Second Grade Length 2015-12-8 www.njctl.org Slide 3 / 270 Slide - - PDF document

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Second Grade

Length

2015-12-8 www.njctl.org

Slide 3 / 270 Table of Contents Page 1

Measuring in Centimeters Measuring in Feet Measuring in Yards

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Introduction to Length Measuring in Inches Measuring in Meters Measuring with a Ruler Which Unit? Which Tool? Using a Tape Measure Lab: Centimeter Sam

Slide 4 / 270 Table of Contents Page 2

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Length Comparison Measuring in Different Units Line Plots Line Plots pt. 2 Estimating in and ft Estimating cm and m Number Stories on a Number Line Number Line as a Ruler Lab: Ring Toss Lab: Packing Peanut Punt

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Standards for Mathematical Practices

MP8 Look for and express regularity in repeated reasoning. MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure.

Click on each standard to bring you to an example of how to meet this standard within the unit.

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Introduction to Length

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Slide 7 / 270 What is Length?

Length is the distance from one end of an object to the other end. The average lion is 8 1/2 feet long.

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How wide is the classroom using student feet?

Measuring Length Slide 10 / 270

Click the book to hear a reading of How Big is a Foot?, by Rolf Myller. After the story, discuss why the bed made by the carpenter did not turn

• ut how the king expected.

There can be problems when measuring with

• bjects that are not always the same size.

How Big is a Foot? Slide 11 / 270

We can measure with our bodies, or parts of our bodies like the carpenter and the king did with their

• feet. However, it doesn't always work because

people are different sizes. To be accurate, we need to use a standard measuring tool that is always the same size and shape. This is called "standard measurement". The problem in the story is that the king's foot was not the same size as the apprentice's foot!

Slide 12 / 270 Standard Measuring Tools

These tools are in standard units and they are what we use to measure length when we want to have a common understanding of the size of something. Measuring Tape Ruler Yard Stick Meter Stick

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Can you see the units on the ruler and measuring tape? They are marked with hash marks and numbers. Each unit is the exact same length. The units are numbered. Measuring Tape Ruler

What is a Standard Unit?

inch units centimeter units

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There is United States Standard Measurement and Metric Standard Measurement. US Standard Measurement:

• Inches
• Feet
• Yard

Metric Standard Measurement:

• Centimeters
• Meters

We will learn about both types of measurement

Standard Measurements Slide 16 / 270

1 If you measured a length of rope with your feet, and then your friend measured the same length of rope with their feet, will you both get the same length? A Yes B No C Maybe

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2 Pick the two units of measurement that are part of the US Measuring System A feet B meter C inches

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3 A hand is a standard measuring tool. True False

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4 Is a meter part of the US measuring system? Yes No

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5 A tape measure is pictured below. True False

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Measuring with a Ruler

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A ruler is a measuring stick used to measure the length of an object or the distance from one point to another. A standard ruler has 12 evenly spaced segments called "inches".

Ruler

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When using a ruler, we start at the left and read the numbers to the right. A ruler starts at 0. Sometimes, the 0 is not printed on the ruler because it is too close to the end but it still starts with 0. Start with End with 12 Sometimes, the last number on the ruler is missing as well. How would you know which number is missing?

Ruler Slide 26 / 270

From the 0 to the 1 is one inch or 1 centimeter. From the 1 to the 2 is one inch or centimeter. From the 0 to the 2 is two inches or centimeters.

Ruler Slide 27 / 270

Most rulers have markings on the top and the bottom. If you look closely, you should see "in" on one side. This stands for inches. The other side should have "cm". This stands for centimeters. Which unit is longer?

Ruler Slide 28 / 270

When using a ruler to measure the length of an object, place the end of the object along the ruler on the 0 mark. Put your finger on the other end of the object and see which number on the ruler is it closest to. This pencil is 4 inches long. How many centimeters is it?

Ruler Slide 29 / 270

Move the paperclip to measure how long it is.

Ruler Slide 30 / 270

Sometimes we need to use a ruler up and down. Move the boot to measure how tall it is.

Ruler

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Move the dog to measure how long it is.

Ruler Slide 32 / 270

How long is the book?

Ruler Slide 33 / 270 Lab: Classroom Measuring

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6 The ruler is correctly placed to measure the basket. True False

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7 What number is missing from the ruler?

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8 A standard student ruler can measure in ______ and ______. A yards B inches C centimeters

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9 When we measure with a ruler, we start measuring at 1. True False

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10 A standard student ruler ends with ______. A 0 B 12 C 11 D 1

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Measuring in Inches

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An inch is a small standard unit of measurement. The abbreviation for inch is "in". An average thumb is 1 inch from the tip to the knuckle. Can you think of any objects about 1 inch?

