Let’s Learn!
What is an addition table, and how can we use its patterns to add?
Goal:
Goal:
Think About It!
Goal: Identify patterns using an addition table to help solve addition equations.
Zoe learned that the calories in food give us energy. She wants to make sure her healthy snacks have enough calories. Zoe can count the calories in her snacks by counting the calories in each ingredient: cheese and whole wheat crackers. For one snack, the cheese has 9 calories, and the cracker has 10 calories. We can add the number of calories to see how many calories the snacks have in all!
\({9+10=?}\)
We will add using an addition table. An addition table is a table that is used to help find the sums of addition equations. You can also call an addition table an addition chart. To use the table, find the first addend in the first column. Then find the second addend in the first row. The sum is where the column and the row meet!
Click on the addition table to see the sum of 5 + 4!
\({5+4=?}\)
5 is the first addend. We find it in the first column. 4 is the second addend. We find it in the first row.
Remember, the order does not matter when we add. If we add 4 + 5 by finding 4 in the first column and 5 in the first row, we will still, get 9!
\({5+4=9}\)
A addition chart the first row starts at the 4 and the first column starts at 5 and they meet at the number 9
\({4+5=9}\)
A addition chart the first row starts at the 5 and the first column starts at 4 and they meet at the number 9
We can also use patterns in an addition table to help us add. A pattern is a set of numbers that follow the same rule. When we can see patterns in the table, we can find a sum quickly and easily. We will look for patterns that will help us predict if a sum will be even or odd, what a sum will be when we add 0, or what a sum will be when we add 10.
When you add two even numbers, will the sum be even or odd?
\({4+4=?}\) \({8+2=?}\)
A addition chart showing solving \({4+4 = 8}\) by going to the 4 in the first column and the 4 in the first row and joining them at 8.
Using the same chart solving \({8+2 = 10}\) by going to the 8 in the first column and then 2 in the first row and joining them at 10
\({4+4=8}\) \({8+2=10}\)
even \({+}\) even \({=}\) even
What happens when we add two even numbers? We will get an even sum! We can see this in the addition table. Look at the first addition equation. Both 4's are even numbers. 4 and 4 meet at 8. 8 is an even number! Now, look at the second addition equation. 8 and 2 are both even numbers. They meet at 10. 10 is an even number!
When you add two odd numbers, will the sum be even or odd?
\({1+3=?}\) \({3+7=?}\)
A addition chart showing solving \({1+3 = 4}\) by going to the 1 in the first column and the 3 in the first row and joining them at 4.
Using the same chart solving \({3+7 = 10}\) by going to the 3 in the first column and then 7 in the first row and joining them at 10
\({1+3=4}\) \({3+7=10}\)
odd \({+}\) odd \({=}\) even
What happens when we add two odd numbers? We will get an even sum! We can see this in the addition table. Look at the first addition equation. 1 and 3 are both odd numbers. They meet at 4. 4 is an even number! Now look at the second addition equation. 3 and 7 are both odd numbers. 3 and 7 meet at 10. 10 is an even number!
When you add an even number and an odd number, will the sum be even or odd?
\({4+3 = ?}\) \({7+2=?}\)
A addition chart showing solving \({4+3 = 7}\) by going to the 4 in the first column and the 3 in the first row and joining them at 7.
Using the same chart solving \({7+2 = 9}\) by going to the 7 in the first column and then 2 in the first row and joining them at 9
\({4+3=7}\) \({7+2=9}\)
even \({+}\) odd \({=}\) odd
What happens when we add an even and an odd number? We will get an odd sum! The order of the even and odd numbers does not matter. We can see this in the addition table. Look at the first addition equation. 4 is an even number, and 3 is an odd number. 4 and 3 meet at 7. 7 is an odd number! Now look at the second addition equation. 7 is an odd number, and 2 is an even number. They meet at 9. 9 is an odd number!
What is the sum when you add 0?
\({6+0 = ?}\) \({0+7=?}\)
A addition chart showing solving \({6+0 = 6}\) by going to the 6 in the first column and the 0 in the first row and joining them at 6.
