Week 5

1
Week 5

• Warm up Problem What did the student do wrong?
• 457 - 29 338
• Explain the error in a sentence.

2
What makes a good answer?

• 457 - 29 338.
• Incomplete answers was supposed to cross out
  the 5 and make it a 4.
• This does not explain mathematically why it is
  wrong. It only says which rule was broken in the
  standard algorithm.
• Better answer In the minuend, we need to
  exchange a ten for some ones. So, 5 tens and 7
  ones is the same as 4 tens and 17 ones. This
  student did not trade the ten away, and so thinks
  that 5 tens and 7 ones is the same as 5 tens and
  17 ones.

3
Types of errors

• 36 28 91
• Possible answers Student added 6 8 14, and
  put the 1 down and the 4 up when it should be the
  4 down and the 1 up. You need to explain why this
  is wrong--otherwise, addition is just a bunch of
  rules!
• Better answer Student added 6 8 14, but
  thought that 14 is 4 tens and and 1 one. But 14
  is really 1 ten and 4 ones. Correct answer is 1
  ten and 4 ones and 5 tens which is 64.

4
Types of errors

• 36 28 514
• Possible answer The student put the 5 next to
  the 14, which is wrong. Answer should be 64.
• Better answer The student added 6 8 which is
  14, or 1 ten and 4 ones. But then the student
  added 3 tens and 2 ones, and recorded this as 5
  hundreds instead of 5 tens. Answer should be 6
  tens and 4 ones, or 64.

5
Types of errors

• 365 287 742
• Possible answer The student added 5 7 12,
  but put the 1 on top of the 3 instead of the 6.
• Better answer The student added 5 7 12,
  which is 1 ten and 2 ones. But the student
  recorded this as 1 hundred and 2 ones. The
  correct answer is 652.

6

• Exam (50 minutes) next class. Bring calculator,
  pen or pencil, and colored pens, pencils,
  markers.
• Dont memorize the names of strategies for mental
  calculation or estimation.
• Do memorize the number systems (Roman, Egyptian,
  Mayan, Babylonian, and Alphabitian) through
  hundreds.
• Answers to sample questions
• Buy the class notes!!!

7
A real problem

• Place the digits 1, 2, 3, 6, 7, 8 in the boxes to
  obtain
• Greatest sumLeast sumGreatest differenceLeast
  difference

8
A quick review of subtraction

• Try this Explain what the student is doing.
• 8 7 8 8- 3 9 --gt - 4 0
• 4 8

9
A quick review of subtraction

• Find a, b, c, and d that will make this
  subtraction problem work. (a, b, c, d all
  different numbers.)
• 6 a b - c 8 b
• 1 d a

10
Use manipulatives or diagrams to show or use
words to explain why

• 9 8 4 9 8 14- 3 6 8 - 3 7
  8
• 6 1 6

11
Alphabitia

• C B A
• D C A
• NO NEW SYMBOLS! You may only use A, B, C, D,
  and 0.
• In any base,
• base 7, you may use 0, 1, 2, 3, 4, 5, 6.
• In base 9 0, 1, 2, 3, 4, 5, 6, 7, 8.
• In base N 0, 1, , N-1.

12
Use pictures or diagrams to explain

• Write 1e716 in base 10.Write 39010 in base
  5.True or false 425 346

13
Why is this a pattern?

• Find the ones digit for 329.
• Can you find the ones digit for the first 10
  powers of 3?
• 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049,
  

14

• So, there are 4 terms that repeat in this
  sequence. To find the 29th term, do 29 4 7
  R 1.
• So, since the remainder is 1, we look for the
  first term, which is 3.
• Now, how do we know this patterns continues? Be
  able to write a sentence for this.

15

• It continues because when we multiply the ones
  digits of each factor by 3, we are always going
  to have one of these
• .3 3 ..9
• .9 3 ..7 (from 27)
• .7 3 ..1 (from 21)
• .1 3 ..3

16
Problem Solving

• I bought 27 apples and oranges. Apples cost
  0.59 each. Oranges cost 0.69 each. Before
  tax, I spent 17.63. How many apples and how
  many oranges did I buy?
• Answer You bought 10 apples and 17 oranges.