Distributive Property Interactive Tool = Visual Learning

This interactive tool makes a great visual representation of the distributive property/partial products for our students!  It is from the Math Learning Center, and it will help you to visually show how the distributive property works.  You put in the array size in the top boxes (max of 30 x 30), and then you can decompose either side by sliding the little widgets on the side.

Quick Videos to aid instruction

MathCuts is a great resource for teachers! These videos model for us how to use visual resources to help students better understand math concepts. It is shared with us through the Charles A. Dana Center at the University of Texas at Austin.

Here is a good one about partitioning for 1st and 2nd grade:





This one helps teachers to introduce the distributive property for 3rd grade:




This video shows how to use visual models to divide decimals.  Students are not expected to master a traditional division algorithm in 5th grade.  This video shows you how to spend time making sense of what is happening:

Visual Math

Another great website resource is available to us in Math is Visual. This website, maintained by Kyle Pearce, and it takes the concept that we continue to learn more about from Jo Boaler and gives us videos we can use in our room to support our teaching.

Math is visual!  When students see HOW math works over just memorizing abstract algorithms, they understand better.  This videos on this site will help guide you as you begin to include more visual examples, but it will support your students in having a clearer understanding of numbers and how they work.

Valentines Would You Rather

I have shared with many of you the website wouldyourathermath.  It offers great opportunities for your students to reason with real math problems.  It also offers them opportunities to explain their reasoning--something that we know is difficult for students. We need to be sure to offer these opportunities to all of our students so they can begin to practice more math thinking.

You might want to offer these to your students and ask them to give verbal explanations for a while before you begin asking them to write their reasoning. Be sure to encourage the use math vocabulary as much as you can, and to explain to them that they need to use math reasoning.  (They might tell you they would buy the M & Ms instead of the Butterfinger because they don't like peanut butter, but they need to acknowledge which one is the better math deal.)

Here is a simple Valentines Would you Rather? that you might want to try with your class.  I have scaffolded the writing portion of it by offering sentence stems at the bottom.  

Would You Rather? Valentines Candy (easier version)
Would You Rather? Valentines Candy

I recommend you take the time to check out the website!  It has a lot of prepared problems that you can use, or it might spark an idea for one of your own!  If you make some and would be willing to share, send me a link or share below.  Enjoy!

Extension Activities for Unit 6

Below are a variety of games, problems, and tools that you might use to help meet your students' needs in Unit 6 of Everyday Math.

1st Grade:
Two-Digit Targets:  This challenging place-value activity has an interactive version, but would be easy to print out for your classroom, too.
What is the Time:  Some extra practice with time
Coded Hundred Square:  Can your students crack the code for the hundred square?
Making Sticks:  This activity has a hands-on component that allows students to manipulate blocks to answer the questions.
Make those Bracelets:  Students are challenged to find as many solutions to the problem as possible.
GregTang books:  Use any of these books to reinforce problem solving and/or to introduce arrays.  This link takes you to the books in case you don't have the physical copy on hand!
Cookie Monster Puzzle:  Video that explains how puzzle works.  Great puzzle to promote perseverance.

2nd Grade:
Create a Bar Graph Online: This site allows students to input data to create a bar graph.Bar Graph examples:  Sample bar graphs to use in whole class or small group
Learn Zillion:  This site is good for introducing or reteaching the partial sums method of addition.
GregTangMath:  This site offers another way for students to look at partial sums.  Most of these problems are laid out vertically, so they may be for your students who have developed a strong conceptual understanding.
GregTang books:  Use any of these books to reinforce problem solving and/or to introduce arrays.  This link takes you to the books in case you don't have the physical copy on hand!
Sweets in a Box:  Great problem solving problem involving arrays layered in a box.
Thinking Blocks:  This visual model helps students to make sense of the story problem they are trying to solve.
Valentine 3 Act Task:  This 3 Act Task works on basic addition/subtraction.  Good for making sense of a story problem.

3rd Grade:
Make 100:  This problem asks students to use flexible thinking to reach 100 in as many ways as possible.
25th Wedding Anniversary: A 3 Act task using subtraction (and my grandparents!)
Would you Rather:  Students must make a choice and defend it mathematically.  This one deals with fractions.
Nim-7:  Not only do students learn how to play this game, they must think about the strategy needed to win.
Tables without Tens:  This problem asks students to find patterns in the multiplication table.
Carrying Cards:  Nrich problem in which students must look for patterns and do basic computation.
Is My Son Going to Win...Again?: Real world problem solving activity where students have a number of details to determine who will win the game of Monopoly Jr.

