Foundations in Fluency
Memorization
Routine
Multiplication 2s, 5s, and 10s
rd
Beginning of 3 grade
Page 1 of 6
Foundations in Fluency Lesson Sequence
STEPS
1
Lesson
Introduction
of the Facts
Student Behaviors
 Write facts in their own notebooks
 Introduces facts (e.g., uses think aloud to
model strategy , includes a visual
representation, etc.)
 Models how to write the facts in the
notebook
 Copy commutative fact/fact family 3-5
times in notebook horizontally (one fact
at a time)
 Chant the facts quietly to themselves
(“whisper time”)
 Quiz the facts with a partner
 Repeat commutative fact/fact family
 Models what memorizing looks like
 Checks for understanding
1-2 minutes
2
Memorization
of the Facts
3-5 minutes
3
4
5
Oral Practice
2 minutes
Application
3-4 minutes
Share
5-8 minutes
Teacher Behaviors
 Covers up facts
 Reads facts
 Initiates whole-group choral response and
then moves to small-group and individuals
 Copy problems vertically into notebooks
 Solve application problems Alone
 Models application problem (process and
vocabulary)
 Checks for understanding
 Compare solutions with a partner (include
explanation of process)
 Rehearse student presentation
 Teach problems to the class
 Checks for understanding
 Randomly selects students to respond
 Teacher prompts students only (students
do the talking)
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Multiplication Strategies
•
Skip counting →
2x7=
2…4…6…8…10…12…14
•
Counting up/down from known fact→6 x 5=
5 x 5 = 25…6 x 5 = 25 + 5 = 30
•
Doubling → 4 x7 =
4 x 7 = twice as much as 2 x 7
•
Breaking a product into sum of know→7 x 8=
7 x 8 = 5 x 8 + 2 x 8 = 40 + 16 = 56
•
Patterns →
1.
Nines pattern
2.
0 times a number equals 0
3.
1 times a number equals the number
4.
5 times a number ends in 0 or 5
5.
Even numbers times 5 end in 0
6.
Odd numbers times 5 end in 5
7.
10 times a number is the same number with a zero on the end
Page 3 of 6
Multiplication 2s, 5s and 10s
Lesson
Facts
Commutative
Facts
Teacher Says
Students Say
Apply Fact to
Whole Numbers
Rewrite in vertical format
1
2x2=4
2x3=6
2x2=4
3x2=6
Two times two equals
Two times three equals
Three times two equals
Two times two equals
Two times two equals four
Three times two equals six
Two times three equals six
Two times two equals four
20 x 3 =
2 x 30 =
2 x 20 =
2
2x4=8
2 x 5 = 10
4x2=8
5 x 2 = 10
Two times four equals
Two times five equals
Five times two equals
Four times two equals
Four times two equals eight
Five times two equals ten
Two times five equals ten
Two times four equals eight
20 x 4 =
40 x 2 =
20 x 5 =
50 x 2 =
3
4
2 x 6 = 12
2 x 7 = 14
5
2 x 8 = 16
2 x 9 = 18
2 x 10 = 20
6
7
Review Lessons 1 & 2 (include word problems and verbal expressions)—examples:
How many legs do three chickens have altogether?
There are two benches. Each bench has four legs. How many legs altogether?
Twice the number five, Double the number three, The product of two and four
6 x 2 = 12
Two times six equals
Six times two equals twelve
7 x 2 = 14
Two times seven equals
Seven times two equals fourteen
Six times two equals
Two times six equals twelve
Seven times two equals
Two times seven equals fourteen
8 x 2 = 16
9 x 2 = 18
10 x 2 = 20
Two times eight equals
Eight times two equals sixteen
Two times nine equals
Nine times two equals eighteen
Two times ten equals
Ten times two equals twenty
Nine times two equals
Two times nine equals eighteen
Eight times two equals
Two times eight equals sixteen
Ten times two equals
Two times ten equals twenty
Review Lessons 4 & 5 (include word problems and verbal expressions)—examples:
There are nine penguins in the water. How many legs do the penguins have altogether?
Double the number eight, The product of ten and two.
