10 more/less and MORE!

Standards Progression

1st Grade

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

2nd Grade

Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900

*Supporting Standard 

 2nd grade-Count within 1000; skip-count by 5s, 10s, and 100s.

This one sounds so simple, yet encompasses so much number sense and understanding!  Where to begin...same place as always, with some math manipulatives of course.

This standard states to "mentally find 10 more/less, without having to count" but that doesn't just happen without some serious instruction and practice where the students do count. They count over and over again until they see and understand the pattern of adding 10 more or subtracting to get 10 less. 

 In 1st grade, the 10 more begins early as the kiddos are adding 10 more to those groups of 10.  This is closely related to the place value standard that has the kiddos counting 10 and some more for teen numbers and multiples of 10 and some more for larger numbers.  When you're doing those activities, it's simple to throw some in tasks where you have the children continue counting past 9 more.  Then that opens the door to "regroup" to make a new group of 10.  It all just goes hand in hand and these place value activities make a smooth transition into the world of 10 more/less. Voila!  Sounds so easy, right? 

Those little firsties can do this in so many forms-using all kinds of counters and tens frames will help to build the understanding of 10 more/less but remember to not just stop there.  Counting is only the first step.  After that, the kiddos have to see the pattern which can be accomplished by pairing those concrete manipulatives with some representational recording of the numbers they are making.  A good way to start is with them doing the counting and the teacher recording the numbers-it's a little neater at first when you record.  So, record a number pattern on the board as your kiddos keep counting those counters.  After a few numbers, call them to the carpet and have them look at the numbers.  Remind them that good mathematicians stop and look for patterns to see if they can be repeated (ding, ding, ding...there's one of the Mathematical Practice Standards). I usually ask them some questions like, 

-What do you see?

-Do you notice a pattern in any of the numbers?

-Can you see something that changed?

-Can you see something that stayed the same?

Some students will see that the number in the tens place changed right away, while others will need to count it, record it and see it many more times before they finally "see" and understand that the number in the tens place changes when you add or subtract 10 (aka, 10 more/less). That's all there is to it right?  You're almost there, but not quite...

So once my kiddos start seeing the pattern then we continue to practice it, with guidance, in small groups and independently. I also make sure MY STUDENTS have plenty of opportunities to practice writing those number patterns themselves.  We practice skip counting by 10's (even though skip counting isn't an actual 1st grade standard I still do it to help solidify the pattern of the numbers) from any given number 23, 33, 43.... 

Finally when I think they've got the pattern down pat, we discuss the different ways this might look.  I show them some skip counting patterns with 10 more/less. I relate it to some +10/ -10 equations, and finally give it to them in chart form for the true mental test! 

Confession of a place value geek...no base 10 blocks were used in the building of this understanding for those little 1st graders.  It seems like it would be so much easier (I know), but I have to remind myself that I must build number sense and understanding of quantity of numbers for those little kiddos and the best practice for building that understanding is counting  all those individual little counters up and down, over and over again.

Now, onto those 2nd graders...hopefully they come to you with the complete understanding from those wonderful 1st grade teachers; however, in all reality we know stuff just slips out of their little brains over that summer break and as much as we try to convince them that they "did learn it in 1st grade," somehow we sometimes have to do some review and then it all starts coming back to them :)

So in 2nd grade, I know it's going to surprise you...but I still don't start with base 10 blocks (insert eye roll 🙄) so once again even though we are doing larger numbers, I still have them count 10 more/less with individual little counters but that doesn't always involve building the WHOLE big, huge 3 digit number.  We might just say the number, then count on 10 more/less like say 346 then use counters and count 347, 348, 349, 350, 351...until we have added/subtracted 10.  In the beginning, I record the number pattern for them as we practice just counting on 10 more/less from several numbers.  Then we have the same discussion as mentioned above.  In 2nd grade this concept usually comes much quicker and some kiddos already have it thanks to those wonderful 1st grade teachers doing such a thorough job (thank you 1st grade teachers). After that we do finally break out the base 10 blocks and practice adding/subtracting those tens rods and eventually move onto the hundreds flats.  We practice skip counting number sequences, adding 10/100 more/less with equations and finally in a chart form for the true mental test!  

                                             

We're almost there...one common issue for the 2nd graders is not being able to cross the hundred.  Now, you might have noticed that I didn't mention the good ole hundreds chart in my above description and that's because it's just not my tool of choice.  While completely acceptable and I do use it, it's just not the first tool I pull from my tool belt.  It is especially helpful when you have some kiddos that just can't seem to "see" the pattern. It's a very tactile tool that allows the kiddos to move up and down to see how the numbers get larger/smaller.  Now in 2nd grade, we use a 1000's chart to help cross over to the next hundred. Some kiddos just need to touch, say and move from the first hundred to the next in order to help them understand how to cross over when learning 10/100 more/less.

And there you have it, fellow teacher friends...mentally finding 10 more/less than a number without having to count! Easy as pie!