4th Grade:
Pebbles:  Students look to continue a pattern using as few pebbles as possible.
Massive Mosaic:  This 3 Act Task looks at area and division.
What's My Angle?: Extra practice measuring angles using a digital protractor
Would you Rather?:  This problem asks students to pick a side and defend their choice.  This problem deals with money.
Area and Perimeter:  These problems ask students to look more closely at area and perimeter.
Star Polygon:  An angle exploration from nrich.  Students investigate their hypothesis.
Alison's Quilt: Story problem with putting square pieces together to form a rectangular quilt.
The Quotient Cafe: App from NCTM that helps students visualize division

5th Grade:
Spiraling Decimals: Students practice knowledge of decimal value in this partner game.
Jumping:  Story problems that involve computations with decimals
Sugar Cubes:  3 Act Task that focuses on 5.NBT.6 and 5.NBT.7
Round the Dice Decimals: This nrich activity lets students think through the value of decimals.
Pick a Path:  This game from NCTM has students use all operations to move the octopus through the maze. Numbers include whole, exponents, and decimals.
Star Wars Phenomena:  This lesson involves a lot of number manipulation on a topic that many students are interested in:  Star Wars!
Carl's Aquarium:  Illustrative Mathematics task that gives real world exposure to volume
Your Number Was:  This machine can guess the number you are thinking of.  Try it with decimals!  
Would you Rather:  Students must make a choice and defend it mathematically.

One step at a time....

Many of us are looking for baby steps to begin our changes in math instruction.

Robert Kaplinsky just wrote an awesome post called, "I Hope You're Embarrassed."  In this post, he discusses how we should be looking back on our math instruction, embarrassed by the methods we used to teach our students in the past.  If we are embarrassed, we know that we have improved!  We might be embarrassed by methods we used in our first years in the classroom, a few years ago, or just last week!  No matter, noting that we can do better is a huge step towards more improvement.

In my talks with teachers, I try to expose them to a number of routines, problems, and best practices that I find in my own professional development, hoping that something I share will spark an idea for teachers to integrate into their own classroom.

Today, my spark is pretty straight forward: My Favorite No.  Watch this video from Teaching Channel and consider ways that you can use it in your classroom.  Ms. Alcala uses this routine daily; maybe for you, it is enough to try it once a week to start?  How can you take this practice and use it to help you transform your learners (and yourself) into better mathematicians?  

Have you tried this routine in your class already?  What were the results?  

Taking steps with CRA

As we work to be more intentional in our use of CRA instruction, there are some things for us to consider:

++All students should be involved in the concrete level of instruction.  

++After creating a concrete model, students should have the opportunity to explain their model to a partner and discuss what is being represented in their model.

++When students are learning in the concrete, they should still be exposed to the representational and abstract models.

++Some students may be in the concrete longer than others.  That is okay, but teachers should support these students in representing their concrete models on paper.

++When working in the representational level, students should again be given opportunities to explain their drawing with a partner and discuss what is being represented.

++Once students move to the abstract level with a concept, they should still be able to represent their thinking about that concept concretely and pictorially.  If they are unable to, then their basis of conceptual understanding is probably not strong enough.

++Remember--these steps are important to students' strong base for future math concepts that are much more complex.  We want our students to feel comfortable in using concrete materials.  We want our manipulatives to be readily available and the norm in our classrooms for all students.

Math talk is so important for our students to better reason through their work so that they gain a stronger conceptual understanding.  As we work to build our CRA instruction, we don't want to skip opportunities for students to discuss their models with others.

This acronym developed by Witzel, Riccomini and Schneider (2008) is a good place to start as you look at your lessons through a CRA lens.

1. Choose the math topic to be taught.
2. Review procedures to solve the problem.
3. Adjust the steps to eliminate notation or calculation tricks.
4. Match the abstract steps with an appropriate concrete manipulative.
5. Arrange concrete and representational lessons.
6. Teach each concrete, representational and abstract lesson to student mastery.
7. Help students generalize what they learn through word problems.

What are you learning about your students through this method of instruction?  What do you think are the hurdles? 

Real World Math

Math@Work offers upper grade teachers some great resources to use in the classroom.  The website offers webisodes and downloadable lesson plans and resources which will help yo ur students begin to understand the connection between math and their future careers!

I watched the webisode with Ty Pennington in New Orleans building a sustainable house.  The connections and the math were real and would be great stepping stones for our students as they begin to think about the future.  In the video, a math "expert" talks through solving the problems, but I think it would be worthwhile to stop the video and have the students see if they can work together to solve the problem before revealing the expert's solution.