William is making cards. He sticks six decorations onto each card and he has 24 decorations. Which of these models will help you find how many cards he can make? How many cards can he make?
We’re given four different models to look at. And one of them is a way of modeling the problem that we’ve been asked. We have what looks like a set of counters organized in groups. We have a number line showing jumps of the same amount. We have a set of squares that have been laid out in an array. And then, finally, we have another number line showing jumps of a different amount this time.
To work out which one of these models fits the word problem, we need to look more closely at the word problem itself and try to understand what it’s asking us. We’re told about a boy, William, who’s making cards. We’re also told that he sticks six decorations onto each card. We’re also told that he has 24 decorations. And we need to calculate how many cards he can make.
So, William starts off with 24 decorations. And to find the number of cards that he makes, we need to divide that number of decorations by six, in other words, to split it up into groups of six. These are the six decorations that he sticks onto each card. And the number of sixes that there are in 24 will be the number of cards that William can make. So, now, we can ask ourselves a slightly different question. Which of these models shows how to work out the answer to 24 divided by six?
If we look at the first model, we can see a number of counters that have been split into groups of six. This is exactly the sort of thing that William’s doing with his decorations. Let’s count in sixes to see how many counters there are in this first model, six, 12, 18. We’ve got three groups of six, which make 18. This first model shows 18 divided by six, doesn’t show 24 divided by six. So, it doesn’t help us with the word problem.
If we look at the squares underneath, we can see that they have been arranged into two rows. And there are 12 squares in each row. That makes 24 squares altogether. So, I suppose these could represent William’s 24 decorations that he starts off with. But this model doesn’t show us how to divide 24 by six. I guess you could say it shows us how to divide 24 by two though, two rows of 12.
What about our number line models? In the top number line, we start at zero, and we skip count in sixes. And we stop when we get to 24. This shows us how many groups of six there are in 24. So, this is the model that will help us find how many cards that William can make. We just need to count in sixes until we get to 24. There’s one lot of six in six. Two sixes are 12. Three sixes are 18. And four sixes are 24. So, William can share his 24 decorations into four groups of six.
And If we just check that we don’t need to use our last number line, we can see that we’re counting in 24s. And it shows us six jumps of 24, all the way up to 144. So, our last number line shows us the answer to 24 times six, not 24 divided by six. So, the model we can use to help us find how many cards William can make is this one, where we skip count in sixes until we get to 24. This shows us how many sixes there are in 24. Now, we can answer the final question.
How many cards can he make?
Williams starts off with 24 decorations, and he divides those 24 decorations into groups of six on each card. We know from the model in the first part of the question that there are four groups of six in 24. So, William can make four cards. So, we used the number line, where we counted in sixes, to find out that William can make four cards.
Here’s a little challenge to end with. We did say that the squares in the bottom left of your screen showed 24 in two rows of 12. And your challenge is this. Draw three straight lines on this model to help you solve the problem. Because you could use this model to help you solve the problem, but not as it looks at the moment. You have to draw three lines. See how you get on.