FactsWise x÷
Multiplying & Dividing with
Fluency, Flexibility & Number Sense
By Valerie Henry, NBCT, Ed.D.
© Valerie Henry, June 2008 … www.ellipsismath.com
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Ellipsis Math
EIGHT GOALS FOR MULTIPLICATION/DIVISION SUCCESS
Once a child is fluent with the multiplication facts in a goal, begin work on the related division facts.
Goal 1 – 10s
Mult: 10 x 2, 10 x 3, 10 x 4, 10 x 5, 10 x 6, 10 x 7, 10 x 8, 10 x 9, 10 x 10
Div: 20÷2, 30÷3, 40÷4, 50÷5, 60÷6, 70÷7, 80÷8, 90÷9, 100÷10,
20÷10, 30÷10, 40÷10, 50÷10, 60÷10, 70÷10, 80÷10, 90÷10
Goal 2 –5s
Mult: 2 x 5, 3 x 5, 4 x 5, 5 x 5, 6 x 5, 7 x 5, 8 x 5, 9 x 5
Div: 10÷2, 15÷3, 20÷4, 25÷5, 30÷6, 35÷7, 40÷8, 45÷9, 10÷5, 15÷5, 20÷5,
30÷5, 35÷5, 40÷5, 45÷5
Goal 3 – 2s
Mult: 2 x 2, 2 x 3, 2 x 4, 2 x 6, 2 x 7, 2 x 8, 2 x 9
Div: 4÷2, 6÷3, 8÷4, 12÷6, 14÷7, 16÷8, 18÷9, 6÷2, 8÷2, 12÷2, 14÷2, 16÷2,
18÷2
Goal 4 – 9s
Mult: 9 x 3, 9 x 4, 9 x 6, 9 x 7, 9 x 8, 9 x 9
Div: 27÷3, 36÷4, 54÷6, 63÷7, 72÷8, 81÷9, 27÷9, 36÷9, 54÷9, 63÷9, 72÷9
Goal 5 – 3s
Mult: 3 x 3, 3 x 4, 3 x 6, 3 x 7, 3 x 8
Div: 9÷3, 12÷4, 18÷6, 21÷7, 24÷8, 12÷3, 18÷3, 21÷3, 24÷3
Goal 6 – 4s
Mult: 4 x 4, 4 x 6, 4 x 7, 4 x 8
Div: 16÷4, 24÷6, 28÷7, 32÷8, 24÷4, 28÷4, 32÷4
Goal 7 – 6s
Mult: 6 x 6, 6 x 7, 6 x 8
Div: 36÷6, 42÷7, 48÷8, 42÷6, 48÷6
Goal 8 – 7s & 8s
Mult: 7 x 7, 7 x 8, 8 x 8
Div: 49÷7, 56÷8, 56÷7, 64÷8
© Valerie Henry, June 2008 … www.ellipsismath.com
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TABLE OF CONTENTS
Section 1: Introduction …………………………………………………………………………………………………..
1.1 Research Findings …………………………………………………………………………………………………..
Section 2: Getting Started …………………………………………………………………………………………….
2.1. FactsWise Overview ………………………………………………………………………………………….
2.2. Pre-Assessing Your Students ……………………………………………………………………………..
2.3. Pre-Assessment and Ongoing Assessment Techniques …………………………………
2.4. Pre-Assessment and Ongoing Assessment Record-Keeping …………………………
Section 3: WHOLE-CLASS ROUTINES AND MINI-LESSONS
3.1 Teaching Basic Facts Every Day …………………………………………………….…………………
3.2 Whole-Class Routines ………………………………………………………………………………………….
Section 4: Individual and Small-Group Practice ………………………………………………………..
4.1 Coordinating Goal-Alike Practice …………………………………………………………………………
4.2 Flashcards and Pairs Practice ……………………….…………………………………………………….
4.3 Online Flashcards, Games and Quizzes ……………………………………………………………
4.4 Whole-Class Powerpoint “Commercials” …………….………………………………………………
Section 5: Moving Basic Facts into Permanent Memory …………………………………………
Section 6: Goal-by-Goal Assessments …………………………………………………………………………
Section 7: Record-Keeping Resources ………………………………………………………………………….
Section 8: Pairs Practice Goals 1 through 8 and Top 21 ……………………………………………
© Valerie Henry, June 2008 … www.ellipsismath.com
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SECTION ONE: INTRODUCTION
For students to continue to succeed mathematically in middle school and high
school, they need to develop a strong number sense and basic facts fluency. This
program is based on research findings about memorization and ways students build
strategies and connections between basic multiplication and division facts.
Some U.S. students develop this same fluency with numbers – but many don’t.
FactsWise provides a systematic approach to basic facts fluency for all our students.
It builds on the research from many countries, including China, Japan, Korea, Singapore,
Australia, and New Zealand. In addition, it incorporates cognitive research on ways to
move facts into long-term memory, and then to help build strong retrieval mechanisms.
As we all know, memorizing a large set of facts works best when we break it up
into smaller chunks. FactsWise breaks the job of memorizing the multiplication and
division facts up into eight goals. These goals are strategic – they work on facts with
easily-recognized patterns early in the program. Once these are learned, there are only
fifteen facts left to memorize. We also know that students find division much less
intuitive than multiplication, particularly when they don’t see the connections between
them. So FactsWise incorporates the related division facts right after each
multiplication goal.
This program is different in one other important aspect – no timed tests! We all
know how much anxiety timed tests can create in our classrooms. But equally
troublesome, timed tests don’t really tell us much about how students are solving their
facts problems. If we want to help students move beyond counting, we need a different
assessment tool. FactsWise provides an easy one-on-one assessment system that can be
implemented by the classroom teacher, classroom aids, or parent volunteers. Teachers
who have used this program are sold on what they can learn about a student’s math
thinking in just a minute or two of one-on-one assessment.
© Valerie Henry, June 2008 … www.ellipsismath.com
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1.1: Research Findings
We have done one small pilot study on this program to date. The results showed
higher fluency for FactsWise students, particularly for the girls.
