Wednesday, April 16, 2014

The Using Doubles Strategy for Addition

Back in November (has it really been that long?) I blogged about the Make a 10 strategy for addition.  I included a little freebie that you can throw in a workstation to help students practice the strategy and develop fluency of harder facts by using facts they already know.

Another great strategy for tackling those harder facts, like 7 + 8, is the Using Doubles strategy.  Students often easily learn their doubles (2 + 2, 3 + 3, 4 + 4, etc.). If your kiddos are still learning their doubles, check out this post for a fun kinesthetic way to practice. The Using Doubles strategy involves decomposing one addend to make a double with the other addend.  For example 7 + 8 is the same as 7 + 7 plus 1 more. Double ten frames are great for exploring the strategy.  Have students build each addend on a different ten frame.  For example, 7 + 8 would look like this:

You can download a ten frame template here.

After you've introduced the strategy and students have had a chance to work with manipulatives to understand the strategy, it's time for a little independent practice! This little freebie includes a set of workstation cards and an "I Can " card for student directions.  Have students record their work in their math journal for accountability and for a quick formative assessment.

Grab your freebie here! :)

Monday, April 14, 2014

Multiplying Fractions

Next year in Texas our 5th grade teachers are wading into unfamiliar waters as our new TEKS (Texas standards) push computation with fractions down to 5th grade.  Now that we've finished our state testing (at least for 5th grade math), we're covering some of those gap skills that our 5th graders will need as 6th graders next year. Enter multiplying fractions.

Our standard requires students to multiply a whole number by a fraction.  Here's some things to keep in mind when introducing this skill:

  • Remind students about the connection between multiplication and repeated addition. The problem 3 x 2/5 is the same thing as 2/5 + 2/5 + 2/5, which is 6/5 or 1 1/5.  
  • Remember to return to the concrete and representational stages of learning since you are introducing a new skill.  Pull out those fraction tiles or strips so students can model 3 x 2/5.  Don't leave out the number line, which is a great representation for fractions.
  • Put the problems in a real life context.  Fractions are very abstract and misunderstood by many students, so you absolutely need to put them in context.  Beth is making 3 picture frames.  She needs 2/5 yards of ribbon for each picture frame.  How many yards of ribbon does Beth need to buy?
Once you've done some modeling and guided practice, your students will be ready for practice.  Grab the fraction cards from this post, a number cube, and these workstation instructions, and you're all set to go!

 Do you have any great tips for multiplying fractions?  Add them in the comments!

Friday, April 11, 2014


I just have one thing to say as I start this post:  If you have not attended an NCTM National Meeting and Exposition, you MUST plan on Boston next year.  What an amazing experience!  Not just the sessions by the leaders in mathematics education, but also the networking with colleagues.  I've met so many wonderful people and had great discussions.  Let me put it in perspective, today I had to choose between a session by Jessica Shumway, author of Number Sense Routines, and a session on how to choose CCSSM aligned materials with one of the authors of the CCSSM, Jason Zimba.  Agonizing choice, especially since I'm on my math rock star tour, hoping to meet as many of my favorite authors as possible.  Ultimately, Jason won, so I'll just have to go to Boston to meet Jessica!

Two great takeaways from Jason's talk:
  • Kindergarten is the beginning of the path to college readiness
  • Parents don't like thinking that everything they have learned about math is now useless; enlist them to help with what they can
Now for the next stop on my rock start tour. I've been attending as many fraction sessions as I can, because in Texas our new standards (TEKS, not Common Core) are pushing a number of fraction concepts down.  This afternoon I attended a session on computing with fractions presented by Suzanne Chapin.  As in the author of Classroom Discussions in Math and Math Matters. Another heavy hitter!!  Coincidentally, I had lunch with a colleague (although we didn't actually eat, because we were too busy chatting), and she asked what my current focus was for learning.  I told her productive math talk and the power of mathematical discussions in the classroom.  So here is my selfie with Suzanne Chapin. :)

A half day tomorrow, and then I'm back to Texas with a brain full of new mathematical ideas!

Thursday, April 10, 2014

Math Rock Stars in the Big Easy

I am in math paradise--the NCTM Annual Meeting and Exposition in New Orleans, LA.  I presented my Quick Daily Routines for Building Number Sense first thing this morning, and I was pleasantly surprised that the 8:00 AM start time and the long trek to the far end of the convention center didn't deter folks from coming to my session.  So great to meet lots of talented, dedicated math teachers and enjoy learning together.  We talked about rekenreks, number bracelets, Shake and Spill, and games for making 10.  I was duly corrected for calling a 10-sided "polyhedral randomizer" a number "cube".  Oops!

After finishing my session, it was a quick trip across the street to change into comfy clothes for the rest of the day.  And what a day!!  First up was a session with Laney Sammons (of Guided Math fame) on math conferences.  I'm a huge fan and I've been reading her new book, so it was such a pleasure to meet her.  And I can tell you she is warm and wonderful in person.

My next session was with another of my math heros, Sherry Parrish, author of Number Talks.  She and co-presentor, Ann Dominick, were presenting on using number talks for developing fractional reasoning.  Which got me to wondering if a number talk book on fractions is forthcoming.  And the answer is YES!!  How exciting is that?  No specifics, but it's in the works.