Using the same chart solving \({7+0 = 7}\) by going to the 7 in the first column and then 0 in the first row and joining them at 7
\({6+0=6}\) \({0+7=7}\)
number \({+ }\) 0 \({=}\) number
What happens when we add 0 to a number? We will get the addend that is not 0 as the sum! The order of the non-zero addend and the 0 does not matter. We can see this in the addition table. Look at the first addition equation. 6 and 0 meet at 6. 6 is the non-zero addend! Now look at the second addition equation. 0 and 7 meet at 7. 7 is the non-zero addend!
What is the sum when you add 10 to a one-digit number?
\({3+10 = ?}\) \({10+4=?}\)
A addition chart showing solving \({3+10 = 13}\) by going to the 3 in the first column and the 10 in the first row and joining them at 13.
Using the same chart solving \({10+4 = 14}\) by going to the 10 in the first column and then 4 in the first row and joining them at 14
\({3+10 = 13}\) \({10+4=14}\)
number
\({+}\) 10
\({=}\)
1 in the tens place and number in the ones
place
What happens when we add 10 to a one-digit number? We will get a sum that has the one-digit number in the ones place and a 1 in the tens place! The order of the 10 and the other addend does not matter. We can see this in the addition table. Look at the first addition equation. 3 and 10 meet at 13. 13 has a 3 in the ones place and a 1 in the tens place! Now look at the second addition equation. 4 and 10 meet at 14. 14 has a 4 in the ones place and a 1 in the tens place!
What is the sum when you add 10 to 10?
\({10 + 10 = ?}\)
A addition chart showing solving \({10 + 10 = 20}\) by going to the 10 in the first column and the 10 in the first row and joining them at 20.
This changes when we add 10 to 10. 10 is a two-digit number and has a 0 in the ones place. Both 10s have a 1 in the tens place. When we add them, their sum will have a 0 in the ones place and a 2 in the tens place.
We can combine patterns to make it even easier to find a sum! We can look at the addends and decide if a sum will be even or odd. Then we can look for the other patterns we learned! If we want to add 8 + 0, we know that 8 and 0 are both even. That means their sum will be even. The pattern we learned about adding 0 tells us that 8 + 0 = 8. The addition table shows that this is true!
A addition chart showing solving \({8+0 = 8}\) by going to the 8 in the first column and the 0 in the first row and joining them at 8.
\({8+0=8}\)
even \({+}\) even \({=}\) even
number \({+}\) 0 \({=}\) number
Let’s use the patterns we learned to count the calories in Zoe’s snacks!
Look for Patterns
Cheese: 9 calories
Cracker: 10 calories
\({9+10=?}\)
Look at the addition equation, \({9 + 10 = ?}\), above. Do you notice any patterns? Look at the addends. Are they even or odd? Do you see a 0 or a 10?
Click the Show Me button to see!
9 is an odd number, and 10 is an even number. 10 is one of the addends. The other addend, 9, is a one-digit number.
Even and Odd
\({9+10=?}\)
odd \({+}\) even \({= ?}\)?
We found that 9 is an odd number and 10 is an even number. Let’s start with what we know about adding an odd number and an even number!
Question
Will the sum of
\({9+10}\)
be an even number or an odd number?
odd
\({+}\)
even
\({=}\)
odd
The sum of 9 and 10 will be an odd
number.
10 or 0
\({9+10=0}\)
odd \({+}\) even \({=}\) odd
number \({+}\) 10 \({=}\) ?
We know that the sum will be an odd number. We also found that one of the addends is a 10 and the other addend is a one-digit number. If we did not find a 10 or a 0, we would skip this step and move on to the addition table.
Question
What is the sum of a one-digit number and 10?
The sum will have the one-digit number in the ones place and a 1 in the tens place. Our sum will have a 9 in the ones place and a 1 in the tens place.
Use the Table
A addition chart showing solving \({9+10 = ?}\) by going to the 9 in the first column and the 10. Where do they join.
\({9+10=19}\)
odd \({+}\) even \({=}\) odd
number \({+}\) 10 \({=}\) ?
We know the sum is an odd number. it should have a 9 in the ones place and a 1 in the tens place. That is the number 19! Let's use the addition table to check our predictions. Click the Show Me button to see!
A addition chart showing solving \({9+10 = 19}\) by going to the 9 in the first column and the 10. They join at 19
\({9 + 10 = 19}\)
Zoe’s snack has 19 calories!
We can use addition patterns and an addition table to help us find sums quickly and easily!