Written solutions to the chapter problems. Check each step, then correct yourself.
1 Counting blocks ★★★
The first group has \(2\) tens and \(3\) ones. The second has \(1\) ten and \(4\) ones.
Ones: \(3 + 4 = 7\). Tens: \(2 + 1 = 3\), which is \(30\).
\(23 + 14 = 37\). Together the blocks make 37.
2 Add the tens and the ones ★★★
Ones: \(1 + 6 = 7\). Tens: \(5 + 3 = 8\), which is \(80\).
\(51 + 36 = 87\).
3 Subtract with no trading ★★★
Ones: \(8 - 5 = 3\). Tens: \(6 - 2 = 4\), which is \(40\).
\(68 - 25 = 43\).
4 Another subtraction ★★★
Ones: \(9 - 6 = 3\). Tens: \(7 - 4 = 3\), which is \(30\).
\(79 - 46 = 33\).
5 Tens and ones puzzle ★★★
\(3\) tens \(8\) ones is \(38\). \(2\) tens \(1\) one is \(21\).
Ones: \(8 + 1 = 9\). Tens: \(3 + 2 = 5\).
\(38 + 21 = 59\). The answer is 59.
6 Basketball points ★★★
Add: \(32 + 45\). Ones: \(2 + 5 = 7\). Tens: \(3 + 4 = 7\).
\(32 + 45 = 77\). The Eagles scored 77 points.
7 Apple stand ★★★
Subtract: \(89 - 54\). Ones: \(9 - 4 = 5\). Tens: \(8 - 5 = 3\).
\(89 - 54 = 35\). There are 35 apples left.
8 True or false? ★★★
- True. \(3\) tens plus \(4\) tens is \(7\) tens, which is \(70\).
- False. Ones: \(6 - 4 = 2\). Tens: \(5 - 2 = 3\). So \(56 - 24 = 32\), not \(42\).
9 Add with regrouping ★★★
Ones: \(8 + 7 = 15\). That is \(1\) ten and \(5\) ones. Tens: \(3 + 2 = 5\), plus \(1\) new ten gives \(6\) tens.
\(60 + 5 = 65\). So \(38 + 27 = 65\).
10 Another regrouping sum ★★★
Ones: \(9 + 6 = 15\), so write \(5\) and make a new ten. Tens: \(4 + 3 + 1 = 8\).
\(49 + 36 = 85\).
11 Trade a ten ★★★
\(71\) is \(7\) tens and \(1\) one. There are not enough ones, so trade one ten: \(6\) tens and \(11\) ones.
Ones: \(11 - 8 = 3\). Tens: \(6 - 2 = 4\).
\(71 - 28 = 43\).
12 Subtracting from a multiple of ten ★★★
\(90\) is \(9\) tens and \(0\) ones. Trade one ten: \(8\) tens and \(10\) ones.
Ones: \(10 - 6 = 4\). Tens: \(8 - 4 = 4\).
\(90 - 46 = 44\).
13 Jumping on a number line ★★★
Start at \(54\). Jump \(20\) to \(74\). Jump \(9\) more to \(83\).
\(54 + 29 = 83\).
14 Find the missing number ★★★
Subtract to find the missing number: \(82 - 47\). Trade a ten: \(82\) is \(7\) tens and \(12\) ones. Ones: \(12 - 7 = 5\). Tens: \(7 - 4 = 3\). So \(82 - 47 = 35\).
Check: \(47 + 35 = 82\). The missing number is 35.
15 Find Leo’s mistake ★★★
Ones: \(5 + 7 = 12\), which is \(1\) ten and \(2\) ones. Leo wrote the \(2\) but forgot the new ten.
Tens: \(4 + 2 + 1 = 7\). The correct answer is \(45 + 27 = 72\).
16 Sticker graph ★★★
- Ava has \(34\) and Cam has \(45\). \(34 + 45 = 79\). They have 79 stickers.
- Cam has \(45\) and Dee has \(18\). \(45 - 18 = 27\), because \(18 + 27 = 45\). Cam has 27 more stickers.
17 Four numbers ★★★
Add two at a time: \(14 + 23 = 37\). Then \(37 + 31 = 68\). Then \(68 + 22 = 90\).
Another way: tens \(1 + 2 + 3 + 2 = 8\) tens is \(80\), ones \(4 + 3 + 1 + 2 = 10\). \(80 + 10 = 90\).
18 Look for tens ★★★
\(18 + 27 = 45\). Then \(45 + 15 = 60\) (the ones \(5 + 5\) make a ten). Then \(60 + 34 = 94\).
Check by adding in a different order: \(18 + 34 = 52\) and \(27 + 15 = 42\). \(52 + 42 = 94\).
19 The library cart ★★★
First, add the returned books: \(63 + 28 = 91\) (ones \(3 + 8 = 11\), tens \(6 + 2 + 1 = 9\)).
Then subtract the books checked out: \(91 - 35 = 56\) (trade a ten: \(8\) tens \(11\) ones, \(11 - 5 = 6\), \(8 - 3 = 5\)).
There are 56 books on the cart.
20 Missing start ★★★
If you take \(38\) away and \(27\) is left, the start was \(27 + 38\).
Ones: \(7 + 8 = 15\). Tens: \(2 + 3 + 1 = 6\). So the start was \(65\).
Check: \(65 - 38 = 27\). The missing number is 65.
21 Check Sam’s answer ★★★
To check, add the answer and the number taken away: \(56 + 47 = 103\). That is not \(93\), so Sam is wrong.
Subtract correctly: \(93\) is \(8\) tens and \(13\) ones. Ones: \(13 - 7 = 6\). Tens: \(8 - 4 = 4\). So \(93 - 47 = 46\).
Check: \(46 + 47 = 93\). The correct answer is 46.
22 The city bus ★★★
First stop: \(58 - 19 = 39\) (since \(58 - 20 = 38\), then add \(1\) back).
Next stop: \(39 + 26 = 65\) (ones \(9 + 6 = 15\), tens \(3 + 2 + 1 = 6\)).
There are 65 riders on the bus now.
23 Two mystery numbers ★★★
The other number is \(71 - 29 = 42\). Check: \(29 + 42 = 71\).
The bigger number is \(42\), the smaller is \(29\). \(42 - 29 = 13\). The difference is 13.
Test yourself: quick challenge for Grade 2
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