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TEKS Refinement 2006 –
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Tarleton State University
e to a Gallon 9-54 Race t o a Gal lon Recording Sheet #
What Units? (circle one) # of Cups
# of Pints
# of
Quarts
# Cups Added to Jug
(This turn onl
y
!)
# Cups Total in the
Jug (Running Total) 1 Cups pint s quarts 2 Cups pint s quarts 3 Cups pint s quarts 4 Cups pint s quarts 5 Cups pint s quarts 6 Cups pint s quarts 7 Cups pint s quarts 8 Cups pint s quarts 9 Cups pint s quarts 10 Cups pint s quarts 11 Cups pint s quarts 12 Cups pint s quarts 13 Cups pint s quarts 14 Cups pint s quarts 15 Cups pint s quarts 16 Cups pint s quarts 17 Cups pint s quarts 18 Cups pint s quarts 19 Cups pint s quarts 20 Cups pint s quarts 21 Cups pint s quarts
Number of Turns to Fill the Ga
llon
Number of Cups in t
h
e Gallon
Number of Cups in the Pint Number of Cups in t
h
e Quart
Race to a Gallon Summary Sheet
1. If you spin 1 pint, how many cups will you be able to add to the jug? 2. If you spin 4 pints, how many cups will you be able to add to the jug?
3. If you could spin 7 pints, how many cups would you be able to add to the jug? 4. Pretend that you added 10 cups to the jug after spinning “pints” (on a different set
of spinners). How many pints must you have spun?
5. If you added 6 cups to the jug after spinning “pints,” how many pints did you spin?
6. If you spin 1 quart, how many cups will you be able to add to the jug?
7. If you could spin 3 quarts, how many cups would you be able to add to the jug? 8. If you could spin 4 quarts, how many cups would you be able to add to the jug? 9. If you spin 2 quarts, how many pints will you be able to add to the jug?
10. If you already have 13 cups in the jug, can you complete the gallon in 1 more turn with this set of spinners? If so, how? If not, why not?
11. If you already have 13 cups in the jug, can you complete the gallon in exactly 2 more turns with this set of spinners? If so, how? If not, why not?
12. If you already have 13 cups in the jug, can you complete the gallon in exactly 3 more turns with this set of spinners? If so, how? If not, why not?
13. If you already have 13 cups in the jug, can you complete the gallon in exactly 4 more turns with this set of spinners? If so, how? If not, why not?
14. If you already have 12 cups in the jug, what do you hope you spin next with this set of spinners? Why?
15. What is the fewest number of turns necessary to complete the gallon with this set of spinners?
Summary Sheet – Answer Key
1. If you spin 1 pint, how many cups will you be able to add to the jug? 2 cups
2. If you spin 4 pints, how many cups will you be able to add to the jug? 8 cups
3. If you could spin 7 pints, how many cups would you be able to add to the jug? 14 cups
4. Pretend that you added 10 cups to the jug after spinning “pints” (on a different set of spinners). How many pints must you have spun? 5 pints
5. If you added 6 cups to the jug after spinning “pints,” how many pints did you spin? 3 pints
6. If you spin 1 quart, how many cups will you be able to add to the jug? 4 cups
7. If you could spin 3 quarts, how many cups would you be able to add to the jug?
12 cups
8. If you could spin 4 quarts, how many cups would you be able to add to the jug?
16 cups – the full gallon!
9. If you spin 2 quarts, how many pints will you be able to add to the jug? 4 pints
10. If you already have 13 cups in the jug, can you complete the gallon in 1 more turn with this set of spinners? If so, how? If not, why not? Yes, spin 3 cups
11. If you already have 13 cups in the jug, can you complete the gallon in exactly 2 more turns with this set of spinners? If so, how? If not, why not? Yes, the following ways would work: 1) spin 2 cups then 1 cup; 2) spin 1 cup then 2 cups; 3) spin 1 pint then 1 cup; 4) spin 1 cup then 1 pint
12. If you already have 13 cups in the jug, can you complete the gallon in exactly 3 more turns with this set of spinners? If so, how? If not, why not? Yes, spin 1 cup then 1 cup then 1 cup
13. If you already have 13 cups in the jug, can you complete the gallon in exactly 4 more turns with this set of spinners? If so, how? If not, why not? Yes… one scenario would be to spin 1 quart (add nothing to the jug), then spin 1 cup then 1 cup then 1 cup.
