Teaching the Introductory Unit - Working Women Community Centre

Transcription

2009 Edition
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B, C and D
Tutor Essentials
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Tutor Essentials
JUMPMath
To Accompany Student Books B, C and D
Contents
Working in Communities
Introductory Unit Using Fractions
Getting Ready for the Introductory Unit
Teaching the Introductory Unit
Show Your Success
Why Mental Math
Mental Math Unit
Appendix 1 Ideas for Math Fun
Copyright © 2009 JUMP Math
All rights reserved. No part of this publication may be reproduced or transmitted in any
form or by any means, electronic or mechanical, including photocopying, recording, or
any information storage and retrieval system, without written permission from the
publisher, or expressly indicated on the page with the inclusion of a copyright notice.
JUMP Math
Toronto, Canada
www.jumpmath.org
ISBN: 978-1-897120-81-1
Printed and bound in Canada
Working in Communities
JUMP Math: Working in the Communities
What is JUMP Math?
JUMP Math (Junior Undiscovered Math Prodigies) is a program designed to help students develop
proficiency in mathematics. Started in 1998 by mathematician, author and award-winning
playwright John Mighton, JUMP Math is a federally registered charitable organization based in
Toronto, Canada. Thus far, JUMP Math has had a significant effect on mathematics success by
increasing achievement and reducing anxiety.
What is at the heart of the JUMP Math program?
Helping children understand mathematics is the fundamental issue that
JUMP Math strives to address. There is a causal link between a child’s
academic success and his or her future contribution to society. JUMP Math
strives to increase a child’s chances of success, to reduce socio-economic
disparities, to engender a sense of belonging and, most importantly, to
endow voiceless children with opportunity. Enhancing the potential in
children by encouraging an understanding and a love of math in students
and educators is at the heart of JUMP Math.
What does JUMP Math believe?
JUMP Math believes that every child can be successful at mathematics.
A prevalent myth in our society is that while some people are born with
mathematical talent, others simply do not have the ability to succeed.
Recent discoveries in cognitive science are exploding that myth of ability.
Building on the belief that every child can be successful at mathematics,
JUMP Math:
• Promotes positive learning environments and builds confidence through praise
and encouragement;
• Maintains a balanced approach to math instruction by focusing on both
conceptual and procedural learning concurrently;
• Achieves understanding and mastery by breaking down concepts and skills into
small sequential steps;
• Keeps all students engaged and attentive by “raising the bar” incrementally; and
• Guides students to explore and discover mathematics.
Tutor Essentials • Working in the Communities • page 4
What makes JUMP Math different?
JUMP Math recognizes the importance of reducing math anxiety. Research in psychology has
shown that our brains are limited: our working memories are poor; we are easily overwhelmed by
too much new information; and, we require a good deal of practice to consolidate skills and
concepts. These mental challenges are compounded when we are anxious. The JUMP Math
approach has been shown to reduce math anxiety significantly.
JUMP Math scaffolds mathematical concepts rigorously and completely. The JUMP Math materials
were designed by a team of mathematicians and educators who have a deep understand of and
a love for mathematics. In JUMP Math, concepts are introduced in rigorous steps, with prerequisite
skills and concepts included in the lesson.
Consistent with emerging brain research, JUMP Math provides materials and methods that
promote guided practice helping tutors to more effectively improve student understanding.
What kind of impact does JUMP Math have?
Although successful for all students, JUMP Math is particularly effective for struggling students,
including those from vulnerable populations.
FACT: Research indicates that JUMP Math is particularly successful for weaker students:
•
In London, UK, after just one school year with JUMP Math, 67% of failing students
improved two math grade levels.
JUMP Math in Lambeth 2007: Evaluation & Impact of the KS2 national test,
Autumn 2007.
•
A University of Toronto study found of JUMP Math that conceptual understanding
of math improved significantly among weaker students. OISE, Ontario Institute for
Studies in Education, 2009
What is the importance of mathematical literacy?
Math presents itself in our every day lives in a variety of ways. For example, calculating change at
a store, knowing when the next bus will come, or making sure a paycheck is correct, all require
adequate numeracy skills. You will face many external situations that demand recall
mathematical facts, so a solid grounding in mathematics is absolutely necessary to be an
engaged, constructive citizen.
FACT: Mathematical literacy is directly linked to participation in the economy and civil society.
•
Mathematics performance is closely related to finishing high school and
participating in post secondary education.
(OECD, PISA 2006: Science competencies for Tomorrow’s World, Volume 1)
•
Taking a math course prior to leaving school is one of the two most significant
indicators on whether a high school dropout will return to school.
(Statistics Canada: 2008: High School Dropouts Returning to School)
How can JUMP Math help in tutoring settings?
In addition to providing curriculum-based resources for teachers and students in classroom
settings, JUMP Math has recently developed student workbooks and tutor guides. These
resources are designed to cover foundational skills and concepts using the JUMP Math approach
to learning. JUMP Math is committed to working with communities to improve student success in
settings such as: homework clubs; after school tutoring programs; one-on-one mentoring
initiatives; and, community centres.
There are three levels of student workbooks:
•
Student Essentials B for grades 3-4;
•
Student Essentials C for grades 5-6; and,
•
Student Essentials D for grades 7-8.
With the generous support of our donors, JUMP Math has launched the Community REACH Fund
to assist non-profit organizations by providing subsidies for student workbooks and
tutor training.
What JUMP principles should a tutor consider?
Take responsibility for learning:
If the student doesn’t understand a concept, it can always be clarified further or explained
differently. The tutor is responsible for a student’s success.
Use positive reinforcement:
Students like to be rewarded when they succeed. Praise and encouragement builds
excitement and fosters an appetite for learning. The more confidence a student has, the
more likely they are to be engaged.
Take small steps:
In mathematics, it is always possible to make something easier. The tutor should break
down the question to a series of small steps. Practice, practice, practice!
Only indicate correct answers:
A student’s confidence can be shaken by a lack of success. Place checkmarks where the
students have answered correctly, and revisit questions the student has failed to complete.
Never use X’s!
Raise the bar:
When students master a particular concept, challenge them by posing a question that is
slightly more difficult. As students meet these challenges, you will see their focus and
excitement increase.
What are some hints for helping students who have fallen behind?
Teach the number facts! It is a serious mistake to think that students who don’t know their
number facts can always get by in mathematics using a calculator. Students can certainly perform
operations on a calculator, but they cannot begin to solve problems if they lack a sense of
numbers: students need to be able to see patterns in numbers, and to make estimates and
predictions about numbers, in order to have any success in mathematics.
How can a tutor make his/her session productive?