Lest you think I'm not enjoying the sights and sounds of NOLA, as soon as I hit publish on this post I'm heading out to enjoy the French Quarter Festival.  More on-the-spot reporting tomorrow. :)

Monday, April 7, 2014

Counting by Tens off the Decade on a 100 Chart

I was planning with my Kinder team today, and the discussion turned to skip counting by tens off the decade. Traditionally, when skip counting by tens was taught, we asked students to count the multiples of ten--10, 20, 30, etc.  Counting by tens off the decade involves counting by tens from a number other than a multiple of ten, for example 7, 17, 27, etc.

The hundred chart is a perfect tool for skip counting by tens because of the arrangement of numbers in rows and columns.  As you move down a column on the hundred chart, each number is ten more than the number above it.  To help students practice skip counting by tens off the decade make two copies of a hundred chart--one on white card stock and the other on a colored card stock.  Laminate the charts for durability.  Cut the colored hundred chart into strips and place the complete chart and strips in a workstation.  Students take turns selecting a strip, placing it on the hundred chart, and reciting the numbers.

Grab a free hundred chart here.

Saturday, March 29, 2014

Making Ten, Easter Style!

One of my most popular freebies is Ghostly Make Ten, so I decided to do an Easter-themed version with the adorable Peeps bunnies I found at Krista Wallden's store. I really like this game because it's concrete practice, but it also connects the abstract (symbolic).

Grab it now at my TpT store.

Wednesday, March 26, 2014

Tips for Effective Remediation

It's testing season (sigh...), and before you get into the meat of the blog post, enjoy a good laugh with this video!  Just click on the picture.

I laugh so hard each time I watch that video, but it's also a bit of a sad commentary regarding how we often 'prepare' our students for standardized tests.  I've been working with some of our 5th graders the past few weeks, helping to remediate before our state testing, and I wanted to share some thoughts about remediation.

Remediate the skill, not the test

It's very common to give some type of benchmark test prior to state testing to determine the areas that students still struggle with, but sitting down with a student or students and 'going over' the items they missed on the test is not remediation. Explaining to a student why they missed the question isn't likely to help them gain any additional understanding of the underlying skill.  If a student missed a question on fractions, you have to find out what they know and don't know about fractions. What's the best way to do that?  Talk to them!  Given the student a similar fraction problem and have them talk through their process for solving it.  You'll know immediately when they stray off the path of understanding, and you can step right in with corrective steps.  Then be prepared with a few additional practice problems that they can work first with your support (through questioning, not telling), and gradually on their own.

Don't resort to tricks

We've all been tempted.  It's two weeks before the test and your students still can't compare fractions.  Time to teach them to cross multiply!  Please. Don't.  We owe it to our students to give them quality instruction, and that means teaching for understanding.

Help students recognize their strengths and weaknesses as mathematicians

This is huge!  Students need to hear that they have strengths and they also need to be aware of their weaknesses.  Consider this conversation I had while remediating a student on subtraction with regrouping:
I notice that one of your strengths as a mathematician is that you REALLY know your facts!  You knew that 15 minus 8 was 7 without even hardly thinking. That's a huge strength!  Here's what I noticed.  You really struggled regrouping when there was a zero in the problem.  Did you notice that?  (nods head) When you thought hard about it, you could remember what to do, but it was harder for you than the other subtraction problems wasn't it.  If that's a weakness you have as a mathematician, what should you do when you come to a problem like that?  Slow down?  Absolutely!  That's a great idea. Just being aware that that's a problem for you and that you need to slow down will help you do better.  What about checking with addition?  Would that be a good idea, too?  Oh, yeah, I think that would be good. Great!  Thanks for all of your hard work today. 
Contrast that discussion with this one I had with a student who was working on multi-digit multiplication:
You've just worked five multiplication problems for me, and you've got the process nailed!  You know exactly what to do, how to regroup--EVERYTHING!  But you got the wrong answer on three of the five problems. (looks shocked)  Really?  Yes, these three (pointing them out) are wrong.  Let's look at this first one.  Walk me through your work.  8 times 6 equals (long pause and much thinking)...Oh!  It's 48 not 52.  That's right!  8 x 6 = 48.  How well do you know your facts?  Not too well.  That's what I was thinking.  It looks like you missed these other two because of fact errors, too.  First, I want to suggest you practice when you can, because knowing your facts makes everything in math easier, but let's talk about some strategies you can use on the test.  If you aren't sure of a fact, should you guess?  No. That's right!  Let me show you this tic-tac-toe strategy you can use when you're not sure of a fact.  It would just be a shame to miss a multiplication problem because of a fact error when you can do all the really hard math, right? Yeah (sheepish smile). Awesome!  Thanks for working with me today. 

Realize how much YOUR attitude matters! 

Think of yourself as a mirror, because your attitude and outlook reflects directly on your students.  Keep your conversations upbeat and positive.  SMILE!  Let your students know that you think the tests are exciting, because it's a chance to really shine.  I like to compare it to the Super Bowl--sure the players have butterflies when they take the field, but their strongest emotion is excitement, not fear.  Remind them that they all have strengths as mathematicians and that they've learned strategies for overcoming their weaknesses.

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