14. If you already have 12 cups in the jug, what do you hope you spin next with this set of spinners? Why? 4 cups or 2 pints or 1 quart…. Any of these spins would complete the gallon.
15. What is the fewest number of turns necessary to complete the gallon with this set of spinners? 2 turns; 2 quarts then 2 quarts – 2 turns to complete the
gallon; 4 pints then 4 pints – 2 turns to complete the gallon; 8 cups then 8 cups – 2 turns to complete the gallon
TEKS: See Appendix for student version of this activity with correlated TEKS.
Overview: An important concept in understanding the relationship between volume
and capacity is that an object submerged in water will displace a volume of water equal to the volume of the object that was submerged. In this lesson, participants will investigate the relationship between the volume of a centimeter cube (1 cubic centimeter) and the amount of water displaced when the cube is submerged in water (1 milliliter). Another outcome from this lesson is that participants will develop and refine their familiarity with the milliliter – one of the commonly encountered standard units for capacity in the metric system. At the conclusion of the lesson, the participants will use what they have learned about displacement to measure the volume of an irregularly shaped object. This lesson addresses the TEKS refinements by helping to build a conceptual
understanding of volume. A strong conceptual understanding of volume serves as preparation for the development and use of volume formulas (of rectangular prisms) in the refined 5th grade TEKS. The lesson also
strengthens the conceptual development of the relationship between volume and capacity. Finally, the lesson ties in well with the concept of finding density (mass per unit of volume) in science.
Materials: Handout 1-My Tub Runneth Over! Skit Script, 4 copies (pages 9-65 – 9-
67)
Handout 2-Recording Sheet #1 (page 9-68) Handout 3-Recording Sheet #2 (page 9-69) Handout 4-Recording Sheet #3 (page 9-70)
Handout 5-Recording Sheet #3 Answer Key (page 9-71) Handout 6-Recording Sheet #4 (page 9-72)
Graduated cylinder calibrated in milliliters – either 25 milliliter or 50 milliliter capacity, 1 per group
Graduated cylinders with larger capacities, 1 per group if needed Water in a container that allows participants to pour easily
Eyedroppers, 1 per group Dishpans, 1 per group Paper towels
Centimeter cubes, about 30 cubes per group – make sure that you have Rainbow cubes or the plastic centimeter cubes that are
approximately 1 gram each so that the cubes will sink
Collection of small objects such as marbles, small toys such as soldiers or dinosaurs, and so on (waterproof, non-floating, able to fit into the
graduated cylinder)
Time: 30 – 45 minutes Lesson:
Procedures Notes
1. Select four participants to participate in the skit: My Tub Runneth Over (page 9-65 – 9- 67). You will need readers for the following characters:
Narrator King Hiero Goldsmith Archimedes
This story has been shared through the ages. The skit was adapted from a printed version found in The Book of Virtues: A Treasury of Great Moral Stories on pages 562 – 564.
Have participants act out the skit if you wish, or just have them read the parts.
2. Give each group of participants a graduated
cylinder that is calibrated in milliliters. The 25 milliliter cylinders and the 50 milliliter cylinders work well. Make sure that the increments show markings for single milliliters.
3. Have each group pour some water into the cylinder, filling it from one-third to two-thirds full.
Make sure to pour over a dishpan to catch any spills. Participants should work over dishpans as well in case a cylinder gets turned over.