Measuring in Inches

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One Inch Tall If you were only one inch tall, you'd ride a worm to school. The teardrop of a crying ant would be your swimming pool. A crumb of cake would be a feast And last you seven days at least, A flea would be a frightening beast If you were one inch tall. If you were only one inch tall, you'd walk beneath the door, And it would take about a month to get down to the store. A bit of fluff would be your bed, You'd swing upon a spider's thread, And wear a thimble on your head If you were one inch tall. You'd surf across the kitchen sink upon a stick of gum. You couldn't hug your mama, you'd just have to hug her thumb. You'd run from people's feet in fright, To move a pen would take all night, (This poem took fourteen years to write-- 'Cause I'm just one inch tall).

By: Shel Silverstein

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• 1. Make sure the ruler has inches on the top

Steps when measuring in inches with a ruler Slide 45 / 270

• 1. Make sure the ruler has inches on the top
• 2. Place the object above the ruler

Steps when measuring in inches with a ruler Slide 46 / 270

• 1. Make sure the ruler has inches on the top
• 2. Place the object above the ruler
• 3. Line up the end of the object to the 0 mark on

the ruler

Steps when measuring in inches with a ruler Slide 47 / 270

• 1. Make sure the ruler has inches on the top
• 2. Place the object above the ruler
• 3. Line up the end of the object to the 0 mark on the

ruler

• 4. Place your finger at the other end of the object

and see which number it is closest to on the ruler

Steps when measuring in inches with a ruler Slide 48 / 270

• 1. Make sure the ruler has inches on the top
• 2. Place the object above the ruler
• 3. Line up the end of the object to the 0 mark on

the ruler

• 4. Place your finger at the other end of the object

and see which number it is close to on the ruler

• 5. Label your measurement

4 inches

Steps when measuring in inches with a ruler

Slide 49 / 270 Practice

How long is the bike?

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How long is the frame?

Practice Slide 51 / 270

How long is the crayon?

Practice Slide 52 / 270

How long is the football?

Practice Slide 53 / 270

Billy said the car is 9 inches long. Is he correct?

Practice Slide 54 / 270

Work with a partner, use your rulers to see if you can find items in the classroom that are about: 2 inches 4 inches 8 inches 10 inches What did we find? 2 in 4 in 8 in 10 in

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Work with a partner to measure the lengths of the following items in inches:

• 1. Workbook
• 2. Desk
• 3. Student Computer
• 4. Bookshelf

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• 1. Workbook: _____ in
• 2. Desk: _____ in
• 3. Student Computer _____ in
• 4. Book Shelf _____ in

What were our measurements?

Should we all have the same or different measurements?

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11 How many inches is this pencil?

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12 About how many inches is this crayon?

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14 Aisha measured this line to be 3 inches. Is she correct? Yes No

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15 Theo measured this line to be 4 inches. Is it really 4 inches? Yes No

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Measuring in Feet

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Slide 65 / 270 Measuring in Feet

Long ago before they had rulers, people used their feet to measure. Today we don't use our own foot as much but we use a standard foot. This ruler is a standard foot. Why do you think they stopped measuring with their actual foot?

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How many inches are in a foot long ruler? How does your foot compare to a foot long ruler? Is it bigger? Is it smaller? Did you know that the largest foot on a human is about 15 inches long! Now that's huge! A standard foot is larger than an inch. The abbreviation for foot is ft.

Measuring in Feet

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First, trace your foot on paper. Then, cut out the traced foot. Next, measure it with a ruler. How many inches long is it?

How Long is My Foot? Slide 68 / 270

Use both your foot and a ruler to measure these objects. Width of door Window White board/ Chalkboard Table

Measure Objects Slide 69 / 270

Student Feet Actual Feet Door Window Board Table

Use the chart to document your findings Slide 70 / 270

16 A foot is larger than an inch. True False

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17 A standard foot is ______ inches.

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18 Which items could you measure in feet? A eraser B car C couch D plate

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19 A standard student ruler is 1 foot. Yes No

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20 Twelve ______ equals 1 foot. A feet B centimeters C inches D yards

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Measuring in Yards

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The class is going to work together to measure some distances around the school in yards. Let's measure the length of:

• Our classroom, first the longer wall, then the

shorter wall

• The length of the hallway
• The length of the cafeteria/gym

Measuring in Yards Slide 81 / 270

Classroom Longer wall __________ yards Shorter wall __________ yards Hallway __________ yards Cafeteria __________ yards

Results

Should we all have the same measurements or different?

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21 A yard is ______ than a foot. A shorter B longer

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22 Which items could you measure in yards? A shoe B football field C house D cat

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23 How many feet are in a yard?

