### Understanding Place Value & Addition and Subtraction

```Do Now
Solve the problems in the most efficient
way you can.
3 + 8 = ____
10 – 7 = ____
6 + 3 + 4 = ____
18 – 9 = ____
36 + 22 = ____
84 – 40 = ____
How to Become a More Efficient
Mathematician
• Master a number of different
• Choose the strategies that work best for
him/her and for the particular problem.
• Be flexible with strategies and choose ones
that are efficient.
• Check work with another strategy.
Full Model
Prompt: How can you use a picture to solve this problem?
Counting objects, counting on fingers, drawing a
picture
• Crossing off for subtraction
Taking away objects, taking away fingers, crossing
off in a picture
Counting On/Counting Back
Prompt: How can you use a number line and/or
counting to solve this problem?
• Adding and subtracting are like counting up and
back
back (“hop”/”jump” forward or back)
• Efficient strategy for solving single-digit addition
and subtraction problems
• Show your work with a number line or drawing
Examples: 3 + 8 = ___
8 – 2 = ___
Using Facts We Know (Fluency)
Prompt: How can you use facts you know to solve this
problem?
• Combinations of 10
6 + 3 + 4 = ____
I know 6 + 4 = 10 and 10 + 3 = 13
• Doubles and Near Doubles
8 + 7 = _____
I know 7 + 7 = 14, so one more is 15
• Fact Families – using what we know about addition to help with
subtraction
10 – 7 = ____
I know 7 + 3 = 10, so 10 – 7 = 3
Keep One/Break One
Prompt: How can you break a number into helpful
parts to solve this problem?
• Break one number into two parts so that you can
make a landmark number
(e.g., 10 or a multiple of 10)
9 + 7 = ____
18 – 9 = ____
36 + 8 = ____
Using Place Value
Prompt: How can you use what you know about 10s and 1s to
solve this problem?
36 + 22 = ____
• Base 10 Model: Using or drawing base 10 blocks
• Expanded Form: Breaking numbers into 10s &1s
30 + 6
20 + 2
50 + 8 = 58
• Keep One/Break One: Adding multiples of 10 first
36 + 20 = 56 56 + 2 = 58
```