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How to Add Depth and Rigor to Addition and Subtraction

Hello everyone! I’m been on a LONG vacation from the blogging world and I am so excited to be back! This is my first in a series of blog posts about ways to increase the rigor of your math instruction, so be sure to check back for more ideas and FREEBIES!

Today I want to share a tried and true idea to use with your high achievers in addition and subtraction.  If you’re like me, you are passionate about providing rigor to all students, but it is especially vital to challenge your high achievers. If a child isn't challenged, how will he/she learn the correlation between effort and achievement?To many of us, increasing rigor seems like a daunting task and we don't even know where to begin.  We may question that if a student already knows his or her addition and subtraction facts, shouldn't we just go ahead and teach them multiplication?  You can, but before branching out to multiplication, how about providing those high achievers challenge by increasing the rigor of the grade level tasks we assign? 

What do you mean by rigor? 

By rigor, I mean to increase depth and complexity or the intellectual demand of your instructional tasks.  This is easily accomplished by providing opportunities for students to apply what they have learned through tasks that require them to analyze, evaluate, and create (think Bloom’s Taxonomy). 

How can I add rigor to my math instruction?

Provide Open Ended Math Challenges:  I particularly enjoy providing students with open ended challenges, and making pumpkin paths is a great open ended activity!  You can download this activity for FREE when you click the picture below.  

In this activity, students start at the pumpkin next to the boy. In each pumpkin, they   put a number and either a subtraction or an addition sign to show the operation. Their final number must equal the number on the pumpkin by the pumpkin patch sign.
The first time you introduce this type of puzzle, you need to model it with the entire class. I have included a demo sheet which you can use to model how to solve these puzzles. Simply project a challenge onto the whiteboard and work the puzzle with the class together. The thing to demonstrate is that there is NO ONE CORRECT WAY to create your pumpkin path. There are multiple ways to arrive at the ending number! I also suggest "thinking out loud" so the kiddos can hear your though processes as you go about completing the task. 

One thing I suggest is to write the numbers beside each pumpkin  to help the kiddos keep up with where they are along the path. I challenge my advanced kiddos to try to find at least 5 different ways to solve the puzzle - there are probably thousands, but 5 will do!  I chose to do this activity with pumpkins since it is November, but you can use Christmas ornaments, hearts, flowers, shamrocks, etc. for any other season.

As an extra challenge, you can have your students write a story about a visit to the pumpkin patch, and they have to include the problems in their pumpkin path in their story.  (see example below). I have included both black and white and color versions of all the puzzles, a blank puzzle so your can create your own challenges, AND a recording sheet. 

There are several ways you can use this activity with your students:

Morning Challenge With the Whole Class:
I like to project a puzzle up on the whiteboard and have the students work to complete it.  There is a recording sheet for the students to write their answers.  You can give the kiddos a copy of the worksheet, or have them use their whiteboards to figure it out.  When I use the product this way, I  have each student come up with one solution to the problem, but you can tell you high achievers to see how many different paths they can create! 

In a Center:
When I place these challenges in a center,  I like to print them out in color and then laminate them so students can write on the sheets with dry erase markers and then record their answers on an answer sheet.

End of the Day Wrap Up:
I like to give one of these out during the last 5-10 minutes of class.  According to research, kids remember best the first and last things they do at school, so this is a great way to keep your kiddos on the ball and have something neat to share with parents at home.

Let the kiddos take one of the puzzles home to work on, or better yet, have them create their own puzzle!

Many of your high achievers are probably used to sailing through most of their assignments, and this activity will take some real thinking.  They might have to erase and/or start over at times.  Then there will always be those kiddos who want to rush through and so they do things like 2 plus 1 plus 1 plus one plus 1....  With those types of kiddos I have to make some guidelines like - you can't use any number more than twice or you have to use at least 3 two digit numbers.   I like to challenge them to use BIG numbers.  How about 2 plus 68? and things like that.  If this activity seems to be daunting to some of your kiddos, this is the perfect time to talk about those habits of mind such as persistence. 

Be sure to download your free copy of these challenges and have a great week!  Check back next week for another freebie and another challenge to add rigor to your addition and subtraction lessons.  

Until then, remember to always...

Keep 'em Thinking!

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