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24 There are more feet than inches in a yard. True False

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25 Would it be a good idea to measure a room in yards? Yes No

Quiz

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Measuring in Centimeters

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Centimeters are part of the metric measurement system. A centimeter is about half the size of an inch. The abbreviation for centimeter is cm. A fingernail is about 1 cm wide. 1 cm

Measuring in Centimeters

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Let's brainstorm some items that you think might be 1 cm.

Centimeters Slide 92 / 270

We measure centimeters with a ruler just like we measure inches.

• 1. Make sure the ruler has centimeters on the top
• 2. Place the object above the ruler
• 3. Line up the end of the object to the 0 mark on the ruler
• 4. Place your finger at the other end of the object and see

which number it is close to on the ruler

• 5. Label your measurement

11 cm

Measuring in Centimeters Slide 93 / 270 Practice

How long is the foot?

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How long is the ant?

Practice Slide 95 / 270

How long is the pencil?

Practice Slide 96 / 270

How long is the fork?

Practice

Slide 97 / 270 Measuring in centimeters

A playing card _____ cm. An unsharpened pencil _____ cm. A book _____ cm.

Slide 98 / 270 What were our measurements?

• 1. Playing Card:

_____ cm

• 2. Pencil:

_____ cm

• 3. Book

_____ cm

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26 Max used his centimeter ruler to measure this line. How long is it in centimeters? A 8 cm B 18 cm C 17 cm D none of the above

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

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27 Yolanda used her ruler to measure this line. She thinks it is 14 cm long. Is she correct? Yes No

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28 How many centimeters long is this line?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

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29 How many centimeters long is this line?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

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30 Eric found a broken ruler and used it to measure a line. How long do you think it is? A 6 cm B 10 cm C 5 cm D 16 cm

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Slide 104 / 270 Lab: Centimeter Sam

Click here for complete directions Students will practice measuring in centimeters.

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Measuring in Meters

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100 centimeters = 1 meter

Meters

To measure something a little larger in metric units, use meters. The abbreviation for meter is m. What are some thing we can measure using meters?

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Measuring with the centimeter rulers when you are measuring something long is not as efficient as it can

• be. This is why we have meter sticks. They are longer

than centimeter rulers and are more efficient when you want to measure something longer.

Measuring with Meter Sticks Slide 110 / 270

Let's try both! First, we will measure something really long in centimeters and use a centimeter ruler. Next, let's measure the same thing we measured with the centimeter ruler but this time in meters with a meter stick. What did you notice? Was it more efficient to measure long things with a meter stick? Note: We can use a meter stick to measure centimeters too. When it would be best to use a meter stick?

Centimeter Ruler or Meter Stick Slide 111 / 270

Usually, measuring things that are long work better with a longer tool like a meter stick. Let's list other objects in the classroom that we can measure with a meter stick.

Centimeter Ruler or Meter Stick Slide 112 / 270

The class is going to work together to measure some distances around the school in meters, just like we did with yards. Let's measure the length of:

• Our classroom, first the longer wall, then the

shorter wall

• The length of the hallway
• The length of the cafeteria/gym

Measuring in Meters Slide 113 / 270

Classroom Longer wall __________ meters Shorter wall ________ meters Hallway _________ meters Cafeteria __________ meters Should we all have the same measurements or different?

Practice Slide 114 / 270

31 Which of the objects below would you use a meter stick to measure? A An eraser B A pencil C A hallway D A cat

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32 Which object is best to measure with a centimeter ruler? A a book B a hallway C a white board D a room

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33 If the height of the door was measured in centimeters and in meters, which would there be more of? A centimeters B meters

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34 Tony measured his toy car and got 6 meters. Is he correct? Yes No

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35 Many second graders are more than 1 meter tall but less than 2 meters tall. True False

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Using a Tape Measure

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Slide 122 / 270 Using a Tape Measure

Here are two different types of tape measures. This type is made from metal. Many people who build things like to use this kind because it can be really short like in the photograph

• r it can be pulled out to measure

things really long. This type is made from cloth and is useful for measuring things that are curved or round.

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When we want to measure things that are round, we use a cloth measuring tape. 1) First, make sure you know what unit you are measuring in. (This photo shows measuring in inches.) 2) Next, wrap it around what you are measuring. 2) Carefully, see where the end that represents zero is touching the measuring tape. In this case, this wrist is 7 inches around.

Tape Measure Slide 124 / 270

What objects around the room could we measure with a tape measure. Many cloth tape measures have centimeters on one side and inches on another.

Tape Measure Slide 125 / 270

We can also use a tape measure to measure very long

• bjects.

