1i) a.
1g) A three-digit number has three places: the ones' place at the right, the tens' place in the middle, and the hundreds' place at the left.
1f) A two-digit number has two places: the ones' place and the tens' place. A three-digit number has three places: the ones' place, the tens' place, and the hundreds' place.
2i)
d.
2g) If the two-digit number is, for example, 17, the addition might be as follows, depending on the order of the digit cards: 17 + 2 = 19; 19 + 7 = 26; 26 + 4 = 30; 30 + 6 = 36; 36 + 1 = 37; 37 + 5 = 42; 42 + 3 = 45; 45 + 8 = 53; 53 + 9 = 62. In all cases, the final sum will be 45 more than the two-digit number.
2f) There are several ways to make exactly 20 from six numbers from 1 to 6; among them are 1 + 2 + 3 + 4 + 6 + 4 and 2 + 2 + 5 + 5 + 3 + 3.
3i) c.
3g) The greatest number has the greatest digit in the hundreds' place, the next-greatest digit in the tens' place, and the least digit in the ones' place.
3f) Your child may either subtract the number left from the original number or count up from the number left to the original number.
4i) b.
4g) A meterstick is 100 centimeters long.
4f) Be sure your child aligns the ruler properly to find accurate measurements.
5i) d.
5g) 0 x any number = 0
1 x any number = the number
2 x: 2 = 4, 3 = 6, 4 = 8, 5 = 10, 6 = 12, 7 = 14, 8 = 16, 9 = 18
5 x: 2 = 10, 3 = 15, 4 = 20, 5 = 25, 6 = 30, 7 = 35, 8 = 40, 9 = 45
5f) When joining equal groups, multiplication is quicker and more efficient than adding or counting.
6i) d.
6g) For example, 308,425 in words is three hundred eight thousand, four hundred twenty-five; in expanded form it is 300,000 + 8,000 + 400 + 20 + 5.
6f) Your child should not use the word and when reading the numbers.
7i) a.
7g) So that all measurements are consistent, all students should measure in a straight line from one point to another, for example, from the center of the heel to the farthest point of the toe.
7f) A measurement to the nearest quarter inch may be recorded as a whole-inch, half-inch, quarter-inch or three-quarter-inch measurement.
8i) b.
8g) For example, if the two prices are $5.79 and $1.98, $5.79 + $1.98 = $7.77 and $5.79 - $1.98 = $3.81.
8f) Encourage your child to explain each addition and subtraction.
9i) c.
9g) divided by 6 with no remainder: 54, 48
divided by 7 with no remainder: 63, 56
divided by 8 with no remainder: 48, 56
divided by 9 with no remainder: 54, 63
9f) 18 ÷: 2 = 9, 3 = 6, 4 = 4 r 2, 5 = 3 r 3, 6 = 3, 7 = 2 r 4
10i)
a.
10g) Answers will have either three or four digits.
10f) Be sure your child writes the dollar sign and decimal point in the answer.
11i) b.
11g) 3 sides: triangle; 4 sides: quadrilateral (or square or rectangle); 5 sides: pentagon; 6 sides: hexagon; 8 sides: octagon
11f) A polygon is a closed, flat figure with straight sides.
12i) d.
12g) 48 pennies can be arranged in 2 equal rows (1/2; 24 in each row), 3 equal rows (1/3; 16 in each row), 4 equal rows (1/4; 12 in each row), 6 equal rows (1/6; 8 in each row), 8 equal rows (1/8; 6 in each row), 12 equal rows (1/12; 4 in each row), 16 equal rows (1/16; 3 in each row), or 24 equal rows (1/24; 2 in each row).
12f) 1 quart = 32 fluid ounces; 1 pint = 16 fluid ounces; 1 cup = 8 fluid ounces
13i) b.
13g) Some answers will have remainders. The remainder is always less than the divisor.
13f) For example, if the one-digit number is 6 and the secret number is 572, 6 x 572 = 3432 and 3432 ÷ 6 = 572, the secret number.
14i)
a.
14g) Students may use calculators to check their paper-and-pencil computations.
14f) Your child should subtract the total cost from the amount given.
15i)
c.
15g) For example, an estimate of 34 x 27 is 30 x 30 = 900. The exact answer of 34 x 27 is 918.
15f) To estimate a product of two two-digit numbers, round each factor to the nearest ten; then multiply.
16i) b.
16g) Students can use the "guess and check" or "trial and error" strategy to find appropriate numbers.
16f) To find the average, add the numbers, and then divide the sum by the number of addends.
17i) d.
17g) Decimals to tenths have one place to the right of the decimal point. Decimals to hundredths have two places to the right of the decimal point. The decimal points should be lined up before addition or subtraction.
17f) An example of a daily record is as follows: began with $5.00, spent $2.25 on baseball cards, earned 50¢ taking out trash: total is $3.25.
18i)
d.
18g) for example, 2/8 + 4/8 = 6/8 and 4/8 - 2/8 = 2/8
18f) To add or subtract fractions with the same denominator, add or subtract the numerators.
19i) c.
19g) If, for example, there is a total of 45 squares in the bag and 5 of them are red, the probability of picking a red square is 5 out of 45, or 5/45, or 1/9. If students only pick 45 times in all, it is unlikely that their tallies will match the probabilities. However, the more times they try the experiment, the closer the tallies will come to the probabilities.
19f) The probability of a coin's coming up either heads or tails is 1 out of 2, or 1/2. This means no matter how many times the coin is flipped, the probability remains 1/2 for each flip. So if a coin comes up heads 3 times in a row, there is still a 1 out of 2 chance that it will come up heads on the next flip.
20i)
three hundred twenty-one million, seven hundred nine thousand,
twelve
20g) Commas should be placed after the words million and thousand.
20f) Seven-, eight-, and nine-digit numbers are numbers in the millions.