**Grade 1: 11 + 12 = ___**

There are two ways to think about 11 + 12, both require mastery of doubles facts. Think about the double, then add 1 or take away 1. So, for 11 + 12 start with 11 + 11 and add 1. 11 + 11 is 22, so 11 + 12 is 23. Or start with 12 + 12 and take away 11. 12 + 12 is 24, so 11 + 12 is 23.

**Grade 2: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = ___ **

Since 10s are easy to add up, find pairs that add up to 10. 1 plus 9 is 10, and 2 plus 8 is 10. It's a pattern. 3 plus 7 is 10, etc. Add up all the 10s (the four 10s from the pairs and the single 10) and you get 50, plus the 5 left over = 55.

**Grade 3: How much is 99 plus 99 plus 99? **

100s are almost as easy to add as 10s. Since 99 is one less than 100, adding three 99s gives you 3 less than 300 = 297.

**Grade 4: If 2 candies cost 5¢, how many candies can you buy for 35¢?**

14 candies. To solve, reason in groups. here are 7 nickels (5¢) in 35¢. So, 2 candies, 7 times is 14 candies.

**Grade 5: Which is greatest: ^{17}⁄_{18}, ^{23}⁄_{30}, or ^{18}⁄_{19}? Explain how you got your answer.**

A fraction shows what part of a whole.

^{23}⁄

_{30}is out of the running because it isn't even close to a whole (1), whereas

^{17}⁄

_{18}and

^{18}⁄

_{19}are almost 1. When you divide something into more parts, each piece is smaller (think of cutting up a pie into a hundred pieces - each piece would be really small!). So, a piece of a pie with 19 pieces is smaller than a piece of pie with 18 pieces, so

^{18}⁄

_{19}is bigger than

^{17}⁄

_{18}because "the smaller the missing piece, the more that is left."

**Grade 6: Halfway through the second quarter, how much of the game is left?**

The game is divided into 4 parts, called "quarters." If we divide each quarter in half, we get 8 eighths. The first quarter is ^{2}⁄_{8}. Half of the next quarter is another ^{1}⁄_{8}. That's ^{3}⁄_{8}. After the first 3 eighths, there are 5 more eighths left in the game. In other words, ^{5}⁄_{8} of the game is left.

**Grade 7: How much is 6 ^{1}⁄_{2}% of 250?**

Percent means “’

*for each*’ ‘

*hundred*.’” There are two and a half hundreds in 250. So, it’s 6

^{1}⁄

_{2}; for the first hundred, plus 6

^{1}⁄

_{2}for the second hundred, plus half of 6

^{1}⁄

_{2}(which is 3

^{1}⁄

_{4}) for the fifty, or 6

^{1}⁄

_{2}+ 6

^{1}⁄

_{2}+ 3

^{1}⁄

_{4}= 16

^{1}⁄

_{4}.

**Grade 8****: If a = 5, b = 2 and c = 7, evaluate 3a2 + 5b (c – 4).**

105. Substitute the values into the expression. Try to use mental math whenever possible. 75 + 10(3) = 105.

**Grade 9****: Solve for x: -3(2x + 7) = 39.**

*x*= -10. Before diving in and distributing the -3, take a moment and see if a mental math approach would work. Dividing both sides by -3 leaves 2

*x*+ 7 = -13. Subtract 7 from both sides to get 2

*x*= -20. Divide both sides by 2 to get

*x*= -10.

**Grade 10****: Factor the polynomial: ***x*2 – 5*x *+ 6.

When factoring a quadratic polynomial where a = 1, the factored polynomial is always in the form (*x* + ) (*x* + ), where the blank spaces are filled in with the numbers that multiply to make *a* x *c* and add to make *b*. First, identify the values of *a*, *b*, *c*: *a* = 1, *b* = -5, *c* = 6. Create a list of all factor pairs for *a* x *c* (1 x 6 = 6) and determine which pair add to make *b* (-5). The factor pair for 6 that adds to make -5 is -3 and -2. We can “split” the middle term and factor the resulting polynomial by grouping, or simply fill the factors into the form (*x* – 3)(*x* – 2).