Second Grade. Slide 1 / 270. Slide 2 / 270. Slide 3 / 270. Length. Table of Contents Page 1

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1 Slide 1 / 270 Slide 2 / 270 Second Grade Length Table of Contents Page 1 Introduction to Length Measuring with a Ruler Measuring in Inches Measuring in Feet Measuring in Yards Measuring in Centimeters Lab: Centimeter Sam Measuring in Meters Using a Tape Measure Which Unit? Which Tool? Click on the topic to go to that section. Slide 3 / 270

2 Slide 4 / 270 Table of Contents Page 2 Click on the topic to go to that section. Length Comparison Lab: Ring Toss Measuring in Different Units Estimating in and ft Estimating cm and m Lab: Packing Peanut Punt Number Line as a Ruler Number Stories on a Number Line Line Plots Line Plots pt. 2 Standards for Mathematical Practices Slide 5 / 270 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. MP8 Look for and express regularity in repeated reasoning. Click on each standard to bring you to an example of how to meet this standard within the unit. Slide 6 / 270 Introduction to Length Click to return to Table of Contents

3 What is Length? Slide 7 / 270 Length is the distance from one end of an object to the other end. The average lion is 8 1/2 feet long. Slide 8 / 270 Measuring Length Slide 9 / 270 How wide is the classroom using student feet?

4 Slide 10 / 270 How Big is a Foot? There can be problems when measuring with objects that are not always the same size. 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 out how the king expected. The problem in the story is that the king's foot was not the same size as the apprentice's 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". Standard Measuring Tools Slide 12 / 270 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. Yard Stick Ruler Measuring Tape Meter Stick

5 What is a Standard Unit? 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. inch units Ruler Slide 13 / 270 centimeter units Measuring Tape Slide 14 / 270 Standard Measurements Slide 15 / 270 There is United States Standard Measurement and Metric Standard Measurement. We will learn about both types of measurement US Standard Measurement: - Inches - Feet - Yard Metric Standard Measurement: - Centimeters - Meters

6 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? Slide 16 / 270 A Yes B No C Maybe 2 Pick the two units of measurement that are part of the US Measuring System Slide 17 / 270 A feet B meter C inches 3 A hand is a standard measuring tool. Slide 18 / 270 True False

7 4 Is a meter part of the US measuring system? Slide 19 / 270 Yes No 5 A tape measure is pictured below. Slide 20 / 270 True False Slide 21 / 270

8 Slide 22 / 270 Slide 23 / 270 Measuring with a Ruler Click to return to Table of Contents Ruler Slide 24 / 270 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".

9 Ruler Slide 25 / 270 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 0 End with 12 Sometimes, the last number on the ruler is missing as well. How would you know which number is missing? Ruler From the 0 to the 1 is one inch or 1 centimeter. Slide 26 / 270 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?

10 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.

11 Ruler Slide 31 / 270 Move the dog to measure how long it is. Ruler How long is the book? Slide 32 / 270 Slide 33 / 270 Lab: Classroom Measuring Click to return to Table of Contents

12 6 The ruler is correctly placed to measure the basket. Slide 34 / 270 True False 7 What number is missing from the ruler? Slide 35 / A standard student ruler can measure in and. Slide 36 / 270 A yards B inches C centimeters

13 9 When we measure with a ruler, we start measuring at 1. Slide 37 / 270 True False 10 A standard student ruler ends with. Slide 38 / 270 A 0 B 12 C 11 D 1 Slide 39 / 270

14 Slide 40 / 270 Slide 41 / 270 Measuring in Inches Click to return to Table of Contents Measuring in Inches Slide 42 / 270 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?

15 One Inch Tall Slide 43 / 270 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 Steps when measuring in inches with a ruler Slide 44 / Make sure the ruler has inches on the top Steps when measuring in inches with a ruler Slide 45 / Make sure the ruler has inches on the top 2. Place the object above the ruler

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

17 Practice Slide 49 / 270 How long is the bike? Practice Slide 50 / 270 How long is the frame? Practice How long is the crayon? Slide 51 / 270

18 Practice Slide 52 / 270 How long is the football? Practice Slide 53 / 270 Billy said the car is 9 inches long. Is he correct? Work with a partner, use your rulers to see if you can find items in the classroom that are about: Slide 54 / inches 4 inches 8 inches 10 inches What did we find? 2 in 4 in 8 in 10 in

