Lesson 2.2 · Word Problems
Put-together and take-apart problems
Some stories don't have anything coming or going. Two kinds of things are just sitting together, like red and blue blocks in one box. These are put-together and take-apart problems.
Put together
When you have two parts, you can put them together to find the total.
"There are 5 red blocks and 4 blue blocks. How many blocks in all?"
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Nothing moved. We just count both parts together: blocks.
Part + part = total
Two parts make a whole group, called the total.
If you know both parts, add to find the total.
If you know the total and one part, subtract to find the other part.
Take apart
Sometimes you know the total and one part. You need the other part.
"There are 9 blocks. 5 are red. The rest are blue. How many are blue?"
The total is 9 and one part is 5. So . There are 4 blue blocks.
You can also think . The missing part is 4.
Worked example: Pets in a class
A class has 7 dogs and 6 cats as pets. How many pets in all?
We know both parts, so add: . That is a near double: , and one more is . There are 13 pets.
Worked example: Socks in a drawer
There are 15 socks in a drawer. 8 are white. The rest are black. How many socks are black?
We know the total (15) and one part (8). Subtract: . Check: . ✓ There are 7 black socks.
Worked example: Many ways to split
Zoe has 6 flowers. Some are pink and some are yellow. What could the parts be?
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Lots of answers work! , , , and all make 6. Every way to split 6 into two parts is a take-apart story.
Common mistake
Look for the word total or in all. If the story tells you the total, don't add it to a part. Subtract the part you know from the total.
Practice
There are 3 boys and 5 girls at the park. How many kids are at the park?
Type a number.
There are 10 fish in a tank. 4 are orange. The rest are gray. How many fish are gray?
Type a number.
A plate has 7 green grapes and 7 purple grapes. How many grapes are on the plate?
Type a number.
Nora has 12 pencils. 9 are sharp. The rest are not. Which number sentence finds how many are not sharp?
A farmer has 9 cows and 8 pigs. How many animals does the farmer have?
Type a number.
There are 16 cars in a lot. 7 are red. The rest are blue. How many cars are blue?
Type a number.
Eli has 10 toy cars. Some are in his room and some are outside. The same number are in each place. How many are in his room?
Type a number.