FactsWise 3rd Grade Pilot Project (Multiplication & Division)
21 Grade FactsWise students (2 classrooms) and 20 Control students (2 classrooms)
Mean Differences – Independent Samples T-Test
Control Students : FactsWise Students
Difference in Average
Percent Fluent
(Control:FactsWise)
Multiplication Fluency
All Students (n=20:21)
Boys (9:12)
Girls (11:9)
Division Fluency
All Students (n=20:21)
Boys (9:12)
Girls (11:9)
Total Fluency
All Students (n=20:21)
Boys (9:12)
Girls (11:9)
*
11% (79:89)
4% (81:85)
18% (77:95)
19% (66:84)*
19% (62:81)
21% (68:89)
15% (72:87)
11% (72:83)
19% (73:92)
Statistically significant at p < .05 based on independent samples t-test
All Students
Total Fluency - Control
Division Fluency - Control
Mult Fluency - Control
15%
30%
30%
20%
50-79
<50
<50
<50
50%
50-79
50-79
80-100
80-100
80-100
60%
65%
10%
20%
Mult Fluency - FactsWise
Division Facts - FactsWise
5%
5%
10%
19%
10%
80%
Total Fluency - FactsWise
23%
<50
<50
<50
50-79
50-79
50-79
80-100
80-100
76%
© Valerie Henry, June 2008 … www.ellipsismath.com
80-100
72%
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No. of
Students
1st
Quartile
Median
3rd
Quartile
Control Girls
(blue)
11
47.6
85.7
100
Control Boys
(red)
9
35.7
85.7
97.6
FactsWise MD
Girls (green)
9
90.45
100
100
FactsWise MD
Boys (black)
12
76.2
98.85
95.2
© Valerie Henry, June 2008 … www.ellipsismath.com
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SECTION TWO: GETTING STARTED
2.1: FactsWise Overview
FactsWise is a very flexible program. You can start off very simply, and add
instructional strategies, materials, and technology as you choose. The core of the
program revolves around: 1) quick one-on-one assessments, 2) whole-class routines and
mini-lessons, and 3) goal-specific practice and games.
Pre-assessment
Whole-class routines
& mini-lessons
Communicating
with Parents
Individual/small group
practice & games
Ongoing
assessment
Before you begin this program, be sure that your students have developed a good conceptual
understanding of both multiplication and division. It is very important that students not
work on memorizing math facts before they understand what the operations mean.
Be sure to have students do the cumulative reviews. Teachers have reported that when
these are skipped, students tend to forget earlier goals.
© Valerie Henry, June 2008 … www.ellipsismath.com
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2.2 Pre-Assessing Your Students
To get started, you have two good options:
1) Start everyone at Goal 1 multiplication and be ready for some students to move
quickly through one or more goals.
2) Do a quick-start FactsWise Pre-Assessment (Section 7) with each student to gain a
good sense of which goal each student is ready to work on. This generally takes 3 to
5 minutes per student.
2.3 Pre-Assessment and Ongoing Assessment Techniques
When you do one-on-one assessments with your students, you will want to have made
some decisions ahead of time:
1) Will you be asking the students the questions verbally? Will you also be showing the
students the problems in writing (see FactsWise Pre-Assessment Visuals)? Or will
you simply be asking your students to look at the problems in writing? We have
found a great deal of success using verbal prompts while also showing the students
the problems in writing, If, however, you have second-language students who have
learned their numbers and at least some of their facts in their first language, you
may want to avoid saying the problems aloud in English. For these students, this
necessitates that they then translate them into their first language, and then back
again when they state the answers. You may get a truer sense of their fluency if
they don’t have to make that first translation. Be aware that the need to translate
their answers into English may still cause these students to have a certain time lag.
2) What are your criteria for passing students on a goal?
a. If a student is counting on one or more problems, then he or she is not ready
to move on yet. Sometimes you’ll be able to see the student using fingers or
sub-vocalizing the counting.
b. In all cases where you’re not sure what a student is doing, ask “How did you
get that?” Most students will be able and willing to tell you. If they say “I
just knew it”, it’s most likely that they are retrieving from long term memory.
If they say they were counting in their heads, they’re still not ready to move
on. Remember, our goal is to help students develop part-whole strategies and
ultimately memorization!
c. If a student is retrieving from long-term memory, or using a part-whole
strategy, you have one last decision to make – was it fluent enough? Your
criteria for fluency (speed of response) may differ depending on the grade
you’re working with.
© Valerie Henry, June 2008 … www.ellipsismath.com
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i. For fourth grade and above, we recommend setting a standard of two
seconds or less for response time (just mentally count “one thousand
one, one thousand two” while you’re waiting for the response). If the
student is taking longer than this, then their retrieval or part-whole
strategy is still cognitively demanding.
ii. For third grade, you may want to set a more forgiving fluency
expectation – perhaps three seconds. One thing we definitely want to
encourage at this age is part-whole thinking. If we demand that they
answer too quickly during this developmental phase, we may simply
encourage guessing.
2.4 Pre-Assessment and Ongoing Assessment Record Keeping
You’ll find a couple of different recording options in the Record-Keeping Resources
(Section 7).
1) If you do the quick-start pre-assessment, you’ll want copies of the FactsWise PreAssessment form for all of your students.
2) Once you have started the program, and are conducting weekly or bi-weekly ongoing
assessments, we recommend that you use individual student records (FactsWise
Progress Chart). These allow you to notice students who are not making steady
progress, and also provide good information for parent conferences.
3) In addition, we have provided a FactsWise Class Progress Chart that can provide you
with flexible grouping options for small-group instruction and for FactsWise
stations. You can write students’ initials or class numbers on small dots with
removable adhesive (available at most office supply stores). These dots are able to
move from goal to goal as students progress. We generally recommend that this
chart be reserved for the teacher’s eyes only.
