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3 Math Routines to Build Number Sense

Are your students having great difficulty counting and understanding number relationships with numbers beyond 100?  Well, I definitely understand!

Building number relationships and number sense can be a struggle.

According to the common core standards, students in the 1st grade should be able to count to 120.  By 2nd grade students are expected to understand multi-digit numbers up to 1,000. For struggling students, there is a huge number sense gap that needs to be filled.

To help fill this gap, I want to share 3 math routines that have helped me in the past.

Many of the routines are counting sequences that will ultimately help your students better understand relationships among numbers.

 

What is the Number Bounce Routine?

The Number Bounce Routine is a quick counting routine in which students and teachers count forward and backward in a given sequence.

How does the Number Bounce Routine Work?

Begin this routine by telling your students that you will count forward or backward by ones starting with a specific number and ending with a specific number.  Let your students know that when you tap them, they will have to say the next number. Here is one example using the start number 213 and the end number 235. I start counting forward by ones like: 213, 214, 215, 216. Next I tap a student on the shoulder. The student says 217. Then I continue counting: 218, 219, 220.  I tap a different student. The student says 221.  I continue to count in this way until I have given most of the students an opportunity to answer.  The student who says the last number in the sequence says, “235. Bounce” and gets the opportunity to do a 20-second celebratory dance.

I especially like this routine because my students are very attentive. They all want to say “Bounce” and dance. This is powerful routine to practice counting forwards and backward.  It is pretty simple and offers flexibility.
 

Modify this Routine with Decimals and Fractions

This routine also works well for fractions and decimals.  Since decimals are pretty difficult for students it is critical that we infuse this type of counting method.  Check out the example below:

 
number bounce routine using decimals

How long will the Number Bounce Routine take?

This routine should ideally take 3 – 5 minutes.  It is meant to be a quick activity that can be used at any time during the school day including transitions, restroom breaks or the beginning of a math lesson.
 

What is the Base Ten Toss Routine?

The Base Ten Toss Routine is a quick counting routine that includes counting using place value language.  It is intended to build base ten language and ultimately foster place value understandings.

 

How does the Base Ten Toss Routine work?

A beach ball or bean bag is recommended when implementing this routine. Begin this routine by telling your students that they will count in base ten language until they reach a base ten decade with no ones (example: 3 tens 0 ones or 30, 4 tens 0 ones or 40).
 
For this routine, students stand in a circle. After one student counts in base ten language (ex. 7 tens 5 ones…75), he or she passes a beach ball or bean bag to the person standing next to them. When a student says a base ten decade with no ones (ex. 8 tens 0 ones…80) they get the opportunity to toss the beach ball to any classmate of their choice. My students love that part of the game! For more details, check out the illustration below.
base ten toss routine using 2 digit numbers

Modify this routine with Larger Numbers and Decimals

This routine works for larger numbers and decimals as well. Students can add on hundreds (ex. 6 hundreds 9 tens and 8 ones…698) or hundredths (ex. 6 tens 7 ones and 37 hundredths…67.37).  For more of a challenge, they can count backward.
 

How long will the Base Ten Routine take?

This routine should around 5 – 10 minutes.  It can be used anytime during the day when students need to get out the wiggles or as a daily opening to your math lesson.

 

What is the Amazing Race Routine?

This routine is intended to help students break down numbers in various ways.

How does the Amazing Race Routine work?

Students work in pairs to decompose a given number in as many different ways as they can.  You should provide each partner pair with a blank piece of paper or sheet like the one in the photo.

You can give your students 5 – 10 minutes to record as many different ways to represent the number as possible.  After the time is up, 1 or 2 partner pairs can randomly be selected to share what they recorded, in front of the class.

As a quick tip, you can award team points to partner pairs that had the most inventive and correct ways. It’s very important check for accuracy.

Click on the picture for to opt in for the FREE download. There is one for younger children (big circles) and older children (smaller circles).

 
number of the day worksheet shows the number 136 with multiple representations

I really enjoy this activity because my students had an opportunity to communicate their mathematical thinking with one another. This is also a very open-ended routine.

Students get a chance to be as creative as possible when recording.  There were times when I was reviewing my students’ answers and thought, I would have never come up with that!

When you first start this routine, your students may only have 2 or 3 different ways. That’s OKAY…..  If you consistently use this routine your students will evolve and ultimately fill the page!

Use this Routine with Fractions and Decimals

This routine can easily be adapted to fractions or decimals.  For example, you can write 7/10 or 0.7 as the number of the day.

How long will the Amazing Race Routine take?

This routine should around 5 – 10 minutes.  It can be used as a daily opening to your math block or as a morning sponge activity. 
 

This wraps up the 3 routines to build number sense. I hope you enjoyed all of these tips to help with your kids.

Do you have any number sense math routines you use in your classrooms? Tell me about it in the comments section below.

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