Sunday, January 24, 2016

Making a 10 to Add

Making a 10 to Add is a great math strategy to help students mentally add bigger numbers. It's a skill I picked up somewhere along the way in elementary school and have used on a daily basis ever since. I never realized I was composing and decomposing numbers but I've done it all my life and it's so helpful!


That being said, holy moly is it a hard concept for some kids to grasp!

If you can guide them there, though, I think it's a great mental math strategy for them to have in their toolkit. So I'm going to try to explain, step by step, how to get them there. :)

1) Master all facts within 10, especially making 10
I wrote a huge blog post recently with a ton of ideas and resources for how to build students' fact fluency. There's really no way getting around this step - they have to be fluent in their facts to truly use this strategy. If they're not there yet, keep working on it before you attempt the next steps.

2) Adding to 10
The next step is that students need to learn how to add one digit numbers to 10.

This step is WAY easier because students are pretty quick to realize that they just replace the 0 with the number. It's good to explain why, too, with base 10 blocks. Get out the base 10 blocks and show them a problem like 10 + 4. Show them how 10 has no ones so when you add 4 ones to it, it simply becomes the ones place.

A great way to show this is for them to put the numbers on top of the 0s as well. I made some cut and paste activities where they simply paste the number on top of the 0 to replace it.


Then, to build their automaticity, center games like Rollin' Facts are a great way to practice the skill over and over but in a way they think is just a game. :)


You may remember this game from my fact fluency post because I have it for all the numbers 0-10. It's just an awesome station! They can play it over and over and it's always different. In order to make it a game, you can have students partner up and each roll dice. Whoever made the bigger number gets to circle their number sentence and the person with the most circles when the page is full wins.



Then, of course I recommend doing worksheets to practice and also to assess. If you're familiar with my math units, you know I give every worksheet in 3 levels: on level (B), below level (A), and challenge level (C). You can always see what level a worksheet is by looking in the star in the upper right corner.


My worksheets also have the self-assessment at the bottom so they can tell you how they felt they understood the concept - that's a whole other blog post though! :)


3) Adding 9 (moving 1 to make 10)
Woohoo! Now they're ready for a little compensation practice now!

I recommend starting with JUST 9 where they take 1 from the number they're adding to 9 to make a 10 and practice that A LOT. A lot a lot a lot.

To show them what you mean, use twenty frames and red and yellow counters to demonstrate what exactly you're doing. If you tell them to just move the number, they're going to look at you like you're crazy. :)

First, have students take a problem strip. Next, have them build each number in its own ten frame in a different color like this:



Then, tell them since adding 10 is so easy, we could make the problem so much easier if we made the 9 into a 10. Show them how you can just move the yellow chip from the second number to the 9 to make it a 10. DO NOT FLIP IT. You want them to be able to see that it's borrowed. Now ask them what the problem is now and guide them that it's now 10+4. Talk about how you borrowed 1 from the 5 and made it a 4 to give it to the 9 to make it a 10. I know it may sound confusing but they'll get it when you show them how you're borrowing from one number to give to another.


Last, have them write the new number sentence at the bottom. Practice with several problem strips until you think they've got it. This is definitely a concept I recommend introducing in small groups rather than whole group so you can watch each child move the piece and "change" the problem.

Once you feel like they have it down, give them a worksheet on their level to practice the skill.


A lot of them will still need the ten frames at this point. Give them something small like 2 different kinds of beans or any small thing they can use as counters to use with the ten frames at the top of their worksheet. Have them build the problem then physically move one over to make a ten.



Then it's time for centers to hopefully have it become a mental math skill for them!

For this center, kids simply match the cards that show an original adding 9 problem and the card that moved 1 to make a 10. For example, they would match the 9+6 card to the 10+5 card like this:



Then, they write the problem on their recording sheet like this to solidify it:



I also have cut and pastes of course because I do cut and pastes for everything :)



The more practice with this skill they get, the better! It's a really important step in them understanding the mechanics of making a 10 before jumping in to do it with any number so make sure you spend an adequate amount of time on it.

The goal is for them to understand what they're doing but also for it to become a mental math strategy. If you ask them 9+5, they should quickly be able to move the 1 in in their head to make it 10+4 and know it's 14 right away because of it.

Okay... so now we're ready for.... [drumroll please]

4) Making a 10 to Add!
First, bring out the twenty frame mat and red and yellow counters again!

Remind them about how you borrowed from a number to make a 10 when adding 9. Explain that you can borrow as many as you need to in order to make a 10.

