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Category: Algebra

Power Packs: Building Number Sense in Grades 4/5

Power Packs: Building Number Sense in Grades 4/5

I’m excited to share with you that our Building Number Sense in Grades 4-5 Power Pack is now available.  All of our Power Packs are filled with games that teach parents strategies and tools to help their children build strong math skills.
As I mentioned in an earlier post, there have been a lot of changes in mathematics curriculum and pedagogy in recent years and a lot of parents don’t feel as prepared as they’d like to be when it comes to helping their child in math.  The power of these Power Packs comes in the integration of strategies and tools that parents use as they play the games with their children.  While playing the games, not only are parents learning about the new standards, they’re also gaining strategies they can use to help their child in math.

The strategies and tools in our 4/5 Power Pack are:

  • Partial Products Multiplication
  • Partial Quotients Division
  • Distributive Property for single- and multi-digit multiplication
  • Front End Estimation
  • Fraction Bars
  • Multiplying Fractions on a Number Line
  • Rounding
  • Order of Operations
  • Standard Algorithms for addition, subtraction, multiplication, division
  • Multiplication Strategies for Multiples of 10

 

I’ve been using games from each of our Power Packs during my recent Family Math Night events with great success.  Participants learn to play some of the games at the event and then get to walk away with a Power Pack of their own to continue the learning at home.  Click here to get a pdf describing how to use the Power Packs at your Family Math Night event.

In addition to using the Packs at your Family Math Night event, they can also be used as take-home math packs in the classroom and as classroom math centers.

If you have any questions about our Power Packs, or any of our Family Math Night products, feel free to contact us.  Our number one goal is to help you host the best event of the school year.

 

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 2

Rubber Stampin’ Math Part 2

Last time in Part 1 of Rubber Stampin’ Math we talked about dusting off those rubber stamps and using them to create expressions, equations, and arrays.  In Part 2, I’m going to share how I used them in second and third grade to introduce multiplication and how that translated to algebraic functions in fourth and fifth grade.

Part 2:  Multiplication and Functions

For these next activities, the type of rubber stamps students use is very important.  So let’s start with something fun.  Take a close look at the stamps in the photo below. One of them does not belong with the group.  Can you figure out which one?

rubber stamp3

You probably came up with several options for the incorrect stamp.  Maybe it’s the orange star stamp because it’s a circle…or it’s plastic…or it’s in full color.  But that’s not the one.

Maybe it’s the yellow star to the left because it’s the only one that doesn’t have eyes?  (I’m grasping here…but kids will, too!).

Nope, that’s not the one.

It’s actually the octopus.  Why that one? Although we know that an octopus has 8 legs, it’s hard to look at that stamp and be able to count each one.  The stamps we need for these next activities must have “parts” that can be counted.  The legs on the spiders can easily be counted.  The wings on the butterfly and dragonflies can be counted…the points on the star…  But the octopus?  Well those legs are hard to count so that stamp is out.

Now that we have a bunch of stamps with parts that are easy to count, we’re going to explore beginning multiplication.  For this activity, I created a t-table where students could stamp in rows starting with one stamp in the first row, two stamps in the second row, etc.  In the photo below, Miranda chose to stamp butterflies.  In the second column, she needed to write the total number of wings on all the butterflies in each row.  Notice how easy it is to count the wings.

rubber stamp5

The next step was to have her transfer the numbers in the ‘wings’ column to a multiplication table.  That’s what you see in the photo below the t-table.  She created a t-table for each of the numbers 2-9 and transferred the numbers.  We didn’t stamp the numbers 1 or 10 since they were pretty easy.

When all of Miranda’s numbers had been transferred to the 10 x 10 grid, what she ended up with was the multiplication matrix.  But not just any multiplication matrix.  A matrix where each of the numbers had meaning.  ’24’ became 6 butterflies each with 4 wings.  Or maybe it was 3 spiders with 8 legs each. The connection between multiplication and repeated addition was solidifying.

rubber stamp6

At this point, there were some students who were ready for the next level of abstraction.  Miranda was one of them and that’s where the yellow post-it comes in.  Now we’re getting into algebra.  B = butterflies and W = wings.  In the left column, she wrote the number to represent the butterflies.  In the right column she wrote the total number of wings for the particular number of butterflies.  No more counting wings.

In fourth and fifth grade I take it a level higher and we start moving towards functions.  I do a few quick activities like the ones described above and then everything becomes abstract.  We switch from ‘Number of Butterflies’ and ‘Total Number of Wings’ to ‘In’ and ‘Out’.  It looks something like this:

IN OUT
1 4
2 8
3 12
4 16

From there it’s a simple morph into ‘X’ and ‘Y’ columns and creating equations:  4x = y. Once they understand the ‘Y’ column is a function of the ‘X’ column (and the same thing needs to happen to each number in the ‘X’ column), we move to equations such as 2x + 2 = y.  Easy peasy.  Really.  They love it!

rubber stamp9

Although we’ve been using rubber stamps in all these activities, stickers with parts that can be easily counted, work just as well.  For example, here’s an activity that I did in…are you sitting down…Kindergarten:

rubber stamp8

The students got so into looking for number patterns on the hundreds chart that I thought I’d give this activity a go.  Turns out, they loved it!  I included a number grid below the t-table so they could circle the numbers that showed up in the second column.  Next time, I would arrange the numbers to look more like the hundreds chart.

Then I used strips of graph paper taped together to represent the ones and the tens column.  The students who were ready for this part wrote the numbers in the columns and then looked for patterns.  It’s hard to see in the photo but this particular kindergartner got sooooo into this that, once he discovered the pattern, he took the numbers all the way to 4,110.  Yup. That’s four thousand one hundred ten.  Amazing. And my rubber stamp collection started the whole thing!

rubber stamp7

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~