Be vague as to the amount of water to pour into the cylinder. You want some variety throughout the large group so that the
participants can see that the relationship between volume and the amount of water displaced does not depend on the original amount of water in the cylinder. 4. Explain how to read the markings on the
graduated cylinder.
The participants should read the cylinder at eye level. If necessary, the participants may want to put a sheet of paper behind the
cylinder to make the markings easier to read. The water will form a “meniscus” – it will be higher at the sides of the cylinder than it is in
You may wish to provide food coloring to color the water so that the participants can read the markings more easily.
the center of the cylinder. The participants should read the marking on the cylinder that is level with the bottom of the meniscus. If the reading from the graduated cylinder falls between two milliliter markings, participants should use the eyedropper to add a small amount of water to the cylinder to raise the water level to a milliliter marking. 5. Each group should read the markings on the
graduated cylinder and record how many milliliters of water are in the graduated cylinder on Handout 2-Recording Sheet #1 (page 9-68).
Ask each group to share how many milliliters of water they have in the graduated cylinder.
By having each group share, the leader can assess if the
participants understand how to read the markings on the graduated cylinder.
An interesting discussion can come about because of the different sizes of graduated cylinders. For example, 20 milliliters in a 25-milliliter capacity cylinder will appear different than 20 milliliters in a 50-milliliter capacity cylinder.
6. Give each group about 30 centimeter cubes. Lead the class in a brainstorming session to recall the attributes of the centimeter cube that were developed in the activity Skeletons in the Closet (pages 9-14 – 9-22).
Sample list:
12 edges measuring one centimeter each in length
6 faces with an area of 1 square centimeter each
1 cube with a volume of 1 cubic centimeter
7. Ask: What do you think will happen to the water level if we drop 1 centimeter cube into the water in the graduated cylinder?
The water level should rise.
What do you think the reading on the graduated cylinder will be after we drop 1
Procedures Notes
centimeter cube into the water? Predict to your partner and then record your prediction on Recording Sheet #1.
8. Now have each group drop a centimeter cube into the water in the graduated cylinder, read the marking from the graduated
cylinder, and record on Recording Sheet #1. 9. Ask: How much did the water level rise
when we dropped 1 centimeter cube into the water?
The water level rose 1 milliliter.
Have participants write a statement about their observation on Recording Sheet #1.
Sample participant response: The water level rose 1 milliliter when we dropped 1 centimeter cube into the water.
10. Ask: If we drop 1 more centimeter cube into the water, what do you think will happen to the water level?
The water level should rise another milliliter. Have participants record the water level for 0 cubes and 1 cube on Handout 3-Recording Sheet #2 (page 9-69). Then have
participants drop in another centimeter cube to see if their predictions were correct. Record the results on Recording Sheet #2. 11. Have participants continue to drop in
centimeter cubes, 1 at a time, to complete the table on Recording Sheet #2.
Each group of participants should only have about 30 centimeter cubes, so they should be looking for a pattern to emerge fairly quickly.
12. Ask: How many centimeter cubes would you have to drop into the water to raise the water level to the top marking on the graduated cylinder?
Answers will vary, depending on the capacity of the cylinder and the amount of water initially poured into the cylinder. 13. Let’s summarize what we have
discovered…. We’ll record our summary on Handout 4-Recording Sheet #3 (page 9-70).
Handout 5-Recording Sheet #3 Answer Key (page 9-71) is
Ask: How much water is displaced by each centimeter cube?
1 milliliter of water is displaced by each centimeter cube.
Ask: What is the volume of each centimeter cube?
The volume of each centimeter cube is 1 cubic centimeter.
Make sure that participants use correct units during class
discussions, and that participants write the units when recording measurements. We as teachers should model good
communication skills by always indicating the unit as well, not just the quantity.
14. If one of our centimeter cubes were a hollow box without a top, how much water do you think it would take to fill it?
It would take 1 milliliter of water to fill a hollow centimeter cube.
So, what is the capacity of a centimeter cube?