A builder will use a tape measure to very large

• bjects. Maybe they need to measure the

height of a door or how long a table is. Can you think of some large objects that you could use a tape measure to measure?

Tape Measure Slide 126 / 270

A lot of times, a seamstress will use a tape measure to measure a person he is making clothes for. Besides on measure around all the different parts of the body, they also need to measure how tall the person is. Let's use a tape measure to measure our bodies!

Tape Measure

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Measure the length around your partner's neck, wrist, ankle, and head in inches and centimeters. Neck Ankle Wrist Head

Measuring Our Body

Object Measured Inches Centimeters neck wrist ankle head

Record your measurements on the worksheet

Teacher Notes & Math Practice

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36 A tape measure is used to measure objects that do not bend. True False

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37 Is it better to use a tape measure or a ruler to measure your wrist? A tape measure B ruler

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38 Do you line the end of the tape measure up to the 1 to get a final measurement? Yes No

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Which Unit? Which Tool?

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Slide 134 / 270 Which Tool Should We Use?

We have learned about each of the tools below. Under each item list things that can be measured using each. Ruler Tape Measure Yard stick

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Before we decide which tool to use, we need to decide which unit we will be measuring in. First, will us be using the US measurements or Metric? Second, the length of the object helps decide which unit to use. Very large objects are better measured with larger units such as yards or

• meters. A football field is measured in yards.

Small objects will be measured with inches or centimeters.

Which Unit? Slide 136 / 270 Which Tool?

Once you know what unit you will be measuring in, pick your tool. If you are measuring in inches or centimeters and it is small, pick a ruler. If you need to measure in inches or centimeters and it is a longer, pick a tape measure or yard/meter stick. When measuring larger items, most of the time a tape measure or yard/meter stick is best.

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Pedro and Carla want to build a playhouse

• ut of cardboard. They want it to be about

the length of a long table. They also want to cut windows out so that their heads could easily fit through them. What measurement tools would you suggest Pedro and Carla use to build the house and to cut windows out? Draw a picture and use words and numbers to explain your thinking.

Building a Playhouse Slide 138 / 270

39 Which tool would be best to measure a room with? A standard ruler B your foot C a yard stick

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40 It is best to measure a pencil in ______ or ______. A feet B inches C meters D centimeters

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41 You should use a yard stick to measure a penny. True False

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42 Which tool should Bob use to measure the soccer ball? A standard ruler B tape measure C yard stick

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43 Which objects would you measure with a yard stick? A eraser B football field C large window D book E classroom rug

Quiz

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Length Comparison

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Slide 146 / 270 How Much Longer?

We often want to know how much longer something is. When you measured your neck, wrist, ankle, and head didn't you want to know how much longer (or shorter) your measurement was compared to your friend's? When comparing two measurements, we simply subtract.

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First, make sure you measure the two items you are comparing in the same unit (inches, centimeters, feet, etc). Then, measure both objects and record the measurement. Last, subtract the smaller measurement from the larger measurement.

How Much Longer? Slide 148 / 270 Let's Try it

Pick any book from your desk and measure it in inches with your ruler.

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Next, write down your measurement. Don't forget to write in. for inches after the number. This tells everyone what unit you measured in. My book is 6 inches. Then, ask someone close to you what their book length is in

• inches. Write it down.

Beth's book is 10 inches.

How Much Longer? Slide 150 / 270

Subtract the smaller measurement from the larger one. 1 0

• 6

smaller measurement larger measurement 4 You book is 4 inches smaller than your partner's book.

• r

Your partner's book is 4 inches longer than your book.

How Much Longer?

Slide 151 / 270 Did you know?

Did you know that Robert Wadlow, the tallest man ever, had hands that measured a little more than 32 cm long from the wrist to the tip of his middle finger. How much longer were his hands than yours? Measure your hand with your ruler!

Slide 152 / 270 How Much Longer Practice

The green frog hopped a distance of 21 cm. The red frog hopped a distance of 15 cm. How much farther did the green frog hop? Let's work through it on the next page.

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Step one: What unit are you using? Step two: Measure and write down the measurements. (Since they already told us the measurements we do not have to measure) Step three: Subtract Answer:

How Much Longer? Slide 154 / 270 How Much Longer Practice

Work to solve these problems. Be ready to share your solution. The Book was 12 in. high and 6 in. wide. How much longer is the height than the width? Elisha's ribbon is 11 feet long. Joann's ribbon is 18 feet. How much shorter is Elisha's ribbon? Doug had a piece of rope that was 65 cm long. He needed one that was 100 cm long. How much more longer was the rope he needed?

