Counting Stars Objectives • Students will learn a method for counting objects as numerous as the stars. • Students will gain an understanding of the immense size of our universe. Suggested Grade Level 8th grade Subject Areas Science Math Timeline Two 50-minute periods Background Knowledge Students need to understand that space is 3-dimentional. Students will need to be able to multiply small and large numbers. Students will need an understanding of area. Area relationships are needed for calculations. Students will also need knowledge of the area formula and the use of a metric ruler for a more challenging experience. Materials Paper Pencil Small bags of pretzels Paper towels Triple beam balance Large bag of pretzels Note card Lab sheets 1,2 and 3 (see Addendums 1,2,3) Lesson 1. Pose the key question of the lab: How do scientists count the stars? Accept all answers. 2. Tell the students they are going to perform a method of estimation that scientist use to estimate large quantities such as the number of stars. 3. Lab question-What is the total number of grains of salt attached to the pretzels in the large bag? Accept all answers. 4. Ask the students how they might come up with the answer. Are any of their methods practical? 5. Tell students that they are going to use one method for counting and hand out the lab sheet. (See lab sheet for steps)

6. After completing the lab, have the students brainstorm how scientists could use a method similar to this to estimate the number of stars in the sky. You are looking for a response that details how a scientist might choose small parts of the sky and count only that portion, then choose another section and use the average to estimate the total number of stars in the sky. You can use a topic as simple as multiplication or a concept such as ratios and proportions for the more advanced. 7. Discussion questions: Why use 10 samples? Could you get an answer with 1 sample? What about 100 samples? Is your solution the exact answer? Is an exact answer needed? 8. Estimates for the number of stars in space is between 100 billion-400 billion, how many 2 kg bags of pretzels are needed to have 100 billion salt grains attached? Day 2 1. Hand the students lab sheet 2 and a note card with a 1-cm square cut out. 2. Have students trace the 1-cm square at some location on the lab sheet. 3. Repeat 9 more times. 4. Have the students count and record the number of “stars” located in each box. 5. Have students find the average number of “stars” per box. 6. If the entire “sky” has an area of 100 cm, then about how many “stars” are on the page? Use multiplication, ratios, and proportions… 7. Discuss why it is 100 times more. 8. Assessment of understanding- Hand out Lab Sheet 3 to be done individually. You may or may not want to give the dimensions of the star field. 9. Key Question-How could this method be used to estimate the number of stars in the Universe? 10. As a class, in groups or individually, brainstorm the method that scientist might follow. Extensions Use the method for counting various things (trees in a forest, people in a crowd, bees in a honeycomb, bacteria). Evaluation/Assessment Evaluation of student learning will be assessed by the completion of the 3-lab sheets with higher consideration to lab sheet three, the individual task. Are the estimates reasonable? Resources http://www.stargazing.net/david/constel/howmanystars.html http://www.esa.int/esaSC/SEM75BS1VED_extreme_0.html

Addendum 1

Lab Sheet 1

1. Carefully remove each pretzel from the bag and place it on a paper towel. Label each pretzel 1-10. 2. Carefully count the number of salt grains on each pretzel and record that number below. Pretzel

Grains of Salt

1 2 3 4 5 6 7 8 9 10 3. Find the average number of salt grains per pretzel by adding the grains of salt column and dividing by 10. (Round to the nearest whole number) 4. The average number of salt grains is ______________. 5. Carefully transfer all ten pretzels to the triple beam balance. Find the mass. 6. The mass of the ten pretzels is ____________. 7. Find the average mass of one pretzel. (Rounded to the nearest whole number) 8. The average mass of one pretzel is ______________. 9. If the mass of the large bag of pretzels is 2-kg (2000g), about how many pretzels would you expect to be in it? 10. The number of pretzels in the large bag is about ______________. 11. About how many total grains of salt are attached to all of the pretzels in the bag? 12. The number of salt grains attached to the pretzels in the bag is about ____________.

Addendum 2

Lab Sheet 2 10 cm x 10 cm

1.

Place the note card inside the square; trace the square onto the star field. Label this # 1.

2.

Count and record the number of stars in box #1.

3.

Repeat steps 1 and 2 nine more times, record the data below.

4.

What is the average number of stars in a box? (Round to the nearest whole number)

5.

If the area of the entire square is 100 times more than the area of the note card’s square, about how many stars are there?

Box 1 2 3 4 5 6

# of stars

7 8 9 10

Average # of stars per 1-cm square: _____________________ Estimated total # of stars on the page: ___________________

Addendum 3

Lab Sheet 3

1. About how many stars are inside the rectangle? _______________________