19 Work with a partner to measure the lengths of the following items in inches: 1. Workbook 3. Student Computer Slide 55 / Desk 4. Bookshelf What were our measurements? Slide 56 / Workbook: in 2. Desk: in 3. Student Computer in 4. Book Shelf in Should we all have the same or different measurements? 11 How many inches is this pencil? Slide 57 / 270

20 12 About how many inches is this crayon? Slide 58 / 270 Slide 59 / Aisha measured this line to be 3 inches. Is she correct? Slide 60 / 270 Yes No

21 15 Theo measured this line to be 4 inches. Is it really 4 inches? Slide 61 / 270 Yes No Slide 62 / 270 Slide 63 / 270

22 Slide 64 / 270 Measuring in Feet Click to return to Table of Contents Measuring in Feet Slide 65 / 270 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? Measuring in Feet A standard foot is larger than an inch. The abbreviation for foot is ft. How many inches are in a foot long ruler? Slide 66 / 270 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!

23 How Long is My Foot? Slide 67 / 270 First, trace your foot on paper. Then, cut out the traced foot. Next, measure it with a ruler. How many inches long is it? Measure Objects Use both your foot and a ruler to measure these objects. Slide 68 / 270 Width of door Window White board/ Chalkboard Table Use the chart to document your findings Slide 69 / 270 Student Feet Actual Feet Door Window Board Table

24 16 A foot is larger than an inch. Slide 70 / 270 True False 17 A standard foot is inches. Slide 71 / Which items could you measure in feet? Slide 72 / 270 A eraser B car C couch D plate

25 19 A standard student ruler is 1 foot. Slide 73 / 270 Yes No 20 Twelve equals 1 foot. Slide 74 / 270 A feet B centimeters C inches D yards Slide 75 / 270

26 Slide 76 / 270 Slide 77 / 270 Measuring in Yards Click to return to Table of Contents Slide 78 / 270

27 Slide 79 / 270 Measuring in Yards Slide 80 / 270 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 Results Slide 81 / 270 Classroom Longer wall Shorter wall yards yards Hallway yards Cafeteria yards Should we all have the same measurements or different?

28 21 A yard is than a foot. Slide 82 / 270 A shorter B longer 22 Which items could you measure in yards? Slide 83 / 270 A shoe B football field C house D cat 23 How many feet are in a yard? Slide 84 / 270

29 24 There are more feet than inches in a yard. Slide 85 / 270 True False 25 Would it be a good idea to measure a room in yards? Slide 86 / 270 Yes No Quiz Slide 87 / 270

30 Slide 88 / 270 Slide 89 / 270 Measuring in Centimeters Click to return to Table of Contents Measuring in Centimeters Slide 90 / 270 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

31 Centimeters Slide 91 / 270 Let's brainstorm some items that you think might be 1 cm. Measuring in 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 Practice Slide 93 / 270 How long is the foot?

32 Practice Slide 94 / 270 How long is the ant? Practice Slide 95 / 270 How long is the pencil? Practice Slide 96 / 270 How long is the fork?

33 Measuring in centimeters Slide 97 / 270 A playing card cm. An unsharpened pencil cm. A book cm. What were our measurements? Slide 98 / Playing Card: cm 2. Pencil: cm 3. Book cm 26 Max used his centimeter ruler to measure this line. How long is it in centimeters? Slide 99 / 270 A 8 cm B 18 cm C 17 cm D none of the above

34 27 Yolanda used her ruler to measure this line. She thinks it is 14 cm long. Is she correct? Slide 100 / 270 Yes No How many centimeters long is this line? Slide 101 / How many centimeters long is this line? Slide 102 /

35 30 Eric found a broken ruler and used it to measure a line. How long do you think it is? Slide 103 / 270 A 6 cm B 10 cm C 5 cm D 16 cm Lab: Centimeter Sam Slide 104 / 270 Students will practice measuring in centimeters. Click here for complete directions Click to return to Table of Contents Slide 105 / 270

36 Slide 106 / 270 Slide 107 / 270 Measuring in Meters Click to return to Table of Contents Meters Slide 108 / 270 To measure something a little larger in metric units, use meters. The abbreviation for meter is m. 100 centimeters = 1 meter What are some thing we can measure using meters?

37 Measuring with Meter Sticks Slide 109 / 270 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. Centimeter Ruler or Meter Stick Let's try both! First, we will measure something really long in centimeters and use a centimeter ruler. Slide 110 / 270 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.

