Addition, Subtraction

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? (Play the video, pause again) How many are there now?  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.

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