Unknown Addition and Subtraction Equations

1. Unknown Addition and Subtraction Equations Objectives: I can determine the unknown whole number in addition and subtraction problems.

2. Set up your notes Guess and Check Related Equation for Missing Addend Unknown Equations (vocabulary goes here too) Related Equation for Missing Minuend Related Equation for Missing Subtrahend

3. Vocabulary Review • Addend – a number that is added to another number. • Subtrahend – a number that is subtracted from another number. E.g. In 15 – 6, 6 is the subtrahend. • Minuend – a number from which the subtrahend is subtract from. E.g. In 15 – 6, 15 is the minuend. • Sum – the answer to an addition problem. • Difference – the answer to a subtraction problem.

4. Unknown Equations • We are used to seeing typical addition and subtraction equations, such as: 346 + 432 = Or 42 – 13 = In these equations, the sum or difference is missing. Sometimes, though, it is the addend, minuend, or subtrahend that is missing, and it is these that we need to figure out.

5. Unknown Equations Represented • The missing number in these equations are represented in a few different ways. • Empty box: 12 + = 24 • Questions mark: 24 - ? = 12 • Variable: x – 12 = 12 0

6. Guess and Check Method • We can attempt to solve these problems using the guess and check method: • 12 + = 24 First, I am going to just guess that the missing number is 10 since the number goes from 12 to 24. 12 + 10 = 22 After guessing 10, I realize it would be wrong since 12 + 10 is 22, not 24. I’m just 2 off, so I’m going to guess that the missing number is 12. 12 + 12 = 24 0

7. Related Number Sentence • The problem with guess and check is it is difficult to use when we deal with larger numbers, and especially numbers that require us to regroup. This is where we can use our knowledge of related number sentences to help us. • ? + 42 = 258 This would be way too difficult to guess and check. I can create a related subtraction problem to help me though. A rule of thumb to remember is this: The sum of an addition problem is the minuend of a subtraction problem. The addend simply becomes the subtrahend. So… 258 - 42 = ? From here, we could use all the cool subtraction strategies we learned throughout the year. Let’s use a number line. We’ll check our work after. 258

8. Practice Solve. 254 + ? = 365

9. Related Number Sentence • It can get confusing when you’re trying to turn a subtraction problem into a related number sentence. Sometimes it’s a good idea to turn it into an addition problem, but sometimes it’s better to turn it into another subtraction problem. • ? - 42 = 258 Remember what we said about the minuend? The minuend is the sum of an addition problem. Here we do not know that minuend (sum), but we do have the other two numbers that would make the addends. So… 258 + 42 = ? When we’re missing the minuend it is easy to turn it into an addition problem. But what if we’re missing the subtrahend? • 435 - ? = 27 If we tried to turn this into a related addition problem, we’d end up with: 27 + ? = 435 That got us nowhere. In this case, it is easier to just take the difference, and swap it with the subtrahend, like so: 435 – 27 = ?

10. Think of it Like This

11. Related Number Sentence Solve. • ? – 35 = 56 • 74 - ? = 23

12. Word Problems • Charlotte had 345 cupcakes. She needed to buy a few more so that she should give all 635 students at Irwin a cupcake. How many cupcakes did she need to buy? 2. A local store had 633 song birds for sale. Jimmy, seeing a sale sign on a tree by the brook, went to the store and bought a bunch of song birds. A little later, a dear lady heard whispering in the wind about the sale, and bought the remaining 456 song birds. How many song birds did Jimmy buy?