38 Measuring in Meters 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 Practice Slide 113 / 270 Classroom Longer wall Shorter wall meters meters Hallway meters Cafeteria meters Should we all have the same measurements or different? 31 Which of the objects below would you use a meter stick to measure? Slide 114 / 270 A An eraser B A pencil C A hallway D A cat

39 32 Which object is best to measure with a centimeter ruler? Slide 115 / 270 A a book B a hallway C a white board D a room 33 If the height of the door was measured in centimeters and in meters, which would there be more of? Slide 116 / 270 A centimeters B meters 34 Tony measured his toy car and got 6 meters. Is he correct? Yes No Slide 117 / 270

40 35 Many second graders are more than 1 meter tall but less than 2 meters tall. Slide 118 / 270 True False Slide 119 / 270 Slide 120 / 270

41 Slide 121 / 270 Using a Tape Measure Click to return to Table of Contents Using a Tape Measure Slide 122 / 270 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 or 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. Tape Measure Slide 123 / 270 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.

42 Tape Measure Slide 124 / 270 Many cloth tape measures have centimeters on one side and inches on another. What objects around the room could we measure with a tape measure. Tape Measure Slide 125 / 270 We can also use a tape measure to measure very long objects. A builder will use a tape measure to very large objects. 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!

43 Measuring Our Body Record your measurements on the worksheet Neck Ankle Wrist Head Slide 127 / 270 Teacher Notes & Math Practice Measure the length around your partner's neck, wrist, ankle, and head in inches and centimeters. Object Measured Inches Centimeters neck wrist ankle head 36 A tape measure is used to measure objects that do not bend. Slide 128 / 270 True False 37 Is it better to use a tape measure or a ruler to measure your wrist? Slide 129 / 270 A tape measure B ruler

44 38 Do you line the end of the tape measure up to the 1 to get a final measurement? Slide 130 / 270 Yes No Slide 131 / 270 Slide 132 / 270

45 Slide 133 / 270 Which Unit? Which Tool? Click to return to Table of Contents Which Tool Should We Use? Slide 134 / 270 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 Which Unit? Slide 135 / 270 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.

46 Which Tool? Slide 136 / 270 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. Building a Playhouse Slide 137 / 270 Pedro and Carla want to build a playhouse out 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. 39 Which tool would be best to measure a room with? Slide 138 / 270 A standard ruler B your foot C a yard stick

47 40 It is best to measure a pencil in or. Slide 139 / 270 A feet B inches C meters D centimeters 41 You should use a yard stick to measure a penny. Slide 140 / 270 True False 42 Which tool should Bob use to measure the soccer ball? Slide 141 / 270 A standard ruler B tape measure C yard stick

48 43 Which objects would you measure with a yard stick? Slide 142 / 270 A eraser B football field C large window D book E classroom rug Quiz Slide 143 / 270 Slide 144 / 270

49 Slide 145 / 270 Length Comparison Click to return to Table of Contents 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. How Much Longer? Slide 147 / 270 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.

50 Let's Try it Slide 148 / 270 Pick any book from your desk and measure it in inches with your ruler. How Much Longer? Next, write down your measurement. Don't forget to write in. for inches after the number. This tells everyone what unit you measured in. Slide 149 / 270 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 larger measurement smaller measurement You book is 4 inches smaller than your partner's book. or Your partner's book is 4 inches longer than your book.

51 Did you know? Slide 151 / 270 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! How Much Longer Practice Slide 152 / 270 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. How Much Longer? Slide 153 / 270 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:

52 How Much Longer Practice Slide 154 / 270 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? 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? Elisha's ribbon is 11 feet long. Joann's ribbon is 18 feet. How much shorter is Elisha's ribbon? 44 Rabbit jumped 20 cm. Frog jumped 12 cm. How many more centimeters did rabbit jump? Slide 155 / 270 A 32 cm B 20 cm C 8 cm D 12 cm 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? Slide 156 / 270 A 20 cm B 38 cm C 18 cm D None of the above

53 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? Slide 157 / 270 cm 47 Look at the rectangle. How much longer is the longest side? Slide 158 / cm 7 cm 48 Compare these two lines. How much shorter is the red line? Slide 159 / cm 31 cm

54 Lab: Lord of the Ring Toss Slide 160 / 270 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. Click here for complete directions Click to return to Table of Contents Slide 161 / 270 Slide 162 / 270

55 Slide 163 / 270 Measuring in Different Units Click to return to Table of Contents Different Units Slide 164 / 270 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?

