Megan FortgangPage 110/12/2018

Math Trailblazers Unit 16: Volume

Unit Goals: SWBAT…

Measure volume using a graduated cylinder.

Collect, organize, graph, and analyze data.

Make and interpret bar graphs.

Solve addition, subtraction, multiplication, and division problems involving volume.

Demonstrate fluency with the multiplication facts for the 2s, 5s, and 10s.

PA State Standards:

2.2.3.B. Add and subtract single- and double- digit numbers with regrouping and triple-digit numbers without regrouping, including problems with money.

2.2.3.D. Estimate values, sums, and differences of quantities and conclude the reasonableness of those estimates.

2.3.3.A. Demonstrate an understanding of measurable characteristics and the need to quantify those characteristics.

2.3.3.B.Identify a measurable characteristic of an object, select an appropriate standard or non-standard unit of measurement and tool, and determine the measurement to a specified level of accuracy.

2.3.3.D. Identify equivalent measurements within the same system.

2.3.3.F. Estimate and verify measurements of length, area, weight, and capacity.

2.4.3.A. Use models and number facts to draw conclusions and explain the reasons for conclusions.

2.5.3.A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer made sense, and explain how the problem was solved in grade appropriate contexts.

2.5.3.B. Use appropriate mathematical vocabulary when explaining how to solve a problem.

2.6.3.A. Gather data from surveys and observations within the classroom or homes.

2.6.3.B. Organize and display data using pictures, tallies, charts, bar graphs, and pictographs.

2.6.3.C. Describe data displayed in a diagram (e.g., Venn), a graph or a table.

2.6.3.D. Analyze data shown in tables, charts, diagrams, and graphs; compute the data from two categories displayed in a graph and compare representations of a set of data in different graphs

Assessments:

Observational Assessment Record

Unit 16 Assessment

Megan FortgangPage 110/12/2018

Math Trailblazers Unit 16: Volume

Unit Vocabulary:

Cubic centimeter (cc)

Displacement

Graduated cylinder

Liter (l)

Meniscus

Milliliter (ml)

Volume

Cup

Gallon

Pint

Quart

Megan FortgangPage 110/12/2018

Math Trailblazers Unit 16: Volume

Lesson 1, Day 1: Measuring Volume

Goals:

  • Estimate volume using centimeter connecting cubes.

Materials:

  • Variety of small objects (that can be placed in and taken out of graduated cylinders)
  • Connecting cubes
  • Student Guide

Introduction:

  • Prompting volume v. mass questions
  • Which is heavier, 1 lb. of popcorn or a 1 lb. rock?
  • Which is heavier, 10 lbs. of cotton balls or a 10 lb. weight?
  • Which is heavier, 5 lbs. of books or 5 lbs. backpack?
  • Neither is heavier, they both weigh 1 lb.
  • If the mass of both is ___ lb., what is the difference between them? (volume)
  • Show 1 connecting cube for 1 cubic centimeter, graduated cylinder for milliliter and liter.
  • Student to come up to the document camera to use ruler to measure cube to prove it is 1 cm long.
  • The volume would be 1 cubic centimeter.

Activity:

  • Demonstrate building a shape or cube with cm connecting cubes.
  • Show students the cube shape and ask: how can we measure the volume of the cube? (count the number of cubes)
  • Show students the SG p. 237
  • Students should build the models, then count the number of cubes to find the volume.
  • How could we use centimeter connecting cubes to estimate the volume of one of the small objects? (Make a model about the same size as the object. Find the volume by counting the number of cubes in the model).
  • SG p. 238 - Estimate the volume of several objects by making models and record the volume of the models in the table (do at least 4; and a shape of at least 10 pieces)  fill in the first two columns but not the third.

Conclusion:

  • Share the volumes of the objects that we found.

Homework:

  • DAB p. 244 – Unit 16: Home Practice Parts 1 & 2

Lesson 1, Day 2:

Goals:

  • Use graduated cylinders to measure volume by displacement.

Materials:

  • Graduated cylinders
  • Water
  • Eyedroppers
  • Variety of objects

Introduction:

  • Introduce term meniscus
  • Practice reading scale and meniscus on document camera (URG p. 26)
  • Point out…
  • Double line appearance of meniscus and point out reading the lower line.

