Monday, April 28, 2014

POTD1. Which choice is equal to 1.3?

a) 1 b) 1 3 3 100

c) 1 6 d) 13 100 10

2. The sum of the interior angles of a triangle equals 180 degrees. If you have an isosceles right triangle and one angle that measures 90 degrees, what is the measure of the other two angles?

4.MD.14.MD.2

In measurement problems, it is sometimes important to convert from one unit to another within a system.

UNITS OF LENGTH Customary • 12 inches = 1 foot • 3 feet = 1 yard Metric • 1,000 millimeters = 1 meter • 100 centimeters = 1 meter • 10 millimeters = 1 centimeter • 1 kilometer = 1,000 meters

Example:

Convert to feet: 5 yardsSolution:

Since 3 feet equal 1 yard, multiply 5 times 3 to find how many feet are equal to 5 yards.

• 5 × 3 = 15 • So, 15 feet are equal to 5 yards.

UNITS OF CAPACITY Customary 8 fluid ounces = 1 cup 2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon Metric 1,000 milliliters = 1 liter

Example :

Convert to cups: 8 pints Solution:

Since 1 pint equals 2 cups, multiply 8 by 2 to find how many cups are equal to 8 pints.

• 8 × 2 = 16• So, 16 cups are equal to 8 pints.

UNITS OF WEIGHT Customary 16 ounces = 1 pound Metric 1,000 milligrams = 1 gram 1,000 grams = 1 kilogram

Example:

Convert to ounces: 3 pounds Solution:

Since 16 ounces equal 1 pound, multiply 3 times 16 to find how many ounces are equal to 3 pounds.

• 3 × 16 = 48 • So, 48 ounces are equal to 3 pounds.

UNITS OF TIME • 12 months = 1 year• 365 days = 1 year • 7 days = 1 week • 24 hours = 1 day • 60 minutes = 1 hour • 60 seconds = 1 minute

Example:

Convert to minutes: 4 hoursSolution:

Since 60 minutes equal 1 hour, multiply 4 times 60 to find how many minutes are equal to 4 hours.

• 4 × 60 = 240 • So, 240 minutes are equal to 4 hours.

• In measurement problems, it is important to know how the sizes of units within a system compare to one another.

Example:

Gerry wants to know how much water his mop bucket holds. So, he filled a one-pint container of water and poured it into the bucket. It took 16 full one-pint containers to fill the bucket. If he had used a one-cup container, what would have happened?

• Solution:

Since there are 2 cups in 1 pint, cups are smaller than pints.

Therefore, it would have taken more containers to fill up the bucket.

Example 2:

Julio wants to know the distance from his room to the bathroom.

Which length of rope should he use if he wants to use it the fewest number of times to measure the distance?

A. one inchB. one footC. one yardD. It would take the same amount of times with any length of rope.

• Solution:

One yard is longer than one foot and one inch.

Therefore, he would need to use the one-yard piece of rope the fewest number of times.

Example 3:

Lillian measured her purse to weigh 16 pounds.

What would happen to the number of units if she measured her purse in ounces?

• Solution:

One ounce is smaller than one pound.

Since the units are smaller, there would be more units.

Length• Length tells how long an object is or the

distance between two objects.Example 1:• Harold and John took turns flipping coins up in

the air. Harold's coin went 1.1 meters into the air, and John's coin went 1.5 meters into the air. How much farther did John's coin go into the air than Harold's coin?

Solution:• Since the problem is making a comparison,

use subtraction to find how much farther John's coin went into the air than Harold's coin.

• 1.5 meters - 1.1 meters = 0.4 meters• So, John's coin went 0.4 meters farther into

the air than Harold's coin.

Example 2:• Ginny has a piece of string that measures 1/5

of a foot. Rachael has a string that measures 3 times as long as Ginny's string. How long is Rachael's string?

Solution:• Since Rachael's string is 3 times as long as

Ginny's, use multiplication to find the total length of Rachael's string.

• So, Rachael's string is 3/5 of a foot long.

Mass

• Mass tells how much matter an object is made of.

