days that Cavin works, he has 2 days off of work. If Cavin had 8 days off last month, how many days did he work?
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IDENTIFY PROPORTIONS AND SIMPLIFY/REDUCE RATIOS NOTES: Part one:
Ratios are proportional if the conversion on the top and the bottom is the same. PROPORTIONAL – the conversions are the same
3 goats x7 21goats = 2 ponies x7 14 ponies NOT PROPORTIONAL – the conversions are different
3 goats +7 10 goats = x7 2 ponies 14 ponies Directions: Explain whether or not these ratios are proportional. If it’s not proportional, rewrite it to make it true.
2.
1.
3.
Part two:
Simplifying or reducing ratios means to divide both the top and the bottom by the same conversion as completely as you can. You have to keep the same order and return the answer in the same form! Simplify this ratio: 36 to 52
=
36 ÷4 9 = 52 ÷4 13
= 9 to 13
Reduce this ratio: 16 : 30
=
Simplify/reduce this ratio:
16 = 30 =
=
20 10
20 = 10
=
10
PRACTICE: Directions: Simplify/reduce each ratio to its simplest form.
Directions: Explain whether or not these ratios are proportional. Then rewrite the proportion to make it true. 1. 11 to 9, 44 to 36
2. 5:6, 23:18
3. 5 to 10, 2 to 1
4. 2:1, 28:14
5. 2:3, 24:36
6. 7 to 3, 8 to 4
11
7.
2
24 =
1 8.
12
45
3 =
15
1
9. 1:7, 4:28
10.
45
2 =
30
3
11. 1 to 3, 16 to 48
12. 12:39, 2:5
13. 6:30, 1:5
14.
5
10 =
2
4
15. 5 to 8, 24 to 15
16. 2:14, 28:1
17.
45
9 =
43
7
18. 36 to 21, 12 to 7
19. 33:12, 11:4
20. 7:5, 14:10
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FIND UNIT RATES NOTES: A unit rate has a denominator of one. RATE
36 pages 1notebook
NOT a Rate Read “36 pages per notebook”
144 pages 3 notebooks
Read “144 pages in every 3 notebooks”
To find a unit rate, divide the value of the original denominator on both the top and the bottom. 34 miles ÷ 2 17 miles = 2 hours ÷ 2 1 hour
17 miles per hour
72 cakes ÷ = 6 cups of milk ÷
________ cakes per cup of milk
PRACTICE: Directions: Find the unit rate (by making a proportion with a ratio over 1. 1. 164 miles in 4 hours
2. 106 pages in 1 day
3. 30 calls in 6 hours
4. 11 seats in 1 row
5. 243 meters in 3 seconds
13
cakes cup of milk
6. 152 miles in 2 hours
7. 64 calls in 16 hours
8. 2,080 pages in 20 days
9. 178 meters in 2 seconds
10. 14 seats in 1 row
11. 156 seats in 12 rows
12. 342 meters in 6 seconds
13. 40 calls in 20 hours
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14. 138 pages in 2 days
15. 395 miles in 1 hour
16. 48 calls in 16 hours
17. 135 pages in 1 day
18. 567 meters in 9 seconds
19. 108 seats in 4 rows
20. 970 miles in 2 hours
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Homework: Unit 3.Week 1.1 Part One: READ AND WRITE RATIOS Directions: Write each ratio in all five ways. Then tell whether it’s a part to a part or a part to a whole. 1. 4 gallons compared with 5 cups 2. twelve pencils compared with twenty pens 3. 8 computers compared with 40 laptops
Part Two: MULTIPLY AND DIVIDE FRACTIONS 4.
3 5
• 35 =
5.
1 35 • 35 =
6.
3 35 •1 43 =
Part Three: MULTIPLY AND DIVIDE DECIMALS 7. 2.4 x 3.4 =
8. 0.45 x 1.2 =
9. 3.1 x 6.52 =
Part Four: ADD AND SUBTRACT FRACTIONS 10.
3 5
+ 71 =
11.
3 21 + 34 =
12.
132 + 2 31 =
Part Five: ADD AND SUBTRACT DECIMALS 13. 2.4 x 3.4 =
14. 0.45 x 1.2 =
15. 3.1 x 6.52 =
Part Six: USE THE RUBRIC 16. Milissen is having a barbecue. The hamburger packs she is buying contain 8 hamburgers per pack. If she would like to serve 27 hamburgers, how many packs will she need to buy? EXPLAIN WHY WE SHOULD BELIEVE YOUR ANSWER IS CORRECT!
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Homework: Unit 3.Week 1.2 Part One: SOLVE PROPORTIONS 1. A KIPPster has to complete at least 15 assignments every 3 days. How many assignments does she have to complete in 21 days? 2. The moon is full for four days every month. How many full moons is there in one year? (Remember, there are 12 months in a year.) 3. Ms. Taylor has five cups of coffee every day. How many cups of coffee does she have every week?
Part Two: MULTIPLY AND DIVIDE FRACTIONS 4.
3 5
÷ 35 =
5.
135 ÷ 35 =
6.
2 35 ÷135 =
Part Three: MULTIPLY AND DIVIDE DECIMALS 7. 4.92 ÷ 3.28 =
8. 96.4 ÷ 9.64 =
9. 91.2 ÷ 1.52 =
Part Four: ADD AND SUBTRACT FRACTIONS 10.
