• Most people will add 40 + 30;
• 70;
• then add 8 + 9;
• 17;
• then add 70 + 17.

Or

• A more efficient strategy would be to add 48 + 30;
• 78;
• then 78 + 9;
• 87.

Or

Take one from 48 and add to 39 to make 40;

then 47 + 40 = 87.

• Add 2 to 98 to make an easy number of 100;
• subtract 113 - 100;
• 13;
• Then add the 2 back;
• 13 + 2 = 15.

Or

• Add 2 to both numbers and get
• 115 - 100;
• Then subtract and get 15.

• Factor 14;
• 2 * 7 * 5 * 7;
• rearrange (commutative property);
• 2 * 5 * 7 * 7;
• multiply (2 * 5) and (7 * 7);
• 10 * 49;
• multiply;
• 490

Or

• Break apart 14 and multiply 5 * 7;
• (10 + 4) + 35;
• multiply;
• 350 + (4 * 35);
• Use double double to multiply by 4 (35 + 35 = 70; 70 + 70 = 140)
• 350 + 140

• Add one to 249;
• 4 * 250;
• Subtract 4 * 1;
• 1000 - 4;
• 996.

• Add 37 + 63;
• 6 * 100 + 18;
• multiply;
• 600 + 18
• 618.

• Think of .25 as 1/4;
• and 9 as 8 + 1;
• (14 of 8) + (1/4 of 1);
• 2 + 1/4;
• 2 1/4.

Or

• 1/4 of 8 = 2.
• 1/4 of 10 is 2.5
• ∴ 1/4 of 9 = 2.25

• Think of a clock
• 1/2 = 30 minutes;
• 1/3 = 20 minutes;
• ∴ either
• 30/60 + 20/60 = 50/60.
• or 3/6 + 2/6 = 5/6

• Remove 2;
• 150 - 75 = 75;
• Add 2 back;
• 75 + 2;
• 77.

• 39 * 2 = 78;
• 78 + 39 = 100 + ___;
• If 85 is closer to 78 (2) than 39 (1) or one hundred something (3), then the answer is ...
• Two.

• 12.03 + .4;
• 12.43 + 2.36;
• 14.79

• ($2 + $3 + $4) - .04;
• $9 - .04 but before subtracting the 4 cents.
• I think that it will be the change that will be needed with the dollar;
• ∴ the change would be $1.04.

Additional comment

The ability to think of the 4 cents as money that isn't owed and money that will be change is one of the landmarks that Piaget identified in child development. To expect children to think in this manner before second grade is problematic.

• Ten percent of 160 = 16;
• 90% = 100% - 10%;
• ∴ 160 -16;
• 144.

• 50% = 1/2;
• 25% = 1/4;

 

• 1/2 of $50 = $25;
• 1/4 of $25 = $12.50;

 

• Round $49.35 to $50;
• Round $12.50 to $13;
• ∴ $50 - $13 = $37.

• (1 + 19) = 20;
• (3 + 17) = 20;
• (5 + 15) = 20;
• (7 + 13) = 20;
• (9 + 11) = 20;
• that's five pairs of integers that have a sum of 20.
• ∴ 5 * 20;
• 100.

• Square with perimeter of 20;
• Square has four equal sides;
• 4 sides * 5 units long = 20 units long;

 

• If a square is 5 units long in each side;
• then its areaa wold be;
• 5 units * 5 units;
• 25 square units.

• If the radius = 1;
• then the length of each side of the square is 2;
• ∴ the area of the square is 4 square units.
• If the radius = 1;
• then the area of the circle is π * 1²;
• π or 3.14 square units.
• The ratio would be 3.14 : 4;
• a little more than 3/4 or .75
• ∴ .8.

• Try 90.
• If 90 is the mean, then the total above and below should be the same.
• There is 11 more above 90 and 6 below 90.
• Since there are five numbers and 11 is 5 more that means there would be one more for each 5 to raise the average to 91.

 

• If the average is 91, then the total above is 9 and the total below is 9
• 82 + 2 = 91;
• 85 + 6 = 91; total below 91 = 9
• 90 + 1 = 91;

 

• 94 - 3 = 91;
• 97 - 6 = 91; Total above 91 = 9

 

• If 16 is 4 * 4;
• then 4/6 * 4/4;
• 16/24
• ∴ X = 24

• If 2 * 10 = 20 and 20 + 3 = 23;
• then 10 is too low.
• Try 2 * 11 = 2 and 22 +3 = 25;
• ∴ X = 11

• If 82 = 64 and 92 = 81;
• 64 + 11 = 75;
• 81 - 6 = 75;
• ∴ 9 is closest to √75.

• 10% of #80.00 is $8.00;
• 1/2 of $8.00 = $4.00'
• $8.00 + $4.00 = $12.00