Measurement and Data

1
Measurement and Data

• Everyday Mathematics Unit 10
• Mr. Brumfield
• Lawnton Elementary

2
Table of Contents

• 10.1 Review Length
• 10.2 Volume
• 10.3 Exploring Volume
• 10.4 Weight
• 10.5 Weight and Volume
• 10.6 Capacity
• 10.7 The Mean and the Median
• 10.8 Calculating the Mean
• 10.9 Calculator Memory
• 10.10 Frequency Distributions
• 10.11 Coordinate Grids
• 10.12 Unit Review and Assessment

3
Review Length
Lesson 10.1

• Why units and tools to we use to measure?

4
Mental Math
5 x 7 3 x 3 5 x 5 4 x 9 9 x 7 9 x 9

• 40 (20s)
• 30 (70s)
• 20 (100s)
• 60 (20s)
• 40 (80s)

5
Math Message

• The inch is a unit of length.
• List as many other units of length as you can.

6
Categorizing Units of Measurement

• Metric Units

• U.S. Customary Units

7
Finding Measurement Equivalencies
Metric System
1 Kilometer
meters
1 Meter
decimeters
1 Meter
centimeters
1 Meter
millimeters
1 Decimeter
centimeters
1 Centimeter
millimeters
8
Finding Measurement Equivalencies
U.S. Customary Units
1 Mile
yards
1 Mile
feet
1 Yard
feet
1 Yard
inches
1 Foot
inches
9
How would you categorize these tools?
Car odometer
Category
10
Thinking About Measurement

• Would it make sense to measure the distance
  between two cities with a yardstick?
• How could you measure the circumference of
  (distance around) the lid of a jar?
• How would you measure the diameter of a ball?
• How would you estimate the height of a three
  story building?

11
Renaming Measurements

• Is 18 inches more or less than a foot?
• What fraction of 1 foot is 6 inches?
• 2 yards is equal to how many feet?
• 2 feet is equal to how many inches?
• Give another name for 2 feet 3 inches
• Give another name for 5 feet

12
Independent Practice
Math Journal Page 246

• Practice measuring in centimeters and inches,
  renaming measurements, and finding the areas of
  rectangles.
• Remember to begin measuring at the 0 mark.

Math Boxes on page 248
13
Group Work
Math Journal Page 247

• With a partner you will read about the layers of
  the earth. You will need to use the distance key
  and the information in the reading to help you
  answer the four questions.

14
Exit Slip What have you learned today?

15
Volume
Lesson 10.2

• What is volume and how is it measured?

16
Mental Math

• Write three and nine hundredths.
• Underline the digit in the tenths place.
• Four and fifty hundredths
• Circle the digit in the hundredths place.
• Underline the ones.
• Seventeen and ninety-three hundredths
• Underline the ones digit.
• Put an X through the tenths.

17
Introducing the Volume of a Rectangular Prism
This arrow is showing ___________________
These arrows are showing ___________________

• Bases of a Prism
• Remember that bases are any two pairs of
  opposite faces. The bases are rectangular and
  parallel and have the same area.
• Height of a Prism
• The height of a prism is the distance between
  the two opposite bases.

18
Group Work
Math Journal Page 249 Part One Only

• Each student will need 10 cm cubes.
• We will break into groups of 4 students. Each
  group will get a copy of math masters 166. Each
  student is responsible for cutting out and taping
  a rectangular prism (A, B, C, or D).
• Discuss the prisms from your group and estimate
  how many cubes you think it will take to fill
  each of the rectangular prisms.
• How will you find out how many cubes would fill
  the prisms?

19
Group Work Follow Up
Math Journal Page 249 Part One

• What do you notice about the cubes in the
  rectangular prisms?
• Is there an algorithm we could use to easily
  find the number of cubes in a prism?
• The number of cubes needed to fill a box is the
  volume of the box. The algorithm for volume is
• Area of Base X Height

20
Finding Volume Practice
10
7
4
2
3
3
5
6
4
Area of Base______ Height ___________ Volume
__________
Area of Base______ Height ___________ Volume
__________
Area of Base______ Height ___________ Volume
__________
Is it possible for two different size
rectangular prisms to have the same volume?
21
Independent Practice

• Complete part two of math journal page 249. You
  will be finding the volume of three different
  rectangular prisms.
• Remember area of base X height
• When you have finished, complete the
  multiplication problems on math journal page 250.
  
