#### Addition and Subtraction

How to use:

- Watch and ask: What do you notice? What do you wonder?
- Ask: What is addition? What is subtraction? How are they the same? How are they different?

#### Adding 2 Digit Numbers (42 + 35)

How to use:

- Watch and ask: What do you notice? What do you wonder?
- Watch the visual on the bottom, then replay and watch the equation on the top. Ask: How do they show the same thing?
- Ask: How does the number bond work in this problem?
- Watch the second video (with notes) and ask: How could you show your work on a problem like 25 + 32?

#### Make 10 by Filling the Tens Frame

How to use: Ask: What do you notice? What do you wonder? Why did it take 3 from the 5? Could you use this strategy for 8+7? How do the number bonds work? How can you show make 10 with an equation?

How to use: Ask: What do you notice? What do you wonder? Why did it take 2 from the 6? Could you use this strategy for 9+5?

#### Parts and Whole with 5 plus 2

How to use: Ask: What do you notice? What do you wonder? What would this look like with other numbers, like 3 and 6? Can you draw it or act it out with cubes?

#### Parts and Whole with Number Bonds and Equations

How to use: Ask: What do you notice? What do you wonder? What would this look like with the parts 5 and 3? Can you draw it?

#### Count On and Count Back (No Numbers or Sound)

#### Count On and Count Back (Regular Version)

How to use:

- Watch and ask: What do you notice? What do you wonder?
- No Numbers or Sound Version: What problem is he solving? How do you know? What equation would match?
- Regular Version: How does count on/back work? What are the parts and whole and how do you know? What other problems could you solve using one of these strategies?

#### Related Addition and Subtraction

How to use:

- Watch and ask: What do you notice? What do you wonder? What is the same? Different
- Ask: What is addition? What is subtraction? How are they the same? How are they different?

#### Story Problem Equations: Missing Part

#### Open Number Line: Solve 52-28 Version A

#### Make 10

How to use:

- Watch and ask: What do you notice? What do you wonder? and What is the same? What is different?
- Questions and Big Ideas:
**What is the same?**They both start with 8 and 6. The total stays the same both times: 14**What is different?**The second one takes 2 from the 6 and puts it with the 8 to make 10. Then there is 4 left.**Which one is easier to add, 8+6 or 10+4?**10+4 could be easier if you know how to break up the 6 and put the 2 with the 8, because it is easier to add with 10 than with 8.**What would 9 + 5 look like in this machine? What about…**- 9+4
- 9+8
- 8+7
- etc

**Would this (new strategy) work for 19+7?**

#### Make 10 with 3 Addends

#### Make 10 Mountain

How to use:

- Watch and ask: What do you notice? What do you wonder?
- Questions and Big Ideas:
**Make a prediction about where you think the balls will land – what number will they fill up to?****Why did the mountain break up the 7 that way?**The mountain broke the 7 into 1 and 6 because there was one more space on the left side of the mountain, and 9 plus 1 makes 10. Then, there were 6 left from the 7, and that filled up the other side to 16.**Where would 9 and 5 fill up to on the mountain? How do you know?**It would fill up to 14 because you could take 1 from the 5 and put it with the 9 to make 10, then add the 4 left over from the 5 to make 14.**Where would _____ land? How do you know?**- 9+4
- 9+8
- 8+7
- etc

**What if the tip of the mountain went to 20, where would 19+7 land?**

#### Equal or Not?

#### Difference Between 13 and 16, with Equations

Download the PDF printout here: Double Number Path Printout

#### Doubles, Doubles Minus 1

How to use: Ask: What do you notice? What do you wonder? Can you figure out what 8+9 is, based on what you noticed with 8+8 and 8+7? What other equations would this work for?

#### What Equations Match?

How to use: Watch all of the options (on the left), then pause and ask: What matches? How do you know? Then ask for other equations that could match these pictures.

#### Many Ways to See a Number

#### 4+3 using Count All and Count On

How to use:

- Watch and ask: What do you notice? What do you wonder? and What is the same? What is different?
- Questions and Big Ideas:
**What is the same?**Both are adding the numbers (parts) 4 and 3. Both are counting up, the numbers are getting bigger. Both get the same total/whole: 7.**What is different?**When you count all, you say every number as you count, 1, 2, 3, 4, 5, 6, 7, but when you count on, you start at the part 4 and count on three more times: FOUR, 5, 6, 7. Counting on is faster because you don’t have to count all of the numbers.