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44 Rabbit jumped 20 cm. Frog jumped 12 cm. How many more centimeters did rabbit jump? A 32 cm B 20 cm C 8 cm D 12 cm

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45 The largest foot in the world is about 38 cm. If Kyle's foot is 18 cm long, how much shorter is his foot? A 20 cm B 38 cm C 18 cm D None of the above

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46 Melissa was cutting string for a bracelet. Her string was 40 cm long. She cut 10 cm off to make it shorter. How long is the string for her bracelet now? ___ cm

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47 Look at the rectangle. How much longer is the longest side? 15 cm 7 cm

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48 Compare these two lines. How much shorter is the red line? 20 cm 31 cm

Slide 160 / 270 Lab: Lord of the Ring Toss

Click here for complete directions Students get points for a “ringer”, but also get points for getting close (like in horseshoes). To get their score, students need to measure distance to the rings in Metric.

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Measuring in Different Units

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Jim measured the pencil and got a measurement of 4. John measured the same pencil and got a measurement of 10. Why do they have different measurements?

Different Units Slide 165 / 270

Inches Centimeters Which are bigger, inches or centimeters? Which ruler shows more numbers?

Different Units Slide 166 / 270

When we measure an object using two different units, we will get two different measurements. The smaller the unit, the more units in a measurement. Since, centimeters are smaller than inches, an

• bject will have more centimeters than inches

when measured. A standard soccer ball is: 27 inches around 69 centimeters around

Different Units Slide 167 / 270

Why are there fewer yards than feet on a football field? A football field is:

• 100 yards
• 300 feet

Different Units Slide 168 / 270 Comparing Measurements in Centimeters and in Inches

Assign each student a partner. Each pair needs a centimeter ruler, an inch ruler, a sheet of white paper, a bag with a new eraser, a new crayon, and a new pencil. Assign partners 'A' and 'B'. A will measure in inches, B will measure in centimeters. Students will record the measurements in inches and in centimeters on the "Different Unit Different Measurement" chart.

Slide 169 / 270 Are there more inches or centimeters?

Discuss with your partner what patterns you see in your measurements using different units. "For each object, the number of inches is always______________. The number of centimeters is always __________________." "The smaller the unit means ______________________________. The bigger the unit means _______________________________."

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49 Kim measured her bike in feet and said her bike was 3 feet long. Then she wanted to measure her bike in

• inches. Before she measured it, she predicted that her

bike would have less inch units than feet units. Is she correct? Yes No

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50 Jessica measured her book in inches. Josh measured the same book in centimeters. Who would get a higher number? A Jessica B Josh

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51 Tom's pencil is 6 inches. Jose's pencil is 11 centimeters. Jose said his pencil is longer since he got a higher

• number. Is he correct?

Yes No

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52 Centimeters are bigger than inches. True False

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53 If you measure the same object in feet and inches. Would you have more feet or inches in your final measurements. A feet B inches

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Estimating Inches and Feet

Slide 178 / 270 Estimation

We don't always have a measuring tool with us when we need to measure something! Sometimes estimating the length of something is good enough. When you estimate the length of something you make a close guess about how long it might be.

Slide 179 / 270 Benchmark for an Inch

Try holding your thumb and index finger so that they are about an inch apart. Now, measure that space with a ruler. Adjust it as needed to come closer to an inch. Once you know this distance, it can be a benchmark for estimating length in inches.

Slide 180 / 270 Try it!

1) Estimate the length of your folder in inches. Then, measure it with your ruler. How close were you to the actual measure? 2) Now estimate the length of your pencil. Think about your measurement of the folder. How can it help you with your pencil estimate? Then, measure it with your ruler. As you practice this way, you will strengthen your ability to estimate in inches!

Slide 181 / 270 Benchmark for a Foot

As we make benchmarks for one foot, we need to think about things that we know well that are about a

• foot. This might be a part of your body!

Use a foot long ruler to find a body part that you can use as a benchmark.

Slide 182 / 270 Try it!

1) Estimate the length of your desk in feet. Then, measure it with your ruler. How close were you to the actual measure? 2) Find something longer than your desk. How can your desk measurement help you with the next estimate? Estimate the new object in feet. Then, measure it with your ruler. As you practice this way, you will strengthen your ability to estimate in feet too! Just as we tried out our estimates in inches, we will do the same in feet.