• (You can use either partial products or the
  lattice method)

22
Math Boxes

• Complete the review math boxes on page 252 of
  your math journal.

23
Exploring Volume
Lesson 10.3

• Can rectangular prisms of different sizes have
  the same volume?

24
Mental Math Riddles

• If you take ½ of me, I will be an odd number.
• I am less than 20.
• One of my factors is 5.
• Who am I?

Solve the Problem
25
Mental Math Riddles

• If you double me, I will be a 3-digit number
• The sum of my digits is 6
• 2, 3, 4, 5, and 6 are some of my factors
• Who am I?

Solve the Problem
26
Mental Math Riddles

• 1/3 of me is equal to ½ of 16
• Who am I?

Solve the Problem
27
Math Message

• A rectangular prism is made of 45 cubes
• The base has 15 cubes
• How many layers of cubes does the prism have?

What operation is needed to solve this
problem? What information do you have? What
information is needed?
Fact Triangle
28
Reviewing the Volume of a Rectangular Prism
This arrow is showing ___________________
These arrows are showing ___________________

• Bases of a Prism
• Remember that bases are any two pairs of
  opposite faces. The bases are rectangular and
  parallel and have the same area.
• Height of a Prism
• The height of a prism is the distance between
  the two opposite bases.
• Volume of a Rectangular Prism
• Multiply the area of the base X the height of
  the prism

29
Practicing Finding Volume Review
12
5
4
2
2
3
5
9
6
Area of Base______ Height ___________ Volume
__________
Area of Base______ Height ___________ Volume
__________
Area of Base______ Height ___________ Volume
__________
Is it possible for two different size
rectangular prisms to have the same volume?
30
Exploring Volume

• You and your assigned partner will be given 36
  cubes which will be your volume.
• You need to use these blocks to build different
  bases and heights with the same volume
• (36 cubic units).
• Record your findings on math masters 168

31
Same Volume, Different Prisms
Prism Area of Base Height Volume
A 36
B 36
C 36
D 36
E 36
F 36
G 36
32
Exit Slip Volume
What have we learned about volume today?
33
Math Boxes

• Complete the review math boxes on page 254 of
  your math journal.

34
Weight
Lesson 10.4

• What are the different tools we can use to
  measure weight?

35
Mental Math

• Louise had 10 quarters. She gave 2/5 of her
  quarters to her brothers. How many did she give
  him?
• Number Model _________________
• Answer _______________
• Ricks dad made two apple pies. Six people
  shared the pies equally and finished them. What
  fraction of a pie did each person get?
• Number Model _________________
• Answer _______________

36
Math Message
Measuring Weight
What do we already know about weight? What units
of measurement can you list?
37
Categorizing Units of Weight

• Metric Units

• U.S. Customary Units

38
Examining Kinds of Scales

• Lets look at different types of scales found in
  your SRB, on pages 147 and 148.
• There are two things we need to know about
  scales.
• Capacity of a Scale
• the weight a scale can measure.
• Precision
• the size of the unit of measurement. The smaller
  the unit the more precise the scale.

39
Group Work Exploring Scales

• You will be working with a partner to complete
  math journal page 255.
• You will be brainstorming objects that can be
  measured or weighed by the different scales that
  are categorized.
• When you have finished you may complete math
  journal pages 256 and 257 independently. You will
  be working with weight on these pages also.

40
Math Boxes

• Complete the review math boxes on page 258 of
  your math journal.

41
Weight and Volume
Lesson 10.5

• How can we organize objects by weight and volume?

42
Mental Math

• 49 candies shared by 5 friends. How many candies
  for each friend?
• Answer __________________________
• 6 boxes of crayons with 8 crayons in a box. How
  many crayons altogether?
• Answer________________________
• 9 tables with 4 children at each table. How many
  children?
• Answer ___________________________
• 300 pennies shared by 10 children. How many
  pennies per child?
• Answer __________________________

43
Examining 4 Objects

• I will be displaying four objects. You need to
  evaluate them and estimate the order of the items
  by weight.
• Use part one of math journal page 251.
• Then estimate and rank the order of items by
  volume, using part two of the same page.

