Sam is collecting cards. He wants to collect 100 cards altogether. Last week he collected 50 cards. This week he collects 30 cards. How many more cards does he need?
There are a lot of words to get through with this problem. So, let’s read through it again slowly and underline any pieces of key information that might be important to us. Firstly, we’re told that Sam is collecting cards. And then, we’re told that he wants to collect 100 cards altogether. The 100 cards is important. This is the target that Sam has. He wants to be able to collect 100 cards.
And then, we’re told two pieces of information about the cards that Sam has collected already. Last week, he collected 50 cards. 50 cards is important. And this week, he collects 30 cards. And the question asks us how many more cards does he need. Let’s draw a bar model to help us understand the question.
Here is the 100 cards that Sam wants to collect altogether. This bar represents the 50 cards that Sam collected last week. And here are the 30 cards that he’s collected this week. And this bar represents the amount we need to find out. 50 plus 30 plus what is equal to 100?
First, we can add together the cards that Sam has already. We know that five plus three equals eight. And so, if we know this fact, we also know that five 10s plus three 10s equals eight 10s. 50 plus 30 equals 80. So, Sam has collected 80 cards already. How many more cards does he need to collect to get to 100? What do we add to 80 to get to 100?
Eight 10s plus two 10s equals 10 10s. 80 plus 20 equals 100. We know Sam collected 50 cards last week and 30 cards this week, so we added these two amounts together to find the total number of cards that Sam has collected already. We know Sam has a target of wanting to collect 100 cards. So, we thought about what number we needed to add to 80 to get to 100.
Another way we could’ve found the same answer is to start with 100 and take away 80. This would leave behind 20. Sam needs to collect 20 more cards until he’s collected 100 cards altogether.