Building addends is fun!

Or is that building addends are fun? Building walls is yet another way for students to practice math and have fun. (By addends I mean single digit numbers that add together to make or build other numbers. In other words all the different combination for adding 1 through 9, to themselves or to other numbers. Seems everybody knows 1+1 and 9+9 but the ones in between seem to cause a few problems.)

base ten blocks, math manipulatives, Mortensen Math

From 2 to 10 there are ONLY 25 single digit combinations. Young students look at this as a puzzle, or game: it's fun.

From 11 to 18 there are 20 more.

That means (doing a little math) there are only 45 of them. How it is that I made it out of grade school and then high school without knowing them by heart and not having to think about adding single digits together at all, escapes me. Most students, yourself included, may have to think about certain combinations for a second or more...7 + 5 for example...once you get these 45 combinations (addends) down it all starts getting easier.

You need a password but there are plenty of videos on the Sample Lessons page (That Tab right there to your left that says "Sample Lessons.") covering addends, and how to build them effectively. There are also vids for free on my blog but they are much shorter.



Doing the pairs leads to multiplication, specifically the twos times table...but that's another lesson.

base ten blocks, Mortensen Math

Students can race building a single wall each 10 high in any order they want...or make a game of who can build the highest wall before it falls over. Of course once you build a wall, knocking it over is the funnest part. In fact there are lots of games that can come out of building walls and then knocking them over...

This shirtless student called this his Ice Cream Truck...it wasn't a wall at all. Let them use their imagination and they will. This is a 10 ton truck; all the other trucks can be built (and driven around) for a fun math experience. With a white board you can draw roads and depots where blocks can be picked up and dropped off. Just make the simple rule that only two blocks can fit per level, and remember there's no wrong way to play.

You direct their discovery, they do the discovering.


kindergarten math actvities,

Students can work together and make a “math house” with four walls and a roof out of a ten, a nine, an eight and a seven...or you can give this as a task for a single student to complete. The rules are simple each wall has to be made of two blocks not more, and the walls can't overlap. They can go up 7 or 8 high.


kindergarten math actvities

This takes quite a bit of manual dexterity, it refines the motor skills while the brain learns math facts. Or perhaps the students are learning math while refining their motor skills. Students without "fine motor skills' may get frustrated because they knock over walls while building other walls. Help them. Allow as much time as needed.


kindergarten math actvities

There is no right way to play math. Some students will build one wall at a time some will build all walls level by level. It doesn't matter. DO NOT try to get them to build it exactly the way you see it built here. The object is to practice the combinations 7 through 13, while having fun. Young students may take the better part of an hour on this task. Let them.


kindergarten math actvities

The student building this took almost 40 minutes to complete this exercise, there was no "fooling around" as it were, he was on task the whole time. He was quite proud of himself when he was done. He also asked if we could do it again another time. (We did only the next time we did it it was 8 through 14 instead.) It would have been more fun if there were a couple of playmates to help him. Everyone would have learned about all of the addends here, even the the ones they weren't building and it would have been done a lot faster.

Use your imagination. Set up fun foundations. Sometimes I use a white board and put the symbols next to the walls (ie a "7" next to the seven wall etc)...they could also get out toys like trucks or cars (make a garage) or little construction workers. I personally refrain from allowing toy soldiers or 'army men' into my math lessons but that's just me.


kindergarten math actvities

Learning takes place in the sub-conscious mind, the mind that never sleeps and doesn't miss much of anything presented to it.


base ten blocks, fun math activities, Mortensen Math

Completed with finishing touches. It was a radar station after all, not a math exercise. Note the math cup in the back ground.

Get them off their fingers!

There are only 20 more addends they have to master: 11 through 18. The point is there are only so many combinations, 7+8 ALWAYS equals 15. So doing 37+8 is a snap it's going to be 45, because the student knows 7+8 is 15, then the jump to “carrying” or adding the ten is simple because they aren't trying to figure out what eight and seven is...they know it ends in 5. Then 37+18 is easy too...ends in five carry two tens or 55...they will be able to do it their heads without their fingers, with practice. Practice that's fun and easy, not dull and boring drudgery. Try to keep it fun. With more students you can bring out their natural competitiveness and have them race, and do it over and over again to try and get faster...and they want to do it. Be sure to keep it fun, a little healthy competition is a great motivator...but make sure everybody wins and no one fails.

Other combinations to watch for are 7+5 and 8+5 for some reason these two seem to give students pause, older students will often take a extra few seconds to figure these out or worse count on their fingers and if careless are off by 1.

Here is an offsite page I built pn Myspace showing how to take the next step with addition, I started with 7 + 8 (but it doesn't really matter). It's the method that is important. Don't forget to come back and if you are on MySpace add me as a friend.

Be reminded that we did a lot of play with blocks up to 10 first. Once they get comfortable here go higher. You can tell them 8 + 7 is ALWAYS 15 and start showing them 18 + 7 and 28 + 7 etc...but that's a "whole 'nother lesson" and we don't want to spend the whole hour on addition. Move on to something else and come back to it next time.

Base ten blocks, Base ten manipulatives, pre-school math activities

Here are the addends past 10 neatly arranged in order.

As you progress the house you make them build can have longer walls; one side nine, another ten, another eleven and another twelve as they begin to master addition past 10. Again we place emphasis is on 9 and 10, but all 45 addends should be mastered.


Manipluatives for addition, Mortensen Math, addends,

Another drill is to put out 11 to 18 using the tens blocks and and have them build the combinations flat. The idea here is to use two hands and go for speed.

All of these exercises can be done by students of any age...on up to adults. (Adults usually like building two handed for speed.) They are not just for kids. Also remember if you are tutoring or having math time, NOT TO spend the whole hour on addition or addends. There should be a whole lot of activities done in an hour... multiplication, division, fractions, measuring, factoring, building squares and rectangles, completing the square, place value etc. If you are working with a very young student or your own child you could do just one of these things a day...five or ten minutes and that's it. It's all the same language: MATH. You will see it all goes together simply and beautifully.



Use addends in the classroom.

Go from addends to the Addition main page.


Go from addends back HOME, CRHOM.


Do not…keep children to their studies by compulsion but by play. ~Plato, Greek philosopher, 427-347 BC