An average tutoring session is usually 45 minutes to an hour. To keep your student engaged and
attentive, consider breaking up your session into thirds:
•
First 10 – 15 Minutes: Use this time to focus on Mental Math. This will sharpen
their mental number skills, and students will find the remainder of the session
much more enjoyable if they are not constantly struggling to remember their
number facts.
•
Second 10-15 Minutes: Use this time to work on grade-specific material. These
tutoring materials have been designed by mathematicians and educator to fill
gaps in learning, strengthen basic skills and reinforce fundamental concepts.
•
Final 10-15 Minutes: Save this portion of the session for math games or optional
worksheets.
It is important to remember that tutoring sessions must be fun! Most of the time, students have
been at school for the entire day and may be tired. Liven up your session by conversing casually
with your student, playing games, and being as active as possible. If the opportunity to visually
demonstrate a concept arises, jump at it! Have your student sort out change, look around them
for geometric objects, or pace out a perimeter.
What is the purpose of the Introductory Unit?
In recent years, research has shown that students are more apt to do well in subjects when they
believe they are capable of doing well. It seems obvious, then, that any math program that aims
to harness the potential of every student must start with an exercise that builds the confidence of
every student. Getting Ready for JUMP Math: Introductory Unit Using Fractions was designed for
this purpose. It has proven to be an extremely effective tool for convincing even the most
challenged student that they can do well in mathematics.
The method used in the Introductory Unit can be described as guided discovery.
The individual steps that tutors will follow in teaching the unit are extremely small, so even the
weakest student needn’t be left behind. Throughout the unit, students are expected to:
•
Discover or extend patterns or rules on their own;
•
See what changes and what stays the same in sequences of mathematical
expressions; and
•
Apply what they have learned to new situations.
Students become very excited at making these discoveries and meeting these challenges as they
learn the material. For many, it is the first time they have ever been motivated to pay attention to
mathematical rules and patterns or to try to extend their knowledge in new cases.
How does the Introductory Unit build confidence?
The Introductory Unit Using Fractions has been specifically designed to build confidence by:
•
Requiring that students only possess a very small amount of simple skills.
To achieve a perfect score on the final test in the unit, students need only possess three
skills. These skills can be taught to the most challenged students in a very short amount
of time. Students must be able to:
1.
Skip count on their fingers;
2.
Add one-digit numbers; and
3.
Subtract one-digit numbers.
Tutor Essentials • Introductory Unit Using Fractions • page 10
•
Eliminating heavy use of language. Mathematics functions as its own symbolic
language. Since the vast majority of children are able to perform the most basic
operations (counting and grouping objects into sets) long before they become expert
readers, mathematics is the subject in which the vast majority of kids are naturally
equipped to excel at an early age. By removing language as a barrier, students can
realize their full potential in mathematics.
•
Allowing the tutor to continually provide feedback. Moving on too quickly is both a
hindrance to a student’s confidence and an impediment to their eventual success. In the
Introductory Unit, the mathematics is broken down into small steps so that the tutor can
quickly identify difficulties and help as soon as they arise.
•
Keeping the student engaged through the excitement of small victories. Children
respond more quickly to praise and success than to criticism and threats. If students are
encouraged, they feel an incentive to learn. Students enjoy exercising their minds and
showing off to a caring tutor.
How long should we work on the Introductory Unit?
The introduction Unit using Fractions has been an integral part of the JUMP Math approach since
its inception more than 10 years ago. Teachers and tutors have consistently had positive results
in reducing math anxiety and improving confidence. Struggling students tend to believe that
fractions are the most challenging part of mathematics. It is a booster of confidence to start with
fractions and begin to experience small successes right away. Try to complete the unit, but if it is
taking longer than six weeks consider moving on. While you are working on the introductory unit,
concurrently work on mental math during every session.
How can my student show success?
The following section of this tutor guide has tips for teaching the Introductory Unit Using
Fractions. By following the suggestions, you will be able to work with your student to ensure they
will be successful and at the end of the section you will find the unit test which we called “Show
Your Success”. If the student has completed the unit they will be able to do well at this task and
show off!
Fractions Unit Content Listing
Fractions Skill 1: Naming Fractions
Fractions Skill 2: Adding and Subtracting Fractions with the same Denominator
Fractions Skill 3: Adding and Subtractions Fractions with Different Denominators
Fractions Skill 4: Adding and Subtracting Fractions – Changing Only One
Denominator
Fractions Skill 5: Adding and Subtracting Fractions – Distinguishing the Three
Methods
Fractions Skill 6: Adding and Subtracting Three Fractions
In my experience teaching the Introductory Unit Using
Fractions, I’ve learned that it’s natural to experience a
setback or two on occasion. Solving problems
sometimes takes a great deal of trial and error. Once
students develop a sense of confidence in math and
know how to work independently, you can provide
them a series of graduated challenges. Remember,
stick to your T.U.T.O.R. principles!
Getting Ready for Fractions Unit
Getting Ready for Introductory Unit
Addition (where one number is a single digit)
NOTE TO TUTOR: Before starting the Introductory Unit Using Fractions, make sure your student
can add single digits, subtract single digits and multiply by 2, 3, 5. Practice these skills on pages
xxx and xxx.
Example: 16 + 3 =
Step 1:
Say the greater number (16) with your fist closed.
Step 2:
Count up by ones raising first your thumb, then one finger at a time until you have the
same number of fingers up as the lower number.
Step 3:
The number you say when you have the second number of fingers up is the answer
(in this case, you say 19 when you have three fingers up so 19 is the sum of 16 & 3).
17
18
19
A great bonus question would be to add a multi-digit number to a single digit number (e.g. 1653 + 8).
Just make sure your student can count high numbers.
Subtraction (where the answer is a single digit)
Example: 11 – 8 =
Step 1:
Say the lesser number (8) with your fist closed.
Step 2:
Count up by ones raising first your thumb, then one finger at a time until you have
reached the higher number (11).
Step 3:
The number of fingers you have up when you reach the final number is the answer (in
this case, you have three fingers up so 3 is the difference between 8 & 11).
9
10
11
A great bonus question would be double- or triple-digit subtractions whose difference is a single
digit (e.g. 462 – 458). Just make sure your student can count high numbers!
Tutor Essentials • Getting Ready for Introductory Unit • page 14
Worksheet
Counting by 2, 3 and 5
F-1
1. Complete the following hands:
2
3
5
BONUS: Try to do it when the top of this page is covered!