Have them take a problem strip and build both numbers in its own frame like this:



Then ask: how many more do we need to add to 7 to make 10?
If they know their facts to 10, especially those that make 10, they should be able to tell you that they need 3 because 3 and 7 makes 10. They'll also be able to confirm that visually by seeing that there are 3 spots empty in their top ten frame. If any of your kids need more help with this, review Making 10 (Chapter 3.3 in First Grade Math Unit 3) with them.

When they tell you 3, have them slide the yellow counters into the top frame to fill it. Don't flip them so they can see they're borrowed, just like you did with adding 9.



Now ask them what their problem is now. This part is important! They made a 10 so they should be able to tell you that their problem is now 10 + 3 because there is a full ten frame and 3 left over in another ten frame. Keep practicing until all these steps are quick.

You can also use other fun things instead of red and yellow counters like fuzzy balls or mini erasers:



Okay so now they're hopefully ready to put it into practice!

Show them a problem. Have them look at the first number (in this example: 8) and ask them how many more they need to make 10.



When they tell you 2, tell them you're going to borrow 2 from the other number to make the first number 10 to make it easy to add. Next, ask them if the number they're borrowing from is 2 or if they'll have numbers leftover, to which hopefully they'll say yes.

Draw 2 lines from the number like above and write a 2 under one of the lines. Ask them: "What do you have to add to 2 to get 7?" Again, this is where their fact fluency from Step 1 becomes really important! They should be able to tell you 5 because 2 and 5 makes 7. You can do this with red and yellow counters for students who are really struggling. Put out 7 red counters and have them flip over 2 so they now have 2 yellow counters and 5 red counters to show how 2 and 5 makes 7.

Once they tell you that 2 and 5 make 7, write the 5 at the end of the next line so it now shows 7 is 2 and 5 like above.

Circle the 8 and 2 to show that you put them together to make a 10. Point out how the 5 is leftover.
So that makes the new problem 10 + 5 = 15.

Practice this with them a lot until they get quick at it.

I recommend practicing with this center... Make a Ten to Add!



Laminate the cards and give students dry erase markers. Have them do the steps themselves on the card: Look at the first number and figure out how many more to make 10, break apart the 2nd number to give it that number, circle the 10 they made and add it to the leftover number, write their new addition sentence.


When you feel like they are ready to practice independently, give them a worksheet at their level.



For your students who need a little bit of extra help, give them the worksheets with ten frames on them and let them use 2 different kinds of something small like mini erasers to help them solve the problems.



No matter what level worksheet they do, have them show their work where they decompose the numbers, circle the numbers to compose a 10, etc. so you can see that they're doing the steps.



Aaaaand cutting and pasting fun because, well, of course :)



So this is another way to make 10 to add that is a little bit different than above but is another GREAT strategy!


Kids can even use this with bigger numbers as they get older. I personally use this strategy any time I do mental math! For example they could do 54+3 by making tens by turning 54 into 50 then adding 50 + (4+3).

Remind students how they know their 10 facts (10+4=14, 10+5=15, etc.) and show them how they already know that 14 is 10 and 4 because 14 is a ten and 4 ones. Then, show them how they can use that to add numbers to 20 in their head.

Using the whiteboard example I show above... 14 + 2 =
Show them how they can break apart 14 into 10 and 4. Then, show them how they have 2 left over so now they have 10 + 4 + 2. Well they know 4 + 2 is 6 because that's a fact they know so then they just have to add 10 and 6 which they know is 16. Easy! Do the circling and all that good stuff like I showed above. I actually think this strategy is easier for them than the other making a ten to add strategy but equally important.

I made cards for these too to practice!



Do the same thing for these where they use a dry erase marker to write on them to figure out the answer, record on their recording sheet, then wipe off when they're done!



As well as a full set of differentiated worksheets of course!



This is definitely a skill that requires a lot of practice so I recommend having all students start at level A to work with the twenty frames and then have them work their way through the level B worksheets without the support. Give level C to those who need a challenge. Once they get it, this one can become really automatic for some kids.



Now it's assessment time to see how well they understood!



I hope this has helped you feel more confident to teach making a 10 to add!
If you have any questions, feel free to ask - I'm happy to help! If you want to share what you do to teach this difficult skill in the comments, I'd love that as well! The more we all help each other, the better mathematicians the world will have when these littles grow up :)

If you want the activities from this post, you can get EVERYTHING I showed in this post as well as the materials in the fact fluency post I talked about in my First Grade Math Unit 10.



Want to read more MATH ideas from me?
Check out some of these fun posts:
Building Number Sense
Place Value
Telling Time
Fractions
Adding 3 Numbers
Fact Fluency
Money (available in U.S., Australian, Canadian, and U.K. coins!)
Graphing and Data

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