MENTAL MATH
from the TCDSB
Mathematics
Department
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JANUARY 2014
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Addition Strategies
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thinkMATH@home
What
Mental
Math?
Thereisare
a number
of ways to
Calculators
and
computers
areinto
only
work mental math practice
useful
when
people
know
what
everyday situations. For example,
information must be entered and if they
doubling a recipe, counting change,
know the answer is reasonable. Knowing
double-checking
till receipts
reasonableness
includes
the use and
of some
scoring
a game
of Scrabble all
sort
of mental
math.
involve using a knowledge of basic
mathsmath
operations
to workestimating
out the
Mental
is calculating,
answers.
and
or visualizing with and without the
use of pencil/paper, calculators or tools.
What is Addition?
Addition is the joining or combining of
two or more numbers (or addends) to
make a new number (or sum).
Mental
Addition
Strategies
There are
a number
of ways to
• Some strategies are better suited for
work mental math practice into
particular sets of numbers. Try all
everyday
situations. For example,
strategies to figure out which strategies
doubling
recipe,
are bettera for
whichcounting
numbers.change,
double-checking
till
receipts
and
• Numbers to use for:
scoring
a
game
of
Scrabble
all
o grade 2 (1-digit; sum to 18)
o gradeusing
3 (2-digit
or less) of basic
involve
a knowledge
o
grade
4
(3
digit
or
less) out the
maths operations to work
o
grade
5
(4
digit
or
less)
answers.
Home
Making 5s and 10s
If you know know these sums:
5 => 1+4, 2+3
10=> 1+9, 2+8, 3+7, 4+6
5+5
2+8+3+6+4
= 10 +3+10 = 20+3 = 23
5+7+9+4+8+6
= 5+5+1+1+9+4+8+2+4
= 10+1+10+4+10+4
= 30+5+4+39
Front-End (Left to Right)
Adding the front-end digits
(adding larger place value
digits first) towards the right
(smaller place value digits)
and keeping a running total
in your head.
124+234 ->1+2 hundreds + 2+3
tens + 4+4 ones -> 3 hundreds +5
tens + 8 ones -> 300+50+8 = 358
Break Up the Numbers
Use when regrouping is
required. One of the
addends is broken up into its
expanded form and added
in parts to the other addend.
57+37 = 57+30 +7 =87 +7
= 87+3+4 = 90+4=94
87+8=87+3+4
=90+4=94
Making Jumps of Ten
Keep one number whole
and jumps of ten are
added to it
28 + 44 = 44 + 10 + 10 + 8
(decompose 8 into 6 and 2)
3 486 + 1 214 = 3 486 + 1 000 +
200 + 10 + 4
o grades 6 to 9 (any size digit number)
Try These!
a) 4+9; 6+6+5; 3+4+2+4;
b) 1+2+3+4+5; 3+6+7+4+9+6
c) 4+9+10+6+5+8; 20+9+6+5+4+8
d) 29+39; 39+19+29; 15+26+37
e) 11+22+33+44+55
f) There
111+222+333+444+555
are a number of ways to
g)work
351+249+111;
mental math 419+131+236
practice into
h)everyday
1111+2222+3333+4444+5555
situations. For example,
i) doubling
What’s the
relationship
between
(b),
a recipe,
counting
change,
(e),
(f),
and
(h)?
double-checking till receipts and
scoring a game of Scrabble all
Now, create your own challenges!
involve using a knowledge of basic
maths operations to work out the
answers.
Moving to the Next
Friendly Number
Compensation
Units are added first to
reach a friendly number
Substitute a compatible
number for a number you
can calculate more easily
(usually a ten)
98 + 37 = 98 + 2 + 35 = 100 + 35
= 135
36 + 118 = 34 + 120
227+164=230+161
27 + 49 = 26 + 50
47 + 29 -> (47 + 30) – 1 -> 77-1
= 76
Helping Your Child Learn Mathematics AT HOME …
Developing Students’ Mathematical Understanding, Reasoning and Communication
Strategy #1 - Have your child solve math problems in different ways, such as using different number
combinations, different sets of operations in calculations or different models of representation like
the number line, set of objects, or square grid.
Strategy #2 - Ask your child to explain their solutions to math problems that they solved during class
lessons or are working on for practice at home. As they explain their thinking, they are developing
reasoning, proving and communication.
Strategy #3 – Do mathematics with your child. Solve the problems they have from their class lesson
or homework in 2 different ways. Compare your solution(s) with your child’s solution(s). Discuss how
the solutions are mathematically similar and different.
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learning resources
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