6
9
4
5
8
2
Worksheet
Counting by 2, 3 and 5
F-1
1. Complete the following questions. (Hint: Use your 2 hand)
3 ¯ 2 = _____
1 ¯ 2 = _____
4 ¯ 2 = _____
3 ¯ 2 = _____
1 ¯ 2 = _____
5 ¯ 2 = _____
2 ¯ 2 = _____
4 ¯ 2 = _____
3 ¯ 3 = _____
2 ¯ 3 = _____
4 ¯ 3 = _____
3 ¯ 3 = _____
1 ¯ 3 = _____
3 ¯ 3 = _____
5 ¯ 3 = _____
2 ¯ 3 = _____
3 ¯ 5 = _____
2 ¯ 5 = _____
4 ¯ 5 = _____
3 ¯ 5 = _____
1 ¯ 5 = _____
3 ¯ 5 = _____
5 ¯ 5 = _____
2 ¯ 5 = _____
4. Diagnostic Quiz: Complete the following questions.
3 ¯ 3 = _____
2 ¯ 2 = _____
4 ¯ 5 = _____
4 ¯ 2 = _____
1 ¯ 5 = _____
3 ¯ 5 = _____
2 ¯ 5 = _____
5 ¯ 3 = _____
3 ¯ 2 = _____
2 ¯ 3 = _____
4 ¯ 3 = _____
2 ¯ 2 = _____
1 ¯ 3 = _____
3 ¯ 5 = _____
4 ¯ 5 = _____
5 ¯ 5 = _____
5 ¯ 3 = _____
1 ¯ 2 = _____
2 ¯ 2 = _____
1 ¯ 5 = _____
1 ¯ 8 = _____
1 ¯ 21 = _____
1 ¯ 23 = _____
1 ¯ 296 = _____
1 ¯ 663 = _____
1 ¯ 0 = _____
1 ¯ 1 = _____
1 ¯ 12,035 = _____
46 ¯ 1 = _____
127 ¯ 1 = _____
2 ¯ 0 = _____
0 ¯ 189 = _____
1,905 ¯ 1 = ________
104,761 ¯ 0 = _____
0 ¯ 1 = _____
1 ¯ 6 = _____
BONUS:
TUTOR: Do not move on until all of your students have gotten 100% on the diagnostic quiz
(Q 4) on this page. Make sure your students can add and subtract one digit numbers. Students
can learn the skills required to do well in this unit very quickly—do not move on until you have
taught the skills covered in this section.
Fractions Skill 1
Explain how to represent a fraction.
3
8
Step 1:
Count the number of shaded regions.
Step 2:
Count the number of pieces the pie is cut into.
Remember, each step should be taught separately (allowing for repetition) unless your student is very
quick.
Here are some questions your student can try:
What fraction of each figure is shaded?
1
1
Teach your student how to draw 2 and 4 with circles.
1
Teach them how to draw 3 as follows:
1
1
Ask your student how they would draw 2 and 4 in a square box. Make sure they know that in drawing a
fraction, you have to make all the pieces the same size.
1
For instance, the following is not a good example of 4 :
1
Your student should be able to recognize when a shaded piece of pie is less than 2 of a pie.
1
To see that the fraction is less than 2 ,
continue one of the lines.
Tutor Essentials • Teaching the Introductory Unit • page 18
Fractions Skill 2
Rule: Add the numerator and leave the denominator the same.
For example,
1 piece plus 2 pieces gives 3 pieces
1
4
2
4
+
3
4
=
Make sure your student knows why
the denominator does not change:
the pie is still cut into 4 pieces – you
1
are still adding up 4 size pieces.
Allow for lots of practice. Only introduce one step at a time.
Whenever possible, you should allow the student to figure out how to extend a concept to a case they
haven’t seen. This is easy to do with the addition of fractions.
Ask your student what they might do if:
There were three fractions with the same denominator?
2
4
1
7 + 7 + 7 = ?
(If your student guesses what to do in this case, point out that they are smart enough to figure out
mathematical rules by themselves. It is essential that you make your student feel intelligent and capable
right from the first lesson.)
If they had subtraction?
1
3
4 – 4
= ?
Demonstrate this with a picture:
1
2
taking away 4 leaves 4
If they had mixed addition and subtraction?
5
1
3
7 + 7 – 7 =?
Fractions Skill 3
If the denominators are different, then you can’t compare piece sizes. It’s not clear how to add fractions
with different denominators:
1
2
1
3
+
=
?
Tell your student that after you have shown them how the operation works with pictures you will show
them a much easier method that they cannot fail to perform. (You should, however, return to this sort of
pictorial explanation when your student has fully mastered the operation).
Solution:
Cut each of the two pieces in the first pie into three, and cut each of the three pieces in the second pie into
two. This will give the same number of pieces in each because 2 × 3 = 3 × 2 = 6.
3
6
2
6
+
=
5
6
Draw the above picture, and ask your student to write the new fractions corresponding to the way pies are
1
3
1
2
now cut. Make sure they notice that 2 is the same as 6 of the pie, and that 3 is the same as 6 (and
one out of three pieces is the same as two out of six). Once you have discussed this, your student can
perform the addition. The one thing the student should take away from this explanation is that to produce
pieces of the same size in both pies (which is necessary for adding fractions), one has to cut each pie into
smaller pieces.
Tell your student you will now teach them a very easy way of changing the number of pieces the pie is cut
into without having to draw the picture.
Step 1:
Multiply each denominator by the other one. The numerator also has to be multiplied,
because now you are getting more pieces.
3× 1
3× 2
+
1×2
3×2
Have your student practise this step before you go on. The student should just practise setting the right
numbers in the right places. Remember you can make this step easier if necessary by having the student
move one denominator at a time.
Step 2:
Perform the multiplication.
3×1
3×2
+
1 ×2
3
3 ×2 = 6
2
6
+
Practise Step 1 alone, then Step 1 and Step 2 together, before you go on.
Step 3:
Perform the addition.
3× 1
3× 2
+
1× 2
3
3× 2 = 6
2
5
6 = 6
+
Now have the student practise all three steps.
For students who know higher times tables, gradually mix in higher denominators like 6 and 7 (make sure
the smaller denominator does not divide the larger).
NOTE: Two numbers are relatively prime if their least-common multiple (the lowest number they both
divide into evenly) is their product. For instance, 2 and 3 are relatively prime but 4 and 6 are not (since the
product of 4 and 6 is 24, while their least common multiple is 12). The method of adding fractions taught in
this section is only really efficient for fractions whose denominators are relatively prime (as is the case for
all of the examples directly above). For the case when one denominator divides into the other, a more
efficient method is taught in the next section.
Fractions Skill 4
Tell your student that sometimes you don’t have to change both denominators (i.e. there’s a short-cut)
when you add fractions. How can you tell when you can do less work?
Step 1:
Check to see if the smaller denominator divides into the larger. Count up on your fingers
by the smaller denominator and see if you hit the larger denominator — if you do, the
number of fingers you have up is what you multiply the smaller denominator by.
1
2
+
1
10
=
5× 1
5× 2
+
1
10
Counting up by 2s, you “hit” 10.
You have 5 fingers up.