1 milliliter
15. Ask: How does the space taken up by the centimeter cube and the space taken up by 1 milliliter of water compare?
The centimeter cube and 1 milliliter of water each take up the same amount of space. Ask: So, how does a volume of 1 cubic centimeter compare with 1 milliliter of water? A volume of 1 cubic centimeter and 1
milliliter of water each take up the same amount of space.
Reinforce that capacity is the
same as maximum volume.
Remind participants of Full to Capacity (pages 9-31 – 9-43) where this concept was
developed.
16. Give each group a small object that is not a rectangular prism (so the participants will not have a formula with which to find the volume of the object).
Suggestions for objects would be marbles, small toys such as soldiers or dinosaurs, and so on. Make sure that the objects do not float in water. Also, make sure that the objects are waterproof
Procedures Notes
and small enough to fit into a graduated cylinder.
17. Have each group identify their object on Handout 6-Recording Sheet #4 (page 9-72). Then have them predict the volume of their object in cubic centimeters. The predictions should be recorded on Recording Sheet #4 as well.
Have each group devise a plan to measure the volume of the object in cubic centimeters, reflecting on the displacement properties they have just observed. The groups should explain the plan in writing on Recording Sheet #4.
18. After the groups have written their plans, have each group carry out the plan at their tables.
Depending on the size of the object with which the group is working, the group may want to use a larger graduated cylinder. After completing the plan, the group should complete Recording Sheet #4 by recording their measurement for the volume of the object.
It is important that the object be completely submerged.
19. As participants reflect on the lesson, have each group share their results.
Assessment: Assessment is done throughout the lesson, as groups discuss, share,
and refine their understanding of the concepts.
Extensions: Ask participants to devise a plan to find the volume of a 2nd object
without removing the 1st object from the cylinder. How would you modify your plan if the 2nd object won’t fully submerge with the original amount of water?
Given a set of objects, predict which has greater volume. Then, test your prediction.
virtues: A treasury of great moral stories (pp. 562-564). New York: Touchstone.
My Tub Runneth Over!
Adapted from Eureka! As retold by James Baldwin and published in The Book of Virtues: A Treasury of Great Moral Stories (William J. Bennett, Editor)
Narrator: There was once a king of Syracuse whose name was Hiero. The country
over which he ruled was quite small, but for that reason he wanted to wear the biggest crown in the world. So he called in a famous goldsmith, who was skillful in all kinds of fine work, and gave him ten pounds of pure gold.
King Hiero: Take this and fashion it into a crown that shall make every other king want
it for his own. Be sure that you put into it every grain of the gold I give you, and do not mix any other metal with it.
Goldsmith: It shall be as you wish. Here I receive from you ten pounds of pure gold.
Within ninety days I will return to you the finished crown which shall be of exactly the same weight.
Narrator: Ninety days later, true to his word, the goldsmith brought the crown. It was a
beautiful piece of work, and all who saw it said that it had not its equal in the world. When King Hiero put it on his head it felt very uncomfortable, but he did not mind that – he was sure that no other king had so fine a headpiece. After he admired it from this side and from that, he weighed it on his own scales. It was exactly as heavy as he had ordered.
King Hiero: You deserve great praise. You have wrought very skillfully and you have
not lost a grain of my gold.
Narrator: There was in the king’s court a very wise man whose name was Archimedes.
When he was called in to admire the king’s crown he turned it over many times and examined it very closely.
King Hiero: Well, what do you think of it?
Archimedes: The workmanship is indeed very beautiful, but – but the gold –
King Hiero: The gold is all there! I weighed it on my own scales.
Archimedes: True, but it does not appear to have the same rich red color that in had in
the lump. It is not red at all, but a brilliant yellow, as you can plainly see.
King Hiero: Most gold is yellow. But now that you speak of it I do remember that when
this was in the lump, it had a much richer color.
Archimedes: What if the goldsmith has kept out a pound or two of the gold and made
working.