Mathematics is often described as the science of pattern. Through looking for, reasoning about, and describing numeric and geometric patterns, students come to realize that mathematics reflects order and predictability. This is a significant discovery because students who understand the power of patterns in math are more confident in their ability to do math. So when the Common Core State Standards first came out and I didn’t see a whole lot about pattern and patterning activities in the early years, I wondered why.
And I’ve been wondering why until recently when I read a fabulous article about teaching math. The article was an interview with Bethany Rittle-Johnson, a professor of psychology and human development at Vanderbilt University in Tennessee. Her studies focus on early math and the importance of teaching young children about patterns. Here’s what she said about why pattern was not included in the standards:
“Patterns were mostly left out of the Common Core Math Standards in the early grades (kindergarten and 1st grade) due to a lack of evidence that they helped children understand later math concepts.”
But then she goes on to say that a lot of research since then proves that pattern should actually be included. I agree. In fact, I would argue that there had already been a lot of research underscoring the importance of teaching pattern in the early years yet for some reason, it was ignored.
Here’s why I think teaching pattern in those early years is important:
- The study of pattern is the foundation of mathematics. As I mentioned earlier, mathematics is described as the science of pattern.
- It is the thread that binds all parts of mathematics together.
- Discovering patterns makes life easier; patterns are predictable.*
- Searching for patterns trains the brain to look critically.
- Looking for patterns helps make connections between concepts in mathematics and other curricular areas.
- Looking for patterns helps encourage students to be persistent and better problem solvers – they know there is predictability in mathematics and that mathematics makes sense.
- Pattern can be used as a self-check device.
- Patterns help students when they begin to make generalizations about number.
* to predict is to use known information to predict unknown information
Now, to be fair, the CCSSM Mathematical Practices (MP7 and MP8) do mention looking for patterns. But pattern isn’t specifically called out in the content standards and I think that’s a mistake. The word ‘pattern’ needs to be a part of the mathematical vocabulary so much so that looking for patterns becomes a natural part of what students do in math class.
Let me give you some examples. All of the What Do You Notice? posters that I include in my Family Math Night events are perfect examples of looking for and describing patterns. What I love about these posters is that they can be accessed on a variety of levels but all of those levels require looking for patterns. In addition, some of the posters clearly show the connections between arithmetic and geometry making pattern the thread that binds all parts of mathematics together.
On a higher level, describing patterns helps lead us into making generalizations – the foundation for algebra. By making generalizations, math changes from isolated bits and pieces to an organized and much more manageable body of information. For example, through patterns, the numbers 1 through 100 are no longer 100 separate and isolated pieces of information to learn. Instead, students simply need to learn 1 – 20 and then each of the decade names.
So we need to be doing pattern-specific activities in those early years. Make AB patterns with teddy bears. Sort blocks into different categories. And always, always, always use the word ‘pattern’ when describing math.
By the way, I feel so strongly about pattern in the early grades that we devoted a station in our Nifty Numbers kit to it. It’s important. Without pattern, math simply does not exist.
One of my goals for the beginning of the new school year was to get my students excited about math from the moment they walked in the door. To do this I started our math lessons in the area (no pun intended!) of geometry through hands-on activities and projects. I discovered that through allowing kids to design, create, and build – something all kids love – I could sneak in important ideas in math.
But the other thing I discovered was that it was a great way to build their mathematical confidence right from the very start. And in a subject area where too many kids feel they aren’t “good” enough, this confidence can go a long way.
So I’ve listed below some activities you can do to support the geometry standards. Most of the activities require the use of manipulatives so you’ll want to make sure that you give students enough time to “free explore” before getting into the lesson. This helps minimize distractions with the manipulatives when you’re ready to focus the lesson. While students are exploring, walk around the room, ask questions about their work and talk about the math you see. But make it pretty informal. I love how you used two triangles to create a parallelogram! And have students who are interested share their work with the class. Again, you’re building that confidence which is so important for success in math.