This means 5 × 2 = 10.
Multiply the smaller denominator by the
number of fingers you have up.
Give lots of practice at this step before you move on.
Step 2:
Perform the multiplication.
1
2
Step 3:
+
1
10
=
5
10
+
1
10
Perform the addition.
5
10
+
1
10
=
6
10
1
1
BONUS: Ask your student how they would solve 2 – 10 = ?
Here are some sample questions you can use during this lesson:
a)
1
1
2 + 10
b)
3
1
4 + 8
c)
1
1
5 + 10
d)
1
1
8 + 2
e)
1
1
3 + 6
f)
1
1
4 + 12
g)
2
1
3 + 15
h)
1
1
5 + 20
i)
7
2
25 + 5
j)
1
1
2 – 4
k)
2
1
3 – 9
l)
7
1
15 – 3
If you think your student might have trouble with this section, you
should start with the following exercise: tell your student that the
number 2 “goes into” or “divides” the numbers they say when they
are counting up by twos (i.e. 2 divides 2, 4, 6, 8, 10... etc). Write
several numbers between 2 and 10 in a column and ask your
student to write “yes” beside the numbers that 2 goes into, and “no”
beside the others. When your student has mastered this step,
repeat the exercise with numbers between 3 and 15 (for counting
by threes) and numbers between 5 and 25 divisible by 5 (for
counting by fives). Tell your student that when they are adding
fractions, they should always check to see if the smaller
denominator divides into the larger.
Fractions Skill 5
This is an important section. For many students, it may be the first time they are taught how to decide
which of several algorithms they should use to perform an operation.
As a warm-up exercise, write a number on the board. Have your student tell you whether
Step 1:
they say that number while counting by 2. Repeat the exercise but counting by 3s
and then by 5s.
Do not move on until your student gets 100% on the exercises on this (Questions 1, 2 & 3).
Step 2:
Identify the lesser denominator.
Step 3:
Count up by that number and see if you “hit” the greater denominator (i.e. see if the lesser
divides or goes into the greater evenly). If yes, write “yes.” If not, write “no.” In other words,
the student is identifying whether or not they will have to change one fraction (short-cut) or
both fractions (no short-cut) before adding.
Practise these steps on a variety of different pairs of fractions before going on.
Note on Question 11: If your student has written “same,” add the fractions using the procedure in F-2. If
they should change both denominators, follow the procedure in F-3. If they should change only one
denominator, follow the method in F-4.
Sample Exercise: Which method should be used in each case?
2
1
7 + 7
3
1
5 + 15
3
1
4 + 5
Fractions Skill 6
Let your student know that this is an enriched unit. Adding triple fractions is normally not covered until
Grade 6 or 7.
Give questions where two smaller denominators go into the larger. For example:
1
2
+
1
3
+
3×1
3×2
+
2× 1
2× 3
3
6
2
6
+
+
1
6
1
6
+
=
1
6
6
6
NOTE: When you first teach this section, always place the fractions with the two lowest denominators first.
After your student has mastered this, you can change the order and ask them to identify which
denominators have to be changed.
Here are some sample questions you can use during this lesson:
a)
1
1
1
2 + 3 + 6
b)
2
1
1
3 + 5 + 15
c)
3
1
1
4 + 2 + 8
Tutor Essentials • page 26
Show Your Success!
Show Your Success!
1. Name the following fractions.
a)
b)
c)
2. Add or subtract.
a)
2
1
7 + 7
b)
3
1
5 + 5
c)
3
5
11 + 11
d)
2
1
5 + 2
e)
1
1
3 + 2
f)
1
1
2 + 10
g)
2
1
3 – 9
h)
1
2
+
1
3
+
1
6
Tutor Essentials • Show Your Success • page 28
Show Your Success!
93. Name the following fractions.
a)
b)
c)
4. Add or subtract.
a)
2
1
5 + 5
b)
3
1
11 + 11
c)
3
5
17 + 17
d)
1
1
3 + 2
e)
1
2
3 + 5
f)
1
2
2 + 6
g)
1
1
3 – 9
h)
1
2
+
1
5
+
1
10
That wasn’t
so hard!
Tutor Essentials • Show Your Success • page 29
Why Mental Math?
Why Mental Math?
What is the importance of mental math?
Mental math is the foundation for all further study in mathematics. Students who cannot see
number patterns often become frustrated and disillusioned with their work.
Mental math confronts people at every
turn, making the ability to quickly calculate numbers
an invaluable asset. Calculating how much change
you are owed at a grocery store, or deciding how much
of a tip to leave at a restaurant are both real-world
examples of mental math in action. For this reason, it
may be the single most relevant strand of mathematics
to everyday life.
What is “automaticity,” and how does it help in the
study of mathematics?
Automaticity is the ability to carry out a task fluently
without considering the very small details. Usually,
automaticity comes as a result of continuous practice
and repetition. In reading this, you likely aren’t using any
comprehension strategies or deconstructing prefixes and
suffixes, as a beginner reader would. That is because you have developed automaticity. In much
simpler words, automaticity means to know something well enough to not have to think about it.
In mathematics, automaticity is required. Having to frequently recall low level details in a simple
question would slow down a student’s learning momentum, in much the same way having to
deconstruct a sentence phonetically would slow down reading. Consistent practice in mental
math allows students to become familiar with the way numbers interact, enabling them to make
simple calculations quickly and effectively without always having to recall their number facts. It
helps students become effective and efficient problem solvers.
Tutor Essentials • Why Mental Math? • page 32
Why Mental Math?
Mental Math Unit Content Listing
Mental Math Skill A
Mental Math Skill B
Mental Math Skill C
Mental Math Skill D
Mental Math Skill E
Mental Math Skills 1, 2, 3, and 4
Mental Math Skills 5 and 6
Mental Math Skills 12, 13, and 14
Multiples of 10
Mental Math is extremely important.
Remember to allow your student sufficient
time to hone their skills during tutoring
sessions. It will be worth it, as your
student will be considerably sharper and
more focused. When in doubt, stick to
your T.U.T.O.R. principles.
Tutor Essentials • Why Mental Math? • page 33
Mental Math Unit
Mental Math Unit Manual
Mental Math Unit
SKILLS A – E:
For this section, allow your student to count on their fingers initially. Once they are comfortable
with this, they should be able to do Skills 1 – 18 without using their fingers. Teach your student to
use the following steps to add.
Example:
5 + 3 =
?
2
1
5
1
6
Step 1:
Say the greater number (5)
with your fist closed.
2
3
1
7
5 + 3 =
8
8
Step 2:
Count up by ones until
you have the same number
of fingers up as the
lesser number (3).
Step 3:
The number you say
when you have the lesser
number of fingers up is
the answer (8).