Example 3:• The mass of a cupcake is 96 grams. If the

cupcake is cut into 4 equal slices, what will be the mass of one slice?

Solution:• Divide the number of grams in one cupcake,

96, by the number of slices to find the mass of one slice.

• 96 grams ÷ 4 slices = 24 grams per slices• So, one slice will measure 24 grams.

Capacity

• Capacity tells how much an object can hold.

• Rodney mixed 7/3 liters of water with 1/3 liters of fruit juice. How much liquid did he have in all?

• Since the question is looking for how many liters he has in all, use addition to solve.

• So, Rodney has 8/3 liters of liquid in all.• Simplify your answer

• When measuring length, use tools such as a ruler or a yardstick.

• What is the length of the wallet in millimeters?

Solution:• Note that centimeters are along the top of the ruler.

The smaller marks between the centimeters are millimeters and there are 10 of them between each centimeter.

• Line up the left end of the object with the left end of the ruler, 0 millimeters.

• The right end of the wallet is at 67 millimeters on the ruler.

• So, the length of the wallet is 67 millimeters.

Example• The scale below measures weight in kilograms.

How much do the books weigh in grams?

Solution• The scale measures weight in kilograms, and

the needle on the scale is pointing to the "2", so the books weigh 2 kilograms.

• There are 1,000 grams in a kilogram, so 2 x1000= 2,000 grams.

• The scale below measures weight in pounds.How much does the porcupine weigh in ounces?

Solution• The scale measures weight in pounds, and the

needle on the scale is pointing to the "6", so the porcupine weights 6 pounds.

• There are 16 ounces in a pound. 16 x 6 = 96 ounces. So, the porcupine weighs 96 ounces.

• The short hand points to the hour.The long hand points to the minute.

• Look at the clock below. The long hand is pointing to the 1, so it is 5 minutes past the hour.The short hand is between 7 and 8, so the hour is 7. The clock below reads 7:05

Elapsed Time

• Elapsed time is how much time has passed.It is the difference from one point in time to another point in time.

Example 1:• Look at the 2 clocks below. The clock on the left shows

the time an event started. The clock on the right shows what time the event ended. How much time has elapsed?

Solution:• The start time is 3:35. The end time is 4:50.• The elapsed time from 3:35 to 4:35 is 1 hour.• The elapsed time from 4:35 to 4:50 can be

found by subtracting 35 minutes from 50 minutes.

• 50 minutes - 35 minutes = 15 minutes.• So, the elapsed time is 1 hour and 15 minutes.

Example 2:• Debbie went to the mall at 3:15. She stayed at

the mall for one and a half hours. What time did she leave the mall?

Solution:• Figure out the time she left the mall by adding

together the minutes and the hours. One and a half hours is 1 hour and 30 minutes. Add the minutes first.

• Next, add the hour.

• So, Debbie left the mall at 4:45.

Example 3:• Marcy started working on her math

homework at 3:35. She finished working on her math homework at 4:50.

• How long did it take Marcy to finish her math homework?

Solution:• Marcy started working on her math homework at 3:35. This is

the same as 25 minutes before 4:00.• She finished her math homework at 4:50. Add 25 minutes to

50 minutes.• 25 minutes + 50 minutes = 75 minutes• Since 60 minutes equals one hour, subtract 60 minutes from

75 minutes.• 75 minutes - 60 minutes = 15 minutes• It took Marcy 1 hour and 15 minutes to finish her math

homework.

Example 6: • Betty spends 0.75 hour running each day. How

many hours does Betty spend running over 7 days?

• Solution:• To find how many hours Betty ran in 7 days,

multiply.

• So, Betty spent 5.25 hours running over 7 days.

Money EXAMPLES OF U.S. CURRENCY Penny (1¢ or $0.01) (one-hundredth of a dollar 1/100 = 0.01)

Nickel (5¢ or $0.05)

Dime (10¢ or $0.10) (one-tenth of a dollar 1/10 = 0.1)

Quarter (25¢ or $0.25)

One Dollar bill ($1.00)

Five Dollar bill ($5.00)

Ten Dollar bill ($10.00)

Twenty Dollar bill ($20.00)

• Example• Mark bought a new CD for $13.37.

