Title: Mental Math
1Mental Math
A Life Long Skill
A program developed by Lynn Sinclair Grade 7
Teacher EPEC, Dartmouth, NS lsinclai_at_staff.ednet.n
s.ca 4628401 Ext 143
2The following power point is designed to assist
teachers with the presentation and delivery of
Mental Math at the Junior High/Middle School
level. Please realize the Mental Math program
is a work in progress. Not all topics related to
outcomes are represented in the tests. Most tests
have been student tested however, I will
apologize in advance for any errors or omissions
you may encounter. Lynn
3MENTAL MATHAN OUTLINE OF THIS RESOURCE
 The program itself consists of 140 mental math
tests.  The program was created for a grade seven
classroom, but can easily be adapted for other
grade levels.  It is important to note that this program is
meant to be a resource for teachers however,
classroom teachers need to plan and prepare in
order to establish daily mental math routines for
their students that will effectively promote the
development and use of Mental Math strategies.
4MENTAL MATHAN OUTLINE OF THIS RESOURCE
 The following are guidelines and suggestions
established by the Department of Education for
implementation of a Mental Math program.  As well, an explanation and guidelines of how the
mental math program I developed is utilized in my
classroom.  This includes the preparation, leadup and ground
work required to administer the designed mental
math tests.
5WHY MENTAL MATH?
 Calculating in you head is a practical life
skill.  Mental math can make written computation easier
or quicker  Proficiency in mental math contributes to
increased skill in estimation  Mental calculation can lead to a better
understanding of place value, mathematical
operations, and basic number sense.  Mental math can be challenging and rewarding
lifelong skill.  OUR BRAIN IS WITH US WHEREVER WE GO, OUR
CALCULATOR IS NOT!!!
6MENTAL MATHOVERVIEW OF THE DEPARTMENT
 Mental Math is an integral component of our
mathematics program.  All students are to engage in 5 minutes of mental
math per day.  Mental math strategies develop and improve over
years of regular practice, therefore  Mental math should be a planned program of
instruction.
7MENTAL MATHOVERVIEW OF THE DEPARTMENT
 A variety of mental math resources have been
provided by the Department to assist with
planning for classroom teachers.  In particular, the mental math text resource
entitled Mental Math in Junior High (Dale Seymour
Publications) has been provided.  In addition, Mental Math in the Middle Grades
(Dale Seymour Publications) is another excellent
resource.
8MENTAL MATHOVERVIEW OF THE DEPARTMENT
 In order for students to complete mental math
activities as suggested by the curriculum
document and the Mental Math text resources,
students must be proficient with the following
key concepts Numbers Sense, Estimation, Basic
Fact Recall.  It may be necessary to review/teach if students
do not have these essential understandings.  When completing an assessment of learning at the
end of a strategy development, a three to five
second response time is expected
9MENTAL MATHOVERVIEW OF THE DEPARTMENT
 Students must have multiple representations of
numbers if they are to complete mental math
activities.  They should be able to visualize manipulative
materials in order to help them solve mental math
questions.  Therefore, the use of manipulatives in your math
classroom is critical to the development of
mental math skills.
10MENTAL MATHOVERVIEW OF THE DEPARTMENT
 Strong mental math skills rely on students being
able to see the mathematics in all five
representations.  Connecting concrete, pictorial, verbal, symbolic
and contextual representations is key to helping
students develop strong mental math skills.  Mental math strategies can be taught, as well as,
be developed and shared by students.
11MENTAL MATHOVERVIEW OF THE DEPARTMENT
 Students can often suggest a variety of mental
math and estimation strategies.  As an alternative to teaching the strategies,
have students attempt to solve problems
independently to see what strategies they may
develop on their own.  Sharing these strategies improves the development
of thinking it through in other ways, and
establishes that there is more than one way to
attack a mental math problem.
12MENTAL MATHOVERVIEW OF THE DEPARTMENT
 Class discussion is a crucial component of
teaching mental math.  By students developing and sharing strategies
they are more likely to take ownership of the
strategy.  Talking about the thought processes is the only
way to know if students understand and can apply
strategies.
13GUIDELINES FOR MENTAL MATH IN MY CLASSROOM
 The Mental Math program developed centers on a
series of tests I have created.  Tests are based on class lessons and activities
related to the achievement of curriculum outcomes
and/or specific strategies developed from the
text resource Mental Math in Junior High.  Mental math is DAILY, however, students do not
necessarily complete a test daily.  Alternatively, students engage in activities to
promote development and sharing of strategies
that encourage success during testing.
14GUIDELINES FOR MENTAL MATH IN MY CLASSROOM
 The test themselves each consist of 10 questions
 Students have 5 seconds to answer each question
 Test questions are not on a timer for entrance,
but can be if users desire.  Tests are self corrected by students and results
are recorded by students.
15GUIDELINES FOR MENTAL MATH IN MY CLASSROOM
 Names go in for biweekly draws (1, 2 or 3
chances each test)  If students correct incorrectly, no chance to win
during the next draw.  Any talking during the test, result in tickets
for the day being eliminated.  If students have no red pen for correcting, then,
no tickets for that day.  Unprepared for three classes (homework or
materials) eliminates you from that weeks draw.
16GUIDELINES FOR MENTAL MATH IN MY CLASSROOM
 Strategies used are shared, discussed and
reinforced after test completion.  Mental math lessons are consistently delivered
during the first period of the day that I see
each group of students.  Lessons last from approximately 5 to 15 minutes.
 This establishes a classroom routine that the
students become accustomed to.
17GUIDELINES FOR MENTAL MATH IN MY CLASSROOM
 The procedures I use for delivery of Mental Math
in my classroom, work for me!  If interested feel free to use my ideas, or make
adjustments based on what would work best for
you.  Key to remember is that Mental Math MUST be a
planned program of instruction, focusing on
strategy development with connections to the
outcomes  The designed tests are meant to be a complement
to your mental math program, not your program
itself.
