Transcript x 3 - Chatsworth Avenue School

Computational
Fluency
Grade 4 and 5
Understanding versus Memorization
Children need to understand what it
means to multiply and divide before facts
can become automatic
 Understanding is necessary but not
sufficient
 When isolated multiplications and
divisions are practiced, the emphasis is on
recalling the answers
 Teaching facts for automaticity relies on
thinking

Grade Level Expectations
By the end of third grade students are
expected to have mastered all the facts for
multiplication and division within 100
By the end of fourth grade students are
expected to multiply a whole number up to 4
digits by a 1-digit whole number and two 2digit numbers
By the end of fifth grade students are expected
to be fluent with multi‐digit multiplication
Grade 3 Big Ideas

Multiplication is a fundamental operation
that is used to solve everyday problems.

Multiplication has been described as
rectangular array, repeated addition, and
area.

There are patterns and relationships in
multiplication facts and multiplication and
division are related
Common Multiplication Strategies
I can use a multiplication fact I know, to figure out one I don’t…
Using the commutative property:
2x4=4x2
4 groups of 2
2 groups of 4

Common Multiplication Strategies

Doubling: 2 x (3 x 6) = 6 x 6
3 groups of 6 doubled
Common Multiplication Strategies

Halving and doubling: 4 x 3 = 2 x 6
4 groups of 3
2 groups of 6
Common Multiplication Strategies
Using the distributive property: 6 x 4 =
(5 x 4) + (1 x 4) = 20 + 4 = 24

Common Multiplication Strategies
Using the distributive property: 6 x 4 =
(5 x 4) + (1 x 4) = 20 + 4 = 24
Number bond

Common Multiplication Strategies
Using the distributive property with tens:
9 x 4 = (10 x 4) – 4

Part/Whole relationships
A guitar has 6 strings. How many strings are
there on 3 guitars? Write a multiplication
sentence to solve.
Grade 4 Big Idea

To find the products for multi-digit
multiplication, I can break apart the numbers
using place value.
The “Place” of Place Value
4
x3
12
4 ones x 3 = 12 ones
The “Place” of Place Value
40
x 3
120
4 tens x 3 = 12 tens
The “Place” of Place Value
400
x 3
1200
4 hundreds x 3 = 12 hundreds
The “Place” of Place Value
4000
x
3
12,000
4 thousands x 3 = 12 thousands
Multiplying Larger Numbers
4 x 13 = 4 groups of 13 or 13 groups of 4?
How would you model this
problem?
I am retiling my hallway. The dimensions are
4 feet by 13 feet. Each tile is one square
foot. How many tiles do I need?
My 4’ x 13’ hallway
The Open Array
Now let’s try bigger numbers

1,423 x 3

Show 1,423 chart with the disks
Area Model
3
1,000
400
3 x 1,000
3 x 400
3,000
1,200
20
3
3 x 20 3 x 3
60
9
Understanding the Standard Algorithm
starting with Partial Products
1423
x
3
9
60
1200
3000
4269
3 x 3 ones
3 x 2 tens
3 x 4 hundreds
3 x 1 thousand
Understanding the Standard Algorithm
1
1423
x
3
4269
Two-digit x 2-digit
Area Model with Base Ten Blocks
Leads to the…
Open Array or Area Model
Open Array
20
10
3
7
20 x 10
7 x 10
20 x 3
7x3
20 x 10 = 200
20 x 3 = 60
7 x 10 = 70
7x3=
21
Multiplying Decimals
Multiplying Decimals by rounding
2 x 2.4
“2.4 is closer to 2. My answer
should be more than 4.”
* Now I know where to put the decimal.
Multiplying Decimals
Multiplying Decimals by renaming
2 x 2.4
= 2 x 24 tenths
= 48 tenths
= 4.8
* What are you actually doing to the numbers?
With Blocks
Build 2 groups of 2 and 4 tenths (2.4)
= 1 whole
Area Model
Division with Disks
Model this problem using the disks.
396 ÷ 3
How do the disks support
understanding of division with large
numbers?
Great Websites for Math Practice
sheppardsoftware.com/math.htm
 topmarks.co.uk/maths-games/
 Arcademicskillbuilders.com/games
 FactMonster.com/math/flashcards.html
 Multiplication.com
 IXL.com