44
Discussing your Estimates

• Take a minute to discuss your predictions with
  your partner.
• Why did you rank certain objects as heavier or
  lighter?
• How did you rank your volume? Explain your
  thinking.

45
Conducting the Volume Experiment

• We are going to test the volumes of our four
  objects using containers and water. We will be
  measuring how much water is displaced from the
  container after each object is inserted. The more
  water displaced, the greater the volume of the
  object.

46
Discussing the Experiment

• How you would explain the relationship you
  noticed?

Can you name two objects for which the heavier of
the two also has a greater volume? Can you
name two objects for which the heavier of the two
has the smaller volume?
47
Independent Work

• Complete the parentheses puzzles on the bottom
  of page 251. Remember that the parentheses tell
  you what operation to do first.
• Complete the review math boxes on page 259 of
  your math journal.

48
Capacity
Lesson 10.6

• What is the capacity of a container?

49
Mental Math

• We are going to compare fractions to ½. You need
  to mark whether the fraction is greater, less
  than, or equal to ½.

1/2
1/4
7/8
1/2
2/3
1/2
3/6
1/2
How did you solve the comparison?
1/2
3/5
1/2
5/8
50
Math Message

• The pint is a unit of measure for liquids such
  as milk and juice.
• List as many other units as you can that are
  used to measure liquids.

51
Capacity

• We have learned about the capacity of scales,
  what they are able to weigh. Today we are
  learning about the capacity of a container, how
  much liquid it can hold. Measures of capacity are
  special measures of volume.

52
Capacity Equivalencies
1 Gallon _______ Quarts _______ Pints _______
Cups
G
Q
P
Q
P
P
P
C
C
C
C
C
C
C
1 Quart _______ Pints _______ Cups
C
Q
Q
P
P
P
P
C
C
C
C
C
C
C
C
1 Pints _______ Cups
53
Working with Capacity

• You can turn to SRB pages 142 and 143 to view a
  capacity equivalency chart.
• You will complete math journal page 260 using
  this chart, identifying units of measurement.
• We will work together to complete the metric
  weights on math journal page 261.

54
Online ConversionEnrichment

• http//www.onlineconversion.com/

55
Math Boxes

• Complete the review math boxes on page 262 of
  your math journal.

56
Mean and Median
Lesson 10.7

• How do we find the median and the mean of a set
  of data?

57
Mental Math

• Lets read and solve word problems using the
  internet.
• http//www.iknowthat.com/com/L3?AreaWordProblems
  
• Tip When the website asks you to sign in, you
  can skip the registration and go straight to the
  activity.

58
Math Message

• Make a bar graph of the data in the table on
  page 263 in your journal.
• What is the median of this set of data? How did
  you find it?

59
Math Message Follow Up

• We are going to use our bar graph and pennies to
  find the average or mean of the set of numbers.
• We are first going to find the average by
  placing pennies on each shaded square.
• After covering each shaded block, rearrange the
  pennies to level them off across the bar graph.
• That is one way to find the mean.

60
Finding the Mean with Pennies

• Link to Smart Notebook Activity

61
Group Work

• You and your assigned partner or partners will
  work together to find the mean of a set of data.
• You will use the penny method we practiced.
• Turn to math journal page 264.
• Work together cooperatively!
• When you finish, complete the math boxes on page
  265.

62
Calculating the Mean
Lesson 10.8

• Is there an easier way to find a mean number
  (average)?

63
Mental Math

• Find the capacity and volume equivalencies
• 1 gallon ________ quarts
• 1 cup __________ ounces
• _____ ounces ½ cup
• 1 gallon ________ pints
• 3 gallons _______ cups
• 4 cups ________ ounces

64
Math Message

• We are going to find the mean or average length
  of our arm spans.
• You will need your tape measure and a partner.
• First, spread your arms and have your partner
  measure the distance from your middle finger
  across your body to the opposite middle finger.
• Then write the measurement in inches on the
  sticky note that I provide you. Write big and do
  not include your name.
• Switch positions and measure your partners arm
  span.

65
Lets find the Median arm-span
Follow along and fill in our findings on math
journal page 266
We will arrange our post it notes on a poster or
large piece of paper. What are the two things I
need to remember to do when finding the
median? First____________________________________
_________ Then __________________________________
__________
Our Median is ________ inches
66
How will we find the Mean or Average?