56 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 object 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: yards feet Comparing Measurements in Centimeters and in Inches Slide 168 / 270 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.

57 Are there more inches or centimeters? Slide 169 / 270 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." 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? Slide 170 / 270 Yes No 50 Jessica measured her book in inches. Josh measured the same book in centimeters. Who would get a higher number? Slide 171 / 270 A Jessica B Josh

58 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? Slide 172 / 270 Yes No 52 Centimeters are bigger than inches. Slide 173 / 270 True False 53 If you measure the same object in feet and inches. Would you have more feet or inches in your final measurements. Slide 174 / 270 A feet B inches

59 Slide 175 / 270 Slide 176 / 270 Slide 177 / 270 Estimating Inches and Feet Click to return to Table of Contents

60 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. Benchmark for an Inch Slide 179 / 270 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. Try it! Slide 180 / 270 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!

61 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. Try it! Slide 182 / 270 Just as we tried out our estimates in inches, we will do the same in feet. 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! 54 If someone said your front door was about 3 inches wide, would that be a good estimate? Slide 183 / 270 Yes No

62 55 What would be a good estimate for the height of the classroom door? Slide 184 / 270 A 7 feet B 7 inches C 7 yards 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. Slide 185 / 270 A A lion B a mouse C a bear D a snake 57 Many adults are between 5 and 6 tall. Choose the best answer that fits in the blank. Slide 186 / 270 A inches B feet C yards

63 58 It is best to estimate a pencil in Slide 187 / 270 A inches B feet C yards Slide 188 / 270 Slide 189 / 270

64 Slide 190 / 270 Estimating in Centimeters and Meters Click to return to Table of Contents 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. Slide 191 / 270 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! Your finger as a benchmark 1 cm Slide 192 / 270 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. 2) Next, measure the index card with a cm ruler. How close were you to the actual measurement? How can you figure this out?

65 To Do: An eraser as a benchmark Slide 193 / 270 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. 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? Your hand span as a benchmark Slide 194 / 270 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. 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. Once you know the length of your hand span, you can use that to estimate the length of longer objects. Click here for a ten second video clip of using hand spans to measure on YouTube. Longer Benchmarks: Your Arm span Slide 195 / 270 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 of 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.

66 A doorknob's height can be a longer benchmark Slide 196 / 270 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? Word Problem 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. 59 A good estimate for the height of a door might be Slide 198 / 270 A 2 cm B 2 m C 20 cm D 20 m

67 60 A good estimate for the length of the envelope is 20. A cm B m Slide 199 / A good estimate for the height of a basketball hoop is 3. A cm B m Slide 200 / A benchmark for estimating a centimeter is Slide 201 / 270 A the width of your finger. B your arm span.

68 63 It is best to estimate the width of your desk in meters. Slide 202 / 270 True False Quiz Lab: Packing Peanut Punt Slide 203 / 270 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

69 Slide 205 / 270 Slide 206 / 270 Number Line as a Ruler Click to return to Table of Contents Number Lines Slide 207 / 270 You may have used number lines before. There are many different kinds! The numbers can be written on the top or the bottom Some don't start with zero Number lines are useful for many things. You can count with them. You can measure with some. You can add or subtract with them.

70 Number Lines Slide 208 / 270 A number line often has arrows at the ends. This shows that numbers can go on and on forever. 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. 0 The numbers get bigger as you go to the right. The distance between the hash marks must be equal Missing Points on a Number Line Slide 209 / 270 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? click to reveal The left endpoint is missing 0 and the other endpoint is missing 30. Number Lines Slide 210 / 270 We can also zoom in to see only part of the number line 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?

71 Number Lines Slide 211 / 270 Some number lines label a missing number with a letter. 10 A B 30 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 Click to reveal answer. one 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. Number Lines Slide 212 / 270 Remember, number lines don't have to start at zero. 50 A B 70 Point A is located right in the middle of 50 and 70. What is the value of A? Click The value to reveal of point the answer A is 60. Point be is right in the middle of point A and 70. What is the value of B? Click The value to reveal of point the answer B is 65. Unit Spacing The hash marks on number lines are always spaced in equal units but the units are not always in ones. Slide 213 / 270 Look carefully at the number line below. What do you think the units are between the hash marks? What is the value of A? 20 A 40 A is half way between 20 and is in the middle of 20 and 40 so A must Click be to 30. reveal Therefore, the answers the equal units are worth 10.

