Know the strategies:
Add up from 8 until you get to 14:
8+2=10
10+4=14
so 8+6=14
and 14-8=6
Know what facts each strategy is an efficient choice for.
Sample questions:
- Describe or list all of the facts for which using doubles to add is an efficient strategy
using doubles is efficient for the facts that are close to being doubles: the addends are only 1 or 2 apart. These are the facts: 1+2, 1+3, 2+3, 2+4, 3+4, 3+5, 4+5, 4+6, 5+6, 5+7, 6+7, 6+8, 7+8, 7+9, 8+9
- Write 5 math facts for which using 10 to add is an efficient strategy
8+5, 9+6, 9+7, 8+6, 8+4
- Identify two efficient strategies you could use to solve 12-8, and show how to use them to find the sum
The only appropriate strategies are:
- build up through 10 to subtract (add 2 to 8 to get 10, and add 2 to 10 to get 12, so the difference is 2+2=4)
- count up to subtract (say "8". Put up fingers as you count on, stop when you get to 12: "9, 10, 11, 12". The number of fingers up (4) is the difference.
- think addition: 12-8 means 8+__=12, and 8+4=12, so 12-8=4.
- Explain the difference between counting back to subtract and counting up to subtract. Which strategy is more efficient for subtracting 12-8?
- With counting back to subtract, you are starting with the minuend and counting back by the subtrahend, and the number you end at is the difference.
- With count up to subtract, you start with the subtrahend and count up until you get to the minuend. The number of counts is the difference
- The difference between 8 and 12 is less than 8, so counting up to subtract is more efficient.
Know how other facts can be derived from memorized facts including partners of 10, doubles and decompositions of numbers less than 10.
Sample questions:
- How can knowing partners that make 10 help you with other addition facts? Explain and give a specific example.
- If you know partners that make 10, then if one of your addends is just a little bit less than 10, you can add on to make 10 and then add on the rest. Knowing how much you add on to make 10 tells you how much to add the first time.
- Example: 8+5=? If you know 8+2=10, then you can start with 8+2=10 and then add on the rest of the 5 to get 13.
- How does knowing decompositions of numbers less than 10 help you with using the strategy use 10 to add. Explain and give a specific example.
- When you use 10 to add, you are taking one of the addends, and adding onto it part of the other addend to make 10. You have to break up the other addend into two parts, which is making a decomposition of the numeber.
- Example: 8+5=? 8+2=10, so you need to decompose 5 into 2+3 and first add on the 2: 8+2=10 and then add on the 3: 10+3=13
- How can knowing partners that make 10 help you with subtraction facts where the minuend is greater than 10? Explain and give a specific example.
- If the minuend is greater than 10, and the subtrahend is just a little less than 10, then you can figure out how much bigger 10 is than the subtrahend and add that on to the difference of the minuend and 10.
- Example: 14-9=? If you know that 9+1=10 then you know that 14-9 is just one more than 14-10, so you can add 4+1=5 for the difference
- How can knowing doubles help you with other addition facts? Explain and give a specific example.
- If there is another fact that is close to being a double, like doubles +1 where one addend is 1 bigger than the other, then you can figure out the double of the smaller number and add 1 because the sum will be 1 more than the double.
- Example: 7+8=? If you know 7+7=14, and you notice that 8 is one more than 7, then you know 7+8 is one more than 14, so 7+8=15
Sample questions (make diagrams and write number sentences for):
It would be fine to also have ?-9=3, but it's not necessary.
It doesn't matter whether you have ? or _ in your number sentences, but you should have both a subtraction and a missing number addition problem for this one.