SKILL 1: Adding 2 to an Even Number
This skill has been broken down into a number of sub-skills. After
teaching each sub-skill, you should give your student a short diagnostic
quiz to verify that they have learned the skill. Included are sample
quizzes for Skills 1 to 4.
NOTE TO TUTOR: Teaching the material on these worksheets
may take several sessions. Your student will need more practice
than is provided on these pages. These pages are intended as a
test to be given when you are certain your student has learned the
materials fully.
i)
Naming the next one-digit even number
Numbers that have ones digit 0, 2, 4, 6 or 8 are called the even
numbers. Ask your student to imagine the sequence going on in a
Tutor Essentials • Mental Math Unit • page 36
circle so that the next number after 8 is 0 (0, 2, 4, 6, 8, 0, 2, 4, 6, 8… ) Then play the
following game: name a number in the sequence and ask your student to give the next
number. Don’t move on until your student has mastered the game.
ii)
Naming the next greatest two-digit even number
CASE 1: Numbers that end in 0, 2, 4 or 6
Write an even two-digit number that ends in 0, 2, 4 or 6. Ask your student to name the next
greatest even number. Your student should recognize that if a number ends in 0, then the next
even number ends in 2; if it ends in 4 then the next even number ends in 6, etc. For instance, the
QUIZ
number 54 has ones digit 4 so the next greatest even number will have ones digit 6 (56).
Name the next greatest even number.
a) 52 : ______
b) 64 : ______
c) 36 : ______
d) 44: ______
CASE 2: Numbers that end in 8
Show your student the number 58. Ask them to name the next greatest even number.
Remind your student that even numbers must end in 0, 2, 4, 6, or 8. But 50, 52, 54 and 56 are
all less than 58 so the next greatest even number is 60. Your student should see that an even
number ending in 8 is always followed by an even number ending in 0 (with a tens digit that is
QUIZ
one higher).
Name the next greatest even number.
a) 58 : ______
b) 68 : ______
c) 38 : ______
d) 78: ______
iii) Adding 2 to an even number
Point out to your student that adding 2 to any even number is equivalent to finding the next
even number (example: 46 + 2 = 48, 48 + 2 = 50, etc.). Knowing this, your student can easily
QUIZ
add 2 to any even number.
Add.
a) 26 + 2 = ____ b) 82 + 2 = ____ c) 40 + 2 = ____
d) 88 + 2 = ____
SKILL 2: Subtracting 2 from an Even Number
i)
Finding the preceding one-digit even number
Name a one-digit even number and ask your student to give the preceding number in the
sequence. For instance, the number that comes before 4 is 2 and the number that comes
before 0 is 8.
REMEMBER: The sequence is circular.
ii)
Finding the preceding two-digit number
Write a two-digit number that ends in 2, 4, 6 or 8. Ask your student to name the preceding
even number. They should recognize that if a number ends in 2, then the preceding even
number ends in 0; if it ends in 4, then the preceding even number ends in 2, etc. For instance,
QUIZ
the number 78 has ones digit 8 so the preceding even number has ones digit 6.
Name the preceding even number.
a) 48 : ______
b) 26 : ______
c) 34 : ______
d) 62 : ______
Show your student the number 80 and ask them to name the preceding even number. They
should recognize that if an even number ends in 0 then the preceding even number ends in 8
QUIZ
(but the ones digit is one less). So the even number that comes before 80 is 78.
Name the preceding even number.
a) 40 : ______
b) 60 : ______
c) 80 : ______
d) 50 : ______
iii) Subtracting 2 from an even number
Point out to your student that subtracting 2 from an even number is equivalent to finding the
QUIZ
preceding even number (example: 48 – 2 = 46, 46 – 2 = 44, etc.).
Subtract.
a) 58 – 2 = ____
b) 24 – 2 = ____
c) 36 – 2 = ____
SKILL 3: Adding 2 to an Odd Number
i)
Naming the next one-digit odd number
Numbers that have ones digit 1, 3, 5, 7, and 9 are called the odd numbers. Using drills or
games, teach your student to say the sequence of one-digit odd numbers without hesitation.
Ask Your student to imagine the sequence going on in a circle so that the next number after 9
is 1 (1, 3, 5, 7, 9, 1, 3, 5, 7, 9…). Then play the following game: name a number in the
sequence and ask your student to give the next number.
ii)
Naming the next greatest two-digit odd number
Write an odd two-digit number that ends in 1, 3, 5, or 7. Ask your student to name the next greatest odd
number. Your student should recognize that if a number ends in 1, then the next odd number ends in 3; if it
ends in 3, then the next odd number ends in 5, etc. For instance, the number 35 has ones digit 5: so the
QUIZ
next greatest odd number will have ones digit 7.
Name the next greatest odd number.
a) 51:____
b) 65: ____
c) 37: ____
d) 23: ____
Write the number 59. Ask your student to name the next greatest odd number. Remind your student that
odd numbers must end in 1, 3, 5, 7, or 9. But 51, 53, 55, and 57 are all less than 59. The next greatest
odd number is 61. Your student should see that an odd number ending in 9 is always followed by an odd
QUIZ
number ending in 1 (with a tens digit that is one higher).
iii)
Name the next greatest odd number.
a) 59 : ______
b) 69 : ______
c) 39 : ______
d) 49 : ______
Adding 2 to an odd number
Point out to your student that adding 2 to any odd number is equivalent to finding the next odd
QUIZ
number (example: 47 + 2 = 49, 49 + 2 = 51, etc.).
Add.
a) 27 + 2 = ____
b) 83 + 2 = ____
c) 41 + 2 = ____
SKILL 4: Subtracting 2 from an Odd Number
i)
Finding the preceding one-digit odd number
Name a one-digit odd number and ask your student to give the preceding number in the sequence. For
instance, the number that comes before 3 is 1 and the number that comes before 1 is 9.\
REMEMBER: The sequence is circular.
ii)
Finding the preceding odd two-digit number
Show your student a two-digit number that ends in 3, 5, 7, or 9. Ask your student to name the preceding
odd number. Your student should recognize that if a number ends in 3, then the preceding odd number
ends in 1; if it ends in 5, then the preceding odd number ends in 3, etc. For instance, the number 79 has
QUIZ
ones digit 9, so the preceding odd number has ones digit 7.
Name the preceding odd number.
a) 49 : ______
b) 27 : ______
c) 35 : ______
d) 63 : ______
e) 79 : ______
Show your student the number 81 and ask them to name the preceding odd number. Your student
should recognize that if an odd number ends in 1 then the preceding odd number ends in 9 (but the
QUIZ
ones digit is one less). So the odd number that comes before 81 is 79.