3 5
+ 51 =
11.
3 5
− 51 =
12.
2 35 − 151 =
Part Five: ADD AND SUBTRACT DECIMALS 13. 4.92 – 3.28 =
14. 96.4 – 9.64 =
15. 91.2 – 1.52 =
Part Six: USE THE RUBRIC 16. Jamie and Dave grew miniature pumpkins in their garden this year. They had a total of four vines that produced fruit. If the first vine produced thirteen pumpkins, the second vine produced eight pumpkins, the third vine produced thirteen pumpkins, and the fourth vine produced sixteen pumpkins, how many pumpkins did they grow altogether? If they sell the pumpkins for $3.81 each, how much money will they make? EXPLAIN WHY WE SHOULD BELIEVE YOUR ANSWER IS CORRECT!
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Homework: Unit 3.Week 1.3 Part One: IDENTIFY AND SIMPLIFY/REDUCE PROPORTIONS Directions: Explain whether or not these ratios are proportional. 1.
3 5
=
3 5
2.
3 5
=
3 15
=
3.
3 5
5 15
40 88
6.
27 99
161 ÷ 35 =
9.
2 35 • 2 35 =
Directions: Reduce each of these ratios to its simplest form. 4.
3 15
5.
Part Two: MULTIPLY AND DIVIDE FRACTIONS 7.
1 5
• 63 =
8.
Part Three: MULTIPLY AND DIVIDE DECIMALS 10. 2.94 x 4 =
11. 5.4 x 3.4 =
12. 1.24 x 4.1 =
Part Four: ADD AND SUBTRACT FRACTIONS 13.
135 + 71 =
14.
3 21 − 34 =
15.
132 + 2 41 =
Part Five: ADD AND SUBTRACT DECIMALS 16. 5.45 + 38.15 =
17. 38.15 - 5.45 =
18. 500.45 + 38.1 =
Part Six: USE THE RUBRIC 19. Eric wanted to alter his bedroom so it wouldn't look like a little kid's room. He asked his parents for some money to buy supplies and they gave him $75.00. The paint he wanted cost $12.65 a gallon. Paintbrushes cost $8.68 each. The NFL border cost $5.22 for a 20-foot roll. He needs three gallons of paint, two paintbrushes, and two rolls of border. How much will everything cost? EXPLAIN WHY WE SHOULD BELIEVE YOUR ANSWER IS CORRECT!
18
Homework: Unit 3.Week 1.4 Part One: FIND UNIT RATES 1. 225 miles in five hours 2. 794 words in seven minutes 3. 2.4 miles in 30 minutes
Part Two: MULTIPLY AND DIVIDE FRACTIONS 4.
1 2
• 73 =
5.
1 2
÷ 73 =
6.
1 12 ÷ 173 =
Part Three: MULTIPLY AND DIVIDE DECIMALS 7. 6.5 x 4.21 =
8. 6.15 x 4.1 =
9. 16.51 x 4.1 =
Part Four: ADD AND SUBTRACT FRACTIONS 10.
135 + 51 =
11.
135 − 51 =
12.
135 − 45 =
Part Five: ADD AND SUBTRACT DECIMALS 13. 1.35 + 1.5 =
14. 1.35 – 0.15 =
15. 1.35 – 0.045 =
Part Six: USE THE RUBRIC 16. Grace made four dozen blank cards to use when she wanted to write a compliment to someone. She spent $8.97 for materials. At that price, how much would it have cost her to make one dozen cards? EXPLAIN WHY WE SHOULD BELIEVE YOUR ANSWER IS CORRECT!
20
Homework: Unit 3.Week 1.5 Part One: WEEK REVIEW 1. Write the ratio in all five ways. Then tell whether it’s a part to a part or a part to a whole. a. 8 people compared with three Thanksgiving turkeys 2. Using the ratio above, if there are 21 Thanksgiving turkeys, how many people can it feed? 3. Explain whether or not this ratios is proportional – 3 people to 1 turkey and 9 people to 10 turkey 4. Reduce the ratio from number two to its simplest form 5. If you have ten turkeys to feed 55 people, how many people will one turkey feed?
Part Two: MULTIPLY AND DIVIDE FRACTIONS 6.
4 5
•1103 =
7.
1 45 ÷ 103 =
Part Three: MULTIPLY AND DIVIDE DECIMALS 8. 7.4 x 1.2 =
9. 7.6 ÷ 1.2
Part Four: ADD AND SUBTRACT FRACTIONS 10.
4 34 + 81 =
11.
3 21 − 34 =
Part Five: ADD AND SUBTRACT DECIMALS 12. 7.4 + 1.2 =
13. 7.4 - 1.2 =
Part Six: USE THE RUBRIC 14. Nicole's family of six people decided to spend their summer vacation in San Antonio. They went to Six Flags Fiesta Texas on Tuesday which cost them $50.96 per person. On Thursday, they visited Sea World. The fun they had there cost them $42.98 per person. How much money did Nicole's family spend on admission into these two parks? EXPLAIN WHY WE SHOULD BELIEVE YOUR ANSWER IS CORRECT!
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