72 Unit Value Slide 214 / 270 The more numbers that are given, the easier it is to figure out the unit value. The number line below has six hash marks. How many unit lengths are there? What is the value of B? B 65 Unit Value Some number lines might only give you one number and tell you the unit length. Slide 215 / 270 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? In this number line the length of each unit is again 10. What is the value of the start point D? D 75 Distance Between Points Slide 216 / 270 You can also find the difference between two points. The difference between two points is shown with the arrow. 10 A B 30 How can we find the difference?

73 Distance Between Points Slide 217 / 270 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 A B 30 We can then count the spaces between 13 and ? jumps = 27. We can also use subtraction = the difference Distance Between Points What is the difference in points A and B below? Slide 218 / 270 A B A B A 50 B 65 Word Problem 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?

74 64 How many unit lengths are on this blank number line? Slide 220 / What is the value of A? Slide 221 / 270 A 30 B 35 C 40 D A What is the value of point C? Slide 222 / 270 A 90 B 82 C 85 D C

75 67 What is the unit length for this number line? Slide 223 / Slide 224 / 270 Slide 225 / 270

76 Slide 226 / 270 Number Stories on a Number Line Click to return to Table of Contents Number Stories 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? Number Stories Slide 228 / 270 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.

77 Practice 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? Number Stories 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? Unit Length 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:

78 Unit Lengths 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? Practice Slide 233 / 270 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? Practice Slide 234 / 270 Jen jumped 2 feet. Jill jumped 4 feet more than Jen. How far did Jill jump?

79 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 off the trail and went on a different trail that was 70 meters. How much longer was the second trail? 68 What is the difference between point A and point B? Slide 237 / 270 A 6 B 5 C 4 D 9 A B

80 69 Len was using a number line to show 40 less than 90. Is he starting correctly? Slide 238 / 270 Yes No Slide 239 / John had a rope 65 inches long. He tied a 15 foot rope onto it. How long is the rope now? 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 240 / 270

81 72 Kathy wanted to solve 40 more than 10. Is she starting correctly? Slide 241 / 270 Yes No Slide 242 / 270 Slide 243 / 270

82 Slide 244 / 270 Line Plots Click to return to Table of Contents Line Plots 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. 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 Number of Siblings

83 Analyze the Data Slide 247 / Number of Siblings 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? Line Plots for Height 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 on top of each other for students that are the same height. Student in. Bobby 47 Jessica 44 Henry 46 Lila 48 Cole 44 Leah 46 Bill 44 Teacher Notes Slide 248 / 270 x Class Heights in Inches Our Class Height Data Slide 249 / 270 Class Height

84 73 How many students have pencils that are 6 inches long? Slide 250 / 270 x x x x x x x x Pencil Length in inches 74 Do more kids have pencils 5 inches long or 6 inches long? Slide 251 / 270 A 5 inches B 6 inches x x x x x x x x Pencil Length in inches 75 Do 4 kids have pencils greater than 6 inches? Slide 252 / 270 Yes No x x x x x x x x Pencil Length in inches

85 76 It is not important to label a line plot. Slide 253 / 270 True False 77 How tall are most flowers? Slide 254 / 270 A 14 inches B 12 inches C 16 inches D 11 inches Flower Height (in) Slide 255 / 270

86 Slide 256 / 270 Slide 257 / 270 Line Plots Part 2 Click to return to Table of Contents What is a line plot? Slide 258 / 270 What information can you gather from the line plot below? Number of Pets in Our Class

87 Measuring Arm Spans Slide 259 / 270 Many times when we gather data, we want to keep it organized. 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. Name Arm Span in cm Slide 260 / 270 You can then use your chart to make the line plot. Slide 261 / 270 Class Arm Spans in Centimeters

88 Head Circumference Slide 262 / 270 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 our 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. Line Plot Title Sometimes, the title for the line plot is on the top. What is missing from the line plot? Class Head Circumferences in Inches Slide 263 / Line plots are used to show the frequency of a measurement. Slide 264 / 270 True False

89 79 How many kids have 2 siblings? Slide 265 / Number of Siblings 80 Five or more students have or siblings. (Pick 2 answers.) Slide 266 / 270 A 3 B 1 C Number of Siblings 81 Two students have siblings. Slide 267 / Number of Siblings

90 82 The longest foot is 10 inches. Slide 268 / 270 True False Foot Length in Inches Quiz Slide 269 / 270 Slide 270 / 270