Review Lessons 1-5 (include word problems and verbal expressions)
Page 4 of 6
60 x 2 =
20 x 6 =
70 x 2 =
20 x 7 =
80 x 2 =
20 x 8 =
20 x 9 =
90 x 2 =
Lesson
Facts
Commutative
Facts
Teacher Says
Students Say
Apply Fact to
Whole Numbers
8
5 x 3 = 15
5 x 4 = 20
3 x 5 = 15
4 x 5 = 20
Five times three equals
Five times four equals
Three times five equals
Four times five equals
Three times five equals fifteen
Four times five equals twenty
Five times three equals fifteen
Five times four equals twenty
50 x 3 =
30 x 5 =
50 x 4 =
40 x 5 =
9
5 x 5 = 25
5 x 6 = 30
5 x 5 = 25
6 x 5 = 30
Five times five equals
Five times six equals
Six times five equals
Five times five equals
Five times five equals twenty-five
Six times five equals thirty
Five times six equals thirty
Five times five equals twenty-five
50 x 5 =
60 x 5 =
50 x 6 =
10
Review Lessons 8 & 9 (include word problems and verbal expressions)—examples:
How many nickels in five quarters?
There are give tables in the lunchroom. Each table has four legs. How many legs do the tables have altogether?
Six multiplied by five minus ten, Triple the number five, Double the product of five and five
5 x 7 = 35
7 x 5 = 35
Five times seven equals
Seven times five equals thirty-five
70 x 5 =
5 x 8 = 40
8 x 5 = 40
Five times eight equals
Eight times five equals forty
50 x 7 =
Eight times five equals
Five times eight equals forty
80 x 5 =
Seven times five equals
Five times seven equals thirty-five
50 x 8 =
Rewrite in vertical format
11
12
13
14
5 x 9 = 45
5 x 10 = 50
9 x 5 = 45
10 x 5 = 50
Five times nine equals
Five times ten equals
Nine times five equals
Ten times five equals
Nine times five equals forty-five
Ten times five equals fifty
Five times nine equals forty-five
Five times ten equals fifty
Review Lessons 11 & 12 (include word problems and verbal expressions)—examples:
There are five boxes of pencils on the teacher’s desk.
Each box has ten pencils. How many pencils are there altogether?
Tickets for the raffle cost $5 each. How much money would it cost to buy eight tickets?
Ten plus the product of five and nine
Review Lessons 1-12 (include word problems and verbal expressions)
Page 5 of 6
50 x 9 =
90 x 5 =
Lesson
Facts
Commutative
Facts
Teacher Says
Students Say
Apply Fact to
Whole Numbers
Rewrite in vertical format
15
16
17
18
19
20
3 x 10 = 30
4 x 10 = 40
10 x 3 = 30
10 x 4 = 40
Three times ten equals
Ten times three equals thirty
Four times ten equals
Ten times four equals forty
Ten times three equals
Three times ten equals thirty
Ten times four equals
Four times ten equals forty
6 x 10 = 60
10 x 6 = 60
Six times ten equals
Ten times six equals sixty
7 x 10 = 70
10 x 7 = 70
Seven times ten equals
Ten times seven equals seventy
Ten times six equals
Six times ten equals sixty
Ten times seven equals
Seven times ten equals seventy
Review Lessons 15 & 16 (include word problems and verbal expressions) —examples:
One decade has ten years. How many years in four decades?
Mario is washing his car. One dollar lasts ten minutes. How many minutes will two dollars last?
Double the product of ten and three.
8 x 10 = 80
10 x 8 = 80
Eight times ten equals
Ten times eight equals eighty
9 x 10 = 90
10 x 9 = 90
Nine times ten equals
Ten times nine equals ninety
10 x 10 = 100
10 x 10 = 100 Ten times ten equals
Ten times ten equals one hundred
Ten times nine equals
Nine times ten equals ninety
Eight times ten equals
Ten times eight equals eighty
Ten times ten equals
Ten times ten equals one hundred
Review Lesson 18 (include word problems and verbal expressions)—examples:
What number is equal to five groups of ten?
There are ten cookies on a cookie sheet. If there are 9 cookie sheets, how many cookies are there in total?
Review Lessons 1-19 (include word problems and verbal expressions)
Page 6 of 6