Mental Math

1
Mental Math
A Life Long Skill
A program developed by Lynn Sinclair Grade 7
Teacher EPEC Dartmouth NS lsinclai_at_staff.ednet.n
s.ca 462-8401 Ext 143
2
The 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
3
MENTAL 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.

4
MENTAL 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 lead-up and ground
  work required to administer the designed mental
  math tests.

5
WHY 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
  life-long skill.
• OUR BRAIN IS WITH US WHEREVER WE GO OUR
  CALCULATOR IS NOT!!!

6
MENTAL 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.

7
MENTAL 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.

8
MENTAL 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

9
MENTAL 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.

10
MENTAL 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.

11
MENTAL 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.

12
MENTAL 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.

13
GUIDELINES 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.

14
GUIDELINES 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.

15
GUIDELINES FOR MENTAL MATH IN MY CLASSROOM

• Names go in for bi-weekly 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.

16
GUIDELINES 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.

17
GUIDELINES 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.

18
GUIDELINES 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.

19
DEVELOPING 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.

20
The 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.
21
DEVELOPING 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.

22
DEVELOPING 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
  pre-selected to make the task easier for students
  that may need modifications.

23
DEVELOPING 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.

24
DEVELOPING 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)

25
One and three tenths
1
5.6 - 4.3

1
1
-
1
26

• 3
• 10

130
1
2.6 2
1.3
27
DEVELOPING 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.

28
DEVELOPING 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

29
DEVELOPING 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.

30
0.15
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
31
0.15
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
32
One and nine tenths
1.7
1.4
One and four tenths
1.2
One and two tenths
1.9
One and seven tenths
33
DEVELOPING A MENTAL MATH STRATEGY

• Another option is printing30 as a game
  board and having students take turns placing
  two-sided 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.

34
DEVELOPING 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.

35
Hopefully 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