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54 If someone said your front door was about 3 inches wide, would that be a good estimate? Yes No

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55 What would be a good estimate for the height of the classroom door? A 7 feet B 7 inches C 7 yards

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56 In a book you were reading, the author describes a hole that was 2 inches wide. Choose two animals below that may be able to fit into it. A A lion B a mouse C a bear D a snake

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57 Many adults are between 5 and 6 ___ tall. Choose the best answer that fits in the blank. A inches B feet C yards

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58 It is best to estimate a pencil in A inches B feet C yards

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Estimating in Centimeters and Meters

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Slide 191 / 270 Estimating with Centimeters and Meters Creating Benchmarks

In How Big is a Foot?, the carpenter used his feet to

• measure. Some people still use other parts of their

bodies to measure things when they don't need an exact length. One way we learn to be good estimators is by creating

• benchmarks. What is a benchmark? A benchmark is a

measurement we use to estimate length. We use this benchmark to come close to the measurement of something else. Let's make some benchmarks together!

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2) Next, measure the index card with a cm ruler. How close were you to the actual measurement? How can you figure this out?

1 cm

Look at the width of your pointer finger. Hold it up to your centimeter ruler. Notice that it is about the same

• width. Your finger is about 1 cm wide. How can we use

this benchmark to help us make an estimation? To do: 1) Take an index card and use the width of your index finger to measure the length of the

• card. Share your estimate.

Your finger as a benchmark

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Now, you can use this benchmark to estimate other things. If you knew an eraser was about 6 cm long, and you wanted to estimate the length of a pencil that was a little longer than the eraser, what might your estimate be? 4 cm? Why or why not? 20 cm? Why or why not? 12 cm? Why or why not?

An eraser as a benchmark

To Do: 1) Use your finger to estimate how long the eraser is. Share it with others. 2) Next, measure the eraser with a cm ruler. How close were you to the actual measurement? How can you figure this out? Your eraser can now be a benchmark.

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Another benchmark you can use is the length of your hand

• span. Stretch your thumb and pinky finger as far as they can
• go. This is your hand span.

Once you know the length of your hand span, you can use that to estimate the length of longer objects.

Your hand span as a benchmark

To Do: 1) Put your hand span on a paper and mark where this span starts and ends. Draw a line between the marks. How long do you think your hand span is in centimeters? 2) Measure the length of your hand span with a cm ruler. Click here for a ten second video clip of using hand spans to measure on YouTube.

Slide 195 / 270 Longer Benchmarks: Your Arm span

Stretch out your arms from side to side. This is your arm span. How long do you think your arm span is in meters? Using a meter stick, work with a partner to compare the length

• f your arm span to a meter. Is it longer? Shorter?

Once you know if your arm span is longer or shorter than a meter, you can use it as a benchmark.

Slide 196 / 270 A doorknob's height can be a longer benchmark

Your benchmark: the doorknob is about 1 meter from the floor If you knew the doorknob was about one meter from the floor, and you wanted to estimate the height of the ceiling, what might your estimate be? 2 m? Why or why not? 10 m? Why or why not? 3 cm? Why or why not?

Slide 197 / 270

Tito is measuring things in his bedroom. He thinks his bed is about 5 meters. Is this a reasonable estimate? Explain your answer using pictures, words or numbers.

Word Problem Slide 198 / 270

59 A good estimate for the height of a door might be A 2 cm B 2 m C 20 cm D 20 m

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60 A good estimate for the length of the envelope is 20 ____. A cm B m

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61 A good estimate for the height of a basketball hoop is 3 ___. A cm B m

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62 A benchmark for estimating a centimeter is A the width of your finger. B your arm span.

Slide 202 / 270

63 It is best to estimate the width of your desk in meters. True False

Quiz

Slide 203 / 270 Lab: Packing Peanut Punt

Students estimate and measure how far they can punt a packing peanut! Click here for complete directions

Click to return to Table of Contents

Slide 204 / 270

Slide 205 / 270 Slide 206 / 270

Number Line as a Ruler

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Slide 207 / 270 Number Lines

You may have used number lines before. There are many different kinds!

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10

The numbers can be written on the top Number lines are useful for many things. You can count with

• them. You can measure with some. You can add or subtract

with them.

40 65 50

Some don't start with zero.

• r the bottom.

Slide 208 / 270

0 1 2 3 4 5 6 7 8 9 10

The numbers get bigger as you go to the right. The distance between the hash marks must be equal. When we draw a number line, first we put a little mark at the end. This is called a hash mark. We label it 0. A number line often has arrows at the ends. This shows that numbers can go on and on forever.

Number Lines Slide 209 / 270 Missing Points on a Number Line

A ruler is a type of number line. Some number lines do not have all of the numbers written in. What missing number does each endpoint represent?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

The left endpoint is missing 0 and the other endpoint is missing 30.

click to reveal

Slide 210 / 270

10

30

Number lines don't have to start at zero. Until now, our endpoint has been zero. It didn't disappear, we just aren't using it right now. What number would be in the middle of this number line? What are some strategies you can use to find out?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

We can also zoom in to see only part of the number line.

