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UMI Welcome!

UMI Welcome!. July 8, 2014. Today’s Lesson ah. Place value and algebraic patterns, ratio and proportion, multiple representations, procedural fluency and order of operations. Warm Up ah. a. b. Does one expression have a greater value? 2 x (3 x 4) ( 3 x 2 ) x 4.

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UMI Welcome!

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  1. UMIWelcome! July 8, 2014

  2. Today’s Lesson ah Place value and algebraic patterns, ratio and proportion, multiple representations, procedural fluency and order of operations

  3. Warm Up ah a. b. Does one expression have a greater value? 2 x (3 x 4) ( 3 x 2 ) x 4 c. What is the value of d. 35 x 10 35 x 100 35 x 1000

  4. Warm Up ah As I was going to St. Ives, I met a man with seven wives, Each wife had seven sacks, Each sack had seven cats, Each cat had seven kits: Kits, cats, sacks, and wives, How many were there going to St. Ives?

  5. Place Value ah • Standard Form – when a number is written using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 • Place Value – determined by the position of each digit in the number

  6. Place Value ah • Periods – separation of each group of digits by a comma when a number is written in standard form • The number 3,786,451,294 has four periods • The period names are shown in blue in the place-value chart on previous slide • Try these examples: • Write 25,478,083 in words • Write three hundred thousand three in standard form • Write four hundred fifty-two thousand seven in standard form

  7. Place Value The Hundreds Chart ah • Work in pairs to find patterns on the hundred chart. • What patterns did you find? • Explain another’s discovered pattern.

  8. Multiple Representations ah Other representations of using place value • Expanded form • Try these examples: • Write 23,859 in expanded form. • Write 709,542 in expanded form. 2 Tens 6 Thousands 2 Ten- Thousands 4 Hundreds 9 Ones + + + +

  9. Multiple Representations ah More representations of place value • Building on the understanding of tens and ones to include an understanding that ten tens can be grouped to make a hundred and ten hundreds can be grouped to make a thousand, and so on • Finding the number that is ten more/less and a hundred more/less than a given number, i.e., a specific three digit number • Comparing and ordering of whole numbers • Representing and using decimals

  10. Before we move on to Ratio and Proportion kac Take Two minutes andTell someone you do not know what you like best about teaching math

  11. Procedural Fluencyah • In order to be really fluent, students must understand the mathematics of the facts they are expected to memorize. • Fluency comes at the endpoint of clear learning progressions as documented in the core standards. • Students should experience the use of concrete and pictorial representations of math problems.

  12. Procedural Fluency ah • https://www.youtube.com/watch?v=ZFUAV00bTwA

  13. Ratio and Proportion kac • A ratio is a comparison of two quantities • Comparisons can be part-to-part, part-to-whole or whole-to-part Ratios are written as a fraction Or with a colon 3:8

  14. Ratio and Proportion • 7 males and 12 females at the Dew Drop Inn • In the game room next door there were 14 males and 24 females Let’s practice • Males to females at the Inn • Males to females at the game room • Males in the game room to the number of people in the game room

  15. Ratio and Proportion kac • A proportion is a comparison of two equal ratios or two equal fractions • http://www.mathplayground.com/mv_proportions.html

  16. Ratio and Proportion kac Let’s Practice a. Guess and Check b. Cross Multiply c. Standard Algorithm

  17. Before we move on to Algebraic Order of Operations kac Take two minutes and Tell someone you have not talked to today when you last used Ratio and Proportion

  18. Order of Operations md • What is Operation? • Addition • Subtraction • Multiplication • Division • How to do the problem like this? 8 + (5 × 42 + 7) • What part should you calculate first? • Start at the left and go to the right? • Or go from right to left?

  19. Order of Operations md • Parentheses first-----P • Exponents (i.e. Powers and Square Roots, etc.)-E • Multiplication and Division (left-to-right)---MD • Addition and Subtraction (left-to-right)---AS PEMDAS Please Excuse My Dear Aunt Sally

  20. Order of Operations md Examples: = • P--Parentheses first 2. = • E--Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract.

  21. Order of Operations md Examples: =13 • MD--Multiply or Divide before you Add or Subtract 4. = • Otherwise just go left to right.

  22. Order of Operations md Oh, yes, and what about ? • Start inside Parentheses, and then use Exponents First • Then Multiply • Then Add • 8 + 87Parentheses completed, last operation is an Add • 95 DONE !

  23. Order of Operations md • Let’s practice • 2 + 3 x 6 • (2 + 3) x 6 • 8 – 9 ÷ 3 x 2 + 3 = 4.

  24. Order of Operations md • Let’s play game • Order of Operations Game

  25. Closure kac • Tell someone sitting near you two things • A new piece of information you learned today • Something in math you knew but had not used or thought about in some time

  26. Problem Solving Who is the Liar? Four friends were shown a number. Here is what they had to say about the number. Mascheal: It has two digits. Min: It goes evenly into 150. Angelene: It is not 150. Karen: It is divisible by 25. It turns out that one and only one of the four friends is lying. Which one is it?

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