#### Compensation with 37+29

#### 2 Digit Addition (with Commutative, Associative Properties)

#### 2 Digit Addition with Regrouping (and Commutative, Associative Properties)

#### Decomposing to Subtract 21-7

#### Decomposing to Subtract 35-8

#### Commutative Property

How to use:

- Watch and ask: What do you notice? What do you wonder?
- Questions and Big Ideas:
**What is the same about 3+5 and 5+3?**They have the same parts, 3 and 5. When you combine them they make the same whole/total: 8.**What is different about 3+5 and 5+3?**The parts are switched, one starts with the part 3 and then adds the part 5, and the other starts with the part 5 and then adds the part 3.**What happens to the whole/total when we switch the parts 3 and 5?**The whole stays the same. 3 plus 5 is 8, and so is 5 plus 3.**Does this work for other numbers? How do you know?**Yes, because I could start with 4 and add 2 and it makes 6, or I could start with 2 and add 4 and it also makes 6.**Does this work if you are combining 3 parts? How do you know?**Yes, because I could start with 1 and add 4 and 6 to make 11, or I could start with 4 and add 6 and 1 to make 11, etc.**Which way is easier or more efficient for you to add: 3+5 or 5+3?**(Many possible answers, including the following)- It is easier for me to start at 5 and add 3 more because I only have to count on 3 times.
- Both are easy because I just know that when you combine 3 and 5 it makes 8

**Does this work with subtraction? How do you know?**(Both yes and no could be correct with the right rationale)- (This answer assumes they haven’t been exposed to negative numbers yet) No, because if I start with 7 and take away 3 it makes 4, but if I start with 3 and take away 7 I run out of things to take away. 3 is smaller than 7 so I can’t take 7 away from 3.
- Yes, because if you start with 7 and take away 3 it makes 4, and you could also start with 7 and take away 4, and that makes 3. The 4 and the 3 were switched like when we did addition.

#### Associative Property

How to use:

- Watch and ask: What do you notice? What do you wonder?
- Questions and Big Ideas:
**What is the same about the first and second way of adding?**They both combined all three of the parts and got the same whole/total, 9.**What is different about the first and second way of adding?**They added the parts in a different order. The first way started by adding the 4 and 3 to make 7, then added the 2 to the 7 to make the whole 9. The second way started by adding the 3 and 2 to make 5, then added the 4 to the 5 to make the whole 9.**Does this work when we combine any three numbers?**Yes, because I tried adding 1 and 5 and 7, and no matter which one I started with I still got the total 13.**What about four numbers? Five numbers?****When you are combining three or more numbers, which way is****easier or more efficient for you?**(Many possible answers, including these)- I like to add the biggest numbers first and the smaller numbers last.
- I like to look for combinations I already know, like 1 and 9, since that makes 10 and 10 is easier to add with.

#### Combinations of 8

How to use:

- Watch and ask: What do you notice? What do you wonder?
- Questions and Big Ideas:
**What is happening to the left side?**The left side starts with 8 and each time one is taken away and the number gets smaller by one until there are none left.**What is happening to the right side?**The right side starts with 0 and each time it gets one more until it has 8.**(Pause the video at any point) How many are there altogether?**8**(Play the video, pause again) How many are there now?**8**How many do you think there will be next time I pause it? Why?**I think there will be 8 because every time I count all the dots the total is 8. The left side and the right side always add up to 8.**What is the equation telling us?**The equation is showing us the parts that we are combining to make 8. For example, 5 and 3 make 8.**What are all the combinations of 8? How could you organize them on paper to make it easy to see the pattern?**I could organize them by starting with 0+8, then putting 1+7 underneath, then 2+6 because I see the pattern that shows one side getting smaller and the other getting larger, but each equation combines to make the whole 8.**Does this work with 3 parts? How do you know?**

Thank you to all of the collaborators on Twitter and email who shared ideas and feedback for these visuals.