Primary Counting Puzzles

Recognizing patterns helps students to become better thinkers and problem solvers.  Counting and Cardinality are a big focus in kindergarten.  With this in mind, and taking an idea I saw somewhere, I created these puzzles for primary students.  I think they would be good in a station or as something for the kids to do when they finish other work.  Maybe you would want to use one for classroom management?--the class earns a piece when it reaches a goal, and when the puzzle is complete, they earn a reward.  I am sure you can think of some great ways to use them.  You'll just need to download the file, print it in color, laminate if you wish, and cut! Click on the image below for the entire set of 7 puzzles.

Math Practice Standards--Are you being intentional?

Much like the Engineering Design Practices that are a part of the Next Generation Science Standards, the Standards for Mathematical Practice help us to embed best practices to help our students to grow in their general learning skills.

These standards, unlike the content standards, remain the same for all grade levels, and should be used to help our students to develop better problem solving skills and mathematical practices.

These are the 8 practice standards:

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

It is very easy to find student-friendly language versions of these standards.  I would recommend that you find one that you like and print it and post it in your classroom.

 But, is posting the practice standards enough?  I think that it would be a good idea to look more deeply at them and find ways to embed them into your workshop.  ( I am sure that you will find that many of these are a part of your instruction already.)  The Scholastic website has a nice little guide to helping teachers understand these standards more completely. They are so much more than just the short statements above. The Inside Mathematics website also has some resources to help you with understanding these standards including videos from a variety of grade levels that match each standard. As you watch these videos, you may notice that many math practice standards can be found in just one snippet from a lesson.  Strong math instruction usually has many of these practices included in it.

While you probably won't teach the standards as independent lessons, I think it is worth our while to include the math practice standard(s) along with the math content standard when we are setting the learning intentions for our lessons. Making it more intentional on our part will help our students better begin to understand the value of these practices and allow us to develop stronger mathematicians.

Anchor Charts in Math Class

Anchor charts play an important part in today's instruction.  I see them throughout classrooms for all subjects.  They help us to give students' ownership of the content they are learning.

When I write an anchor chart with my students, I like to have a blueprint in my mind.  This helps me to guide them towards some of the things I want to be sure to include.  Oftentimes, they think of other, even better, ideas for us to put on our chart!  

This Pinterest board has a variety of anchor charts that I have found for grades K-5.  They might help you with a blueprint next time you go to write one with your class!

Growing problem solvers

By 5th grade, many students have figured out how to solve story problems.  Other students remain completely dependent on teacher models and key words.

Teaching kids to follow a model or to look for key words sounds good, but is it really teaching them how to solve problems?  In reality, it is probably only teaching them to solve problems that are presented in the exact same format.  This distracts from the real-world element needed in our math instruction.

A great idea I have heard of recently involves presenting the story problems as a reading situation.  Present the problem with the numbers covered up, and ask the students to visualize what is happening and determine what they are to do with those numbers before even knowing what the numbers are.  This causes them to "make sense" of the problem before they begin manipulating numbers.  It is a great strategy, and one that is used in most 3 Act Tasks.  

This SMART notebook was created with this idea and CCSS 5.MD.1 in mind.  The problems were found in various places, but the notebook presents them all in a format with the numbers covered.   This should allow for classroom collaboration and discussion before students solve the problems.  After discussion, you can reveal the numbers by clicking on the white boxes.  I did not create it thinking that a person would do all of the pages at one time or in the order presented;  you can use these notebook pages however you wish, as they vary in difficulty and measurement units.  

 To go along with the notebook, I created problem labels.  Each page of the labels go with a page in the SMART notebook document.  You can just print and peel the labels (Avery 18662) to hand  to the students to complete independently or with a partner in their math notebooks.

Good luck!  

5.MD.1 SMART Notebook

5.MD.1 story problem labels

Building Mathematicians through Number Talks

I have had a number of teachers show interest in adding Number Talks into their classrooms next year.  That is awesome!

Many of you already use Number Talks regularly.  For those of you who don't, I think you will find that you already do forms of this.  The difference between about what you are doing now and a number talk is generally just one thing--intentionality of instruction.

In this video, you will see a 3rd grade Number Talk.  I think you will be able to recognize the intentionality he uses in this lesson.

https://www.teachingchannel.org/video/multiplication-division-in-the-core
There are many things that I like about this video. I like the classroom culture and the way that everyone is engaged in the activity. I think it is wonderful the number of ideas that they share and the way that the teacher acknowledges each one. I love the way the hand signals give the teacher feedback, but don't distract everyone else's thinking.  However, my favorite part, I believe, is when the student says, "I revised my thinking..." How powerful is that?

 There are lots of ways that you can use Number Talks in your classroom. You might use it as a mini-lesson. It might be an opening or closing activity. It might be designated for a certain time of day outside of math time. You might use it once a week, or you might use it every day. All of that is up to you and what works best for you and your students.

Sherry Parrish's book is a great resource. Many teachers and buildings have copies of this great book. This link also will also give you some ideas of different Number Talks you can use in your classroom. 

 As always, I would love to explore this more with you. If your class uses Number Talks regularly, let me know! I would love to visit if you are comfortable with that. If you would like to learn more, or sharpen your skills at these, I'd be happy to chat with you.

TEN FRAMES: For more than just K-1

Most of us are familiar with ten-frames as a structure for making sense of numbers in the primary grades.  Students use it to learn facts, to represent numbers, and to help them think through problems.

This is a ten frame representing the number 4. It also could be used to represent a variety of facts including 10 - 6 = 4. These ten frames make sense to our little kiddos.  They are prevalent throughout our classrooms. They are the concrete representation of numbers when students use the manipulatives to build the numbers and the pictorial representation when put onto paper.  The concrete and representational stages are very important to conceptual understanding before our students move into the abstract stage which just uses numbers and symbols.

But what if we tried to bridge the gap by using ten frames with our older students in grades 3, 4, and 5?  Certainly, there might be some of our students who still need this ten frame to help them make sense of some basic number problems, but what if we looked at it differently?  What if the frame represents 100 and the counters are each worth 10? This ten frame could help our kiddos make to see that 40 is closer to 0 than to 100.  It might help them to better conceptualize our base ten system.  Similarly, the counters could represent 100 and the frame could be worth 1000...

Having some manipulatives and visuals that are common with our students from K-5 should lead to a stronger conceptual understanding of numbers.  Our students use base ten blocks well, but I believe this would be a next step to help them build their deep understanding of our numbers and how they work. Besides, a ten frame is often easier for a student to draw independently to represent their thinking than base ten blocks or a 100 grid. To show ones in the grid above, students could break one of the ten squares into a smaller ten frame as shown below.

This ten frame could represent 43.  It could represent 430.  Using these frames in a variety of contexts will help our students to better understand how numbers work.

Whole numbers in ten frames are great, but what if we used the above ten frame to show 4.3?  Students can easily visualize the 4 ones and then the next one has been decomposed into 10 parts/tenths.  Using these visuals would help adding, subtracting, and rounding easier.

Similarly, the above ten frame could represent o.43 with each counter being worth a tenth and each of the little counters representing a hundredth.

Using these ten frames in a variety of ways will help our students to gain a stronger foundation of place value.  By changing the whole of the ten frame, the number being represented inside changes.  For some of our kids, it will provide them with an easier way to record numbers.  For others who struggle with place value, it might offer them a familiar format that they can understand.

Do you have other ideas for using ten frames throughout grade school?  Please feel free to share in the comments below.