
Written solutions to the chapter problems. Check each step, then correct yourself.
1 Cross out the ladybugs ★★★
Cross out 2 of the 6 ladybugs. Count the ladybugs with no cross: 4 are left.
The equation is \(6 - 2 = 4\). 4 ladybugs are left.
2 Apples in the basket ★★★
Start with 5 and take away 1. Taking away 1 gives the number just before 5, which is 4.
\(5 - 1 = 4\). 4 apples are left.
3 Read the equation ★★★
a) “Seven minus two equals five.” You start with 7, take away 2, and 5 are left.
b) “Four minus one equals three.” You start with 4, take away 1, and 3 are left.
4 Take away nothing, take away all ★★★
a) Taking away nothing changes nothing: \(3 - 0 = 3\).
b) Taking away all 3 leaves nothing: \(3 - 3 = 0\).
c) \(8 - 0 = 8\).
d) \(8 - 8 = 0\).
5 Finish the facts ★★★
a) \(4 - 2 = 2\).
b) \(5 - 3 = 2\).
c) \(3 - 1 = 2\).
d) \(2 - 1 = 1\).
You can check each one by drawing the starting group and crossing out the number you take away.
6 Fish in the pond ★★★
Cross out 3 of the 8 counters. The counters with no cross are the fish that stay.
\(8 - 3 = 5\). 5 fish stay in the pond.
7 Match the story ★★★
“Gives away” means some stickers go away, so we subtract. The matching equation is B) \(6 - 2 = 4\). Mia has 4 stickers left.
Equation A uses a plus sign, which would make the group bigger.
8 Taking 7 apart ★★★
The orange cars are the part we do not know. Whole minus the known part gives the other part.
\(7 - 3 = 4\). 4 cars are orange.
9 Blocks of two colors ★★★
The whole is 10 and one part is 6. Subtract the known part from the whole.
\(10 - 6 = 4\). There are 4 yellow blocks.
Check: 6 green and 4 yellow make 10 blocks.
10 Cupcakes at the party ★★★
Draw 9 circles and cross out 5. Four circles have no cross.
\(9 - 5 = 4\). 4 cupcakes are left on the tray.
11 Hop back on the number line ★★★
Hop back one step at a time: 7, 6, 5. You land on 5.
\(8 - 3 = 5\).
12 True or false? ★★★
a) False. Six minus two is 4, so \(6 - 2 = 4\).
b) True. Taking away all 5 leaves nothing.
c) False. Taking away nothing leaves 4, so \(4 - 0 = 4\).
13 Fact fluency challenge ★★★
a) \(5 - 2 = 3\) b) \(4 - 3 = 1\) c) \(3 - 3 = 0\) d) \(5 - 4 = 1\) e) \(4 - 2 = 2\) f) \(2 - 0 = 2\)
Trick: \(5 - 2 = 3\) and \(5 - 3 = 2\) use the same two parts of 5.
14 Find Leo’s mistake ★★★
Leo added 6 and 4 instead of taking away. The minus sign means we take away, so the answer must be smaller than 6.
The correct equation is \(6 - 4 = 2\).
15 All the subtractions from 5 ★★★
Take away 1, 2, 3, and 4 from 5 in turn.
\(5 - 1 = 4\), \(5 - 2 = 3\), \(5 - 3 = 2\), \(5 - 4 = 1\).
Notice the pattern: when the number you take away goes up by 1, the answer goes down by 1.
16 Birds leave in two steps ★★★
First step: \(10 - 3 = 7\), so 7 birds are on the fence.
Second step: \(7 - 2 = 5\).
5 birds are still on the fence.
17 How many were lost? ★★★
Hop back from 9 until you reach 6: 8, 7, 6. That is 3 hops, so she lost 3 crayons.
\(9 - 3 = 6\). Ana lost 3 crayons.
Check: 9 minus 3 leaves 6, which matches the story.
18 Which leaves more? ★★★
Story A: \(8 - 3 = 5\) balloons left.
Story B: \(8 - 5 = 3\) balloons left.
Since 5 is more than 3, Story A leaves more balloons. The more you take away, the fewer are left.
19 Two facts from one picture ★★★
Take away one part to find the other.
\(7 - 4 = 3\) and \(7 - 3 = 4\).
20 Write your own story ★★★
Many stories work. Here is one: “There are 10 frogs on a lily pad. Six frogs jump into the water. Four frogs stay on the lily pad.”
A good story starts with 10, something goes away (6), and 4 are left.
21 Make 5 left ★★★
If the answer is 5, the first number is 5 more than the number you take away.
\(10 - 5 = 5\), \(9 - 4 = 5\), \(8 - 3 = 5\), \(7 - 2 = 5\), \(6 - 1 = 5\), \(5 - 0 = 5\).
Both numbers go down by 1 each time, and the answer stays 5.
Test yourself: quick challenge for Kindergarten
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