Transcript 3rd-and-4th-Multiplicationx

Multiplication
Standards
Third Grade Common Core
3.3 NBT Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60)
using strategies based on place value and properties of operations.
Third Grade CA Standards
NS 2.4 Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers
(3,671 x 3 = __).
Fourth Grade Common Core
4.5 NBT– Multiply a whole number of up to four digits by a one-digit whole number, and multiply two
two-digit numbers, using strategies based on place value and the properties of operations. Illustrate
and explain the calculation by using equations, rectangular arrays, and/or area models.
4.5.1 NBT - Solve problems involving multiplication of multi-digit numbers by two-digit numbers.
Fourth Grade CA Standards
NS 3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a
multi digit number by a two-digit number and for dividing a multi digit number by a one-digit
number; use relationships between them to simplify computations and to check results.
NS 3.3 Solve problems involving multiplication of multi digit numbers by two-digit numbers.
Multiplication
• Students should use methods they understand and can
explain while multiplying.
– Visual representations such as area models that students draw
and connect to equations are useful for this purpose.
• By reasoning repeatedly about the connection between
math drawings and written numerical work, students can
come to see written algorithms as abbreviations or
summaries of their reasoning about quantities.
• In mathematics, an algorithm is defined by its steps and not
by the way those steps are recorded in writing. With this in
mind, minor variations in methods of recording standard
algorithms are acceptable.
Area Models
Area models enhance the understanding of geometry and multiplication. This is
an area model of 7x5 using built using base ten blocks. The red base ten blocks
represent the factors as if we were making a square with a length of 7 and a
width of 5. The product is represented by the blue base ten blocks.
Build an area model of 10 x 5 using base ten blocks.
10 x 5
Build an area model of 10x10 using base ten blocks.
10 x 10
Build an area model of 12x15 using base ten blocks.
10 x 10
2 x 10
10 x 5
2x5
4.5 NBT– Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two
two-digit numbers, using strategies based on place value and
the properties of operations.
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
x
12
15
10
10
+
2
+
5
10 x 10 = 100
10x5 = 50
10x2= 20
2x5=10
100 + 50 + 20 + 10 = 180
4.5 NBT– Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two
two-digit numbers, using strategies based on place value and
the properties of operations.
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
x
30
40
+
2
42
31
+
1
1,200
40
60
2
1,200 + 60 + 40 + 2 = 1,302
Connecting the area model to the algorithm
Two-Step Solution
1) Multiply all the numbers and
record the answers.
2) Add the numbers from the top
and record the final answer.
246
7
x
200
4
x
246
7
2
1,400
7
2 4
x
246
7
82
+
40
+
280
6
42
2 4
2 4
246
x
7
1, 4 8 2
246
1
7
1, 4 8 2
+
24 0
x
1, 7 2 2
Connecting the area model to the algorithm
x
4
3, 246
7
2 4
3, 2 4 6
x
7
2
1
3, 2 4 6
x
7
82
Two-Step Solution
1) Multiply all the numbers and
record the answers.
2) Add the numbers from the top
and record the final answer.
2
1
4
2
4
3, 2 4 6
x 1
7
2 1, 4 8 2
+ 1, 2 4 0
3, 2 4 6
x
7
4 8 2
2 2, 7 2 2
3,000
7
21,000
+
200
1,400
+
40
280
+
6
42
Connecting the area model to the algorithm
x
4
2, 358
6
3 4
2, 3 5 8
x
6
8
1
2, 3 5 8
x
6
08
Two-Step Solution
1) Multiply all the numbers and
record the answers.
2) Add the numbers from the top
and record the final answer.
3
1
4
3
4
2, 3 5 8
x1
6
1 2, 8 0 8
+ 1, 3 4 0
2, 3 5 8
x
6
8 0 8
1 4, 1 4 8
2,000
6
12,000
+
300
1,800
+
50
300
+
8
48
Multiply a whole number of up to four digits by a one-digit
whole number, and multiply two two-digit numbers, using
strategies based on place value and the properties of
operations.
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Two-Step Solution
1) Multiply all the numbers and
record the answers.
2) Add the numbers from the top
and record the final answer.
1
3
One-Step Solution
Multiply each number and add the
number from the top before
recording a final answer answer.
4
2, 3 5 8
x1
6
1 2, 8 0 8
+ 1, 3 4 0
1 4, 1 4 8
2
3
4
2, 3 5 8
x
6
1 4, 1 4 8
We are multiplying by a one-digit whole number.
Mathematicians prefer to complete this problem
in one step.
4.5 NBT– Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two
two-digit numbers, using strategies based on place value and
the properties of operations.
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
x
36
23
20
30
+
6
+
3
600
90
120
18
600 + 120 + 90 + 18
4.5 NBT– Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two two-digit numbers,
using strategies based on place value and the properties of
operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
36
36 x 23 = (30 + 6) x (20 + 3)
23
36 x 23 = (30 + 6) x 20 + (30 + 6) x 3
18
36 x 23 = (30 x 20) + (6 x 20) + (30 x 3) + (6 x 3)
90
120
600
+ ____
828
x
Step one:
Step two:
Step three:
Step four:
Step five:
(3 x 6)
(3 x 30)
(20 x 6)
(20 x 30)
3 x 6 = 18
3 x 30 = 90
20 x 6 = 120
20 x 30 = 600
828
4.5 NBT– Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two two-digit numbers,
using strategies based on place value and the properties of
operations. llustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
1
1
1
x
36
23
8
x
1
36
23
98
x
1
1
1
1
36
23
x
98
20
98
6 20
36
23
x
1
+
36
23
98
6 20
7 1 8
+ 1 1 0
8 2 8
Step one:
Step two:
Step three:
Step four:
Step five:
3 x 6 = 18
3 x 30 = 90
20 x 6 = 120
20 x 30 = 600
828
Notice how step five was
two addition problems.
The next slide will show us
how to do step five with
only one addition problem.
4.5 NBT– Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two
two-digit numbers, using strategies based on place value and
the properties of operations.
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
1
1
1
x
36
23
8
x
36
23
1 08
1
x
36
23
1 08
20
1
1
1
1
x
36
23
1 08
7 20
x
+
36
23
1 08
7 20
8 2 8
Step one:
Step two:
Step three:
Step four:
Step five:
3 x 6 = 18
3 x 30 = 90
20 x 6 = 120
20 x 30 = 600
828
This is the preferred
method, and this is how we
will do all future
multiplication problems.
4.5 NBT– Multiply a whole
of Iup
tothefour
digits
by
a one-digit
add
40 500
from
step
40number
240. Then
706xx40
isis2800.
Then
I add
the
from
step
and
whole
multiply
twoand
This
is
8 tens
one
and IInumber,
have 3,300.
280. and
This
is
3 hundreds
three
and
have
2 hundreds.
Notice how based
288 is the
of value and the
two-digit numbers,
usingNotice
strategies
ontotal
place
3 thousands.
how 3,360 is the total of
operations.
stepsproperties
one and twoof
below.
Why is that?
steps three and four below. Why is that?
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5
4
4
x
48
76
8
x
4
48
76
x
48
76
2 88
60
2 88
5
5
4
4
x
48
76
2 88
3 3 60
x
1
48
76
2 88
+
3 3 60
3, 6 4 8
Step one:
Step two:
6x 8=
6 x 40 =
48
240
Step three: 70 x 8 = 560
Step four: 70 x 40 = 2,800
Step five:
3,648
What is the best method for solving
this problem? Why?
368,423 x 7,286