multiplying and dividing in the common core (grades 3-5) julia doverspike, armando rodriguez,...
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Julia Doverspike, Armando Rodriguez, Maricela Garcia
Multiplying and Dividing in the Common Core (grades 3-5)
SecondGrade• Iden'fynumbers(upto20)asOddorEven• Countby2s,5s,10s,and100supto1000• Showrepeatedaddi'onwithobjectsandnumbersupto5groupsof5
ThirdGrade• Mul'plyandDivideupto100usingpictures• Understandtherela'onshipbetweenmul'plica'onanddivision• Relateareaofashapetomul'pica'on• Knowfrommemorymul'pica'onfactsupto9X9=81
FourthGrade• Interpretamul'plica'onequa'onasacomparison• Mul'plynumberswithupto4-- digits‐bya1-- digit‐numberor2-- digit‐by2--‐digitusingdrawingsandequa'ons• Dividenumbersupto4--‐digitby1-- digit‐usingdrawingsandequa'ons
Fi1hGrade• Mul'plymul'-- digit‐wholenumbers• Dividenumbersupto4-- digit‐by2-- digit‐usingdrawingsandequa'ons• Relatevolumeofa3Dshapetomul'plica'on• UnderstandplacevalueusingPowersof10Libby Schwaegler 2015
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Reasoning with numbers
Arrays
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Creating Arrays
3 rows
2 columns
2 + 2 + 2 = 6
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Area
How many different
rectangles can I make with an area
of 12?
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Area Models
Five rows of 3
3 + 3 + 3 + 3 + 3 = 15
5 x 3 = 15
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Equal Groups Model
2 groups of 4
4 + 4 = 8
2 x 4 = 8
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Using Manipulatives
Modeling Division
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Quotative Division
Uses repeated subtraction Provides student with a total number and the number of objects in each group
Focus on the question, “How many equal groups can you make?”
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Partitive Division
Provides student with a total number and the number of groups
Focus on the question, “How many objects are in each group so that the groups are equal?”
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Number Line
There are 12 cookies on the counter. If you put 3 cookies in each bag, how many bags will you fill?
12
3 6 90
- 3
- 3
- 3
- 3
12 ÷ 3 = 4
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Tape Diagram
There are 12 brownies on the plate. If you are sharing the brownies equally among three bags, how many brownies will go in each bag?
? ?? = 12
44 4
12 ÷ 3 = 4
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Array Model
If 15 cars are parked 3 in each row, then how many rows will they fill?
3
5
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For Multiplication
Properties of Operations
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Identity Property
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Commutative Property
4 x 5 = 20
5 x 4 = 20
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Associative Property
3 x 5 x 2 = 30
5 x 2 x 3 = 30
2 x 3 x 5 = 30
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Distributive Property
Decomposing rectangles
8 x 6
= (3 x 6) + (5 x 6)
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Multiplication and Division Patterns
Doubles (2)Double-Doubles(4)Double-Double-Doubles(8)HalvesBy 10s and 5s
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Multiplicative Comparison
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Language
18 = 6 x 3
40 is 5 times as much as 8
5 x 8 = 40
18 is 6 times as much as 3
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Bar Model (Tape Diagram)
A tennis ball costs $2. A soccer ball costs six times as much as a tennis ball. How much does the soccer ball cost?
6 x 2 = n
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Try These
Manny has lived in Illinois for 21 years and that is 7 times as many years as Lucas. How many years has Lucas lived in Illinois?
A tree in Ashton’s yard is 15 feet tall. Ashton is 3 feet tall. The tree is how many times as tall as Ashton?
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Place Value
Each place value is ten times as much
as the previous place value
Including Prime and Composite
Factors and Multiples
Rectangles
How many different rectangles can I make with an area of 7?
How many different rectangles can I make with an area of 12?
Composite
Prime
Number Line
Show the multiples of 4
1 2 3 4 5
20
16
12
840
Factors
Multiples
Table
1 6
2 12
3 18
4 24
x 6
Multi-digit Multiplication
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Digi Blocks
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Base Ten Blocks (or Digi-blocks)321 x 3 =
963
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Base Ten Area Model
31 x 24 X
= 744
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Area Model
24 x 35
= (20 + 4) x (30 + 5)
204
30
5
20
120
100
600
= 840
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Partial Products
24X 36
24
6 x 412
06 x 2 tens12
03 tens
x 4600
3 tens x 2 tens864
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Column Method
Regroup
4 4
2 6
4
2
62
8 08
44
1
11
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Multi-digit Division
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Base Ten Blocks (or Digi-blocks)My team earned $175. There are 5 people on my team. We decided to split the money up evenly between the 5 of us. How much money will we each receive?
$35 each
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Area Model
966 ÷ 7
9667
Hundreds
Tens Ones100
966- 700 266
30
266- 210 56
8
56- 56 0
= 138
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Partial Quotient
3 745 20
0- 600 145
40- 120 25
8- 24 1
745 ÷ 3
248 remainder 1
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Interpreting Remainders
Sam wants to hide 40 eggs for his cousins to find. How many dozen eggs must he buy?
Sam buys 2 dozen packages of chocolates for his cousins. Each package has 22 chocolates. He has 9 bowls to hold the chocolates. If he wants to have the same number of chocolates in each bowl, how many chocolates will be in each bowl?
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Base Ten Area Model
231 ÷ 21
X
Divisor
Quotient
Dividend
= 11
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Column Division - introduction231 ÷ 21
21
231
1
210-21
1
21-0
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Column Division (long division)231 ÷ 21
21
231
1
-2121
1
- 210
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Teaching is more than imparting knowledge,It is inspiring change.Learning is more than absorbing facts,It is acquiring understanding.
William Arthur Ward