18GUIDELINES FOR MENTAL MATH IN MY CLASSROOM
 Before administering any of the designed tests,
students MUST have the opportunity to explore,
practice and share skills that will promote
confident mental math learners.  The followings will provide an example of
the ground work that leads to the testing of a
mental math strategy in my classroom.
19DEVELOPING A MENTAL MATH STRATEGY
 The strategy Searching For Compatible Decimals
(Lesson 10 Mental Math in Junior High)
encourages students to recognize pairs of decimal
numbers whose sums equal a whole.  The leg work for this strategy begins early in
September with a game played using a standard
deck of cards.  The game modifies the Solitaire game where the
player attempts to clear the playing field by
making pairs of number with a sum of 13. The
modification is using a sum of 10.
20The playing field continues to a base of seven
cards. The game is then played following the
normal solitaire rules with the exception of
using a sum of 10 as opposed to 13. The object of
the game is to clear the playing field by making
pairs of numbers that have a sum of 10,
therefore, reinforces the mental math skill of
making compatible numbers to 10.
21DEVELOPING A MENTAL MATH STRATEGY
 The game itself covers an early elementary mental
math concept, but it is surprising the number of
students that do not have this skill.  Students enjoy the game and it is a good ice
breaker for the beginning of the year.  Once this game is played we talk about viewing
the cards as 10, 20, 30 . . ., so making
compatibles to 100, then, making compatibles to
1000 etc.
22DEVELOPING A MENTAL MATH STRATEGY
 This game sets the stage for several other games
that are played using cards.  Another game is to have students (working in
pairs) count out 10 cards and time each other to
see how long it takes for them to find the sum.
They soon realize, using compatibles makes the
job quicker and easier.  The game can be extended to include more than ten
cards or modified with sets of 10 cards
preselected to make the task easier for students
that may need modifications.
23DEVELOPING A MENTAL MATH STRATEGY
 Before introducing the strategy Searching For
Compatible Decimals, it would also be necessary
to ensure decimal understanding.  Prior to this strategy, students would engage in
activities allowing them to build (using base ten
blocks), recognize, illustrate, explain and
express decimals in alternative forms.  Essentially, achievement of outcomes related to
decimals, allow students to understand as well as
visualize the decimals while trying to find
compatibles.
24DEVELOPING A MENTAL MATH STRATEGY
 One activity used to reinforce multiple
representation of decimal numbers is a card game
created where students have to sort the cards
based on the decimal they represent.  The cards can be used individually, with a
partner or in small groups and various games can
be played (limited only by the imagination of the
user).  Students can simply sort the cards.
 Play like 5 card rummy the student who collects
5 cards that represent the same decimal wins  Concentration, Go Fish, etc. (examples of cards
on next 2s)
25One and three tenths
1
5.6  4.3
1
1

1
26130
1
2.6 ? 2
1.3
27DEVELOPING A MENTAL MATH STRATEGY
 Before covering the strategy of compatible
decimals, we would cover Lesson 6 of Mental
Math in Junior High, which is Searching For
Compatibles.  This strategy is a natural progression to
compatible decimals, as it deals with identifying
compatible numbers for multiples of 10 and 100.  As well, the strategy is easily extended to
finding compatible money amounts, which tend to
help students grasp the concept of compatible
decimals easier.
28DEVELOPING A MENTAL MATH STRATEGY
 When presenting a strategy from Mental Math in
the Junior High or Mental Math in the Middle
Schools, I usually  Present, review, discuss and practice the
strategy using the information provided in the
text.  Orally do the TRY THESE IN YOUR HEAD
 Do a timed test using Power Builder A
 Assign Power Builder B for homework or do a timed
test using Power Builder B the following day
29DEVELOPING A MENTAL MATH STRATEGY
 Another activity to strengthen the concept of
compatible decimals is a matching game.  Essentially, the game allows students to make
pairs of compatible decimals.  Using the cards, student can simply find
compatible decimals or use the cards to play a
game of concentration with a partner(s) where
they take turns turning over cards looking for a
compatible pairs.  Thes that follow are examples of two sets
of cards used.
300.15
0.7
5.1
1.47
3.4
1.6
0.64
0.2
0.92
10.8
0.85
5.5
0.27
0.08
0.53
4.9
0.63
1.5
0.36
0.3
310.15
0.7
5.1
1.47
3.4
1.6
0.64
0.2
0.92
10.8
0.85
5.5
0.27
0.08
0.53
4.9
0.63
0.36
0.3
1.5
32One and nine tenths
1.7
1.4
One and four tenths
1.2
One and two tenths
1.9
One and seven tenths
33DEVELOPING A MENTAL MATH STRATEGY
 Another option is printing30 as a game
board and having students take turns placing
twosided counters on a pair of compatible
decimals attempting to get four counters in a
row.  Or, thecan be presented via LCD/overhead
and compatible pairs can be discussed  The cards can easily be adjusted to make more
difficult or easier pairs of compatibles or to
make cards reflect money amounts.
34DEVELOPING A MENTAL MATH STRATEGY
 Connecting concrete, pictorial, verbal, symbolic
and contextual representations is key to helping
students develop strong mental math skills.  Notice these card games do not have multiple
representations, but . . .  With the previous work covered, students should
be able to visualize manipulative materials and
make connections that would allow them to solve
the questions mentally.
35Hopefully you will find this information
beneficial. Feel free to make use of any or all
of the resources provided. If you have any
questions dont hesitate to contact me and
hopefully Ill be able to help out. Happy Mental
Mathing? Lynn Sinclair