Homework Explanations - PowerPoint PPT Presentation

1 / 20
About This Presentation
Title:

Homework Explanations

Description:

We have pigs and chickens in our barnyard. I count 24 heads and 80 feet. ... Each pig has 4 feet and each chicken has 2 feet, so 4p 2c = 80. Four 4s ... – PowerPoint PPT presentation

Number of Views:33
Avg rating:3.0/5.0
Slides: 21
Provided by: suzannew7
Learn more at: https://math.arizona.edu
Category:

less

Transcript and Presenter's Notes

Title: Homework Explanations


1
Homework Explanations
  • Problem A school play charges 2 for students
    and 5 for adults. For the three days of the
    play, 20 tickets were sold and 85 was raised.
    How many student tickets were sold?

2
Unacceptable Answers
  • 15 tickets for 5, 5 tickets for 2
  • The school sold fifteen 5 tickets and five 2
    tickets.
  • I did the work in my head.
  • I did the work on my calculator.

3
More Unacceptable Answers
  • 2x 5y 85 x y 20.
  • I just tried a bunch of things. Arent I
    lucky--I got it on the first try.
  • This is a stupid problem and I am not going to
    waste your time explaining it to you.

4
So, what is a good answer?
  • I know there are 20 tickets. So I tried to find
    out numbers that add to 20 that also made 85
    dollars.
  • if x 10 and y 10, then 2 10 5 10 70
  • If x 12 and y 8, then 2 12 5 8 64
    this is too small. So, try y gt 10.
  • If x 6 and y 14, then 2 6 5 14 82.
    Still too small.
  • If x 5 and y 15, then 2 5 5 15 85!
  • The school sold 5 tickets for 2 and 15 tickets
    for 5.

5
Another good answer
  • If we let x number of 2 tickets, and if we let
    y number of 5 tickets, then
  • x y 20 is the equation for the number of
    tickets and 2x 5y 85 is the equation for the
    amount of money.
  • We can rewrite x y 20 as x 20 - y.
  • Substitute 2(20 - y) 5y 85.
  • 40 - 2y 5y 85
  • 40 3y 85.
  • Subtract 40 from both sides of the equation 3y
    45 Divide both sides by 3
  • y 15, Therefore, because y represents the
    number of 5, there were fifteen 5 tickets and
    then, because x y 20, there were 5 2 tickets
    sold.

6
Things to Remember
  • Explain what you did.
  • Explain why you did it.
  • Be sure you check to see that the answer does
    really answer the question asked.
  • Check to make sure you have not made arithmetic
    errors.

7
Exploration 1.1
  • Goal of the problem with (24) students in
    class, including yourself, if each student shakes
    hands with every student, how many handshakes
    will there be?

8
How to Solve a Problem
  • Read--understand EVERY ASPECT of the problem.
    What is given, what is to be found, what can be
    assumed, what should not be assumed, all
    vocabulary, what the final answer should look
    like, etc.
  • Plan--ways to get at the final answer
  • Find the answer.
  • Check and extend.

9
Exploration 1.1
  • 1. Work on this problem alone for a few minutes.
    Can you apply ideas discussed in the preface to
    find patterns in this problem? Can you use what
    you see to help you plan a solution?

10
Exploration 1.1
  • 2. Discuss your ideas with everyone at your
    table. Describe new ideas that you like that
    arose from the discussion. (Note if you have
    already solved the problem, do not just tell the
    answer. Tell IDEAS that will allow your peers to
    get the answer on their own.)

11
Exploration 1.1
  • 3. Now solve the problem on your own.
  • 4. With those at your table, compare your
    solution strategies. Which one(s) do you like
    best? Why?

12
Exploration 1.1
  • 4. Continued. As a table, write an explanation
    that shows WHAT you did and WHY you did it. Be
    ready to read this.
  • 5. Can you explain how to find the number of
    handshakes if there are n students in class
    today? Work on this with your table-mates.

13
Pigs and Chickens
  • A farmers daughter likes working math problems
    so he gives her this problem to work on
  • We have pigs and chickens in our barnyard. I
    count 24 heads and 80 feet. How many pigs and
    how many chickens are out there?

14
Using random trial and error
15
Guess-check-revise
  • Organized trial and error.

16
Make a diagram
  • Use pictures to clarify and help solve the
    problem.

17
Use algebra
  • There are 24 animals total p c
    24 p represents the number of pigs and c
    represents the number of chickens.
  • There are 48 feet. Each pig has 4 feet and each
    chicken has 2 feet, so 4p 2c 80

18
Four 4s
  • Use four 4s and the arithmetic operations (, -,
    x, /) plus grouping symbols to create each of the
    counting numbers from 0 to 10.
  • Use exactly four 4s for each number.

19
Principles and Standards of School Mathematics
(NCTM, 2000)
  • Website http//www.nctm.org/standards/
  • Five process standards problem
    solving reasoning and proof communication conne
    ctions representations

20
Homework
  • Due Mon 8/27 Complete and write up Exploration
    1.1 how many handshakes? pp. 26 - 29 3,
    5,14, 21a, 22d,f, 25, 30c, 39.
  • Due Wed 8/29 Complete and write up Exploration
    1.4 darts. pp.
    54-57 11, 12a, 3a
  • Extra practice pp. 59 2, 4, 5, 8, 9, 12
Write a Comment
User Comments (0)
About PowerShow.com