If Mark gave the clerk a $20 bill, what is his change, and what kind of change could he get back?

Solution• To figure out how much change he will receive, subtract the cost of

the CD from $20.00.• $20.00 - $13.37 = $6.63• Next, figure out what kind of bills and coins he could receive.

First, he could receive 1 five-dollar bill and 1 one-dollar bill.For coins, because $0.63 is over $0.50, but under $0.75, he could receive 2 quarters, which leaves $0.13.He could receive 1 dime, which leaves $0.03. Since $0.03 is all that is left, he will receive 3 pennies.

• So, his change could be 1 five-dollar bill, 1 one-dollar bill, 2 quarters, 1 dime, and 3 pennies.

Extra Practice

• Charlie and his 10 friends are planning for a pizza part. They purchased 3 quarts of milk. If each glass holds 8oz will everyone get at least one glass of milk?

• Solution:

• 11 people x 8 ounces= 88 total ounces• 1 quart= 2 pints = 4 cups= 32 ounces

• Therefore, 1 quart = 2 pints= 4 cups = 32 ounces• 2 quarts= 4 pints= 8 cups= 64 ounces• 3 quarts= 6 pints= 12 cups = 96 ounces

• If Charlie purchased 3 Quarts (6 pints) of milk, there would be enough for everyone at his part to have at least one glass of milk. IF each person drank 1 glass then he would have 1- 8 ounce glass left over.

• Susan has 2 feet of ribbon. She wants to give her ribbon to her 3 best friends so each friend gets the same amount. How much ribbon will each friend get?

• Solution: • The answer would be 2/3 of a foot or 8 inches

• 1/3 of a foot is 4 inches and 2/3 of a foot is 2 groups of 1/3

• Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40 minutes on Wednesday. What is the total number of minutes Mason ran?

• A pound of apples cost $1.20. Rachel bought a pound and half of apples. If she gave the clerk a $5.00 bill, how much change will she get back?

• Mario and his two brothers are selling lemonade. Mario bought one and half liters, Javier bought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did the boys have?

Core/Workshop

Tuesday, April 29, 2014

1. Samantha measured the classroom at 15 yards. How many INCHES is the classroom?

2. How many lines of symmetry does a regular hexagon have?

Homework Review

Homework Review Cont’d

Area and Perimeter

4.MD.3

Perimeter is the distance around a flat (2-dimensional) shape.

• Formulas: (2xL) + (2xW)• L +L + W + W

Area is the amount of covered up on a flat (2-dimensional) shape.

• Formulas: A= LxW• Represented in square units

• Find the perimeter and area of the rectangle pictured below.

Solution• The perimeter is the sum of all sides of the

rectangle.

• 6 cm + 4 cm + 6 cm + 4 cm = 20 cm• The area of the rectangle is length times

width.• 6 cm × 4 cm = 24 sq cm

• Hannah is making a wall decoration for her room with the letters of her name as shown in the picture. She wants to put a ribbon border around the H. Assuming the figure is symmetric, how much ribbon will she need?

Solution• Since the figure is symmetric, each leg of the H is 10 inches high

on the outside.Minus the one inch on each side of the interior of the legs, so those heights are 9 inches.The perimeter of the figure, the amount of ribbon Hannah needs, is the sum of all measures around the figure.

• 10 in + 3 in + 2 in + 3 in + 10 in + 3 in + 9 in + 2 in + 9 in + 3 in = 54 in

• Example 3• Using the image from Example 1, what is the

area of the figure?

Solution• Each leg is 10 inches by 3 inches.

The middle piece is 2 inches by 1 inch.Each piece is rectangular, so use length times width for the area of each section.

