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Category: Algebra

Play-N-Take and Make-N-Take Logos

Play-N-Take and Make-N-Take Logos

 

Play-N-Take logo                         Make-N-Take logo

Our logos for our Family Math Night Take-Home kits are done!  A little behind schedule but all good things are worth the wait!

These Take-Home kits were designed to continue the learning at home! Here are the deets:

Send your families home with games they can play over and over. Used to supplement a Family Math Night event or use separately, these Take Home kits are a great way to engage parents in their child’s learning. We have two different kits to choose from.

Click the images above for even more details.

 

Rubber Stampin’ Math – Part 1

Rubber Stampin’ Math – Part 1

I know it’s not quite spring yet but I’m a little anxious for it to start.  It seems like it’s been a long winter.  So, to encourage spring to get a move-on, I did a little spring cleaning.  And that’s when I re-discovered my drawer full of rubber stamps and colorful stamp pads.

rubber stamp1

These stamps and stamp pads were a staple in my third, fourth, and fifth grade classroom.  And when I ran centers in K-2, I used them there, too.  I loved how I was able to touch on so many different math concepts in a way that was fun for kids.

So I’m going to share with you, in two parts, some of the simple, fun, and mathematically powerful activities I did using these fabulous materials.

Part 1:  Equations, Expressions, and Arrays

Every opportunity I get I try to put students in charge of creating their own math problems.  It’s more interesting for them that way.  Plus I learn a lot about their math personalities.  Do they know how to create a problem and then solve it?  Do they stick with simple and easy problems or do they push themselves a little?  Can they explain why they did what they did?

So one day in Kindergarten during centers I pulled out the rubber stamps and stamp pads and had students create their own equations and expressions.  They loved it!  It was a new material for them plus they got to complete the task the way they wanted. The best part for me was that I got to observe how they did it.  A win/win!

Below are examples of what some of their work looked like.  For the bottom activity sheets I asked them to come up with a story to describe one of their expressions to me.  Since my time was limited and my focus was on the math and not the writing, I did the writing.  The bottom left story reads, “1 ladybug went to the park.  Then 5 other bugs came to play.  How many bugs were at the park?”

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In second and third grade, I had students create arrays. This fits so nicely into CCSSM 2.OA.C.4 and 3.OA.A.1.

rubber stamp4

rubber stamp2

The first photo shows how I had second graders use graph paper to record their rows and columns.  It made it a lot easier to line everything up.  Notice how the work on the right, done by third graders, was a little more difficult to keep things lined up.  Next time, I may have them use the graph paper, as well.By the way, as a quick aside, rows and columns are a convention in math.  A convention is just an agreed upon way to do something so that we all do it the same way.  Rows go across and columns, just like on buildings, go up and down.  We need to teach this convention to our students.

Next time in Rubber Stampin’ Math Part 2, we’ll explore generalizing patterns – the foundation to algebra.  Stay tuned.  Until then…

…happy stamping!

 

Pattern and the Common Core State Standards in Mathematics

Pattern and the Common Core State Standards in Mathematics

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.

Happy patterning~

 

The Equals Sign: CCSSM

The Equals Sign: CCSSM

I love activities that are super simple yet pack a powerful punch.  This is one of those.  And the good news is, it can be done no matter what grade level you teach which means it lends itself well to differentiation.  But the even better news is that it covers a lot of standards in a fun and engaging way.

The main objective, however, is to teach the concept of equality in equations. (I should mention that one of my pet peeves is calling equations number sentences.  If you’re interested in why, I explain it here.)

But the basic idea of an equation is that both sides of the equals sign need to have the same value in order for it to be considered valid, or true.  Too often young students think the equals sign means and the answer is.  It’s such an important foundational idea in algebra that it’s included as one of the Common Core Standards in First Grade:

Work with addition and subtraction equations.

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

So here’s an easy and fun way to underscore the equality idea.  Choose 15 – 20 numbers and create two expression cards for each number.  Pair students up and hand out one expression card per pair.  The students need to go around the room and find their matching expression.  Here’s an example of some I made for K-2:

pocket chart3

See how easy it is to adapt this to any grade level.  You can even deliberately hand out the expressions depending on the level of the students in your class.  So if you have student who need a challenge, give them more complicated expressions.

Here are ones I’ve used in upper elementary:

pocket chart1

Notice how the three equations at the bottom require that students know the order of operations!  What a fun way to have them practice that.

An easy extension is to have two expressions already set up and then have students place in the correct symbol:  <, >,=.  (CCSSM: 1.NBT.B.3)

pocket chart2

If you’re familiar with how I like to teach then you know what’s coming next.  Working in pairs, have the students create the expressions.  You’ll have to give them the numbers to work with and make sure that two teams (only!) work on the same number.  But it’s so much fun when they’re doing the activity using the expressions they came up with!

Simple yet powerful.

If you’re interested in some pre-made cards, here are two different sets I created.  They’ll be available to you free for the next week.  After that, you’ll be able to get them on our site.  Equation Cards K-2     Equation Cards 3-5

The idea of balance in equations is so important that we included it in our Nifty Numbers Family Math Night kit.