• The algorithm for finding an average has two
  steps.
• Step 1 Add all of the numbers together
• Step 2 Divide by the number of items being
  compared

67
Finding the Mean of a Set of Data

• Here are 5 students weights. We are going to use
  the weights to find the average or mean, using
  the two step process.
• Weights of Students in Pounds
• Mike 56 pounds
• Thomas 43 pounds
• Jenny 62 pounds
• Davis 75 pounds
• Carrie 47 pounds

Step 1 Add all of the numbers together Number
Model________________________________________ St
ep 2 Divide by the number of items being
compared Number Model__________________________
______________
What is the median of this data?
68
Lets find the Mean arm-span
Follow along and fill in our findings on math
journal page 266
What are the two number models I need to solve to
find the mean or average arm span? First_________
____________________________________ Then
____________________________________________
You can solve the problems using your calculator.
Round your answer to the nearest whole number.
Our Mean is ________ inches
69
Small Group and Independent Practice

• You and your small group will practice finding
  the median and mean of sets of numbers.
• You will start with measuring your heights in
  inches, rounding the nearest whole inch. Use the
  handout to organize your information.
• You will fill in the table on math journal page
  266.
• Then you will solve problems 4-7 independently,
  although you are allowed to use a calculator.

70
Group and Independent Work

• Solve the measurement number stories on math
  journal page 267 with a partner.
• Then complete the review math boxes on page 268
  of your math journal.

71
Calculator Memory
Lesson 10.9

• What is the memory key on a calculator?

72
Mental Math Riddles

• I am an odd number.
• If you double me, I will be between 40 and 50.
• My ones digit is half of my tens digit.
• Who am I?

Solve the Problem
73
Mental Math Riddles

• If you add 5 to me, I will be a multiple of 10.
• If you double me,
• I will be greater than 39 and less than 59.
• Who am I?

Solve the Problem
74
Math Message

• Use your calculator to answer the questions on
  Math Message slip 10.9.
• What does the M key do on the calculator?

75
Adding Subtracting Numbers Stored in Memory

• Store the number 7 in memory.
• Press 4 M
• Press the MRC key
• What happened?
• Without clearing the memory, press 8 M-.
• What do you think we have done?
• Press MRC to check your prediction.

76
Playing Memory Addition and Subtraction

• Turn in your SRB to pages 215 and 216.
• We will read the directions to a memory game.
• We will play a few rounds as a whole group,
  before breaking into partners and playing.

Calculator Memory Practice

• Complete the calculator memory problems on math
  journal page 269.
• Then complete the math boxes on page 270.

77
Frequency Distributions
Lesson 10.10

• What is a frequency table?
• How do we find the median, mean, and mode of a
  set of numbers?

78
Mental Math

• Regina had 20 quarters.
• She lost ¼ of them.
• How many quarters did she have left?
• How much money is that?

Show your work
79
Mental Math

• Henry and his brother bought a 6-pack of soda.
  They each drank 2 cans.
• What fraction of the 6-pack did each boy drink?
• What fraction did both drink together?

Show your work
80
Mental Math

• Antoinette had 3 candy bars. She wanted to share
  equally with herself and 3 friends.
• What fraction of a candy bar did each person
  receive?
• Hint Start with 1 whole candy bar first.

Show your work
81
Math Message

• Work with your partner to use the tape measure
  to find your waist-to-floor height. Do the same
  for your partner.
• Write your measurement on the class table pad
  but do not record your name.

82
Math Message Follow Up

• Record the class waist-to-floor heights in your
  math journal on page 272.
• We are going to be making a frequency table,
  where we keep track of how many times a number is
  occurs using tally marks.
• How many tally marks should we have in total?

83
Finding the Median Mean

• You will work with a partner or a small group to
  find the median and the mean of the classroom
  waist-to-floor heights.
• Decide how you want to find the median and mean,
  and what tools you will use.
• Record your findings on questions two and three
  on page 272 of your math journal.

84
Group Work Follow Up

• How did your group go about finding the median?
• Did anyone use the frequency table?
• How can you use the frequency table only, to
  find the median?
• Which is more efficient, finding the median from
  the unordered data on the class data pad or from
  the frequency table? Why?

