measurement and data
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Measurement and Data
Everyday Mathematics Unit 10Mr. Brumfield
Lawnton Elementary
Table of Contents10.1 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
Review: Length
Why units and tools to we use to measure?
Lesson 10.1
Mental Math
40 (20s)
30 (70s)
20 (100s)
60 (20s)
40 (80s)
5 x 7
3 x 3
5 x 5
4 x 9
9 x 7
9 x 9
Math Message
The inch is a unit of length.
List as many other units of length as you can.The inch is a unit of length.
List as many other units of length as you can.
Categorizing Units of Measurement
Metric Units U.S. Customary Units
Finding Measurement Equivalencies
1 Kilometer
1 Meter
1 Meter
1 Meter
1 Decimeter
1 Centimeter
meters
decimeters
centimeters
millimeters
centimeters
millimeters
Finding Measurement Equivalencies
1 Mile
1 Mile
1 Yard
1 Yard
1 Foot
yards
feet
feet
inches
inches
How would you categorize these tools?
Category:
Car odometer
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?
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:
Independent Practice
Practice measuring in centimeters and inches, renaming measurements, and finding the areas of rectangles.
Remember to begin measuring at the 0 mark.
Math Journal Page 246
Math Boxes on page 248
Group Work
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.
Math Journal Page 247
Exit Slip: What have you learned today?
Volume
What is volume and how is it measured?
Lesson 10.2
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 hundredthsUnderline the ones digit.
Put an X through the tenths.
Introducing the Volume of a Rectangular Prism
Bases of a PrismRemember that bases are any two pairs of opposite faces. The bases are rectangular and parallel and have the same area.
Height of a PrismThe height of a prism is the distance between the two opposite bases.
These arrows are showing:
___________________
This arrow is showing:
___________________
Group Work
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?
Math Journal Page 249
Part One Only
Group Work Follow Up
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
Math Journal Page 249
Part One
Finding Volume Practice
Area of Base:______
Height: ___________
Volume: __________
3
7
5 6
104
4
32
Area of Base:______
Height: ___________
Volume: __________
Area of Base:______
Height: ___________
Volume: __________
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 heightWhen you have finished, complete the multiplication problems on math journal page 250.
(You can use either partial products or the lattice method)
Math Boxes
Complete the review math boxes on page 252 of your math journal.
Exploring Volume
Can rectangular prisms of different sizes have the same volume?
Lesson 10.3
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
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
Mental Math Riddles
1/3 of me is equal to ½ of 16
Who am I?
Solve the Problem
Math Message
A rectangular prism is made of 45 cubesThe 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
Reviewing the Volume of a Rectangular Prism
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
These arrows are showing:
___________________
This arrow is showing:
___________________
Practicing Finding Volume Review
Area of Base:______
Height: ___________
Volume: __________
2
5
9 6
124
5
32
Area of Base:______
Height: ___________
Volume: __________
Area of Base:______
Height: ___________
Volume: __________
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
Same Volume, Different Prisms
Prism Area of Base Height Volume
A 36
B 36
C 36
D 36
E 36
F 36
G 36
Exit Slip: VolumeWhat have we learned about volume today?
Math Boxes
Complete the review math boxes on page 254 of your math journal.
Weight
What are the different tools we can use to measure weight?
Lesson 10.4
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: _______________
Rick’s 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: _______________
Math Message
Measuring Weight
What do we already know about weight? What units of measurement can you list?
Categorizing Units of Weight
Metric Units U.S. Customary Units
Examining Kinds of ScalesLet’s 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.
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.
Math Boxes
Complete the review math boxes on page 258 of your math journal.
Weight and Volume
How can we organize objects by weight and volume?
Lesson 10.5
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: __________________________
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.
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.
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.
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?
Independent WorkComplete 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.
Capacity
What is the capacity of a container?
Lesson 10.6
Mental MathWe are going to compare fractions to ½. You need to mark whether the fraction is greater, less than, or equal to ½.
1/2
1/2
1/2
1/2
1/2
1/2
1/4
7/8
2/3
3/6
3/5
5/8
How did you solve the comparison?
Math MessageThe 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.
CapacityWe 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.
Capacity Equivalencies1 Gallon =
_______ Quarts
_______ Pints
_______ Cups
1 Quart =
_______ Pints
_______ Cups
1 Pints =
_______ Cups
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.
Math Boxes
Complete the review math boxes on page 262 of your math journal.
Mean and Median
How do we find the median and the mean of a set of data?