Activity:

  • Students fill graduated cylinder a little below the desired level
  • 100 cc in 250 cc cylinder
  • 50 cc in 100 cc cylinder
  • Use eyedroppers to get water level to proper level  read it at eye level.
  • Explain that we are going to place objects into the cylinders and the object displaces or pushes aside its volume in the water causing the water level to rise.
  • To find the volume of the object alone, subtract the starting water level from the final water level.
  • If the object floats, have students push it under the surface and hold it in place until they can read the level of the water (use a pencil)
  • SG p. 241 – fill in the table to find actual volume using the displacement method

Conclusion:

  • Share data of different objects.

Homework:

  • SG p. 242-243: Homework reading graduated cylinders

Lesson 2, Day 1: Fill ‘er Up!

Goals:

  • Collect, organize, graph, and analyze data.
  • Measure the volume of large, unusually shaped containers accurately.
  • Measure volume using graduated cylinders.
  • Solve + , - , x , / problems involving volume.
  • +, - , x , / multidigit numbers.
  • Make and interpret a bar graph.
  • Use patterns in data to make predictions and solve problems.
  • Measure precisely and accurately.
  • Use medians to average data.

Materials:

  • 3 containers
  • Graduated cylinder
  • Eyedropper
  • Cup (small container)
  • Dishpan
  • Paper towels

Introduction:

  • Goal is to figure out which container has the larger volume.
  • Group:
  • How can you use the graduated cylinder and the water to find the volume of the container?
  • Draw a picture of the plan.

Activity:

  • Class:
  • Present their plans
  • SG p. 245-248
  • Give each group at least three differently sized containers.
  • Identify the two main variables (the cup and the volume)
  • Groups:
  • Draw a picture of the investigation
  • Purpose is to communicate the details of how they will construct the experiment.
  • Class: Explain they will measure the volume of each container three times. To obtain accurate data. Then they will graph the median.
  • Groups:
  • Collect data in their data table
  • Class (when most groups are at this point)
  • Explain why a bar graph is most appropriate – point graph is for when it makes sense to ask about values between data points.
  • Review finding median.
  • X axis: container
  • Y axis: Volume in cc
  • Groups:
  • Find median
  • Make graph
  • Answer questions

Conclusion:

  • Make group bar graph
  • Extension: SG p. 248

Homework:

  • DAB p. 247 – Volume Hunt (bring containers with them to school)

Name: ______Date: ______

Unit 16, Lesson 2: Fill ‘er Up! Lab

Step 1: Identify your variables

1st. ______

2nd.______

Step 1: Draw a picture of your experiment.

Step 2: Collect Your Data

Container / Volume in ______
unit
Trial 1 / Trial 2 / Trial 3 / Median

Step 3: Graph Data

Title

C

Container

Step 4: Questions About Data

  1. Which container has the smallest volume?
  1. Which container has the largest volume?
  1. Use your graph or your data to predict the number of full small containers you can pour into your large container. How many more cubic centimeters of water do you think you will need to fill the large container. Try to make your prediction as accurate as possible. Explain how you made your prediction.

______

______

______

______

______

______

______

______

Lesson 3: Volume Hunt

Goals: SWBAT…

  • Convert between U.S. Customary Units of Measurement—cup, pint, quart, and gallon.
  • Use addition, subtraction, multiplication, and division to solve problems involving volume.

Materials:

  • Volume Hunt Homework
  • Construction paper
  • 1 cup measuring cup
  • Bottles of different volumes

Introduction:

  • Will be talking about common measurements that we see our food in  cups, pints, quarts, gallons.
  • 2 cups = 1 pint
  • 2 pints = 1 quart
  • 4 quarts = 1 gallon
  • Make fraction strips for conversions.

Activity:

  • Each group gets a different container
  • Measure the number of cups needed to fill the container
  • Record data in DAB p. 248 table

Cup / Pint / Quart / Gallon
# of cups in a… / 1 / 2 / 4 / 16
# of pints in a… / ½ / 1 / 2 / 8
# of quarts in a… / ¼ / ½ / 1 / 4
# of gallons in a… / 1/16 / 1/8 / ¼ / 1

Conclusion:

  • Identify conversions
  • 2 cups = 1 pint
  • 2 pints = 1 quart
  • 4 quarts = 1 gallon
  • Make strips for the number of cups in each

Homework:

  • DAB p. 245 – Unit 16 Parts 3 & 4

Lesson 4: Design Our Chick Experiment

Goals:

  • SWBAT apply their understandings of volume.
  • SWBAT construct an experiment involving volume.
  • SWBAT collect, organize, graph, and analyze data.