Number Lines

Slide 211 / 270

Some number lines label a missing number with a letter.

10 30

A B What are the values of point A and point B? How do you know? Point A is 14 and point B is 28. Since there is

• ne unit in between each hash mark, you can

count up by ones to find the value of point A. You can count down by ones to find the value of point B. Click to reveal answer.

Number Lines Slide 212 / 270

50 70 A B

Remember, number lines don't have to start at zero. Point A is located right in the middle of 50 and 70. What is the value of A? The value of point A is 60. Click to reveal the answer Point be is right in the middle of point A and 70. What is the value of B? The value of point B is 65. Click to reveal the answer

Number Lines Slide 213 / 270

The hash marks on number lines are always spaced in equal units but the units are not always in ones.

20 40 A

A is half way between 20 and 40. 30 is in the middle of 20 and 40 so A must be 30. Therefore, the equal units are worth 10. Click to reveal the answers Look carefully at the number line below. What do you think the units are between the hash marks? What is the value of A?

Unit Spacing Slide 214 / 270

40 65 B 50

The more numbers that are given, the easier it is to figure

• ut the unit value.

The number line below has six hash marks. How many unit lengths are there? What is the value of B?

Unit Value Slide 215 / 270

Some number lines might only give you one number and tell you the unit length. Draw this number line. How many unit lengths do you see?

100

C If you know that the length of each unit is 10, what is the value of endpoint C? 75 D In this number line the length of each unit is again 10. What is the value of the start point D?

Unit Value Slide 216 / 270

You can also find the difference between two points.

10

30 A

The difference between two points is shown with the arrow. How can we find the difference?

B

Distance Between Points

Slide 217 / 270

10

30 A B

First, we must figure out A and B. We know the line is counting up by 1 since if we start and 10 and count by ones we will land on the 30 hash mark when we say 30. So, A is 13 and B is 27. We can then count the spaces between 13 and 27. 13 + ? jumps = 27. We can also use subtraction. 27 - 13 = the difference

Distance Between Points Slide 218 / 270

What is the difference in points A and B below?

40 65 B 50 A

0 1 2 3 4 5 6 7 8 9 10

A B 20 50 40 30 60 A B

Distance Between Points Slide 219 / 270

Beth, Dan, and Richard are jumping rope. Beth and Dan are standing 20 feet apart to turn the rope. Richard is jumping in the middle of them. If Richard is standing the same distance from Beth and Dan, how many feet is Richard from Beth?

Word Problem Slide 220 / 270

64 How many unit lengths are on this blank number line?

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65 What is the value of A? A 30 B 35 C 40 D 50

20 60 A

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66 What is the value of point C? A 90 B 82 C 85 D 100

60 80 C

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67 What is the unit length for this number line?

60 80

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Number Stories on a Number Line

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Slide 227 / 270

Number lines are can help us add measurements or find the difference between measurements. Suppose we are looking at a piece of wood that is 3 feet

• long. We need a second piece that is 6 feet longer. How

long does the second piece of wood need to be? How could use the number line to help?

0 1 2 3 4 5 6 7 8 9 10

Number Stories Slide 228 / 270

0 1 2 3 4 5 6 7 8 9 10

One way is to start at 3 because that is how long the first piece of wood was. Place a dot to mark our start. Then, we move 6 more to show the second piece of wood that has to be, "six feet longer." Our second piece of wood needs to be 9 feet long.

Number Stories

Slide 229 / 270

Dylan built a tower that was two feet tall. His friend Rick later helped him build a tower four feet taller. How tall was the second tower? How would you show this on the number line?

0 1 2 3 4 5 6 7 8 9 10

Practice Slide 230 / 270

Sometimes we have problems that have bigger numbers. We can start with a blank number line and fill it in to suit our needs. In a game of football, the quarterback had the ball on the 10 yard line. He threw it 30 more yards. Where is it now? How might you use the blank number line below?

Number Stories Slide 231 / 270

Remember, the unit lengths don't have to be one. In this case you can count up by tens. You can write an addition sentence to show throwing the ball 30 more yards from the 10 yard line. It would look like this:

Unit Length Slide 232 / 270

We may also have problems where it works better to go up by fives. In another football game, the quarterback threw the ball from the 15 yard line. He threw it 25 more yards. Where is it now? What number should you start the number line with? What should the hash length be? Try it?

Unit Lengths Slide 233 / 270 Practice

Kyle's dad is 72 inches tall. Tom's dad is 75 inches tall. How much taller is Tom's dad than Kyle's dad?

Slide 234 / 270

Jen jumped 2 feet. Jill jumped 4 feet more than Jen. How far did Jill jump?