Lesson 10.7
Mental Math
Let’s read and solve word problems using the internet.
http://www.iknowthat.com/com/L3?Area=WordProblems’
Tip: When the website asks you to sign in, you can skip the registration and go straight to the activity.
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?
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”.
Finding the Mean with Pennies
Link to Smart Notebook Activity
Group WorkYou 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.
Calculating the Mean
Is there an easier way to find a mean number (average)?
Lesson 10.8
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
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 partner’s arm span.
Let’s 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
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
Finding the Mean of a Set of DataHere 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
poundsThomas: 43 pounds
Jenny: 62 poundsDavis: 75 poundsCarrie:47 poundsStep 1: Add all of the numbers together
Number Model:________________________________________
Step 2: Divide by the number of items being comparedNumber Model:________________________________________
What is the median of this data?
Let’s find the Mean arm-spanFollow 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: ____________________________________________
Our Mean is
________
inches
You can solve the problems using your calculator. Round your answer to the nearest whole number.
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.
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.
Calculator Memory
What is the memory key on a calculator?
Lesson 10.9
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
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
Math Message
Use your calculator to answer the questions on Math Message slip 10.9.
What does the M+ key do on the calculator?
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.
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 PracticeComplete the calculator memory problems on math journal page 269.
Then complete the math boxes on page 270.
Frequency Distributions
What is a frequency table?
How do we find the median, mean, and mode of a set of numbers?
Lesson 10.10
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
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
Mental Math
Show your work
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.
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.
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?
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.
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?
Finding the “Mode” of the Data
DefinitionOfMode
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
Independent Work
Use the classroom data to make a bar graph on math journal page 273.
Then complete the math boxes on page 271.
Coordinate GridsLesson 10.11
A B C D E
What do you know about grids?
How would you describe the location of the star on this grid?
5 4
3
2
1
0
Mental Math MultiplicationMental Math Multiplication
8 (40s)
80 (40s)
800 (40s)
9 (80s)
90 (80s)
900 (80s)
6 (50s)
60 (50s)
600 (50s)
Math Message
Talk to your partner about the board game “Battleship”.
How does a player win?
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?
Coordinate Grids5
4
3
2
1
0 A B C D E
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.
Let’s Practice Using Coordinates76543210
0 1 2 3 4 5 6 7
A
B
C
Coordinates for Point A:
____, _____
Coordinates for Point B:
____, _____
Coordinates for Point C:
____, _____
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.
Unit Review and AssessmentUnit Review and Assessment
How well did you learn the information in this unit?
Lesson 10.12
Math MessageTake a copy and complete the math message, using a frequency table.
Scores Tallies Number
70
75
80
85
90
95
100
Total:
Spelling Test Scores
85
95
90
100
70
95
100
75
85
85
90
75
95
100
90
85
95
85
90
100
95
75
85
95
95Median Score: _______
Mean or Average: ____
Mode Score: _____
Math Message Follow Up
Median Score: _______
Mean or Average: ____
Mode Score: _____
Scores Tallies Number
70
75
80
85
90
95
100
Total:
Spelling Test Scores
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
Mental MathWe are going to compare fractions to ½. You need to mark whether the fraction is greater, less than, or equal to ½.
1/2
1/2
1/2
1/2
1/2
1/2
1/4
7/8
2/3
3/6
3/5
5/8
How did you solve the comparison?
Review Ruler Measurements
Link to Smart Notebook Activity
Number Stories9 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:
Number Model:
Number Model:
Answer:
Answer:
Number Model:
Answer:
Answer:
Number Model: Answer:
Fractional Number StoriesMarcia 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:
Number Model: Answer:
Finding the Mean (Average) There are two steps to finding the mean. Describe each step below: First Step: ______________________________________________ Second Step: ____________________________________________ There are also two steps to find the median of a set of numbers. Describe these steps:
First Step: ______________________________________________ Second Step: ____________________________________________
Find the median and the mean of each set of numbers below. Show your work, although you may use a calculator.
A Student’s Grades
86% 74 % 63% 95% 100% 61% 70%
The Mean (Average) grade is: The Median grade is:
Children’s Ages
9 8 8 6 5 4 7 8
Donations
$120.00 $15.30 $105.40 $150.00 $89.32
$65 $62.00 $20.00 $45.72
The Mean (Average) age is: The Median age is:
The Mean (Average) donation is: The Median donation is:
Math Boxes
When you have finished your test, complete the last math boxes in Unit 10: Measurement and Data.
Boxes 10.12
Page 277
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.
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