In this addition table, Sophia colored all the even sums blue and all the odd sums green. Look for patterns in the table to decide if the following sums are even or odd. Four plus three. Five plus six. Nine plus seven. 17 plus eight. And 22 plus 28.
The white column and the white row in this addition table provide us with two numbers that we add together. How the table works is that we can choose one number from the left-hand column. For example, we could choose the number three. And one number from the top row. Let’s choose the number two. And we can work our way across and down the grid until the column and the row meet up. And we can see that they meet at this square here. The square gives us the answer to the addition. Three plus two equals five. Now, as [Sophia] has completed the table, we’re told that she’s colored all the even sums blue and all the odd sums green. Five is an odd number. So this is colored green.
Now, we’re given five different additions. And we’re told to look for patterns in the table to decide if the sums are going to be even or odd. There are lots of patterns to see in the table. Some of them are numerical. For example, if we count the numbers across each row, we can see that they increase by one each time. And the same is true with the columns. Another pattern we might spot is if we look diagonally through the grid, we can see squares with the same number in them. But these patterns aren’t really going to help us to answer the question. We need to look for patterns in even and odd numbers.
Now, if we look at the five different calculations that we need to think about, only one of them appears in the grid. We can find the answer to four plus three using the numbers in the grid. But our grid isn’t large enough to show the six in five plus six. Or any of the numbers in nine plus 7, 17 plus eight, or even 22 plus 28. So how can we use these simple additions? All we’re using is the digits one to five to decide whether these larger sums are even or odd.
Well, to start with, let’s use the grid to show the one calculation that is there. Four plus three. First of all, we find the row that represents four and the column that represents three. Now, if we move down the column and across the row, we can use our fingers to do this. We will eventually get to the square that represents the sum. Here it is. Four plus three is seven. But we don’t need to worry about the number seven really. We’re being asked to decide if the sum is even or odd. So let’s just look at the color of the square. It’s a green square. And so we know that the sum must be odd.
Now let’s concentrate on our second addition, five plus six. Now the answer to this isn’t going to be in the grid. But we can use the grid to help us. What do we know about the numbers five and six? Firstly, we know that five is an odd number. So let’s use the same color coding system that Sophia uses. And we’ll write five in green. Six is an even number. So let’s write six in blue. Now, we can use this information to help us find the answer. What happens if we add together an odd number to an even number. Let’s write all the odd numbers in green to help us see them. One, three, five. And let’s write all the even numbers in blue, two, four.
Now we can use the table to help us to spot what happens if we add an odd and an even number together. Let’s pick any odd number to start with. Why don’t we have five? Because that’s the number in our question. And now, let’s choose an even number to add to it. We don’t have six in our table. But we can pick another even number. Let’s pick two. What do we get if we add an odd and an even number together? The square that we arrive at is green. An odd and an even number make an odd answer or an odd sum.
Our next calculation is nine plus seven. Let’s use the same method to help. Both nine and seven are odd numbers. So let’s choose two odd numbers to add together on our grid. We could make things easy for ourselves and choose one and one. We can see that the sum of these numbers is a blue square. And this is the same for any two odd numbers we choose to add together. An odd number plus another odd number equals an even sum. It always does. It doesn’t matter if it’s nine plus seven or one plus one.
Our fourth calculation is 17 plus eight. 17 ends with the digit seven. So we know it’s an odd number. And we know that eight is an even number. Now, if you remember, we’ve already tried adding an odd number and an even number together already. We found the answer to five plus two when we wanted to work out whether five plus six was odd or even. And we said that five plus six was odd. So we know 17 plus eight, which is another odd number plus an even number, will also be odd.
Our final calculation is 22 plus 28. 22 has a two in the ones place. So we know that’s an even number. And 28 has an eight in the ones place. This is also an even number. What happens if we add two even numbers together? Let’s pick two even numbers in our grid and see which color the sum is. Two plus four equals one of Sophia’s blue squares. The sum is even. And so we know the sum of any two even numbers is also even. It doesn’t matter if we add two and four or 22 and 28. The answer will be even. We use Sophia’s addition table and the pattern inside it to help us understand what happens when we add together odd and even numbers in different ways.
The sum of four plus three will be odd. Five plus six will also be odd. Nine plus seven will be even. 17 plus eight will be odd. And the sum of 22 and 28 will be even.