Guest Blog: Number Talks in a 3rd Grade Classroom

Magen Schott, 3rd grade teacher at Knowles Elementary, is our guest blogger this week! She has been using number talks with her students, so we asked her if she would share her thoughts on the topic. Thank you Magen, for sharing your learning and inspiring others through your experiences.

"Since beginning Number Talks in my classroom, my kids are able to have great conversations about their mental computations. It's easy to have a conversation in Language Arts class about the main idea of the book, the author's purpose, etc.  Before reading Number Talks, we never had REAL conversations in Math about numbers.  It has been amazing to listen to my kids discuss numbers in this way.  Students have learned to reason with numbers, and their mental math ability has greatly increased.  Our classroom is a "safe" place for the kids to be wrong, and they are open to admitting their mistakes.  They all learn from each other, and most have begun to try out and adopt different strategies that others are using.  I feel that they think about numbers differently now-- that numbers can be taken apart and combined with other numbers to make new numbers.  They have great conversations about manipulating numbers to make the problem easier and organizing numbers into groups of thousands, hundreds, tens and ones."


Below is a impromptu video recorded during a recent school improvement visit.  Watch Magen's class in action!

Comment below how you use number talks in your classroom...

Traditional Algorithms VS Invented Strategies

There are significant differences between traditional algorithms and invented strategies.

The traditional algorithms are based on performing the operation on one place value at a time with transitions to the next position. They involve trades, regrouping, "borrows," "carries" or Dead Monkeys Smell Bad!  The procedures are rigid.

Traditional algorithms take the understanding out of place value. They are "digit oriented." They rely on procedures or steps that must be done in a specific order and usually start in the ones place. 

Look at theses examples of traditional algorithms for addition and subtraction. They follow a procedure.

Think about what is being said as you solve this problem: 7 plus 8 is 15. I put down the 5 and carry the 1.  One plus 5 plus 3 is 9. Three plus 2 is 5. The answer is 595.

Think about what is being said as you solve this problem: 3 minus 7, you can't do it so you have to go next door and borrow 1. Since they don't have any to give you they go next door and borrow one. The 3 becomes a 2 and the zero becomes a ten. Now they have one you can borrow so the ten becomes a 9 and the 3 becomes a 13. Now you can subtract! 13 minus 7 is 6, 9 minus 6 is 3 and 2 minus 1 is 1. The answer is 136.

Invented or flexible strategies develop a good understanding of the operations especially the commutative property and the distributive property of multiplication. Students start to see the relationships of addition to subtraction, addition to multiplication, and multiplication to division. What an important concept! 

Invented strategies involve taking apart and combining numbers in a wide variety of ways. They are "number oriented." Most of the partitions of numbers are based on place value and start in the largest place. 

Now look at the examples of the same problems. Although these may look complicated many invented strategies can be done mentally and just recorded on paper.

Think about what is being said as you solve this problem: 300 plus 200 is 500, 50 plus 30 is 80 and 7 plus 8 is 15. I add them together and 500 plus 80 equals 580 plus 10 is 590 plus 5 more is 595. The answer is 595.

Think about what is being said as you solve this problem: 300 minus 100 is 200. Since I know 67 + 33 gets me to 100 then 200 - 67 is 133. But I still have the 3 ones in 303 that I need to give back. 133 plus 3 is 136. The answer is 136.







Your Turn: 
Think about the traditional algorithms for multiplication and division. Are they rigid procedures? Are they "digit oriented?" Do they build understanding of number relationships? 

Be careful: Don't turn an invented strategy into a "procedure." 

Students must be allowed to develop their own strategies based on their own understandings!

What is a Rekenrek?

Directly translated, rekenrek means calculating frame, or arithmetic rack. Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland, designed it to support the natural mathematical development of children and to help them generate a variety of addition and subtraction strategies. 

Students can use the rekenrek to develop computation skills or solve contextual problems. Once children understand the operations of addition and subtraction, and can model various situations, it is important that they automatize the basic facts by finding and using patterns and relationships. 

Unlike drill and practice worksheets and flashcards, the rekenrek supports even the youngest learners with the visual models they need to discover number relationships and develop automaticity.

The rekenrek looks like an abacus, but it is not based on place value columns or used like an abacus. Instead, it features two rows of 10 beads, each broken into two sets of five, much like the ten frames.

How to Make a Class Rekenrek

First get a sturdy board. I used a large foam board (20"by 30") that I purchased from Hobby Lobby for $1.99. The clerk was nice enough to cut it in half for me so I can make two!

Next, I drilled two holes on each of the short ends. The holes are 4 inches in and 2 inches from the ends.

Gather scissors, 20 unifix cubes (10 blue and 10 red and free from your math manipulatives), and string. I used S'getti Strings that came on spool of 50 yards for just $1.99.

Then string them up! 

And tie them in the back! 

Now you have a classroom rekenrek (priceless!)

You can also download a free app called Number Rack. 

Your students each need one too! Use poster board, mat board or any stiff cardboard you can get your hands on. I cut my boards into 8 inches by 4 inches pieces but you can do whatever size works for you. Use red and white beads and the S'getti string just like your classroom board. Now you are ready to go!

Here is a confession from a 2nd grade teacher:

Give it a try and let me know how it works.