Name the preceding odd number.
a) 41 : ______
b) 61 : ______
c) 81 : ______
d) 51 : ______
iii) Subtracting 2 from an odd number
Point out to your student that subtracting 2 from an odd number is equivalent to finding the preceding
QUIZ
odd number (example: 49 – 2 = 47, 47 – 2 = 45, etc.).
Subtract.
a) 59 – 2 = ____
b) 25 – 2 = ____
c) 37 – 2 = ____
d) 43 – 2 = ____
e) 61 – 2 =
Now that you’re getting the hang of this,
try creating your own quizzes for your student
to complete. Three or four questions at the
end of each lesson is sufficient. If you feel it is
necessary, do not hesitate to provide your
students with more practice questions.
SKILLS 5 and 6
Once your student can add and subtract the numbers 1 and 2, then they can easily add and
subtract the number 3: Add 3 to a number by first adding 2, then 1 (example: 35 + 3 = 35 + 2 + 1).
Subtract 3 from a number by subtracting 2, then subtracting 1 (example: 35 – 3 = 35 – 2 – 1).
SKILLS 7 and 8
Add 4 to a number by adding 2 twice (example: 51 + 4 = 51 + 2 + 2). Subtract 4 from a number by
subtracting 2 twice (example: 51 – 4 = 51 – 2 – 2).
SKILLS 9 and 10
Add 5 to a number by adding 4 then 1. Subtract 5 by subtracting 4 then 1.
SKILL 11
Your student can add pairs of identical numbers by doubling (example: 6 + 6 = 2 × 6). Your
student should either memorize the 2 times table or they should double numbers by counting on
their fingers by 2s.
Add a pair of numbers that differ by 1 by rewriting the larger number as 1 plus the smaller
number, then use doubling to find the sum (example: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13; 7 + 8 = 7 +
7 + 1 = 14 + 1 = 15, etc.).
SKILLS 12, 13 and 14
Add a one-digit number to 10 by simply replacing the zero in 10 by the one-digit number
(example: 10 + 7 = 17).
Add 10 to any two-digit number by simply increasing the tens digit of the two-digit number by 1
(example: 53 + 10 = 63).
Add a pair of two-digit numbers (with no carrying) by adding the ones digits of the numbers and
then the tens digits (example: 23 + 64 = 87).
SKILLS 15 and 16
To add 9 to a one-digit number, subtract 1 from the number and then add 10
(example: 9 + 6 = 10 + 5 = 15; 9 + 7 = 10 + 6 = 16, etc.).
NOTE: Essentially, the student simply has to subtract 1 from the number and then stick a 1 in
front of the result.
To add 8 to a one-digit number, subtract 2 from the number and add 10
(example: 8 + 6 = 10 + 4 = 14; 8 + 7 = 10 + 5 = 15, etc.)
SKILLS 17 and 18
To subtract a pair of multiples of ten, simply subtract the tens digits and add a zero for the ones
digit (example: 70 – 50 = 20).
Appendix 1
Ideas for Math Fun
Ideas for Math Fun – Go Fish
Game: Modified Go Fish
Purpose
If students know the pairs of one-digit numbers that add up to particular target numbers,
they will be able to mentally break sums into easier sums.
Example: As it is easy to add any one-digit number to 10, you can add a sum more readily
if you can decompose numbers in the sum into pairs that add to ten.
7 + 5 = 7 + 3 + 2 = 10 + 2 = 12
These numbers add to 10.
To help students remember pairs of numbers that add up to a given target number I developed
a variation of “Go Fish” that I have found very effective.
The Game
Pick any target number and remove all the cards with value greater than or equal to the target
number out of the deck. In what follows, I will assume that the target number is 10, so you would
take all the tens and face cards out of the deck (Aces count as one).
The dealer gives each player 6 cards. If a player has any pairs of cards that add to 10 they are
allowed to place these pairs on the table before play begins.
Player 1 selects one of the cards in his or her hand and asks the Player 2 for a card that adds to
10 with the chosen card. For instance, if Player 1’s card is a 3, they may ask the Player 2 for a 7.
If Player 2 has the requested card, the first player takes it and lays it down along with the card from
their hand. The first player may then ask for another card. If the Player 2 doesn’t have the requested
card they say: “Go fish,” and the Player 1 must pick up a card from the top of the deck. (If this card
adds to 10 with a card in the player’s hand they may lay down the pair right away). It is then Player
2’s turn to ask for a card.
Play ends when one player lays down all of their cards. Players receive 4 points for laying down all
of their cards first and 1 point for each pair they have laid down.
NOTE: With weaker students I would recommend you start with pairs of numbers that add to 5. Take
all cards with value greater than 4 out of the deck. Each player should be dealt only 4 cards
to start with.
I have worked with several students who have had a great deal of trouble sorting their cards and
finding pairs that add to a target number. I’ve found the following exercise helps:
Give your student only three cards; two of which add to the target number. Ask the student
to find the pair that add to the target number. After the student has mastered this step with
3 cards repeat the exercise with 4 cards, then 5 cards, and so on.
NOTE: You can also give your student a list of pairs that add to the target number. As the
student gets used to the game, gradually remove pairs from the list so that the student learns
the pairs by memory.
Tutor Essentials • Appendix 1 Ideas for Math Fun • page 44
Ideas for Math Fun – Binary Code
Step 1- Warm-up
a) Review single digit addition (Basic Number Sense)
i.e. 8 + 2 =
8+4+2=
Put a few questions on the board—have tutors check the students’ work.
b) Review Place Value ( 2 7 3 )
Hundreds
Tens
Ones
Put a few questions on the board—have tutors check the students’ work.
Step 2 - Binary Code Introduction
Talk about the fact that we represent numbers using numerical symbols
(i.e. 2 = two).
However, computers do it differently.
They use a SECRET electricity CODE!!
electricity = 1 ; no electricity = 0
You’re going to teach them how to CRACK THE CODE!!
Step 3 - Binary Code Exercises
Set up the following chart:
Eights
Fours
Twos
Ones
a)
b)
c)
Explain to the kids that if you put a “1” in a column, it means that the number contains the value at
the heading of the column.
For example:
Eights
0
0
0
a)
b)
c)
Fours
0
0
0
Twos
0
1
1
Ones
1
1
0
1=1
2+1=3
2=2
Explanation:
a) There are 0 eights, 0 fours, 0 twos, 1 one. Therefore the code 0001 = 1
b) There are 0 eights, 0 fours, 1 two, 1 one. Therefore the code 0011 = 2 + 1 = 3
c) There are 0 eights, 0 fours, 1 two, 0 ones. Therefore the code 0010 = 2
Put several questions on the board—have tutors check that the kids have the hang of it.