© Valerie Henry, June 2008 … www.ellipsismath.com
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SECTION THREE: WHOLE-CLASS ROUTINES AND MINI-LESSONS
3.1 Teaching Basic Facts Every Day
As you prepare to implement FactsWise, it is important to develop a plan for
incorporating basic facts teaching into your daily routines. To maximize results, it is
also important to understand the keys to helping learners move information into longterm memory. All too often, we see students practice their facts with worksheets,
flashcards, or timed tests over and over, with seemingly no improvement in retention.
Research has identified four keys for effective processing of information in
working memory that increase the probability that basic facts will move into long-term
memory:
1) the information is processed multiple times with 1- or 2-day intervals in between,
2) detail is added,
3) associations are made with other information, and
4) students receive immediate feedback on the accuracy of their practice attempts.
With these four keys in mind, we recommend that you allocate ten to fifteen
minutes every day to basic facts mini-lessons, routines, and individual/small group
practice sessions. Work on the same goal for several days/weeks in a row, providing new
detail and associations with each new mini-lesson. Don’t move too quickly to a new goal –
overlearning leads to accuracy and fluency!
© Valerie Henry, June 2008 … www.ellipsismath.com
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3.2 Whole-Class Routines
Goal 1 – Multiplying and Dividing with 10s
Concrete Routines
1) Abacus Show Me – have student(s) show 10, 20, 30, … , 90, 100 (1st sequentially,
and then later randomly) on the abacus without counting. Encourage students to
share various strategies they use to know how many rows to slide.
2) Base-Ten Blocks Show Me – have student(s) show 10, 20, 30, … , 90, 100 (1st
sequentially, and then later randomly) using base-ten rods on a 10x10 grid (with
some kind of marking between the 5th and 6th rows and the 5th and 6th columns).
Encourage students to share various strategies they use to know how many rows
to show.
Representational Routines
3) Ten-Patterns on the Hundred Chart: Multiplication – have each student place a
marker on his/her individual hundred chart as 10s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
4) Ten-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 10s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
Abstract Routines
5) Clap Facts – Say a fact such as “4 tens” or “40 divided by 10” and then use a hand
signal for wait. Give students 2 or 3 seconds to process, and then clap your
hands, at which time students will choral respond with the answer. Watch
carefully for facts where some students are delaying their answers, and repeat
those several times before you end the activity. Remember to spend equal time
on division facts.
© Valerie Henry, June 2008 … www.ellipsismath.com
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Goal 2 – Multiplying and Dividing with 5s
Concrete Routines
1) Abacus Show Me – have student(s) show 5, 10, 15, … , 45, 50 (1st sequentially, and
then later randomly) on the abacus without counting. Encourage students to
share various strategies they use to know how many beads to slide.
2) 5-Strips Show Me – have student(s) show 5, 10, 15, … , 45, 50 (1st sequentially,
and then later randomly) using paper-strips that are 1x5 squares long on a 10x10
grid (with some kind of marking between the 5th and 6th rows and the 5th and 6th
columns). Encourage students to share various strategies they use to know how
many strips to place.
3) Hands Together – have groups of 5 students work together to hold up the
correct number of open hands to show 5, 10, 15, … , 45, 50 (1st sequentially, and
then later randomly).
Representational Routines
4) Five-Patterns on the Hundred Chart: Multiplication – have each student place a
marker on his/her individual hundred chart as 5s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
product will be even or odd.
b. Ask students to predict and share strategies for determining the tensplace digit for these products.
5) Five-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 5s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
quotient will be even or odd.
Abstract Routines
6) Clap Facts – Say a fact such as “4 fives” or “40 divided by 5” and then use a hand
signal for wait. Give students 2 or 3 seconds to process, and then clap your
hands, at which time students will choral respond with the answer. Watch
carefully for facts where some students are delaying their answers, and repeat
those several times before you end the activity. Remember to spend equal time
on division facts.
© Valerie Henry, June 2008 … www.ellipsismath.com
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Goal 3 – Multiplying and Dividing with 2s
Concrete Routines
1) Abacus Doubles – have students show addition doubles problems, such as 6+6 and
relate this to “2 sixes” and “six 2 times” and “2 times six”. Ask students to recall
their doubles sums, and connect them to the related multiplication products.
2) Abacus Show Me – have student(s) show 2, 4, 6, … , 18, 20 (1st sequentially, and
then later randomly) on the abacus without counting. Encourage students to
share various strategies they use to know how many beads to slide.
3) Base-Ten Blocks Show Me – have student(s) show 2, 4, 6, … , 18, 20 (1st
sequentially, and then later randomly) using base-ten cubes and ten-rods on a
10x10 grid (with some kind of marking between the 5th and 6th columns).
Encourage students to share various strategies that do not require counting.
4) Two’s Paper-Folding – From a 10x10 grid, have students cut out the following
strips of paper: 1x2, 1x4, 1x6, 1x8, 1x10, 2x6, 2x7, 2x8, 2x9, 2x10. Have
students fold each of these paper strips in half, and use them to model problems
such as “12 divided by 2” (using the 2x6 strip) as well as “6 two times”.
Representational Routines
5) Two-Patterns on the Hundred Chart: Multiplication – have each student place a
marker on his/her individual hundred chart as 2s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
product will be even or odd – over time, the goal is for students to realize
that an even number times any other whole number gives an even product.
b. Encourage students to use 2x5 as a benchmark. Ask students to discuss
how this can help them know 2x4 and 2x6 without counting.
c. Also encourage students to use 2x10 as a benchmark to assist with 2x9.
6) Two-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 2s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
quotient will be even or odd.
Abstract Routines
7) Clap Facts – Say a fact such as “2 fives” or “18 divided by 2” and then use a hand
signal for wait. Give students 2 or 3 seconds to process, and then clap your
hands, at which time students will choral respond with the answer.