Materials:

  • ¼ Measuring cup
  • Water
  • Chick food
  • Chick food dispenser
  • Chick water dispense
  • Graph paper
  • Data table

Introduction:

  • We will be designing our own experiment to figure out how much food and water our chicks drink.
  • We need to establish: variables, ways to collect data, & how to display our data

Activity:

  • Discussion of variables  Food consumption & Water consumption
  • Documentation
  • How often do we want to check the food levels? (every day?)
  • Recording  data table
  • Eventually make graphs  discuss what kinds of graphs we might make and the benefits of those graphs
  • Create a class data table to be posted in the classroom.
  • Issues with our variables (errors)
  • Spilled food
  • Spilled water
  • Wood shavings in the water
  • Needing to change the food or water
  • Evaporation

Conclusion:

  • Draw pictures of our experiment  with appropriate labels.
  • The materials  bottles, food, ¼ cup measure, food, water, chicks’ brooder set up.
  • Prediction
  • How much water do we think they will drink?
  • How much food do we think they will eat?

Homework:

  • Fluency Review

Lesson 5: Elixir of Youth

Goals: SWBAT…

  • Measure volume in metric units and customary units.
  • Use multiplication and division to solve problems involving volume.

Materials:

  • Elixir of Youth story in Adventure Book reader
  • Map of the world

Introduction:

  • We are going to be reading a story about a volume hunt
  • We are doing our own investigation of the food and water for the chicks

Activity:

  • Read adventure book stopping to ask questions.
  • Page 97  The winged bull is called a lamassu and they guarded the gates into the cities in Assyria.
  • What modern countries included the regions mentioned (Sumeria, Babylonia, Assyria, and Egypt? (Iraq, Kuwait, Iran, Turkey, and Egypt)
  • Do these regions sound familiar? They are all in Mesopotamia, where a lot of beginning farming began and we discussed in our history of farming.
  • Page 99 How long ago was 685 BCE? 2011 + 685 = 2696 years ago
  • Page 100 
  • If an elephant weighs 4 tons, about how many elephants would it take to equal 40 tons? (about 10)
  • What is an elixir of youth? (a liquid that restores youth to anyone who drinks it)
  • Page 102 
  • Have you ever seen a liquid leave a line on the side of a container?
  • What lab are you reminded of by what Sam and Tess are doing? Explain how so. (Fill ‘Er Up! And our chick experiment)
  • Page 103 How many gallons are there in 50 buckets if each bucked holds 5 gallons? (250 gallons)
  • Page 104 How do Sam and Tess know there were 250 milk containers? (because there were 250 gallons of liquid in the vase and each milk container holds one gallon)
  • Page 107 Who do you think might be the thief?
  • Page 109 
  • If Tanya was the last to use the museum station wagon and if she filed it up when she finished, then why is the tank in the station wagon not full now? (because the thief used the car afterwards and didn’t refill it)
  • How far do you think a car could go on 4 gallons of gas? (12 m/gal, 4 gallons would last 48 miles; 25 m/gal, 100 miles)
  • Page 110 
  • How many miles would the museum station wagon go on 2 gallons? On 5 gallons? On 12 gallons? (40, 100, 240 miles)
  • How do Sam and Tess know the thief’s hideout is about 40 miles away from the museum?(The thief drove a total of 80 miles since the thief had to get to the hideout and back again s/he must have driven 40 miles each way)
  • Page 111 What does the circle show on the map? (the radius is the distance from the center to the outside. The circle indicates all the places that are 40 miles away from the museum)
  • Page 112 
  • Why did Sam say, “That stuff really works!”? (He thought it turned the thief into a baby)
  • Is there really any such thing as an elixir of youth? (No, only in Harry Potter)

Conclusion:

  • Page 114 Who do you think the thief is?
  • Record the evidence that supports your theory
  • Share theories

Homework:

  • Fluency review

Lesson 6: Unit 16 Assessment