NOTE TO TEACHER:
All numbers can be coded in this manner by adding columns to the left of the chart as follows:
32’s
1
16’s
0
8’s
1
4’s
0
2’s
1
1’s
1
32 + 8 + 2 +1 = 43
Ideas for Math Fun – Binary Code
JUMP Binary Code Game (A.K.A. MIND-READING TRICK!!):
•
Here are the boxes you need for the final part of the game.
•
•
Write the following charts on the board.
Have the students pick a number between 1 and 15. They should NOT reveal this
number to you.
Then, have the students tell you which chart contains their number.
If a chart contains the number, then think of it as a “1”, if it doesn’t, think of it as a “0”.
•
•
D
C
B
A
8
9
10
11
4
5
6
7
2
3
6
7
1
3
5
7
12
13
14
15
12
13
14
15
10
11
14
15
9
11
13
15
Chart A represents 1’s.
Chart B represents 2’s.
Chart C represents 4’s.
Chart D represents 8’s.
Example:
They choose “14”.
14 is in Chart D - 1
14 is in Chart C - 1
14 is in Chart B - 1
14 is NOT in Chart A – 0
Therefore the code is 1110, or 8 + 4 + 2 = 14!!
THE KIDS WILL BE AMAZED!!
Ideas for Math Fun – Practice Your Skills
Add One to a Number
7 + 1 = _________
4 + 1 = _________
6 + 1 = _________
5 + 1 = ________
1 + 8 = _________
1 + 9 = _________
12 + 1 = ________
3 + 1 = ________
17 + 1 = ________
15 + 1 = ________
18 + 1 = ________
1 + 16 = _______
23 + 1 = ________
35 + 1 = ________
56 + 1 = ________
42 + 1 = _______
69 + 1 = ________
82 + 1 = ________
93 + 1 = ________
79 + 1 = _______
132 + 1 = _______
156 + 1 = _______
BONUS:
125 + 1 = _______
The Next Even Number
2, 4, 6, ________, ________, ________
12, 14, 16, ________, ________, ________
22, 24, ________, ________, ________
30, 32, ________, ________, ________
40, 42, ________, ________, ________
52, 54, ________, ________, ________
16, 18, ________, ________, ________
24, 26, ________, ________, ________
54, 56, ________, ________, ________
48, 50, ________, ________, ________
64, 66, ________, ________, ________
78, 80, ________, ________, ________
The Next Odd Number
1, 3, 5, ________, ________, ________
7, 9, 11, ________, ________, ________
21, 23, ________, ________, ________
31, 33, ________, ________, ________
41, 43, ________, ________, ________
53, 55, ________, ________, ________
39, 41, ________, ________, ________
65, 67, ________, ________, ________
71, 73, ________, ________, ________
85, 87, ________, ________, ________
Add Two to an Even Number
HINT: What is the next even number?
6 + 2 = _________
4 + 2 = __________
8 + 2 = __________
12 + 2 = ________
16 + 2 = _________
20 + 2 = _________
26 + 2 = ________
30 + 2 = _________
38 + 2 = _________
32 + 2 = ________
18 + 2 = _________
24 + 2 = _________
46 + 2 = ________
50 + 2 = _________
64 + 2 = _________
72 + 2 = ________
58 + 2 = _________
78 + 2 = _________
Add Two to an Odd Number
HINT: What is the next odd number?
3 + 2 = ___________
7 + 2 = ___________
5 + 2 = ___________
11 + 2 = __________
15 + 2 = __________29
21 + 2 = __________
33 + 2 = __________
+ 2 = __________
23 + 2 = __________
41 + 2 = __________
45 + 2 = __________
57 + 2 = __________
67 + 2 = __________
81 + 2 = __________
95 + 2 = __________
2 + 7 = __________
9 + 2 = __________
5 + 2 = __________
25 + 2 = _________
16 + 2 = _________
2 + 24 = _________
36 + 2 = _________
27 + 2 = _________
49 + 2 = _________
2 + 58 = _________
2 + 87 = _________
2 + 79 = _________
133 + 2 = ________
247 + 2 = ________
Add Two to Any Number
BONUS:
124 + 2 = ________
Add Three to Any Number
HINT: Add two, then add one more.
5 + 3 = _________
3 + 3 = _________
7 + 3 = _________
9 + 3 = _________
15 + 3 = ________
16 + 3 = ________
14 + 3 = ________
3 + 17 = ________
3 + 21 = ________
43 + 3 = ________
38 + 3 = ________
57 + 3 = ________
3 + 71 = ________
3 + 64 = ________
89 + 3 = ________
90 + 3 = ________
96 + 3 = ________
82 + 3 = ________
7 – 1 = _________
6 – 1 = __________
4 – 1 = _________
9 – 1 = _________
10 – 1 = _________
15 – 1 = ________
23 – 1 = ________
57 – 1 = _________
28 – 1 = ________
35 – 1 = ________
69 – 1 = _________
80 – 1 = ________
90 – 1 = ________
62 – 1 = _________
75 – 1 = ________
Subtract One from a Number
The Previous Even Number
Write the even number that comes before the given number.
__________, 4
__________, 8
__________, 10
__________, 14
__________, 18
__________, 16
__________, 12
__________, 22
__________, 34
__________, 48
__________, 50
__________, 62
__________, 88
__________, 90
__________, 64
__________, 70
The Previous Odd Number
__________, 7
__________, 5
__________, 3
__________, 9
__________, 11
__________, 15
__________, 17
__________, 21
__________, 33
__________, 27
__________, 25
__________, 37
__________, 39
__________, 41
__________, 53
__________, 67
__________, 81
__________, 95
__________, 93
__________, 99
Subtract Two from an Even Number
HINT: What is the previous even number?
6 – 2 = ___________
4 – 2 = ___________
8 – 2 = ___________
10 – 2 = __________
12 – 2 = __________
16 – 2 = __________
24 – 2 = __________
26 – 2 = __________
32 – 2 = __________
38 – 2 = __________
40 – 2 = __________
56 – 2 = __________
50 – 2 = __________
68 – 2 = __________
74 – 2 = __________
86 – 2 = __________
90 – 2 = __________
98 – 2 = __________
Subtract Two from an Odd Number
HINT: What is the previous odd number?
5 – 2 = ___________
3 – 2 = ___________
7 – 2 = ___________
9 – 2 = ___________
11 – 2 = __________
13 – 2 = __________
19 – 2 = __________
25 – 2 = __________
37 – 2 = __________
41 – 2 = __________
33 – 2 = __________
69 – 2 = __________
71 – 2 = __________
85 – 2 = __________
91 – 2 = __________
Subtract Two from Any Number
7 – 2 = __________
8 – 2 = __________
10 – 2 = __________
15 – 2 = _________
28 – 2 = _________
32 – 2 = __________
46 – 2 = _________
40 – 2 = _________
64 – 2 = __________
59 – 2 = _________
33 – 2 = _________
71 – 2 = __________
60 – 2 = _________
80 – 2 = _________
91 – 2 = __________
Add a Number to a Multiple of Ten
10 + 2 = _________
10 + 3 = _________
10 + 5 = __________
10 + 9 = _________
10 + 1 = _________
10 + 8 = __________
20 + 5 = _________
30 + 3 = _________
40 + 9 = __________
7 + 60 = _________
4 + 80 = _________
2 + 90 = __________
8 + 40 = _________
30 + 6 = _________
70 + 2 = __________
Add a Number to Nine
HINT: Subtract one from the number, then add the result to 10: 9 + 7 = 10 + 6 = 16.
