Another puzzle website!

I have posted before about the algebraic thinking mobile puzzles from Solve Me Puzzles.  They are great for increasing our students' understanding of equality, and they give even our youngest students some exposure to algebra concepts.

Solve Me Puzzles has another great puzzle called Who Am I?  These place value puzzles ask students to figure out the value of the number from the clues.  There is some similarity between these puzzles and our Everyday Math place value puzzles.

On both sites, the puzzles progress in difficulty.  I think both puzzle sites could be used in some way with students in 1-5.

There is a third puzzle available on the Solve Me Puzzles menu.  It is called Mystery Grid.  You might have students who enjoy it, too.  It has some similarities to Sudoku puzzles and KenKen puzzles.  (I don't find it quite as much fun as KenKens...)

These puzzles might work well as an opening or closing activity during your day, a partner activity, or a station during math workshop.  They will definitely help build our students reasoning, thinking, and mathematical skills!

Place Value People

As part of a study of place value, I often do a kinesthetic activity which seems to help everyone "get it" a little better.  

I have digits written on construction paper and laminated:  One number per piece of construction paper.  I also have a piece with a comma that says thousand, a comma that says million, and a decimal point that says and.  

I pass out the digits, commas, and decimal point randomly to students.  Then I make up a number and tell the class.  As I say the number, students with corresponding digits go to the front of the room to make the number. They line up and form the number for us by holding the card in front of their chest so we can see it.  I usually let them collaborate some, but I really want them to do some independent thinking.  It helps me to see who is still struggling with the concept.  Once they think they are set, I have another student who didn't have a digit, read us the number. This is good practice for them as well.

After we are done with that number, students hand out their digits to classmates who don't have one, and we start the whole process all over again.

Sometimes, when they have the number made,  I will say "Let's reduce this number by 20,000."  (or something like that)  Then students have to figure out who is affected by this change and who would come take their place.  I begin this in our beginning stages of place value, but it is a great go-to throughout the year for review. Something to think about trying that gets kids up and moving!

TEN FRAMES: For more than just K-1

Most of us are familiar with ten-frames as a structure for making sense of numbers in the primary grades.  Students use it to learn facts, to represent numbers, and to help them think through problems.

This is a ten frame representing the number 4. It also could be used to represent a variety of facts including 10 - 6 = 4. These ten frames make sense to our little kiddos.  They are prevalent throughout our classrooms. They are the concrete representation of numbers when students use the manipulatives to build the numbers and the pictorial representation when put onto paper.  The concrete and representational stages are very important to conceptual understanding before our students move into the abstract stage which just uses numbers and symbols.

But what if we tried to bridge the gap by using ten frames with our older students in grades 3, 4, and 5?  Certainly, there might be some of our students who still need this ten frame to help them make sense of some basic number problems, but what if we looked at it differently?  What if the frame represents 100 and the counters are each worth 10? This ten frame could help our kiddos make to see that 40 is closer to 0 than to 100.  It might help them to better conceptualize our base ten system.  Similarly, the counters could represent 100 and the frame could be worth 1000...

Having some manipulatives and visuals that are common with our students from K-5 should lead to a stronger conceptual understanding of numbers.  Our students use base ten blocks well, but I believe this would be a next step to help them build their deep understanding of our numbers and how they work. Besides, a ten frame is often easier for a student to draw independently to represent their thinking than base ten blocks or a 100 grid. To show ones in the grid above, students could break one of the ten squares into a smaller ten frame as shown below.

This ten frame could represent 43.  It could represent 430.  Using these frames in a variety of contexts will help our students to better understand how numbers work.

Whole numbers in ten frames are great, but what if we used the above ten frame to show 4.3?  Students can easily visualize the 4 ones and then the next one has been decomposed into 10 parts/tenths.  Using these visuals would help adding, subtracting, and rounding easier.

Similarly, the above ten frame could represent o.43 with each counter being worth a tenth and each of the little counters representing a hundredth.

Using these ten frames in a variety of ways will help our students to gain a stronger foundation of place value.  By changing the whole of the ten frame, the number being represented inside changes.  For some of our kids, it will provide them with an easier way to record numbers.  For others who struggle with place value, it might offer them a familiar format that they can understand.

Do you have other ideas for using ten frames throughout grade school?  Please feel free to share in the comments below.

Building Number Talk

Mr. Elementary Math has a lot of great ideas.  This is one that I thought I would share.  This document  he shared has two templates:  one geared for primary grades and one geared for intermediate grades.

He calls this activity The Amazing Race.  The premise is simple.  Pair students.  Choose a number for them to put in the "Number of the Day" box.  They then work with their partner to come up with as many ways to decompose that number as possible.  He recommends starting with decompositions to help build place value knowledge, but I think as your students' abilities progress, you could begin to ask for other ways.

Teachers can move from very easy numbers to decimals, fractions, or exponents depending on their students and needs.

There are many ways it could be used in a classroom:  in a math rotation, as an opening or closing activity, as a challenge activity, as an early-finisher activity...No matter when you use it, I recommend that you get students to collaborate and talk math. It is a great opportunity to use and build their math vocabulary.