Use four different number cards to complete the number sentences below.
And the number cards are five, 15, 25, 35, 45, and 55. The two number sentences are what plus what equals 60 and then another number sentence that’s exactly the same. In this question, we’re given a set of number cards. And these are going to give us the numbers that we need to complete the answer. We need to use four number cards to complete the number sentences. But notice that the question asked us to choose four different number cards. We can’t use one of the numbers more than once.
To begin with, let’s look at the number sentences that we need to complete. The first thing that we can notice is that they’re both exactly the same. So in other words, we need to complete the sentences in different ways, but ways that get the same answer. The next thing we notice is that the number sentences are additions. We need to add two numbers together. So we’re looking to use our number cards to make totals. And the total that we’re looking to make is 60. So really what the question is asking us is, can we use the number cards to find two different ways of making 60?
What do we know about the number 60? We know that it’s made up of six tens. So when we add our number cards together, we need to make a total that equals six tens. Is there anything that we can notice about the numbers on the number cards? They all end in the number five. They all have five ones. So it doesn’t matter which two numbers we choose. We’re always going to be adding five ones and five ones.
What does five ones plus five ones equal? Five ones plus five ones equal one ten. Remember, we need to make six tens. So by adding any two of the numbers on the number cards, we’re definitely going to make one ten, because the fives on the end will add up to make one of our six tens. The tens digits on our number cards are all different. Five has got zero tens. And then we have one ten in 15, two tens in 25, three tens in 35, four tens in 45, and five tens in 55. What do we need to make when we add our two tens digits together?
Well, you might say we need to make six tens because we have to make 60. But remember, whichever two numbers we add together, we’ll have already made one ten because five ones plus five ones equal one ten. We’ve got one of our six tens. We just need to make another five tens or 50. We’re looking for two number cards where their tens digits make a total of five tens.
How can we make five? Five plus zero, four plus one, three plus two, two plus three. Well, we’ll stop there because we’re starting to repeat ourselves and use the same digits again. Let’s get rid of the last calculation. Let’s start with the first one. Five plus zero equals five. So which two number cards show five tens and zero tens? 55 and five. 55 plus five equals 60. Remember, we could’ve written those number cards the other way around too and it would’ve still been correct.
Now let’s look at the next way of making five tens using our tens digits. Four plus one. 45 has four tens, and 15 has one ten. So 45 plus 15 must equal 60. Remember, the five ones on the end give us our extra ten we’re looking for. And remember, we could’ve written the addition the other way around and it would still be correct. We don’t need to make any more number sentences. But there is one more pair of number cards that we could’ve used in a pair to make 60.
We know three tens plus two tens equal five tens. And so we could’ve paired up 35 and 25. We needed to make six tens. But all our numbers had five ones in them. So we knew when we added two numbers together, we’d make one of those tens already. So all we had to do was look for pairs of numbers where the tens digits added up to five tens. The number cards we could’ve used to complete the number sentences are 55 and five in any order, 45 and 15 in any order, or 35 and 25 again in any order.