9 + 3 = __________
9 + 5 = __________
9 + 8 = __________
9 + 4 = __________
9 + 2 = __________
9 + 9 = __________
9 + 6 = __________
9 + 7 = __________
19 + 5 = _________
19 + 2 = _________
19 + 3 = _________
19 + 8 = _________
29 + 4 = _________
39 + 7 = _________
49 + 6 = _________
8 + 79 = _________
7 + 69 = _________
4 + 59 = _________
Add a Number to Eight
HINT: Subtract 2 from the number, then add the result to 10: 8 + 7 = 10 + 5.
8 + 5 = __________
8 + 3 = __________
8 + 4 = __________
8 + 6 = __________
8 + 7 = __________
8 + 8 = __________
18 + 3 = _________
18 + 6 = _________
18 + 5 = _________
18 + 9 = _________
18 + 7 = _________
28 + 4 = _________
38 + 6 = _________
48 + 7 = _________
5 + 88 = _________
8 + 78 = _________
68 + 3 = _________
78 + 6 = _________
Add 4 to a Number
HINT: Add 2, then add 2 more.
6 + 4 = __________
7 + 4 = __________
17 + 4 = __________
26 + 4 = _________
16 + 4 = _________
27 + 4 = __________
36 + 4 = _________
57 + 4 = _________
66 + 4 = __________
3 + 3 = __________
4 + 4 = __________
5 + 5 = ___________
6 + 6 = __________
7 + 7 = __________
8 + 8 = ___________
9 + 9 = __________
25 + 5 = _________
24 + 4 = __________
37 + 7 = _________
46 + 6 = _________
68 + 8 = __________
Doubles
Double the numbers by doubling the digits.
Number
34
42
23
41
243
4,324
28
15
25
36
47
Double
Double with regrouping.
Number
16
35
Double
Near Doubles
Add 6 + 7 by adding 6 + 6 + 1.
6 + 7 = __________
7 + 8 = __________
5 + 6 = __________
4 + 5 = __________
8 + 9 = __________
16 + 7 = _________
27 + 8 = _________
34 + 5 = _________
47 + 8 = _________
Numbers That Differ by 2
Add 6 + 8 by doubling the number in between: 6 + 8 = 7 + 7.
6 + 8 = __________
4 + 6 = __________
5 + 7 = __________
17 + 5 = _________
26 + 8 = _________
44 + 6 = _________
Numbers That Add to Ten
Fill in the missing numbers.
1+
+ 6 = 10
+ 4 = 10
= 10
+ 8 = 10
+ 2 = 10
5+
=10
Add by finding a number that adds to ten.
6 + 7 = 6 + 4 + 3 = 10 + 3 = 13
8 + 4 = ___________________________ = __________________ = ___________________
6 + 5 = ___________________________ = __________________ = ___________________
4 + 7 = ___________________________ = __________________ = ___________________
5 + 7 = ___________________________ = __________________ = ___________________
5 + 8 = ___________________________ = __________________ = ___________________
Essential Computations
Addition
36 389 527 3285
+56
+314
+137
+1324
Subtraction
38 100 239 2723
–19
– 56
–149
–1819
Multiplication
43 57 468 692
× 3
× 3
× 4
× 7
27 32 92 73
×46
×25
×36
×86
Division
4 235
6 419
7 632
8 1029
One-Digit Number Facts
Addition
2 + 3 = _________
5 + 2 = ___________ 3 + 7 = _________
4 + 6 = __________
9 + 1 = __________
8 + 4 = __________
9 + 6 = __________
7 + 5 = __________
6 + 6 = __________
7 + 8 = __________
6 + 5 = __________
5 + 8 = __________
3 + 6 = __________
5 + 5 = __________
7 + 6 = __________
6 + 9 = __________
4 – 2 = _________
7 – 5 = _________
5 – 4 = _________
6 – 4 = _________
8 – 3 = _________
9 – 4 = _________
6 – 5 = _________
7 – 4 = _________
10 – 7 = _________
9 – 8 = _________
9 – 6 = _________
5 – 2 = _________
8 – 6 = _________
10 – 6 = _________
8 – 5 = _________
8 – 4 = _________
3 × 5 = _________
8 × 4 = _________
9 × 3 = _________
4 × 5 = _________
2 × 3 = _________
4 × 2 = _________
8 × 1 = _________
6 × 6 = _________
9 × 7 = _________
7 × 7 = _________
5 × 8 = _________
2 × 6 = _________
6 × 4 = _________
7 × 3 = _________
4 × 9 = _________
2 × 9 = _________
9 × 9 = _________
3 × 4 = _________
6 × 8 = _________
7 × 5 = _________
9 × 5 = _________
5 × 6 = _________
6 × 3 = _________
7 × 1 = _________
8 × 3 = _________
9 × 6 = _________
4 × 7 = _________
3 × 3 = _________
8 × 7 = _________
1 × 5 = _________
7 × 6 = _________
2 × 8 = _________
10 ÷ 5 = _________
12 ÷ 2 = _________
18 ÷ 3 = _________
18 ÷ 2 = ________
24 ÷ 6 = _________
32 ÷ 8 = _________
24 ÷ 3 = _________
15 ÷ 5 = ________
32 ÷ 4 = _________
45 ÷ 9 = _________
64 ÷ 8 = _________
16 ÷ 2 = ________
42 ÷ 7 = _________
35 ÷ 5 = _________
72 ÷ 9 = _________
36 ÷ 6 = ________
40 ÷ 8 = _________
42 ÷ 6 = _________
54 ÷ 9 = _________
63 ÷ 9 = ________
48 ÷ 8 = _________
56 ÷ 7 = _________
20 ÷ 4 = _________
48 ÷ 6 = ________
20 ÷ 5 = _________
28 ÷ 7 = _________
32 ÷ 8 = _________
54 ÷ 6 = ________
56 ÷ 8 = _________
72 ÷ 8 = _________
63 ÷ 7 = _________
81 ÷ 9 = ________
Subtraction
Multiplication
Division

Teaching the Introductory Unit - Working Women Community Centre

Transcription

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Spring/Summer 2014 - Partners in English Language Learning