© Valerie Henry, June 2008 … www.ellipsismath.com
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Goal 4 – Multiplying and Dividing 9s
Concrete Routines
1) Abacus Nines – have students represent a “9-times” problem in 9 rows. Then
have students calculate 10 rows, and then have them subtract a row. For
instance, 9x7 would be modeled on the abacus as 9 rows of 7. Then students
would calculate 10x7=70, and then mentally subtract a 7 to get 63.
a. This same activity can be done using counters and a 10x10 grid.
Representational Routines
2) Nine-Patterns on the Hundred Chart: Multiplication – have each student place a
marker on his/her individual hundred chart as 9s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
product will be even or odd – over time, the goal is for students to realize
that an odd number times an odd number is odd, and an odd number times
an even number is even.
b. Encourage students to notice the patterns that occur in 9s multiplication
problems:
a. As the tens digit increases by one each time, the ones digit
decreases by one.
b. The sum of the digits always equals 9 (up until 9x10).
c. The tens digit for a 9s fact (up until 9x10) is one less than the other
factor (e.g., for 9x5, the tens digit is 4; and for 9x7, the tens digit
is 6).
d. Note – although there are ways to use fingers to help students find
the 9s facts, we don’t want students to become reliant on this
counting substitute. So if you can help them develop mental math
strategies, that would be preferable.
c. Encourage students to use 9x10 as a benchmark to assist with 9x9.
3) Nine-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 9s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
Abstract Routines – Clap Facts (see directions above)
© Valerie Henry, June 2008 … www.ellipsismath.com
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Goal 5 – Multiplying and Dividing with 3s
Concrete Routines
1) Abacus Threes – have students represent a “3-times” problem in 3 rows. Then
have students calculate 2 rows, and then have them add another row. For
instance, 3x6 would be modeled on the abacus as 3 rows of 6. Then students
would calculate 2x6=12, and then mentally add another 6 to get 18.
a. This same activity can be done using counters and a 10x10 grid.
Representational Routines
2) Three-Patterns on the Hundred Chart: Multiplication – have each student place
a marker on his/her individual hundred chart as 3s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
product will be even or odd – over time, the goal is for students to realize
that an odd number times an odd number is odd, and an odd number times
an even number is even.
b. Encourage students to notice the shifting pattern of 3s products. Each
product from 3x1 through 3x10 ends in a different ones-digit.
3
6
9
12
15
18
21
24
27
30
c. Encourage students to use 3x5 as a benchmark. Ask students to discuss
how this can help them know 3x4 and 3x6 without counting.
d. Also encourage students to use 3x10 as a benchmark to assist with 3x9.
e. Encourage students to notice that the sums of the digits of all of these
products are divisible by 3.
3) Three-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 3s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
quotient will be even or odd.
Abstract Routines – Clap Facts (see directions above)
© Valerie Henry, June 2008 … www.ellipsismath.com
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Goal 6 – Multiplying and Dividing with 4s
Concrete Routines
1) Abacus Double-Doubles – have students represent a “4-times” problem in 4 rows.
Then have students calculate 2 rows, and then have them double that. For
instance, 4x6 would be modeled on the abacus as 4 rows of 6. Then students
would calculate 2x6=12, and then mentally double 12 to get 24.
a. Note: Be sure to have students share their mental math strategies for
doubling double-digit numbers such as 18 doubled for 4x9=2x2x9.
b. This same activity can be done using counters and a 10x10 grid.
Representational Routines
2) Four-Patterns on the Hundred Chart: Multiplication – have each student place a
marker on his/her individual hundred chart as 4s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
product will be even or odd – over time, the goal is for students to realize
that an even number times any other whole number gives an even product.
b. Encourage students to notice the alternating pattern of 4s products ending
in 4 and 8, and then in 2, 6, and 0.
4
8
12
16
20
24
28
32
36
40
c. Encourage students to use 4x5 as a benchmark. Ask students to discuss
how this can help them know 4x4 and 4x6 without counting.
d. Also encourage students to use 4x10 as a benchmark to assist with 4x9.
3) Four-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 4s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
Abstract Routines
4) Clap Facts – Say a fact such as “4 fives” or “28 divided by 4” and then use a hand
signal for wait. Give students 2 or 3 seconds to process, and then clap your
hands, at which time students will choral respond with the answer.
© Valerie Henry, June 2008 … www.ellipsismath.com
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Goal 7 – Multiplying and Dividing with 6s
Concrete Routines
1) Abacus Sixes – have students represent a “6-times” problem in 6 rows. Then
have students calculate 5 rows, and then have them add another row. For
instance, 6x7 would be modeled on the abacus as 6 rows of 7. Then students
would calculate 5x7=35, and then mentally add another 7 to get 42.
a. This same activity can be done using counters and a 10x10 grid.
Representational Routines
2) Six-Patterns on the Hundred Chart: Multiplication – have each student place a
marker on his/her individual hundred chart as 6s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
product will be even or odd – over time, the goal is for students to realize
that an odd number times an odd number is odd, and an odd number times
an even number is even.
b. Encourage students to notice the repeating ones-digit pattern of 6s
products: 6, 2, 8, 4, 0 and then again 6, 2, 8, 4 and 0.
6
12
18
24
30
36
42
48
54
60
c. Encourage students to use 6x5 as a benchmark. Ask students to discuss
how this can help them know 6x4 and 6x6 without counting.
d. Also encourage students to use 6x10 as a benchmark to assist with 6x9.
e. Encourage students to notice that the sums of the digits of all of these
products are divisible by 3 and are also all even.
3) Six-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 6s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
Abstract Routines – Clap Facts (see directions above)
© Valerie Henry, June 2008 … www.ellipsismath.com
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Goal 8 – Multiplying and Dividing with 7s and 8s
Concrete Routines
1) Abacus Double-Doubles – have students represent an “8-times” problem in 8
rows. Then have students calculate 4 rows, and then have them double that. For
instance, 8x6 would be modeled on the abacus as 8 rows of 6. Then students
would calculate 4x6=24, and then mentally double 24 to get 48.
a. Note: Be sure to have students share their mental math strategies for
doubling double-digit numbers such as 28 doubled for 8x7=2x4x7.
b. This same activity can be done using counters and a 10x10 grid.
