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# Place Value, Multiplication, Division

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### Place Value, Multiplication, Division

1. 1. Using Power of Ten as a tool to Understand:<br />Place Value<br />Multiplication<br />Division<br />
2. 2. Place Value<br />N3.1 Demonstrate understanding of whole numbers to 1000 (concretely, pictorially, physically, orally, in writing, and symbolically) including:<br />·representing (including place value)<br />·describing<br />·estimating with referents<br />·comparing two numbers<br />·ordering three or more numbers.<br />N4.1 Demonstrate an understanding of whole numbers to 10 000 (pictorially, physically, symbolically) by:<br />·representing<br />·describing<br />·comparing two numbers<br />·ordering three or more numbers.<br />
3. 3. http://www.rif.org/assets/Documents/readingplanet/ReadAloud_Stories/zero_the_hero.html<br />http://www.youtube.com/watch?v=Nvc2PPTlW7k<br />Number Relationships:<br />Anchoring Numbers to 10<br />·Students need a solid foundation of 'ten'<br />·There are many activities to develop this concept. <br />We are going to experience a few games to practice this concept of 'tenness'.<br />1. Salute <br />2. Advanced Salute<br />http://www.poweroften.ca/index.php?view=video&id=34%3Agrade-3-salute&option=com_jomtube&Itemid=139<br />Credit to drjean.org<br />Once students have mastered 'tenness' then they can move to number relationships of larger numbers.<br />"Zero the Hero" Story<br />
4. 4. Rounding<br />Story of Rounding<br />10<br />9<br />8<br />2<br />4<br />5<br />1<br />3<br />6<br />7<br />
5. 5. 83<br />70<br />90<br />80<br />
6. 6. Who could they be?<br />A<br />C<br />D<br />B<br />What numbers do you think are A,B,C, and D and why?<br />
7. 7. Close, Far and In Between<br />Which two numbers are closest and why?<br />Which number is closest to 200? Why?<br />Name a number in between any of these two numbers. _____ ______ ______<br />How far apart are 184 and 199? Explain how you know.<br />If these are big numbers, what are some small numbers?<br />List 3 numbers that make these numbers seem small?<br />
8. 8. What could we do with these numbers?<br />Connections to Real -World Ideas<br />1 752<br />Population of Langenburg , Germany<br />1 048<br />Population of Langenburg, Saskatchewan, Canada <br />Add the numbers in your head. What were the strategies that you used? <br />
9. 9. Build a number that you see.<br />41<br />37<br />19<br />13<br />9<br />12<br />31<br />22<br />38<br />28<br />
10. 10. Make 50<br />Build a number that you see.<br />41<br />37<br />19<br />13<br />9<br />12<br />31<br />22<br />38<br />28<br />
11. 11. Build a number that you see.<br />565<br />720<br />635<br />185<br />550<br />450<br />815<br />435<br />365<br />760<br />280<br />
12. 12. Make 1 000<br />Build a number that you see.<br />565<br />720<br />635<br />185<br />550<br />450<br />815<br />435<br />365<br />760<br />280<br />
13. 13. Multiplication and Division<br />N3.3 Demonstrate understanding of multiplication to 5 × 5 and the corresponding division statements including:<br />· representing and explaining using repeated addition or subtraction, equal grouping, and arrays<br />· creating and solving situational questions <br />· modelling processes using concrete, physical, and visual representations, and recording the process symbolically<br />· relating multiplication and division.<br />N4.3 Demonstrate an understanding of multiplication of whole numbers (limited to numbers less than or equal to 10) by:<br />· applying mental mathematics strategies <br />· explaining the results of multiplying by 0 and 1.<br />N4.4 Demonstrate an understanding of multiplication of whole numbers (2- or 3-digit by 1 - digit) by:<br />· modeling the distributive property<br />· using personal strategies for multiplication, with and without concrete materials<br />· using arrays to represent multiplication<br />· connecting concrete representations to symbolic representations<br />· estimating products solving problems.<br />N4.5 Demonstrate an understanding of division of whole numbers(1-digit divisor to 2-digit dividend) by:<br />· using personal strategies for dividing, with and without concrete materials<br />· estimating quotients<br />· explaining the results of dividing by 1<br />· solving problems involving division of whole numbers<br />· relating division to multiplication.<br />
14. 14. Students should know their doubles before you begin multiplication and division.<br />http://www.poweroften.ca/index.php?view=video&id=44&option=com_jomtube&Itemid=139<br />http://www.poweroften.ca/index.php?view=video&id=46&option=com_jomtube&Itemid=139<br />
15. 15.
