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 61⁄2% of 250?
Percent means “’for each’ ‘hundred.’” There are two and a half hundreds in 250. So, it’s 61⁄2; for the first hundred, plus 61⁄2 for the second hundred, plus half of 61⁄2 (which is 31⁄4) for the fifty, or 61⁄2 + 61⁄2 + 31⁄4 = 161⁄4.
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 2x + 7 = -13. Subtract 7 from both sides to get 2x = -20. Divide both sides by 2 to get x = -10.
Grade 10: Factor the polynomial: x2 – 5x + 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).
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