2) Next-Door Patterns with Abacus or 10x10 Grid – have pairs of students
create 7x7 and 6x8 on their abacuses or 10x10 grids. Encourage them to notice
that the products are one apart (49 and 48), and that 7x7 is 1 larger than 6x8.
Ask students to continue investigating other sets of numbers that have this same
relationship (2x2 and 1x3; 3x3 and 2x4; 4x4 and 3x5; 5x5 and 4x6; 6x6 and 5x7;
8x8 and 7x9; 9x9 and 8x10). Encourage them to develop conjectures about these
relationships, and to discuss ways to remember which product goes with which
problem.
Representational Routines
3) Eight-Patterns on the Hundred Chart: Multiplication – have each student place
a marker on his/her individual hundred chart as 4s multiplication problems are
called out. Once students have placed their markers, the answer should be
provided and students’ strategies for knowing without counting can be shared.
a. Ask students to predict and share strategies for determining whether a
product will be even or odd – over time, the goal is for students to realize
that an even number times any other whole number gives an even product.
b. Encourage students to notice the repeating pattern of 8s products ending
in 8, 6, 4, 2, and 0.
8
16
24
32
40
48
56
64
72
80
c. Encourage students to use 8x5 as a benchmark. Ask students to discuss
how this can help them know 8x4 and 8x6 without counting.
© Valerie Henry, June 2008 … www.ellipsismath.com
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d. Also encourage students to use 8x10 as a benchmark to assist with 8x9.
4) Eight-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 4s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
5) Seven-Patterns on the Hundred Chart: Division – have each student place a
marker on his/her individual hundred chart as 7s division problems are called out.
Once students have placed their markers, the answer should be provided and
students’ strategies for knowing without counting can be shared.
a. Help students find strategies to distinguish between 7x8=56 and 6x9=54.
This is a pair of problems you will want to have students repeat many times
a day across many days.
Abstract Routines – Clap Facts (see directions above)
© Valerie Henry, June 2008 … www.ellipsismath.com
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SECTION FOUR: INDIVIDUAL AND SMALL-GROUP PRACTICE
4.1 Coordinating Goal-Alike Practice
One of the key principles of FactsWise is that students work with small chunks of
facts to facilitate their memorization. For this reason, we have put together a range of
resources that provide students with multiple opportunities to interact with each goal.
Our objective is to engage students in elaborative rehearsal, where they look at the facts
from many different perspectives. This approach to memorization has been found to be
more effective than simple repetition.
For this reason, it will be important for you to know which students are working on
the same goal. You can use the Whole-Class Progress Chart and reusable dots (similar to
Post-Its) to keep track of your students’ progress. Then, when you want students to work
together, it will be easy to get goal-alike groups together.
4.2 Flashcards and Pairs Practice
Many teachers grew up using flashcards to practice their basic facts, and we often
assume that this is an essential tool in this enterprise. Goal-specific flashcards are
available for this program, in both cardstock and online formats, and they are certainly one
of the many ways students can practice their facts. Cognitive research provides evidence,
however, that elaborative rehearsal is a more powerful method of building long-term
memories than repetitive practice. So while some students may thrive using flashcards,
many others will find other forms of practice more valuable.
Included in this resource are Pairs Practice pages for each of the goals. These
pages are designed to be folded in half, and then held between two students. While one
student is reading and answering the problems, the other student is able to check the
answers by looking at the other side of the folded page. This way, students can get
immediate feedback, even when their partners are not yet experts themselves. These
Pairs Practice pages can be reused many times because no writing is required. Just be sure
to help the students learn to give positive feedback and assistance when using these pages.
Jeff Simpson (http://masterylearningsystems.com), who created this practice method,
encourages students to respond to an error with the phrase “try again”. It can be
particularly helpful to have a Slavonic abacus or ten frames ready for students to use if
they are still in the early learning phases of a goal.
Not only can Pairs Practice pages be used at school, they are also a good option for
at-home practice. Rather than asking parents to cut out and manage flashcards, you may
want to send home Pairs Practice pages – they don’t require any cutting, they’re easy to
store, and just as reusable as flashcards.
© Valerie Henry, June 2008 … www.ellipsismath.com
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4.3
Online Flashcards, Games and Quizzes
Online flashcards, games, and quizzes are available for each of the FactsWise goals.
These can be used both at school and at home, and provide an easy way to have students
working on their appropriate goals.
4.4 Whole-Class Powerpoint “Commercials”
Advertisers know that after watching a commercial 7 times, viewers are likely to
remember large chunks of the message. We’ve developed several basic fact “commercials”
for FactsWise goals --- students seem to enjoy watching and interacting with them. Feel
free to download them from the IUSD Intranet. Once you coach your students on the way
you would like them to interact with the presentations (e.g., choral response, silently, …),
these “commercials” can give you a few minutes to take attendance or set up for your math
lesson!
© Valerie Henry, June 2008 … www.ellipsismath.com
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SECTION 5: MOVING BASIC FACTS INTO PERMANENT MEMORY
(excerpts from Building Background Knowledge for
Academic Achievement by Robert J. Marzano, 2004)
Sensory memory is a (very) temporary repository for information from our senses.
However, we cannot process all of the information from the senses. Rather, we pick and
choose.
Permanent memory contains information that has been stored in such a way that it is
available to us.
Working memory is the third type of memory. Working memory can receive data from
sensory memory (where it is held only briefly), from permanent memory (where it resides
permanently), or from both. The amount of time data can reside in working memory has no
theoretical limit. As long as we focus conscious attention on the data in working memory,
it stays active. … All things being equal, it is the quality and type of processing that
occurs in working memory that dictates whether that information makes it to permanent
memory. If processing does not go well, information does not make it to permanent
memory.
At least three interacting dynamics of working-memory processing dictate whether
information makes it into permanent memory. One is strength of the “memory trace,” or
the pathway to the information. As Anderson (1995) explains: “Memory records are
assumed to have a property called strength, which increases with repeated practice” (p.
