Comparing and Ordering Numbers: practice solutions, Grade 2 – download the PDF

1 Fill in the symbol ★★★

1. Same hundreds. Tens: \(4 \lt 8\). So \(148 \lt 184\).
2. Same hundreds. Tens: \(7 \gt 0\). So \(570 \gt 507\).
3. All digits match, so \(300 = 300\).
4. Same hundreds. Tens: \(1 \lt 5\). So \(615 \lt 651\).
5. 99 has no hundreds and 101 has 1 hundred, so \(99 \lt 101\).
6. Same hundreds. Tens: \(2 \gt 0\). So \(820 \gt 802\).

2 Which digit decides? ★★★

1. The hundreds match, so the tens decide: \(5 \lt 8\). Then \(452 \lt 482\).
2. The hundreds are different: \(7 \gt 6\). Then \(719 \gt 619\).
3. The hundreds and tens match, so the ones decide: \(5 \lt 9\). Then \(835 \lt 839\).

3 Biggest and smallest ★★★

The hundreds digits are 2, 2, 4, 4. The cards 426 and 462 are the biggest group. Tens: \(6 \gt 2\), so \(462 \gt 426\). The cards 264 and 246 are the smallest group. Tens: \(4 \lt 6\), so \(246 \lt 264\).

The greatest number is 462 and the least number is 246.

4 Order four numbers ★★★

Hundreds: 5 and 5, then 8 and 8. Between 580 and 508: \(508 \lt 580\). Between 850 and 805: \(805 \lt 850\).

Answer: 508, 580, 805, 850.

5 Jump by 10 ★★★

1. The tens digit goes up by one: \(346 + 10 = 356\).
2. 9 tens plus 1 ten makes 10 tens, which is 1 more hundred: \(590 + 10 = 600\).
3. \(721 - 10 = 711\).
4. 0 tens, so we take 1 hundred apart into 10 tens: \(804 - 10 = 794\).

6 Jump by 100 ★★★

1. The hundreds digit goes up: \(237 + 100 = 337\).
2. \(650 + 100 = 750\).
3. The hundreds digit goes down: \(912 - 100 = 812\).
4. \(905 - 100 = 805\).

7 Counting on and back ★★★

(a) Each number is 1 more: 697, 698, 699, 700, 701.

(b) Each number is 1 less: 403, 402, 401, 400, 399.

8 The apple orchard ★★★

Hundreds match (3). Tens: \(6 \gt 5\), so \(365 \gt 356\). Green Hill picked more.

\(365 - 356 = 9\).

Answer: Green Hill picked 9 more apples than Sunny Row.

9 True or false? ★★★

1. False. The hundreds match, and the tens are \(0 \lt 9\). So \(509 \lt 590\).
2. False. Mia looked at the ones. The tens decide: \(1 \lt 8\), so \(618 \lt 681\).
3. True. 6 hundreds and 1 hundred make 7 hundreds.
4. True. The hundreds match, and the tens are \(4 \lt 5\).

10 Missing digit ★★★

The hundreds match (4), so compare the tens. We need the tens digit to be 6 or more. With 6 we get \(467\), and \(467 \gt 465\) because the ones are \(7 \gt 5\). With 5 we get \(457\), which is too small.

Answer: the digits 6, 7, 8, and 9 work.

11 Mystery number ★★★

Numbers between 640 and 650 have 6 hundreds and 4 tens. With 7 ones, the number is 647.

Check: \(640 \lt 647 \lt 650\).

12 Skip counting ★★★

1. Add 5 each time: 240, 245, 250, 255.
2. Add 10 each time: 350, 360, 370, 380.
3. Add 100 each time: 375, 475, 575.

13 Read the number line ★★★

1. The labeled marks go by 10 and the small marks are halfway, so they count by 5. Then A is 325, B is 340, and C is 385.
2. Moving right means bigger: \(325 \lt 340 \lt 385\), so A, B, C.
3. Distances to 350: A is \(350 - 325 = 25\), B is \(350 - 340 = 10\), C is \(385 - 350 = 35\). Point B is the closest.

14 Mental math table ★★★

\(478 + 10 = 488\): the tens digit changed.

\(478 + 100 = 578\): the hundreds digit changed.

\(478 - 10 = 468\): the tens digit changed.

\(478 - 100 = 378\): the hundreds digit changed.

15 Five numbers in order ★★★

The hundreds digits are 7, 7, 3, 3, 4. So the order of groups is 3, then 4, then 7.

Group 3: 347 and 374. Tens: \(4 \lt 7\), so \(347 \lt 374\).

Group 4: only 437.

Group 7: 734 and 743. Tens: \(3 \lt 4\), so \(734 \lt 743\).

Least to greatest: 347, 374, 437, 734, 743.

Greatest to least: 743, 734, 437, 374, 347.

16 Number machines ★★★

1. \(285 + 100 = 385\).
2. We need a number minus 10 that equals 385. Go up 10 from 385: \(385 + 10 = 395\). Check: \(395 - 10 = 385\). So put in 395.

17 Find the skipped number ★★★

1. From 540, adding 10 gives 550, not 560. Leo skipped 550.
2. Subtract 100 each time: 800, 700, 600, 500.

18 Compare on a number line ★★★

1. The labeled marks go by 100 and the small marks by 50. So K is 150, L is 450, and M is 850.
2. Distances to 500: K is 350, L is 50, M is 350. Point L is the closest.
3. M is farther to the right, so \(850 \gt 150\). M is greater.
4. \(450 + 100 = 550\).

19 The can drive ★★★

1. \(478 \lt 487 \lt 748\). The order is 2A, 2B, 2C.
2. Rooms 2A and 2B. \(487 - 478 = 9\), so they differ by 9 cans.
3. \(478 + 300 = 778\). Since \(778 \gt 748\), yes, 2A will have more than 2C.

20 Digits 2, 5, and 8 ★★★

Put each digit in the hundreds place in turn.

Hundreds 2: 258 and 285. Hundreds 5: 528 and 582. Hundreds 8: 825 and 852.

In each pair, the smaller tens digit comes first.

Answer: 258, 285, 528, 582, 825, 852.

21 Will I say it? ★★★

1. Yes. 365 ends in 5.
2. No. 702 ends in 2, not 0 or 5.
3. Yes. 1,000 ends in 0.
4. No. When counting by 10s every number ends in 0, and 365 ends in 5.