Lovin on Maths (Pt 5)- Working from Ten to Tens
Okay- are you still with me? Are you beginning to write love letters to the number 10?
I hope that even if you are a mathematician, you enjoy the brain exercises of trying to see things in a different way. It’s what teachers need to do all day, every day- brain calisthenics to try to see something we know and understand in a different way. It’s not about knowing that 5 + 5 is a way of making 10, it’s about explaining it, and teaching it in a way that kids can understand rather than know. Then, when they understand rather than know, people can expand and stretch into other arenas- “generalize” as we say in the the teaching world.
It’s the hierarchy of being a good teacher. It’s one level to know. It’s another to understand well enough to explain it to someone else. It’s a whole extra leap up to understand it well enough to jump out of your eyes and see the topic from a whole new perspective (or 25 whole new perspectives).
I challenge you to start from the first ten frames post and work through. Instead of brushing off the simplicity of adding to ten, see if you can look at how this might add up to the wonder of solving 3,478 + 692 with understanding. If you get 10, really get 10 and its role in our place value system, you can generalize to add greater numbers- and subtract greater numbers, and group greater numbers (YUP, multiplication and division mastery starts with really getting the role of 10).
On to Making Tens
So now that we have mastered making 10- and going over 10, what happens if we work into greater tens.
We will start with passing over 20.
The 7 in the ones place of 17 wants a 3 to get to the next ten. 6 is broken into 3 and 3. 17 and 3 gets us to 20, 3 more to 23. Hopefully that feels straightforward now.
A couple of tips:
- Speak of numbers within their place value. For example, 17 is made up of 1 ten and 7 ones. 23 is 2 tens and 3 ones. Easy- but really valuable for generalizing the information.
- Be as flexible as possible. If a student wants to break up the 7 in the ones place of 17 (so the 6 can get its 4, with 3 left over), that’s fine. Play with it. Let them play and be creative. It may not feel smooth or obvious to you. It might make more sense to them OR it might honor their creativity OR it might allow them freedom, but they may find it tedious later on. Any which way, honoring their ideas and approaches is pretty much always a good idea. Let them make sense in their own heads. Be patient while they do.
More Practice Getting Over 20
Okay- Moving Up a Little Level
What happens if we have different digit in the tens column? Have kids explain to you why what they’re doing makes sense- using place value language!
For example, the 7 ones in 27 want 3 ones to get to the next ten, which is 30. 6 is broken into 3 ones (for the 7 ones) and 3 more ones. So we have 3 tens and 3 ones a.k.a. 33.
A Hundred Chart posted in your classroom is a REALLY good idea. And fun to let them fill in a hundred chart and look for patterns. You could find patterns for days. Let them play. Let them color their patterns. Play with the Hundred Chart!
Oh! This one didn’t make a full ten. Throw oddballs in every once in a while so we keep using our brains and don’t get robotic.
And, mix up the order of the horizontal addition. The greater number CAN go second!
Practice, practice, practice. Play. It’s fun, and it feels good to play with something we understand. It builds confidence- and confidence builds LOVE FOR MATHS!
Resources for Practice:
- Greg Tang’s “Break Apart” is online practice, many levels, perfect.
- While we are on Greg Tang online games, Ten Frame Mania also has many levels, and it’s great practice. And, Math Limbo is great for seeing numbers as their parts.
- Place to print out practice: Math Drills- Look for “Horizontally Arranged Addition”.
- Another spot for printed practice: Math Aids- Look for horizontal set-up, loads of possibilities, including visuals of ten frames.
Just One More Time Leveling Up Today
For one more level up. Even into greater numbers, we still keep the adding horizontally- up to 100, up to 1000 if you like. It reinforces place value- understanding 10 AND place value makes you INVINCIBLE!
