Building Number Sense

Don’t miss the math running record GIVEAWAY near the end of this post!

I’m linking up again this week with Denise from #TeacherMom for her Building Back to School linky party!  This week we’re talking about classroom tools and I’m sharing my favorite tools for building number sense.  These are perfect activities for back to school because:

  • they let you see what number sense skills your new student are coming in with
  • if you do them, you’ll know EVERYBODY has been at least exposed to basic number composition/decomposition & skip counting
  • they are fun and engaging

Counting Routines

Counting Routines for Number Sense, a counting and skip counting activity that fits into those 5 minute chunks of extra timeIf I had a dollar for every time I counted (or skip counted) with kids…!  But that’s the only way for them to really master it, they’ve got to practice and somebody’s got to lead them in the practice.  As a 2nd grade teacher I always devoted a couple of lessons to skip counting but it’s really something that has to be briefly revisited many times. Skip counting routines are just the thing!  Here’s how they work:

  1. Everyone stands in a circle.
  2. Everyone counts aloud together (by 1s, by 5s, starting at 247, backwards, by 10s starting at 480, etc.)
  3. Once student are comfortable with the sequence, count around the circle (only one student says each number).

Management: Set the expectation that everybody needs to count together, nobody purposely tries to go faster or slower.  When you are counting around the circle and only one person is saying a number at a time, let students know that everyone else needs to be counting in their heads.  Teach them that if someone gets stuck, everybody need to give them wait time to think rather than blurting out the number.

This activity is perfect for those little 5 minute blocks of time you find yourself trying to fill every now and then.  It’s important for students to get comfortable with counting and skip counting up to 1000 because it will help them with mental math, telling time, counting money, etc.

This idea comes from the book Number Sense Routines by JessicaShumway.


 

Number Arrangements

Number Arrangements, a number sense activity that helps student internalize combinations that make a numberWhen I was a kid, we learned all the +2 facts, then the +3s, +4s, etc.  In college when I learned about the concept of number combinations (all the combinations that make a number) I found it to be a much better way to learn facts.  If you learn all the combinations that make 5 (0 and 5, 1 and 4, 2 and 3) then it’s easy to do both the addition and the subtraction facts.  Knowing how numbers can be broken apart and put back together also helps with problems solving.

Number arrangement activities help students to internalize number combinations.  It’s perfect for those first few afternoons back at school when everyone is so tired because their bodies aren’t on the school schedule yet.  Here’s how it works:

  1. Students divide a piece of construction paper into 8 parts (fold in half, then in half again, then in half one more time).
  2. Choose something to make arrangements with (I’m using noodles here but you could use strips of paper, toothpicks, foam tiles, etc.)
  3. Tell students the number they are working with for the day.  In the picture I’m using the number 5.  In every rectangle there have to be exactly 5 noodles.
  4. Students arrange and glue down their materials.
  5. Students write an equation to represent each arrangement.

This is a great introduction to the ideaofsubitizing if students haven’t ever done it before.  I like to do the activity a few times using a different materials and a different focus number each time.  This can also become a math center.


Counting with Place Value

Counting with Place Value, using manipulatives with counting to develop a strong understanding of place valueIn my last school it was a 2nd grade rite of passage to write the numbers to 1000.  This seems like a daunting task but it is part of the Common Core standards and when broken up into chunks it’s totally do-able.  I like to get kids started with manipulatives to review the place value they learned in 1st grade and to really get them comfortable with place value in the hundreds.

Here’s what you do:

  1. Students put 1 counter in their ones section and write “1” in a notebook or on a blank hundreds grid.  Then they add a second counter and write the number “2.”  I’m using buttons for counters in the picture but I’ve also used beans or dry macaroni noodles.
  2. They keep going until they get to the number 10.  At this point they group their counters up into a ketchup cup (thanks McDonalds!) and move it over to the tens section.
  3. Keep counting!  Every time a new ten is made, the counters go in a cup and get moved over.  It becomes very clear how the written numeral is related to the counters (ex: we have 3 cups of counters and 5 extras so the written numeral is 35).
  4. When students get to 100, they take their 10 small cups of counters and put them together in a bigger cup.  Then the big cup moves to the hundreds space.

By about 250, kids start asking if they can just write the numbers rather than continuing to use the counters and I let them.  If they get stuck or confused later I have them build the last number they were sure of and use the counters to help themselves keep going.  A lot of “ah-ha” moments happen during this activity!

Counting with Place Value, using manipulatives with counting to develop a strong understanding of place value  Counting with Place Value, using manipulatives while counting to develop a strong understanding of place value   


 

The Hiding Game

Here’s another fun and simple way to practice number combinations:

  1. Students choose (or are assigned) a number to work with between 5 and 10.  They get that many counters.
  2. The first player hides some of the counters in their hand and shows the second player the remaining counters.
  3. The second player tries to determine how many counters are hiding by looking at the counters that are visible.
  4. Students switch roles.

The Hiding Game, a fun and easy game that helps students internalize number combinationsIn this picture, the number 7 is being practiced.  One student hides 3 of the counters in their hand (they would completely close their hand, unlike the picture), leaving 4 visible.  The other students knows there are 7 counters total and can see that 4 are showing.  He/She tries to determine how many counters are hiding.  After several rounds, the students start to internalize all the combinations that can make up the number they are practicing.

 

 

The previous three ideas come from the book Developing Number Concepts #2 by Kathy Richardson.


 

Math Running Records

Math Running Record - these are the steps for this assessment which gives you a look at what math strategies your students are usingMy last must-try number sense tool is the math running record.  Yes, I did just use “math” and “running record” in the same sentence!  When students fill in timed math tests you can measure how many facts they can complete in 1 minute but you really don’t know what strategies they are using and where to guide them next.

If you’re interested in trying math running records, I have assessments and recording forms already made up.  Click the picture to check them out in my TpT shop.

 

 

 

Math Running Record, assess the strategies your students are using

Check out the multiplication and division version here.

Follow my math board on Pinterest for more 1st-3rd math ideas:

Follow Hannah @ The Classroom Key’s board Math on Pinterest.


 

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Hannah Braun
Hannah Braun
Hannah Braun is a former teacher with 8 years of experience in the classroom and a master's degree in early childhood education. She designs engaging, organized classroom resources for 1st-3rd grade teachers.

6 Comments

  1. I love finding the Old Math Their Way games reappearing! I am going to take a look at the book by Kathy Richardson to see what else she suggests. I recommend the Math Their Way program to all kindergarten and grade one teachers. It is fabulous, allows for individualization and different ion. There is too much good to say about it here!

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