193). In simple terms, the more times we engage information in working memory, the
higher the probability that it will be embedded in permanent memory. In educational
terms, the more times a student processes information, the more likely the student will
remember it. … Nuthall found that students require about four exposures to information
to adequately integrate it into their background knowledge. Nuthall also notes that these
exposures should be no more than about two days apart. … However, sheer repetition of
information in working memory is not enough to ensure that it will be stored in permanent
memory.
Depth of processing is the second aspect of effective processing in working memory. …
Deep processing of information adds detail to our understanding of information.
Elaboration is the third aspect of effective processing of information in working memory.
Elaboration deals with the variety of associations we make with information. Although
depth of processing and elaboration are related, depth of processing refers to going into
more detail; elaboration, on the other hand, refers to making new or varied connections.
© Valerie Henry, June 2008 … www.ellipsismath.com
Page 19
Effective processing of information in working memory depends on certain critical
activities: 1) the information is processed multiple times with 1- or 2-day intervals in
between, 2) detail is added, and 3) associations are made with other information.
Based on the above research, you may want to try the following during class:
 Work on a small number of facts several days in a row (perhaps target each
goal for one entire week)
 Help students identify the connections between the facts in each goal
 Help students make connections between the addition and subtraction facts
(try using the part-whole grids)
 Have students solve basic fact problems from classroom-based stories as well
as in “naked number” format
 Have students look for patterns within goals and between goals
 Have students learn to look for clues as to whether a sum or difference will
be odd or even
 Once students have become fluent with the first five goals, begin building
part-whole strategies for the remaining facts
 Focus in particular on part-whole strategies involving tens
 Help students learn names for the types of facts in some goals
© Valerie Henry, June 2008 … www.ellipsismath.com
Page 20
SECTION 6: GOAL-BY-GOAL ASSESSMENTS
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 1M - Memorize the 10s (Version A)
10 x 7
10 x 3
10 x 6
10 x 2
10 x 5
10 x 9
10 x 4
10 x 8
10 x 10
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 1M - Memorize the 10s (Version B)
10 x 8
10 x 6
10 x 10
10 x 5
10 x 9
10 x 7
10 x 4
10 x 3
10 x 2
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 1D - Memorize the 10s (Version A)
30 ÷ 10
20 ÷ 2
100 ÷ 10
70 ÷ 10
30 ÷ 3
90 ÷ 10
80 ÷ 10
60 ÷ 6
60 ÷ 10
40 ÷ 4
40 ÷ 10
80 ÷ 8
20 ÷ 10
50 ÷ 10
90 ÷ 9
70 ÷ 7
50 ÷ 5
10 ÷ 10
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 1D - Memorize the 10s (Version B)
40 ÷ 4
50 ÷ 10
80 ÷ 8
40 ÷ 10
100 ÷ 10
60 ÷ 10
50 ÷ 5
90 ÷ 10
70 ÷ 7
20 ÷ 10
80 ÷ 10
30 ÷ 10
20 ÷ 2
70 ÷ 10
90 ÷ 9
30 ÷ 3
10 ÷ 10
60 ÷ 6
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 2M - Memorize the 5s (Version A)
5x5
5x8
5x4
5x9
5x7
5x3
5x6
5x2
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 2M - Memorize the 5s (Version B)
5x4
5x6
5x3
5x8
5x9
5x2
5x7
5x5
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 2D - Memorize the 5s (Version A)
35 ÷ 5
25 ÷ 5
5÷5
10 ÷ 2
30 ÷ 5
35 ÷ 7
15 ÷ 3
20 ÷ 4
30 ÷ 6
40 ÷ 8
45 ÷ 5
20 ÷ 5
40 ÷ 5
10 ÷ 5
15 ÷ 5
45 ÷ 9
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 2D - Memorize the 5s (Version B)
25 ÷ 5
15 ÷ 5
35 ÷ 7
30 ÷ 5
10 ÷ 2
40 ÷ 5
20 ÷ 5
10 ÷ 5
35 ÷ 5
40 ÷ 8
30 ÷ 6
45 ÷ 5
5÷5
20 ÷ 4
15 ÷ 3
45 ÷ 9
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 3M - Memorize the 2s (Version A)
2x7
2x9
2x4
2x2
2x8
2x6
2x3
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 3M - Memorize the 2s (Version B)
2x6
2x9
2x7
2x3
2x8
2x2
2x4
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 3D - Memorize the 2s (Version A)
4÷2
10 ÷ 2
6÷3
12 ÷ 2
16 ÷ 2
14 ÷ 7
12 ÷ 6
14 ÷ 2
8÷4
6÷2
16 ÷ 8
18 ÷ 9
18 ÷ 2
8÷2
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 3D - Memorize the 2s (Version B)
16 ÷ 2
18 ÷ 9
16 ÷ 8
8÷2
6÷2
14 ÷ 2
8÷4
18 ÷ 2
12 ÷ 2
12 ÷ 6
14 ÷ 7
6÷3
10 ÷ 2
4÷2
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOALS 1,2 & 3 Multiplication
10 x 4
10 x 6
10 x 8
10 x 3
5x7
5x4
5x9
5x6
5x3
5x8
2x7
2x9
2x3
2x6
2x8
2x4
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOALS 1,2 & 3 Division
