UMI Seminar
Saturday, October 11, 2014
•Exemplars
Calculating Calculator Costs
Evan and Maria want to make some money.
They ask their parents to let them work
around the house to earn some. Their
parents agree, since one of the things both
Maria and Evan want to buy are graphing
calculators.
Dad tells Maria that he will give her $10 to
start, and then will give her $5 an hour for
the work she does around the house. Mom
offers Evan a slightly different deal. She will
give him $40 to start, but only $3 an hour for
the work he does around the house.
Who offered the better deal? Support your
conclusion mathematically.
— Page 15 —
Calculator
We Set the
Standards!
.6-8
Mental Math
Strategy
Front-End Addition
• Powerful mental
strategy for adding
numbers with two or
more digits
• Provides students a
better understanding
of place value
• Means adding the tens
first, then the ones
Front-End Addition
• With repeated practice,
students can become
very quick and
efficient adders when
using this strategy
For example…in the equation
24 + 53 =
add 20 and 50 to make 70
then add 4 and 3 to make 7
then add 70 + 7 to get the sum of 77
Let’s try another…
496 + 745=
add 400 and 700 to make 1100
then add 90 and 40 to make 130
then add 6 and 5 to get 11
now add 1100 + 130 + 11
to get the sum of 1241
Now it’s your turn to practice…
+
247
8857
502
542
4758
732
2110
489
192
+
+
835
Now it’s your turn to practice…
247
542
+
192
8857
+
200 + 500 + 100 = 800
40 + 40 + 90 =170
7 + 2 + 2 = 11
800 + 170 + 11 = 981
8000 + 4000 + 2000 = 14000
4758
800 + 700 + 100 = 1600
2110
50 + 50 + 10 = 110
7 + 8 + 15
14000 + 1600 + 110 + 15 = 15,725
Now it’s your turn to practice…
502
732
489
+
835
500 + 700 + 400 + 800 =2400
30 + 80 + 30 = 140
2 + 2 + 9 + 5= 18
2400 + 120 + 18 =2558
FRONT-END ESTIMATION
• Front end estimation of a sum is when
only the left-most digit in the addends is
added
• For example, 85 + 44 becomes 80+ 40
• Another example, 24+35 becomes 20 + 30
• Many people think this strategy is easier
than rounding to the highest place value.
4758
8857
8000
4000
4758
7045
7000
7045
2110
+ + 2110
2000
8857
+
+
8857
8857
8000
4758
4000
4758
7045
7000
7045
2110
+ + 2110
2000
Draw the line after the
first number
In each addend.
8000
• Between 11,000 and 15,000
4000
• Between 16,000 and 20,000
7000
+ 2000
• Between 20,000 and 25,000
• Between 28,000 and 33,000
Estimate to find the best answer.
247
6542
489
+
92
7370
•
A little more than 7,000
•
A little more than 8,000
•
A little less than 9,000
•
A little less than 10,000
Using Front-End Estimation…Try these
examples.
+
+
5524
5000
3452
3000
8000
578
500
+
241
+
200
700
Front-End Addition
and Estimation
247
6542
240
247
6540
6542
489
+
92
480
489
++
90
92
5028
5028
5000
6732
6732
6700
1285
1200
1285
+ 835
+ + 800
835
Estimate and choose the most
reasonable answer.
5000
Between 11,000 and 15,000
6700
Between 16,000 and 20,000
1200
Between 20,000 and 25,000
+ 800
13700
Between 28,000 and 33,000
375+ 26 + 1,427 + 216
375
26
37 0
20
1,427
1,42 0
216
21 0
3,876
4,000
3,000
5,814
6,000
5,000
3,176
3,000
3,000
+ 7,895
+ 8,000
+ 7,000
9,876
9,000
10,000
8,514
8,000
9,000
6,092
6,000
6,000
+ 3,895
+ 3,000
+ 4,000