• (10 in × 3 in) + (10 in × 3 in) + (2 in × 1 in) = 30 in2 + 30 in2 + 2 in2 = 62 in2

Find the Area and Perimeter

Find the Area and Perimeter

Find the area and perimeter

Find the Area and Perimeter

• A plan for a house includes rectangular rooms with an area of 60 square meters and a perimeter of 34 meters. What is the length and width of the room? a) Length=12 meter, width = 5 meters b) Length= 60 meters, width = 5 metersc) Length= 20 meters, width = 3 metersd) Length= 15 meters, width= 4 meters

Area and Perimeter Word Problems

• You have a square toy box with a perimeter of 64 feet. What is the area?

a. Extension: If you double the length of each side what happens to the perimeter? What happens to the area?

2) You want to build a fence for your dog. If you have 60 feet of fencing material, what are three possible dimensions of the rectangle? Which of those dimensions gives you the largest area?

• If the area of a square is 36 inches, what is the perimeter?

• The apartment complex next door has a parking lot that is 92 feet wide and 86 feet long. What is the area of the parking lot?

• You want to build a fence for your dog. If you have 60 feet of fencing material, what are three possible dimensions of the rectangle? Which of those dimensions gives you the largest area?

• You have a square with a perimeter of 20 feet. What is the area?

• If you doubled each side, what is the perimeter of the square?

• You have an octagon with a perimeter of 208cm. What is the length of each side?

• You have a rectangle with a length of 29 inches and an area of 1044 square inches. What is the width of the rectangle?

• What is the perimeter of the rectangle?

Core/Workshop

Location Area PerimeterKitchenBathroomBedroom 1Dining Room XXXXXXXCovered PorchBedroom 2Entry HallLiving RoomBack PorchEntire House

Core/Workshop

TenMarks Assignment

Wednesday, April 30, 2014

1. What is the measurement of each fraction if the entire circle is 360 degrees?

2. What type of angle is shown below? What is the measure of the angle?

Homework Review

Homework Review Cont’d

Represent and Interpret Data

4.MD.4

• A dot plot, also called a line plot, is a graph that shows the frequency of data with dots or marks (x).

Example 1:• In a class, the students were asked to journal

about a writing prompt. The following dot plot shows this data. Each dot represents 1 student.

• What is the difference between the longest fraction of a page written and the shortest fraction of a page written?

Solution:• To find the difference between the longest

fraction of a page written and the shortest fraction of a page written, subtract the shortest fraction of a page written 1/4, from the longest fraction of a page written, 3/4.

• So, the difference between the longest fraction of a page written and the shortest fraction of a page written is 2/4 of a page.

Example 2:• Robert works at a deli. The table below shows how much turkey he used

for sandwiches yesterday.

• If each dot represents two sandwiches, which dot plot below matches the table above.

• Bill looked on a map and measured the length of the streets in his neighborhood. The following dot plot shows the lengths of the streets. Each dot represents 1 street.

• What is the length of the two shortest streets combined?

• Susan has a fish tank with many fish in it. She measured each fish and recorded their lengths. The following dot plot shows the data. Each dot represents 1 fish. If the two smallest fish were laid end to end, how long would the two fish be combined?

• Cynthia asked her friends how long it took them to get ready in the morning. The following dot plot shows what she found. Each dot represents 1 friend. What is the difference between the length of time it took the friend who spent the most time getting ready and the length of time it took the friend who spent the least time getting ready?

• Melissa received some money from her parents to get prizes from the prize machines at the grocery store. The prize machines cost different amounts to use. The following dot plot shows the fraction of a dollar each prize costs. Each dot represents 1 prize. If Melissa bought two prizes from the prize machine that costs the most, what fraction of a dollar did she spend?

• Zach's friends live different distances away from his house. The following dot plot shows this data. Each dot represents 1 friend. What is the difference between the distance to his nearest friend's house and the distance to his farthest friend's house?

• At the hardware store, there are bundles of drywall sheets with different thicknesses. The following dot plot shows the number of bundles of drywall the hardware store has for each thickness. Each dot represents 1 bundle of drywall. If Ricky wants to use one sheet of the thinnest drywall and one sheet of the thickest drywall together, how thick would it be?

• Isabella is wrapping presents. The following dot plot shows how much tape she used for the presents. Each dot represents 1 present.How much tape did she use on the two presents that needed the most tape?