40 ÷ 4
70 ÷ 10
50 ÷ 10
80 ÷ 8
80 ÷ 10
30 ÷ 3
40 ÷ 8
20 ÷ 5
35 ÷ 5
15 ÷ 3
45 ÷ 5
30 ÷ 6
30 ÷ 5
45 ÷ 9
10 ÷ 2
12 ÷ 6
18 ÷ 9
14 ÷ 2
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 4M - Memorize the 9s (Version A)
9x6
9x3
7x9
9x9
4x9
9x8
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 4M - Memorize the 9s (Version B)
9x9
4x9
9x7
3x9
8x9
9x5
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 4D - Memorize the 9s (Version A)
54 ÷ 9
81 ÷ 9
27 ÷ 3
63 ÷ 7
72 ÷ 9
36 ÷ 9
36 ÷ 4
54 ÷ 6
63 ÷ 9
72 ÷ 8
18 ÷ 9
27 ÷ 9
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 4D - Memorize the 9s (Version B)
36 ÷ 9
54 ÷ 6
72 ÷ 8
27 ÷ 3
54 ÷ 9
36 ÷ 4
81 ÷ 9
63 ÷ 9
63 ÷ 7
27 ÷ 9
45 ÷ 9
72 ÷ 9
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 5M - Memorize the 3s (Version A)
3x4
8x3
6x3
3x3
3x7
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 5M - Memorize the 3s (Version B)
7x3
3x3
3x5
4x3
3x6
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 5D - Memorize the 3s (Version A)
24 ÷ 3
18 ÷ 3
12 ÷ 4
21 ÷ 7
21 ÷ 3
24 ÷ 8
18 ÷ 6
12 ÷ 3
9÷3
27 ÷ 3
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 5D - Memorize the 3s (Version B)
21 ÷ 3
18 ÷ 6
12 ÷ 4
27 ÷ 3
9÷3
21 ÷ 7
18 ÷ 3
24 ÷ 3
24 ÷ 8
12 ÷ 3
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOALS 1 - 5 Multiplication
10 x 5
8 x 10
5x9
3x7
7x5
9x8
9x2
2x5
2x7
8x2
9x4
3x6
6x5
3x4
3x3
5x4
9x9
8x3
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOALS 1 - 5 Division
60 ÷ 6
90 ÷ 10
35 ÷ 5
45 ÷ 9
20 ÷ 4
40 ÷ 5
18 ÷ 2
14 ÷ 7
12 ÷ 6
16 ÷ 2
36 ÷ 4
54 ÷ 9
81 ÷ 9
63 ÷ 7
27 ÷ 3
24 ÷ 8
18 ÷ 6
21 ÷ 3
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 6M - Memorize the 4s (Version A)
4x8
4x4
7x4
4x6
GOAL 6M - Memorize the 4s (Version B)
6x4
4x8
4x4
7x4
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 6D - Memorize the 4s (Version A)
24 ÷ 6
16 ÷ 4
28 ÷ 4
32 ÷ 8
32 ÷ 4
24 ÷ 4
28 ÷ 7
36 ÷ 4
GOAL 6D - Memorize the 4s (Version B)
28 ÷ 7
32 ÷ 4
24 ÷ 4
30 ÷ 6
16 ÷ 4
28 ÷ 4
32 ÷ 8
24 ÷ 6
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOAL 7M - Memorize the 6s
6x6
8x6
6x7
GOAL 7D - Memorize the 6s (Version A)
48 ÷ 6
42 ÷ 7
36 ÷ 6
48 ÷ 8
42 ÷ 6
54 ÷ 6
© Valerie Henry, June 2008 … www.ellipsismath.com
Page 48
GOAL 8M - Memorize the 7s & 8s
7x7
7x8
8x8
GOAL 8D - Memorize the 7s & 8s
64 ÷ 8
56 ÷ 7
56 ÷ 8
49 ÷ 7
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOALS 1 - 8 Multiplication
7 x 10
10 x 9
5x8
7x5
2x6
8x2
4x9
6x4
4x7
4x8
6x8
8x3
8x9
7x8
3x6
9x3
6x6
6x9
9x7
7x7
© Valerie Henry, June 2008 … www.ellipsismath.com
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GOALS 1 - 8 Division
80 ÷ 8
40 ÷ 10
45 ÷ 5
30 ÷ 6
14 ÷ 2
18 ÷ 9
36 ÷ 9
28 ÷ 4
32 ÷ 4
24 ÷ 6
56 ÷ 7
24 ÷ 8
72 ÷ 8
48 ÷ 6
27 ÷ 3
21 ÷ 7
54 ÷ 6
42 ÷ 7
63 ÷ 7
81 ÷ 9
© Valerie Henry, June 2008 … www.ellipsismath.com
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TOP 21 Multiplication (Version A)
5x9
6x7
7x3
8x8
4x6
3x9
9x9
7x4
8x7
3x6
6x6
9x7
4x8
8x6
8x9
7x7
7x5
9x4
9x7
6x9
5x8
8x3
© Valerie Henry, June 2008 … www.ellipsismath.com
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TOP 21 Multiplication (Version B)
4x9
6x6
7x7
8x5
3x6
7x9
9x8
5x7
8x3
6x8
9x6
9x9
8x8
8x4
7x9
6x7
4x7
9x5
9x3
3x7
4x6
7x8
© Valerie Henry, June 2008 … www.ellipsismath.com
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TOP 21 Division (Version A)
36 ÷ 4
49 ÷ 7
45 ÷ 9
56 ÷ 8
18 ÷ 3
72 ÷ 9
35 ÷ 5
24 ÷ 8
48 ÷ 6
54 ÷ 6
9x6
81 ÷ 9
64 ÷ 8
32 ÷ 4
42 ÷ 7
28 ÷ 7
40 ÷ 8
27 ÷ 3
21 ÷ 7
24 ÷ 6
56 ÷ 7
72 ÷ 9
© Valerie Henry, June 2008 … www.ellipsismath.com
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TOP 21 Division (Version B)
40 ÷ 5
36 ÷ 6
63 ÷ 7
72 ÷ 8
18 ÷ 6
35 ÷ 7
24 ÷ 3
48 ÷ 8
54 ÷ 9
64 ÷ 8
81 ÷ 9
42 ÷ 6
32 ÷ 8
28 ÷ 4
45 ÷ 5
27 ÷ 9
21 ÷ 3
24 ÷ 4
56 ÷ 8
49 ÷ 7
36 ÷ 9
54 ÷ 6
© Valerie Henry, June 2008 … www.ellipsismath.com
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SECTION 7: RECORD-KEEPING RESOURCES
© Valerie Henry, June 2008 … www.ellipsismath.com
Page 56
Name _____________________________ Grade _________ Teacher ______________ School __________
Pre-Assessment
C=counted, FM=fluent memorized, SM=slow memorized, FS=fluent strategy, SS=slow strategy
G1
G2
G3
G4
G5
G6
G7
G8a
G8b
10s
5s
2s
9s
3s
4s
6s
7s
8s
3x10
5x7
2x9
9x7
3x8
4x4
6x7
7x8
8x9
10x8
5x5
6x2
4x9
6x3
4x7
9x6
7x4
6x8
60÷10
45÷9
14÷2
72÷9
27÷3
24÷4
48÷6
56÷7
64÷8
If student is struggling with above, consider assessing with addition and subtraction goals. When not apparent,
ask student “How did you get that?” (C=counted, FM=fluent memorized, SM=slow memorized, FS=fluent strategy,
SS=slow strategy):
G1
G2
G3
G4
G5
G6
G7
G8
G9
