Mathematics 5 curriculum guide 2015 I table of contents acknowledgements

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MATHEMATICS 5 CURRICULUM GUIDE 2015
Specific Outcomes
ADDING AND SUBTRACTING DECIMALS
Suggestions for Teaching and Learning
Students will be expected to:
Number
Compatible numbers is a method of estimating using “friendly” or 
“nice” numbers, which can be easily calculated mentally. Students have 
used this strategy in Grade 4. In this unit, students use compatible 
numbers in estimating sums and differences of large whole numbers and 
decimal numbers.
e.g., 
(a) 109 543 – 10 257
109 543 – 10 243 = 99 300.
(b) 46.093 + 78.92 + 54.1 (46 + 54) + 79 = 100 + 79 = 179
Model estimating both sums and differences using compatible numbers.
Suppose Roger has $17 986 in the bank and spends $196 buying new 
school clothes. In order to determine about how much money he has 
left his account, students could use compatible numbers.
$17 986 (compatible number $18 000) - $196 (compatible number 
$200)
So, $18 000- $200= $17 800. Roger has about $17 800 left.
Students should also work with problems involving decimals, such as:
To raise money at school, 24 students each sold 6 chocolate bars at 
$1.75 each. Estimate how much money the students collected. This 
problem could be solved using addition while some students may 
choose to use multiplication. Both strategies are acceptable. Teachers 
could remind students that multiplication is just repeated addition. A 
compatible number for $1.75 is $2. The estimate can be found using 
either $2 + $2 + $2 + $2 + $2 + $2 = $12 or 6 x $2 = $12.
Teachers should note that the teacher resource for Math Focus 5 refers 
to 
front-end rounding. Students have already used this strategy but 
the terminology used in Grades 3 and 4 has been 
front-end estimation.
Rounding is another related but separate estimation strategy. To combine 
the terms will be misleading. For clarity of student understanding, teachers 
should refer to this strategy as front-end estimation.
Front-end estimation is a method of estimating computations by 
keeping the first digit (i.e., furthest to the left) in each of the numbers 
and changing all of the other digits to zeros. This strategy can be used 
to estimate sums and differences. Students should recognize that this 
strategy always gives an underestimate for sums,
e.g., 189 523 + 25 812 100 000 + 20 000 = 120 000
Students should apply front end estimation to find sums and differences 
in problems such as: Joshua has a piece of ribbon that is 46.5 cm long 
and he cuts off a piece 22.7 cm long. About how much ribbon does 
Joshua have left?
5N2.3 Estimate a sum, difference 
or product, using compatible 
numbers.
5N2.4 Apply front-end 
estimation to find:
• sums
• differences
• products
• quotients