• Students were measuring their objects around the room to the nearest ½, ¼, and 1/8 inch. What was the total length of all of the objects that were at least ¼ inch in length?

Core/Workshop

WIKI: Line Plot Fractions (1-12) http://mrnussbaum.com/lpf/

Thursday, May 2, 20141. What is the measure of the missing angle? What kind of angle is shown?

2. The Time Warner Cable Arena can hold 35,000 people at a time. The circus came to town and the table below shows the attendance for the last 5 days. If TMC Arena had been at max capacity, how many more people would have attended in the 5-day period? Day Attendance

1 21,0002 25,3003 19,8004 29,5005 26,300

Homework Review

Homework Review Cont’d

Angles

4.MD.54.MD.64.MD.7

ANGLE CLASSIFICATIONAcute

angles with a measure between 0° and 90°Right

angles which are exactly 90°Obtuse

angles with a measure between 90° and 180°Straight

angles which are exactly 180°

• Angle measures can be added and subtracted from one another. What is the measure of A?

Solution:• From the diagram, notice A is the sum of 75°

and 71°. Write this as an equation and solve for A.

• 75° + 71° = A 146° = A

• What is the measure of B?

Solution:• From the diagram, notice 74°A is the sum of

17° and the measure of B. Write this as an equation and solve for B.

• B + 17° = 74° B + 17° - 17° = 74° - 17° B = 57°

• What is the measure of Z?

• Which of the following is made from combining two rays at their endpoints?

A. a point B. a rayC. a line segmentD. an angle

• The circle below is divided into 6 equal parts. What is the measure of the angle shown by the shaded section?

• Find missing angle HFG. • Is this a complimentary or supplementary

angle?

• Find missing angle JGH• Is this angle supplementary or

complimentary?

Find the missing angle

angle 1 is 55 degrees, what is the measurement for angle 2?

• What is the measurement of the angle shown on the protractor? Classify the angle as obtuse, acute, straight, or reflex. Explain your answer.

• What is the measurement of the angle shown on the protractor? Classify the angle as obtuse, acute, straight, or reflex. Explain your answer

• .If angle BOL equals 60 degrees and angle BOD equals 60 degrees, what is the measurement of angle DOF

Find the missing angle

Find the missing angle

Find the missing angle

Find the missing angle

• About what does this angle measure?– Between 60⁰ and 70⁰– Between 170⁰ and 180⁰– Between 90⁰ and 100⁰– Between 130⁰ and 140

• If the two rays are perpendicular, what is the value of m?

• How many obtuse angles are in the shape below?

Angle Word Problems• A sprinkler rotates one-degree at each interval. If the

sprinkler rotates a total of 100 degrees, how many one-degree turns has the sprinkler made?

• A lawn water sprinkler rotates 65 degrees and then pauses. It then rotates and additional 25 degrees. What is the total degree of the water sprinkler rotation? To cover a full 360 degrees, how many times will the water sprinkler need to be moved?

• Joey knows that when a clock’s hands are exactly on 12 and 1, the angle formed by the clock’s hands measures 30 degrees. What is the measure of the angle formed when a clock’s hands are exactly on the 12 and 5?

• A lawn sprinkler rotates 65 degrees and then pauses. It then rotates an additional 25 degrees. What is the total degree of the water sprinkler rotation? To cover a full 360 degrees how many times will the water sprinkler need to be moved?

Core/Workshop

TenMarks Assignment.On the Wiki..

Using a Protractor (1-12) http://mrnussbaum.com/protractor/Missing Angles (1-10) http://mrnussbaum.com/adjacentangles/

Friday, May 2, 2014

POTD1. Sampson purchased 8 types of cookies. He purchased 15

of each kind. He also purchased some cupcakes, but bought 4 times as many cupcakes as cookies. How many cupcakes did Sampson purchase?

2. Ms. Mohler is having an end of the year throw-down. She

needs 500 pounds of cheese for the hamburgers. At the store, she can only buy 4 and 9-ounce packages. What is the least amount of packages Ms. Mohler can buy and still have enough cheese for the party?

Homework Review

Homework Review Cont’d

Quiz Time