In addition to the ideas below, you can also tap into some of my Family Math Night Collaborative Projects which lend themselves well to a classroom environment. These are great hands-on STEAM (science, technology, engineering, art, mathematics) projects. If you have a buddy class, the older students can help the younger ones with their part of the project. This is a great way for them to get to know each other while doing something fun and educational!
Activity 1 – Shapes: Students create shapes according to the attributes you give them. Ex: Design a closed shape with exactly three sides. Share samples, compare different shapes and have the students come up with the definition for ‘triangle’.
Activity 2 – Symmetry: Put one geoband down the center of the geoboard. Students create a design on one side of their geoboard. Their partner needs to use the other side to create the mirror symmetry. (You may need to start by limiting the number of geobands used.)
Activity 1: Students place pattern blocks inside hinged mirrors then re-create what they see in the mirror.
Activity 2: Students create task cards for each other to solve. They do this by creating a design with the blocks on triangle paper, tracing the perimeter and cutting it out. They then re-trace just the perimeter on construction paper. These are now the task cards. As a variation, have students write clues such as the number of hexagons needed.
Activity 1: Students use all 7 of their tangram pieces to fill in the design on their task cards (see Grandfather Tang’s Story for task card ideas).
Activity 2: Students create polygons using a specific number of tangram pieces and fill in the chart (scroll down to ‘Tangrams’ and click on the banner link).
Straws and Twist Ties*
Activity: Provide students with straws and twist ties. Let them build whatever they want. Talk about the attributes of the shapes you see. Discuss the difference between 2-D and 3-D shapes.
*I like to use cocktail stirrers and cut up pipe cleaners if I can’t find twist ties.
Finally, if you’re looking for a fun way to involve parents in some of these hands-on activities, there’s our Gellin’ with Geometry Family Math Night kit. Some of the activities described above are in the kit along with lots more fun stuff!
I know many of you are already in your classrooms planning out the year. Since we have to teach geometry anyway, why not switch it up a bit and start with something different? I know your students will love it!
We all know that when parents get involved in their child’s education, student learning increases. What better way to get parents actively involved in important skills than through fun and engaging games that reinforce classroom learning? That’s the idea behind the newest addition to our Family Math Night kit series: Make-N-Take Station Kit.
Designed to give students practice in important number skills, our Make-N-Take Kit is the perfect way to make sure your K-5 students continue the learning at home.
Similar to our Play-N-Take Station Kit, families will go home with game boards and the game pieces needed to play the games over and over. And all games come INDIVIDUALLY packaged saving you a lot of time and effort!
What’s fun and unique about our Make-N-Take Kit is that families play a role in making their game boards and game pieces! They love that! And teachers and parents love the extra skills practice kids will receive in a fun and creative way – all aligned to the Common Core State Standards in Mathematics.
I invite you to check out this short video where I describe the kit contents and the mathematical learning involved. As always, if you have any questions please do not hesitate to contact me. Our number one priority is to help you host a fun and successful event.
Balloon Bunch Capture and Go 4 the Win reinforce beginning place value, addition and subtraction to 20, and making a 10.CCSSM: K.NBT.A.1; K.OA.A.1; K.OA.A.2; K.OA.A.4; K.OA.A.5; 1.OA.A.1; 1.OA.B.4; 1.OA.C.5; 1.OA.C.6; 1.NBT.B.2
Place Value Shuffle and Number Shuffle reinforce place value to the hundreds place, greater than/less than, even/odd numbers, and basic addition and subtraction skills.CCSSM: 2.NBT.A.1; 2.NBT.A.3; 2.NBT.A.4; 2.OA.B.2
Number Shuffle and Cake Walk reinforce place value to the hundreds place, even/odd numbers, multiples, factors, prime and composite numbers, 1- and 2-digit multiplication, division facts, and fractions on a number line.CCSSM: 4.OA.B.4; 4.NBT.A.1; 4.NBT.A.2; 4.NBT.A.3;4.NBT.B.5; 4.NBT.B.6; 4.NF.A.1; 4.NF.A.2; 4.NF.B.3; 5.NBT.A.1