Practice

Slide 235 / 270

Hank built a tower that was 75 centimeters

• tall. Matt added another 20 centimeters to the
• tower. How tall is the tower?

Practice Slide 236 / 270

Alexis walked 30 meters on a trail. She turned

• ff the trail and went on a different trail that

was 70 meters. How much longer was the second trail?

Practice Slide 237 / 270

68 What is the difference between point A and point B? A 6 B 5 C 4 D 9

0 1 2 3 4 5 6 7 8 9 10

A B

Slide 238 / 270

69 Len was using a number line to show 40 less than 90. Is he starting correctly? Yes No

Slide 239 / 270

70 John had a rope 65 inches long. He tied a 15 foot rope onto it. How long is the rope now?

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71 Kim was knitting a scarf. So far it was 40 inches long. She needed to add 35 more inches. How long would her scarf be then?

Slide 241 / 270

72 Kathy wanted to solve 40 more than 10. Is she starting correctly? Yes No

Slide 242 / 270 Slide 243 / 270 Slide 244 / 270

Line Plots

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Slide 245 / 270

When we used a tape measure, we measured our heights. Was everyone the same height? How many people were 47 inches? How many people were taller than 49 inches? All of our measurements are called data. We can organize our data on a line plot to make it easier to analyze it.

Line Plots Slide 246 / 270

A line plot charts data on a number line with a dot or other mark to show the frequency.

1 2 3 4 5 Number of Siblings

The line plot is labeled tell us what data we are looking at. Each dot tells us how many times a number occurs in the data. The dot is placed above the number of siblings a student has.

Line Plots

Slide 247 / 270

1 2 3 4 5 Number of Siblings

Analyze the Data

How many students have 4 siblings? Which number of siblings is the greatest? Which number of siblings are the same? How many students would have 3 siblings if an additional student was added?

Slide 248 / 270

Student in. Bobby 47 Jessica 44 Henry 46 Lila 48 Cole 44 Leah 46 Bill 44

Line Plots for Height

Class Heights in Inches 44 45 46 47 48

When we are drawing our own line plot, it is sometimes easier to draw an x. Place an x on the line plot to present each height. Make sure to line them up right

• n top of each other for students

that are the same height.

x

Teacher Notes

Slide 249 / 270 Our Class Height Data

Class Height

Slide 250 / 270

73 How many students have pencils that are 6 inches long? Pencil Length in inches 4 5 6 7 8

x x x x x x x x x x x x

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74 Do more kids have pencils 5 inches long or 6 inches long? A 5 inches B 6 inches Pencil Length in inches 4 5 6 7 8

x x x x x x x x x x x x

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75 Do 4 kids have pencils greater than 6 inches? Yes No Pencil Length in inches 4 5 6 7 8

x x x x x x x x x x x x

Slide 253 / 270

76 It is not important to label a line plot. True False

Slide 254 / 270

77 How tall are most flowers? A 14 inches B 12 inches C 16 inches D 11 inches 11 12 Flower Height (in) 13 14 15 16

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Line Plots Part 2

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Slide 258 / 270

What information can you gather from the line plot below?

Number of Pets in Our Class 1 2 3 4 5

What is a line plot?

Slide 259 / 270 Measuring Arm Spans Slide 260 / 270

Name Arm Span in cm

Many times when we gather data, we want to keep it

• rganized. One way to do this is to use a chart.

The chart below has a place for each child's name and their arm span measurement.

Slide 261 / 270

Class Arm Spans in Centimeters You can then use your chart to make the line plot.

Slide 262 / 270 Head Circumference

Imagine that we had to make hats for everyone in

• class. We would have to know what different size

heads we have. For this line plot we will be measuring

• ur head in inches.

Let's gather data! We will use a tape measure to do this. When you get your measurement, record it on paper. Then, we will make our line plot on the next slide.

Slide 263 / 270

Class Head Circumferences in Inches Sometimes, the title for the line plot is on the top. What is missing from the line plot?

Line Plot Title Slide 264 / 270

78 Line plots are used to show the frequency of a measurement. True False

Slide 265 / 270

79 How many kids have 2 siblings? 1 2 3 4 5 Number of Siblings

Slide 266 / 270

80 Five or more students have ____ or ____ siblings. (Pick 2 answers.) A 3 B 1 C 2 1 2 3 4 5 Number of Siblings

Slide 267 / 270

81 Two students have ______ siblings. 1 2 3 4 5 Number of Siblings

Slide 268 / 270

82 The longest foot is 10 inches. True False Foot Length in Inches 8 9 1 11 1 2 1 3

Quiz

Slide 269 / 270 Slide 270 / 270