What’s Covered. How do I know they have number to 10 What’s Covered? How do I know they have number to 10? When given a whole and some parts they can make the connections between adding and subtracting.

I am watching for immediate recognition of what is covered because I know the parts that make the whole. If there is counting by ones, I suspect there is no automatic recognition

? The 5 means think about 5. I started with five dots.

? 4 Only 4 dots are showing

? Some dots are hidden under the question mark. How do you know how many are hidden?

? I know because I know 5

? I know 4 plus one equals 5. 4 + 1 = 5

? If 4 + 1 = 5 then one is hidden or missing.

? I could imagine a flip card or put out 5 dots and cover 1 to see.

? 5 Here’s my flip card. I had 5, I lift some away…..

? 5 Now I see 4.

? 5 How many did I lift away?

? 5 I can explain the lift as subtracting. I took some away. I read and write 5 subtract something Use subtract for the subtraction sign. Taking away may be the action, but the sign is not called a take away sign. 5 – ? = 4

5 ? 5 – ? = 4 5 subtract what (?) equals 4 Use subtract for the subtraction sign. Taking away may be the action, but the sign is not called a take away sign. 5 subtract what (?) equals 4

5 ? 5 – ? = 4 5 subtract one equals 4 because Use subtract for the subtraction sign. Taking away may be the action, but the sign is not called a take away sign. 5 subtract one equals 4 because

? 5 4 + 1 = 5

? 5 If 4 + 1 = 5 Then 5 – 1 equals 4 Use subtract for the subtraction sign. Taking away may be the action, but the sign is not called a take away sign.

? 5 5 – 1 = 4 because 4 + 1 = 5

Try another one.

?

Start thinking about 7. ?

Only 4 are showing. 4 ?

? Some are missing?

4 I need 7, I only have 4. How do I know how many are missing? ?

4 ? I know 4 + 3 = 7 4 plus 3 equals 7

4 ? If 4 + 3 = 7 then 3 are missing or hidden.

4 ? Think of a flip card….. Or put out 7 dots and cover 3 to see how this works.

4 ? 7 Here’s my flip card. I see 7 but when I lift

4 ? 7 Only 4 are left…..

4 ? ? 7 I know I lifted away 3....because

4 ? 7 4 + 3 = 7

4 ? 7 If 4 + 3 = 7 then

4 ? ? 7 Read subtract not take away. then 7 – 3 = 4

I can model inverses with Block Cards, with Dot Cards, with Mystery Frames. I can carry these models to 20, then I move to hundred grids to incorporate a multiplicative model into 2 and 3 digit number.

Make no mistake: The goal is to develop an automatic response to equations written like this: 8 - ? = 5 6 + ? = 9 12 - ? = 8 and to have at fingertips the understanding that if you know addition, you can use it to solve subtractions. 8 – 3 = 5 because 3 + 5 = 8 6 + 3 = 9 because 9 = 6 + 3 or 3 + 3 + 3 12 – 4 = 8 because 8 + 4 = 12 YOU DO NOT WANT TO COUNT BACKWARDS… it wastes time and brain space.

These 2 cards are about the same number facts. Can you explain? ?

Both cards start from 8 ?

? This card shows 3, the rest are missing. This card shows an arrow to break apart at 3. ?

? I know 3 + 3 = 8. I know 5 are missing. I know 3 + 5 = 8 so if I unsnap at 3, there will be 5 ?

I can think 3 + ? = 8 to explain. I can think 8 = 3 + 5. ?

? I know 3 + 5 = 8 so 8 – 5 = 3 I can think 8 = 3 + 5. Then 8 – 3 = 5 and 8 – 5 = 3 ?

? They both link to this flip card.

3 3 5 ? 5 8 3 5 3

Let’s try some cards

?

Did you think 1 + ? = 6 or 6 - ? = 1 ?

?

? Did you think 6 + ? = 7 or 7 - ? = 6

Ready?

?

? Did you think 2 + ? = 8 or 8 - ? = 2

?

? Did you think 3 + ? = 9 or 9 - ? = 3

?

? Did you think 8 + ? = 12 or 12 - ? = 8

?

? Did you think 9 + ? = 14 or 14 - ? = 9 If students do not have automatic recognition of the dot collection they should not be in this card. I see 9 as 5 and 4 or 6 and 3.