Fluency and flexibility with numbers are the hallmarks of mathematical thinking. For our students to excel in mathematics, they must understand how numbers can be composed and decomposed. That’s why learning the combinations for numbers to 10 should be the primary focus in our Kindergarten and 1st-grade classrooms. Not convinced? Check out where a number bond goes after Kindergarten.

Like all instruction, to be effective, composing and decomposing activities, which can also be thought of as part/whole activities, should be differentiated. That is, students should be working on the combinations of a number at their level. It does no good for a student to practice combinations for 8 if they don’t know the combinations for 5. Check out this blog post for more information on differentiating and grab an easy recording sheet.

An activity called the hiding assessment is a useful assessment for determining a child’s number. In this short video, a 2nd-grade teacher is using missing part flashcards to assess a student’s proficiency with the combinations for 4. It looks like the student is quite proficient with 4, so the teacher would next test the student on combinations for 5. When a student can’t fluently provide the missing part, that becomes the student’s number. For example, if a student can’t supply 3 as the missing part for 5 when 2 is shown, 5 is the student’s number, and he will have activities to practice combinations for 5.

Special thanks to Jeannette Rodricks, our instructional coach; Karla Anderson, 2nd-grade teacher; and Evan, student; who generously allowed me to post this video!

Great idea for com and decom but how does a teacher get it done it in two days.

Two days? They don’t! This is something that is ongoing throughout the year, Greg.

What is your recommendation when I have 5th and 6th graders that don’t the combinations. Do I start this low?? I feel like I should but I also feel like it will make them feel insecure. Thanks

In the past I have had fifth graders work with much younger kids, kind of playing the role of the teacher. The repeated exposure helps without destroying their confidence. I also love the fluency game Addition Blocks (google it) because it looks more like an iphone game that adults could get addicted to- yet it builds number sense while reviewing facts.

K

Older students like playing with numberless cards too. It’s a fun way for everyone to share what they ‘see’ when a card is shown. Students hear lots of different ideas and ways to look at numbers.

Do you feel like a K student needs to be able to know all the combinations for a given number without any visual support (no dot cards, cubes, etc?). Should they orally be able to answer “what goes with 2 to make 4?” Or “tell me 2 numbers that make 4, tell me another 2 numbers.” Or is that too abstract for a 5 year old? I’m thinking of the AVMR assessment to determine if a student is facile to 5.

Both Common Core and the TEKS (Texas) state that students should know the combinations of numbers to ten

with objects or pictures/drawings. That said, Common Core does say that students should “fluently add and subtract within 5” and it doesn’t mention objects or pictures.When administering the Hiding Assessment, what is the maximum amount of time (in seconds) a student should be given per hidden number to demonstrate fluency?

It should be almost automatic to be considered fluent. For example, if a student has to count on or do some other calculation, it would be hard to say they are fluent with that combination.

Do you have an example of the recording checklist that you could share? Thanks. Love this assessment!

I do not have the one being used in the video, but this blog post has a recording sheet you can use. It’s basically just a check-list you use to keep track of each student’s “number.”