Place Value, Multiplication, Division Document Transcript
Using Power of Ten as a tool to Understand: Place Value Multiplication Division
Place Value N3.1 Demonstrate understanding of whole numbers to 1000 (concretely, pictorially, physically, orally, in writing, and symbolically) including: ·representing (including place value) ·describing ·estimating with referents ·comparing two numbers ·ordering three or more numbers. N4.1 Demonstrate an understanding of whole numbers to 10 000 (pictorially, physically, symbolically) by: ·representing ·describing ·comparing two numbers ·ordering three or more numbers.
http://www.rif.org/assets/Documents/readingplanet/ReadAloud_Stories/zero_the_hero.html http://www.youtube.com/watch?v=Nvc2PPTlW7k Number Relationships: Anchoring Numbers to 10 ·Students need a solid foundation of 'ten' ·There are many activities to develop this concept. We are going to experience a few games to practice this concept of 'tenness'. 1. Salute 2. Advanced Salute http://www.poweroften.ca/index.php?view=video&id=34%3Agrade-3-salute&option=com_jomtube&Itemid=139 Credit to drjean.org Once students have mastered 'tenness' then they can move to number relationships of larger numbers. "Zero the Hero" Story
Rounding Story of Rounding 10 9 8 2 4 5 1 3 6 7
83 70 90 80
Who could they be? A C D B What numbers do you think are A,B,C, and D and why?
Close, Far and In Between Which two numbers are closest and why? Which number is closest to 200? Why? Name a number in between any of these two numbers. _____ ______ ______ How far apart are 184 and 199? Explain how you know. If these are big numbers, what are some small numbers? List 3 numbers that make these numbers seem small?
What could we do with these numbers? Connections to Real -World Ideas 1 752 Population of Langenburg , Germany 1 048 Population of Langenburg, Saskatchewan, Canada Add the numbers in your head. What were the strategies that you used?
Build a number that you see. 41 37 19 13 9 12 31 22 38 28
Make 50 Build a number that you see. 41 37 19 13 9 12 31 22 38 28
Build a number that you see. 565 720 635 185 550 450 815 435 365 760 280
Make 1 000 Build a number that you see. 565 720 635 185 550 450 815 435 365 760 280
Multiplication and Division N3.3 Demonstrate understanding of multiplication to 5 × 5 and the corresponding division statements including: · representing and explaining using repeated addition or subtraction, equal grouping, and arrays · creating and solving situational questions · modelling processes using concrete, physical, and visual representations, and recording the process symbolically · relating multiplication and division. N4.3 Demonstrate an understanding of multiplication of whole numbers (limited to numbers less than or equal to 10) by: · applying mental mathematics strategies · explaining the results of multiplying by 0 and 1. N4.4 Demonstrate an understanding of multiplication of whole numbers (2- or 3-digit by 1 - digit) by: · modeling the distributive property · using personal strategies for multiplication, with and without concrete materials · using arrays to represent multiplication · connecting concrete representations to symbolic representations · estimating products solving problems. N4.5 Demonstrate an understanding of division of whole numbers(1-digit divisor to 2-digit dividend) by: · using personal strategies for dividing, with and without concrete materials · estimating quotients · explaining the results of dividing by 1 · solving problems involving division of whole numbers · relating division to multiplication.
Students should know their doubles before you begin multiplication and division. http://www.poweroften.ca/index.php?view=video&id=44&option=com_jomtube&Itemid=139 http://www.poweroften.ca/index.php?view=video&id=46&option=com_jomtube&Itemid=139
Division should also be taught along with multiplication. When an array is created or a specific area is calculated, the relevant division questions should always be discussed at the same time. For example: when examining the 24th day of a month during calendar time and discussing the varied groupings possible that equal 24, some students will build an array that shows: 4 groups of 6 or 4 × 6 = 24. This array should at once be related to all the facts in this family of groupings: •4 × 6 = 24 •6 × 4 = 24 •24 ÷ 6 = 4 ·24 ÷ 4 = 6 Some effective teaching strategies for developing multiplication concepts are as follows: •Avoid teaching a multiplication table in a specific order, as this promotes counting strategies. Instead use a doubling strategy such as 2 × 5 = 10, 4 × 5 = 20, and 8 × 5 = 40. •Avoid teaching tables before grade three. •Teach meaning through grouping, calendar time, and meaningful projects. •When teaching the multiplication tables, use many varied strategies including: ÖForming groups ÖMaking arrays ÖGraphing arrays on cm grid paper ÖRelating multiplication to area ÖUsing number lines ÖClapping the facts, and using music and rhymes to reinforce multiplication facts ÖUsing visual tools ÖBreaking numbers up •Relate multiplication equations to other questions that are similar and more readily understandable. •Use kinesthetic approaches (clapping, standing and sitting, and manipulating or handling egg cartons).
bounce ball- rhythmic (Page 112) Teaching the 5 Times Tables First 1 group of 5 2 groups of 5
How many 5's make 20?
I see... I think... This reminds me of...
Next teach the 10 times tables. What patterns do you notice? 0 and 1 5,10,0,1 this leaves 2,3,4,6,7,8,9 (2's are doubles) http://vimeo.com/15261830 You have only half of the remaining due to the commutative property!!!
16x8= 8x8=4x8=32....64 64x2=128 8x6= (halving and doubling strategy) Learning the Difficult Multiplication Facts 6,7,8 http://www.poweroften.ca/index.php?view=video&id=42%3Agrade-3-learning-the-difficult-multiplication-facts&option=com_jomtube&Itemid=139 18x25=9x50
Show What is my question sheet page 59 I am thinking of a question : It is a multiple of 4. The product is greater than 30 and less than 40. The sum of the digits in the product is 5. What is my question?
4,8,16,20,24,28,32,36,40, 3+2=5 3+6=9 The answer is 8x4=32
A hotel has 24 windows on a floor. There are 9 floors. How many windows are there? Is the number of windows more than 240? How do you know? How could you estimate the number of windows? How could you use manipulatives to model the problem? Mental Math ?
Describe a situation when you might divide 50 by 4. Now describe a situation when you are forming groups but don't divide.
Susan says 45-9-9-9-9-9=0 describes division do you agree? Explain.
Partitioning or Fair Sharing The bag has 783 jelly beans, and Maggie and her four friends want to share them equally. How many jelly beans will Maggie and each of her friends each get? Measurement or Repeated Subtraction Concept Jumbo the elephant loves peanuts. His trainer has 620 peanuts. If he gives Jumbo 20 peanuts each day, how many days will the peanuts last?
Jumbo the elephant loves peanuts. His trainer has 20 peanuts. If he gives Jumbo 5 peanuts each day, how many days will the peanuts last? Number of Peanuts Day
The bag has 783 jelly beans, and Maggie and her four friends want to share them equally. How many jelly beans will Maggie and each of her friends each get?
Jumbo the elephant loves peanuts. His trainer has 20 peanuts. If he gives Jumbo 5 peanuts each day, how many days will the peanuts last? ------------------------------------------------------------------ What if he only gave 2 a day, how many days will the peanuts last? Number of Peanuts Day