Name: ______________________________________

Date: _____________________________

ANSWERS Goal #1: I can use appropriate estimates to solve problems involving large numbers. 1) If an individual box of raisin contained 30 raisins, about how many individual boxes of raisins would you need to eat to get to one million raisins? 100 divided by 30 = approximately 3.3 There are 10 000 “hundreds” in one million so for the number of raisins: 3.3 x 10 000 = 33 000 So, you would have to eat approximately 33 000 boxes of raisin to eat one million raisins. 2) Do you think you have ever read a book with one million words? About how many pages would a book with one million words be? A normal chapter book might have 25 lines on it. Each line might contain 10 words. Therefore, one page contains approximately 250 words and four pages would contain 1000 words. Since one million = 1000 thousands a book that had one million pages might have approximately 4000 pages. Since I have never read a book with 4000 pages in it, I have never read a book with one million words.

Goal #2: I can identify and explain patterns within our place value system (including decimals). 3) When you write the number 21.3 million, the left digit is in the ten millions column on the place value chart shown below.

In which column is the leftmost digit for each of these numbers? a. 3.2 million = millions

c. 0.03 million = ten thousands

b. 0.57 million = hundred thousands

d. 58.1 thousand = ten thousand

4) Complete each question: a. 1 ten thousand = 1000 tens b. 1 million = 100 ten thousands c. 1 hundred = 1000 tenths 5) What is the greatest six-digit even number that matches these clues? • The ten thousands digit is twice the tens digit. • The hundred thousands digit is more than six. • The thousands digit is divisible by the ones digit. • No digit is used more than once. I came up with 986 742 (can you think of a larger number that meets the criteria?) GOAL #3: I can use these patterns to represent whole and decimals numbers in standard form, expanded form, in pictures, and in words. 6) Write each number in words. a. b. c. d.

214 135 = two hundred fourteen thousand one hundred thirty-five 1 240 100 = one million two hundred forty thousand one hundred 32 156 002 = thirty-two million one hundred fifty-six thousand two 3 104 016 = three million one hundred four thousand sixteen

7) Write each number in standard and expanded form. a. six hundred sixty-five thousand two hundred eighty-seven = 665 287 665 287 = 600 000 + 60 000 + 5000 + 200 + 80 + 7 665 287 = (6 x 100 000) + (6 x 10 000) + (5 x 1000) + (2 x 100) + (8 x 10) + (7 x 1) b. three hundred two thousand seven = 302 007 302 007 = 300 000 + 2000 + 7 302 007 = (3 x 100 000) + (2 x 1000) + (7 x 1) c. four hundred fifteen thousand ten = 415 010 415 010 = 400 000 + 10 000 + 5000 + 10 415 010 = (4 x 100 000) + (1 x 10 000) + (5 x 1000) + (1 x 10) d. nine hundred seventy-two thousand four hundred = 972 400 972 400 = 900 000 + 70 000 + 2000 + 400 972 400 = (9 x 100 000) + (7 x 10 000) + (2 x 1000) + (4 x 100) e.

= 619 242

619 242 = 600 000 + 10 000 + 9000 + 200 + 40 + 2 619 242 = (6 x 100 000) + (1 x 10 000) + (9 x 1000) + (2 x 100) + (4 x 10) + (2 x 1)

8) Write each number in standard and expanded form. a. thirty four and one hundred twenty-two thousandths = 34.122 34.122 = 30 + 4 + 0.1 + 0.02 + 0.002 34.122 = (3 x 10) + (4 x 1) + (1 x 0.1) + (2 x 0.01) + (2 x 0.001) b. twenty thousand six hundred and seventy-five thousandths = 20 600.075 20 600.075 = 20 000 + 600 + 0.07 + 0.005 20 600.075 = (2 x 10 000) + (6 x 100) + (7 x 0.01) + (5 x 0.001) c. one million four hundred three and six thousandths = 1 000 403.006 1 000 403.006 = 1 000 000 + 400 + 3 + 0.006 1 000 403.006 = (1 x 1 000 000) + (4 x 100) + (3 x 1) + (6 x 0.001) GOAL #4: I can order whole and decimals numbers and plot them on a number line. 9) Compare each pair of decimals. Use an inequality (< or >) symbol. a. 0.931 b. 0.078 c. 3.543

> 0.831 > 0.009 > 3.354

d. 0.590 < 0.591 e. 1.111 > 1.110 f. 0.43 > 0.198

10) Order each set of numbers from least to greatest. a. 6.092 6.187 5.989 6.989 5.989 < 6.062 < 6.187 < 6.989

b. 11.756 10.981 10.643 11.173 10.643 < 10.981 < 11.173 < 11.756

11) Show six ways to use each of the digits from 0 to 4 to make this inequality true.

Some ways include: 0.43 > 0.012 0.43 > 0.102 0.43 > 0.201

0.43 > 0.021 0.43 > 0.210 0.43 > 0.120

12) Write the decimal thousandths for each position on the number line.

a) 0.213

b) 0.222

c) 0.248

GOAL #5: I can round whole and decimals numbers to meaningful benchmarks. 13) Round each decimal to the nearest hundredth. a. 0.216 → 0.22 b. 1.312 → 1.31 c. 3.007 → 3.01 d. 2.635 → 2.64 14) Round each decimal to the nearest tenth. a. 3.418 → 3.4 b. 1.572 → 1.6 c. 8.007 → 8.0 d. 0.001 → 0.0 15) When you round a certain decimal less than one to the nearest tenth, it increases by 37 thousandths. What do you know about the decimal? 100 – 37 = 63 Therefore the number must have 63 thousandths in it. For example, the number 0.063 when rounded to the nearest tenth would equal 0.1… an increase of 37 thousandths.