85
Finding the Mode of the Data

• Look up mode in your student reference book.
• Where would you find the information?
• What is the mode of our class data?
• Fill this in on math journal page 272

Definition Of Mode
86
Independent Work

• Use the classroom data to make a bar graph on
  math journal page 273.
• Then complete the math boxes on page 271.

87
Coordinate Grids
Lesson 10.11

• 5
• 4
• 3
• 2
• 1
• 0

What do you know about grids? How would you
describe the location of the star on this grid?
A B C D E
88
Mental Math Multiplication

• 8 (40s)
• 80 (40s)
• 800 (40s)

• 9 (80s)
• 90 (80s)
• 900 (80s)

6 (50s) 60 (50s) 600 (50s)
89
Math Message

• Talk to your partner about the board game
  Battleship.
• How does a player win?

90
Plotting Points

• Turn to page 274 of your math journal.
• Using the number line for question one, label and
  mark a point for each of these numbers
• -5 3 ½ 6 ¼ 8 10
• Is there a point on the number line for any
  number you can name?

91
Coordinate Grids
There are ways to name points that are not on a
number line. These points can be found on
coordinate grid like the one you see. You name
these points using coordinates, for example
(B,2) You name the point with the horizontal
(across) axis first, then the vertical (up or
down) axis.

• 5
• 4
• 3
• 2
• 1
• 0

A B C D E
92
Lets Practice Using Coordinates
7 6 5 4 3 2 1 0







C
A
B
0 1 2 3 4 5 6 7
Coordinates for Point B ____, _____
Coordinates for Point A ____, _____
Coordinates for Point C ____, _____
93
Group Work

• You will work with your group to complete
  questions 2 thru 5 on math journal page 274.
• When you finish working on coordinates, you can
  turn to page 275 and solve elapsed time questions
  using a train schedule. You may use your tool kit
  clocks.
• Complete the math boxes on page 276
  independently.

94
Unit Review and Assessment
Lesson 10.12

• How well did you learn the information in this
  unit?

95
Math Message
Spelling Test Scores

• Take a copy and complete the math message, using
  a frequency table.

Scores Tallies Number
70
75
80
85
90
95
100
Total

90 100 95 75 85 95 95
85 95 90 100 70 95
100 75 85 85 90 75
95 100 90 85 95 85
Median Score _______ Mean or Average ____ Mode
Score _____
96
Math Message Follow Up
Spelling Test Scores
Scores Tallies Number
70
75
80
85
90
95
100
Total

• Median Score _______
• Mean or Average ____
• Mode Score _____

85 95 90 100 70 95
100 75 85 85 90 75
95 100 90 85 95 85
90 100 95 75 85 95 95
97
Mental Math

• We are going to compare fractions to ½. You need
  to mark whether the fraction is greater, less
  than, or equal to ½.

1/2
1/4
7/8
1/2
2/3
1/2
3/6
1/2
How did you solve the comparison?
1/2
3/5
1/2
5/8
98
Review Ruler Measurements
Link to Smart Notebook Activity
99
Number Stories

• 9 boxes of crayons with 8 crayons per box.
• 6 bags of marbles with 9 marbles per bag.
• 56 candies shared equally with 7 children. How
  many per child?
• 47 pennies shared equally with 9 children. How
  many per child?
• 48 pieces of gum shared with 6 children. How
  many each?

Number Model
Answer
Number Model
Answer
Number Model
Answer
Number Model
Answer
Number Model
Answer
100
Fractional Number Stories

• Marcia had 15 dimes. She lost 1/3. How many did
  she lose?
• Janet had 14 peaches. She gave away half, which
  is how many?
• George had 60 sunflower seeds. He planted 1/5 in
  a sunny place and the rest in a shady place.
• What fraction was planted in the shade?
• How many sunflower seeds were planted in the
  sun?

Number Model
Answer
Answer
Number Model
101
(No Transcript)
102
Math Boxes
Boxes 10.12 Page 277
When you have finished your test, complete the
last math boxes in Unit 10 Measurement and Data.
103
Time for the Test

• If you paid attention in class and studied the
  review outline that was sent home, you should be
  prepared for the test.
• Make sure you work carefully, double-checking
  your work and rereading any questions you think
  sound confusing.