16. 16. Division should also be taught<br />along with multiplication. When an array is<br />created or a specific area is calculated, the relevant<br />division questions should always be discussed at the<br />same time.<br />For example: when examining the 24th<br />day of a month during calendar time and discussing<br />the varied groupings possible that equal 24, some<br />students will build an array that shows: 4 groups of 6<br />or 4 × 6 = 24. This array should at once be related to<br />all the facts in this family of groupings:<br />•4 × 6 = 24<br />•6 × 4 = 24<br />•24 ÷ 6 = 4<br />·24 ÷ 4 = 6<br />Some effective teaching strategies for developing multiplication concepts are as follows:<br />•Avoid teaching a multiplication table in a specific order, as this promotes counting strategies.<br />Instead use a doubling strategy such as 2 × 5 = 10, 4 × 5 = 20, and 8 × 5 = 40.<br />•Avoid teaching tables before grade three.<br />•Teach meaning through grouping, calendar time, and meaningful projects.<br />•When teaching the multiplication tables, use many varied strategies including:<br />ÖForming groups<br />ÖMaking arrays<br />ÖGraphing arrays on cm grid paper<br />ÖRelating multiplication to area<br />ÖUsing number lines<br />ÖClapping the facts, and using music and rhymes to reinforce multiplication facts<br />ÖUsing visual tools<br />ÖBreaking numbers up<br />•Relate multiplication equations to other questions that are similar and more readily understandable.<br />•Use kinesthetic approaches (clapping, standing and sitting, and manipulating or handling egg cartons).<br />
17. 17. bounce ball- rhythmic<br />(Page 112) Teaching the 5 Times Tables First<br />1 group of 5<br />2 groups of 5<br />
18. 18.
19. 19. How many 5's make 20?<br />
20. 20. I see...<br />I think...<br />This reminds me of...<br />
21. 21. Next teach the 10 times tables.<br />What patterns do you notice?<br />0 and 1<br />5,10,0,1 <br />this leaves 2,3,4,6,7,8,9 (2's are doubles)<br />http://vimeo.com/15261830<br />You have only half of the remaining due to the commutative property!!!<br />
22. 22. 16x8=<br />8x8=4x8=32....64<br />64x2=128<br />8x6=<br />(halving and doubling strategy)<br />Learning the Difficult Multiplication Facts 6,7,8<br />http://www.poweroften.ca/index.php?view=video&id=42%3Agrade-3-learning-the-difficult-multiplication-facts&option=com_jomtube&Itemid=139<br />18x25=9x50<br />
23. 23. 8x6=48<br />6x8=48<br />48 6=8<br />48 8=6<br />16x8=<br />8x8=4x8=32....64<br />64x2=128<br />Teach your Fact Families<br />
24. 24. Distributive Property<br />4 x 27<br />=4(20 +7)<br />=4(20) + (7)<br />=80 + 28<br />=108 <br />
25. 25. Show What is my question sheet page 59<br />I am thinking of a question :<br />It is a multiple of 4.<br />The product is greater than 30 and less than 40.<br />The sum of the digits in the product is 5.<br /> What is my question?<br />
26. 26. 4,8,16,20,24,28,32,36,40,<br />3+2=5 3+6=9<br />The answer is 8x4=32<br />
27. 27. A hotel has 24 windows on a floor. There are 9 floors. <br />How many windows are there?<br />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?<br />Mental Math ?<br />
28. 28. Describe a situation when you might divide 50 by 4.<br />Now describe a situation when you are forming groups but don't divide.<br />
29. 29. Susan says 45-9-9-9-9-9=0<br />describes division do you agree? Explain. <br />
30. 30. Partitioning or Fair Sharing<br />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?<br />Measurement or Repeated Subtraction Concept<br />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?<br />
31. 31. Jumbo the elephant loves peanuts. <br />His trainer has 20 peanuts. <br />If he gives Jumbo 5 peanuts each day, how many days will the peanuts last?<br />Number of Peanuts<br />Day<br />
32. 32. The bag has 783 jelly beans, and Maggie and her four friends want to share them equally. <br />How many jelly beans will Maggie and each of her friends each get?<br />
33. 33. Jumbo the elephant loves peanuts. <br />His trainer has 20 peanuts. <br />If he gives Jumbo 5 peanuts each day, how many days will the peanuts last?<br />------------------------------------------------------------------<br />What if he only gave 2 a day, how many days will the peanuts last?<br />Number of Peanuts<br />Day<br />
34. 34. Credits<br />http://www.poweroften.ca/<br />blackline masters<br />http://www.ablongman.com/vandewalleseries/<br />