B. Number · Adding and SubtractingMath Rules: Order, Zero and Adding Three Numbers
B2.1About 25 minutes
Learning goals- I can explain that I can add numbers in any order and get the same sum.
- I can explain what happens when I add 0 or subtract 0.
- I know that a number minus itself is 0.
- I can choose which numbers to add first to make adding easier.
Words to know
order
Which number comes first and which comes next.
zero (0)
None, nothing at all.
property
A math rule that is always true.
Rules that are always true
Math has some rules that always work. Knowing them is like having secret shortcuts! Today we learn four of them.
Rule 1: You can add in any order
Look at this domino. It has 2 dots on one side and 6 on the other.
2 + 6 = 8 and 6 + 2 = 8.
When you add, the order does not change the sum. So if you know one fact, you know its turn-around fact for free!
Start with the bigger number
For 2 + 6, start with the bigger number. Say 6 in your head and count on 2: 7, 8. That's much faster than counting on 6!
Rule 2: Subtracting is different
Order does matter when you subtract. 6 − 2 means start with 6 and take away 2. That gives 4.
2 − 6 would mean start with 2 cookies and eat 6. You can't! So in Grade 1, always start a subtraction with the bigger number, the whole.
Rule 3: Zero keeps it the same
If you have 7 stickers and get 0 more, you still have 7.
- 7 + 0 = 7
- 0 + 7 = 7
- 7 − 0 = 7 (take nothing away, nothing changes)
And if you take away all of them:
⭐⭐⭐⭐⭐⭐⭐
7 stars. Add 0 stars: still 7. Take away 0 stars: still 7. Take away all 7 stars: 0 left.| Fact | What happens | Rule |
|---|
| 5 + 0 = 5 | nothing added | Adding 0 keeps the number the same. |
| 5 − 0 = 5 | nothing taken away | Subtracting 0 keeps the number the same. |
| 5 − 5 = 0 | all taken away | A number minus itself is 0. |
| 3 + 5 = 5 + 3 | order changed | Adding in any order gives the same sum. |
Rule 4: Adding three numbers
When you add three numbers, you can add any two first. Look for a pair that is easy, like partners of 10 or a double.
Worked exampleExample 1: Find the partners of 10
Ella picks 3 red maple leaves, 4 yellow ones and 6 orange ones. How many leaves in all? 3 + 4 + 6
- Look for two numbers that make 10. 4 and 6 are partners of 10!
- Add them first: 4 + 6 = 10.
- Now add the last number: 10 + 3 = 13.
Ella has 13 leaves. 3 + 4 + 6 = 13.
Worked exampleExample 2: Look for a double
- 5 and 5 is a double. 5 + 5 = 10.
- Then add 2: 10 + 2 = 12.
Worked exampleExample 3: Use a rule to check
Noah worked out 8 + 1 = 9. How can he check it another way?
- Turn it around: 1 + 8. Start at 8 and count on 1: 9.
- Or use the fact family: 9 − 1 should be 8. It is!
Both checks give the same answer, so 8 + 1 = 9 is correct.
Just for funRiddle: I am a number. Add me to any number, and nothing changes. Who am I?
Zero! The sneakiest number of all.
Hands-on activityDomino turn-arounds
You need: dominoes, or draw 6 dominoes on paper (2 ends with dots).
- Pick a domino. Say the adding fact, like "3 + 5 = 8".
- Turn it around and say the turn-around fact: "5 + 3 = 8".
- Find a domino with a blank side. What happens when you add 0?
- Find a double (both sides the same). Is the turn-around fact any different?
Math talk: "Why do you think turning the domino doesn't change the total?"
Your turn
14 + 5 = 9. What is 5 + 4?
9. Order doesn't change the sum.
52 + 7 + 8. Which two numbers make 10? What is the sum?
2 and 8 make 10. 10 + 7 = 17.
61 + 6 + 1. What is the sum?
1 + 1 = 2, then 2 + 6 = 8. (Or 6 + 1 + 1: 7, 8.)
7True or false: 3 + 6 = 6 + 3
More practice: warm-up
0. You took them all away.
3You know 6 + 3 = 9. What is 3 + 6?
9. The order doesn't change the sum.
5⭐⭐⭐⭐⭐
Take away 0 stars. How many stars are left?
5. Taking away 0 changes nothing. 5 − 0 = 5.
More practice: on your own
1True or false: 7 − 2 = 2 − 7. How do you know?
False. Order matters when you subtract. 7 − 2 = 5, but you can't start with 2 and take away 7.
21 + 9 + 4 = ? Which two numbers make 10?
1 and 9 make 10. Then 10 + 4 = 14.
33 + 5 + 3 = ? Look for a double.
3 + 3 = 6 is a double. Then 6 + 5 = 11.
4Fill in the blank: 8 + 2 = 2 + __
8. You can add in any order. Both sides make 10.
52 + 9 = ? Which number should you start with when you count on?
Start with the bigger number, 9, and count on 2: 10, 11. The sum is 11.
Challenge
1Owen has 4 red mittens, 5 blue mittens and 6 green mittens. How many mittens in all? Explain how you added.
15 mittens. 4 and 6 are partners of 10, so add them first: 4 + 6 = 10. Then 10 + 5 = 15.
2Find the mistake. Zoe says 9 − 0 = 0. Is she right?
No. Taking away 0 takes away nothing, so 9 − 0 = 9. It is 9 − 9 that equals 0.
3Use the math rules to find each missing number: __ + 5 = 5 + 7 and 6 − __ = 6
7 and 0. 7 + 5 = 5 + 7 because you can add in any order. 6 − 0 = 6 because taking away 0 keeps it the same.
Quiz
1. Which is the same as 7 + 2?
4. For 7 + 5 + 3, which two numbers should you add first to make 10?
6. For 5 + 8 + 5, which two numbers should you add first to make 10?
Big idea: These properties (the order or commutative property, the zero property, and grouping when adding three numbers) are tools children use to make calculations easier and to check their work. They do not need to know the formal names.
Common mistakes:
- Thinking subtraction can also be turned around. Show that 6 − 2 and 2 − 6 are different stories with real objects.
- Thinking adding 0 makes the number 0 (confusing 5 + 0 with 5 − 5). Act it out: "You have 5 grapes and I give you none. How many do you have?"
- Always adding left to right. With three numbers, encourage looking for 10s and doubles first.
How to help: When your child adds, ask "Which number would you start with? Why?" Celebrate when they choose the bigger number or find a 10.