1+4
3+5
4+6
10+4
5+7
7+7
3+6
6+9
4+8
5-3
9-5
10-7
16-6
13-5
14-7
8-6
13-9
15-8
© Valerie Henry, July 2008 … www.ellipsismath.com
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FactsWise Multiplication/Division Pre-Assessment Visuals
Goals 1-3
Goals 4 – 6
3 x 10
72 ÷ 9
5x7
27 ÷ 3
2x9
24 ÷ 4
10 x 8
9x7
8x5
3x8
6x2
4x4
60 ÷ 10
4x9
45 ÷ 9
6x3
14 ÷ 2
4x7
© Valerie Henry, July 2008 … www.ellipsismath.com
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Goals 7 – 8b
6x7
7x8
8x9
9x6
7x4
6x8
48 ÷ 6
56 ÷ 7
64 ÷ 8
© Valerie Henry, July 2008 … www.ellipsismath.com
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MULTIPLICATION FACTS ASSESSMENT
Try these facts in random order. Put a + in the box when you know the fact automatically.
Leave the box blank if you had to use a special strategy or were slower to remember the
answer for that fact.
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
I need to work on the following facts:
© Valerie Henry, July 2008 … www.ellipsismath.com
60
Name:____________________________
FactsWise Progress Chart
Goal 1M
Goal 1D
Goal 2M
Goals 2D
Goal 3M
Goal 3D
Goal 1-3 M
Goals 1-3 D
Goal 4M
Goal 4D
Goal 5M
Goals 5D
W – working to learn the facts; inaccurate on one or more problems
C – counts or skip-counts to solve one or more problems
S - solves all problems using strategies & memorization, some slowly
E – efficiently & accurately solves all problems using strategies &
memorization
© Valerie Henry, July 2008 … www.ellipsismath.com
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Goal 1-5M
Goal 1-5D
Goal 6M
Goals 6D
Goal 7M
Goal 7D
Goal 8M
Goals 8D
Goal 1-8M
Goal 1-8D
Top 21M
Top 21D
W – working to learn the facts; inaccurate on one or more problems
C – counts or skip-counts to solve one or more problems
S - solves all problems using strategies & memorization, some slowly
E – efficiently & accurately solves all problems using strategies &
memorization
© Valerie Henry, July 2008 … www.ellipsismath.com
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FactsWise Class Chart
Multiplication
Division
1
2
3
4
5
6
7
8
Top
21
© Valerie Henry, July 2008 … www.ellipsismath.com
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BASIC FACT GOALS
BASIC FACT GOALS
Progress Report
Progress Report
____________________/_________
Name
Date
____________________/_________
Name
Date
Keep working on Goal _____
Keep working on Goal _____
And/or start on Goal ______
And/or start on Goal ______
BASIC FACT GOALS
BASIC FACT GOALS
Progress Report
Progress Report
____________________/_________
Name
Date
____________________/_________
Name
Date
Keep working on Goal _____
Keep working on Goal _____
And/or start on Goal ______
And/or start on Goal ______
BASIC FACT GOALS
BASIC FACT GOALS
Progress Report
Progress Report
____________________/_________
Name
Date
____________________/_________
Name
Date
Keep working on Goal _____
Keep working on Goal _____
And/or start on Goal ______
And/or start on Goal ______
© Valerie Henry, July 2008 … www.ellipsismath.com
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BASIC MATH FACTS RUNNING RECORD
Student _________________________ ID __________________
Birthdate ____________ Other ___________________________
Grade
Addition
Subtraction
K
Facts to 10
Facts to 5
Multiplication
Division
2s, 5s, 10s
2s, 5s, 10s
1
2
3
4
5
6
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MULTIPLICATION AND DIVISION FACTS FLUENCY
Order of Study: 10s, 5s, 2s, Review 10s-2s, 9s, 3s, 4s, Review 10s-4s, 6s, 7s, 8s, Top 21
(for each goal, first work on multiplication; then the related divisions)
Weekly Test
Monday
Practice (practice charts, pairs practice, flashcards, games, online games, oral quizzing, …)
Tuesday
Wednesday
Thursday
Friday-Sunday
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Monday
Tuesday
Wednesday
Thursday
Friday-Sunday
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Monday
Tuesday
Wednesday
Thursday
Friday-Sunday
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Monday
Tuesday
Wednesday
Thursday
Friday-Sunday
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Goal: _______ M / D
Fluent/Needs More Work
Fluent/Needs More Work
Fluent/Needs More Work
Fluent/Needs More Work
Fluent – each fact answered correctly in 3 seconds or less, without counting-on or skip counting
Level 1
Level 2
Level 3
10s x
9s x
6s x
10s ÷
9s ÷
6s ÷
5s x
5s ÷
2s x
2s ÷
Review 1 x
3s x
3s ÷
4s x
4s ÷
Review 2 x
7s x
7s ÷
8s x
8s ÷
Top 21 x
© Valerie Henry, July 2008 … www.ellipsismath.com
Review 1 ÷
Review 2 ÷
Top 21 ÷
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