Building Fraction Understanding

In a recent webinar by Graham Fletcher, he discussed the enigma of fractions for a student.  He had what I believed to be a great perception. Just like we teach kids to subitize whole numbers, we could dispel the notion that fractions are difficult by having kids learn to subitize fractions.   And, just as we have students subitize whole numbers in many different ways--through dominoes, fingers, dice, tally marks...we should present fractions in many different ways in order for them to be able to better understand their meaning.

The SMART document that I made stems from Graham's idea, but I also made it with Number Talks in mind.  I think these images could bring up some good math discussions and justifications of fractions.  It is made with images that are easy enough for 1st grade, and some that would be relevant in a 5th grade class.

If you decide not to use the image as a number talk, you might print out a page of the SMART document and have it be a collaborative activity for kids to decide.  

No matter how you use the pages in this doc, it would probably be good to print out the image so that students could cut the pieces apart so that they could prove their thinking to themselves and others by manipulating the pieces of the image.

Sample image from Fractions SMART doc. Click to download document.

Do you have other ideas on how you could use the pages in this document?  Feel free to share below.

Toying with Tangrams

Do you enjoy the challenge of a good puzzle?  Sometimes, people really like them, and sometimes--not so much.  However, most people believe that puzzles are a necessary component to child development.  They help children to build spatial relationships as well as problem-solving skills.  Besides that, the hands-on component of puzzles is an important form of learning for some of our students.

Tangrams are the puzzles that especially seem to connect with math because of their geometric shapes.  If you want to introduce  your students to tangrams, this book is a great start!

You might decide to read and discuss this book as part of reading workshop, or it might be part of your listen to reading activities when you send students to this Youtube video of the book.  No matter how you decide to use this book, it is one that students are sure to enjoy!

Another great book to use with younger kiddos is this one:

If your students are older, you might be able to review the legend of the tangram, and then have them move into building with tangrams.  You might have them as a recess activity, an activity that they can choose when they have completed their work, or a math station.

Here are some resources that might help you put tangrams in your students' hands:

Tangram pattern cards

More Tangram pattern sheets

Interactive Tangram puzzles

A web unit for students in grades 4-5

Online Tangram puzzles

More online Tangram puzzles

A friend of mine used to make each of her students a tangram set for the holidays each year.  She would then print out a couple of patterns that they could do at home, too. What a great idea!

Once your students become used to tangrams, you might try a literacy activity I used to use as an option for my kiddos:

After reading a book, they would make a tangram picture that represented the beginning of the book and then write a sentence or two about the beginning.  They would do the same for the middle and the end.  It was a fun option for some of the kids!

Do you have other ideas for Tangrams?  I'd love to hear them. Please comment below if you do.

Area Model Thoughts

I 💗 the area model!  I think it is worth your while to watch this video if you teach this method! (and even if you don't)





 Thoughts?

Looking for Extension Activities for Unit 4?

If you have some students who pretest out of Unit 4 in Everyday Math, you may find some of these activities will help meet their needs.  Even if you don't have students who test out of the unit, these activities will take some of your grade level's unit skills and look at them at a higher level.

1st grade:
Game of Totals --whole day lesson from Youcubed
Snap It--great small group activity that could be used for combinations of 10
Eggs in Baskets--problem solving problem with conditions that make kids make sense
The Brown Family--problem solving activity
Make Ten blog post--this blog post from last year focuses on resources to help teach making ten
Popping Balloons--A 3-Act task that focuses on combos to 10

2nd grade:
How many Times?--problem solving activity about time
Wonky Watches--another problem solving activity about timeWhich is faster?--problem solving about place value and giving supporting evidence for your thinking
That number square--problem solving about numbers to 100
Fruit Shoot--online place value game where students match base ten blocks to numbers. FUN!
Place Values Shapes game--another fun online game for kiddos to think about place value differently.  Challenging!
Place Value Pirates--online place value game
Would you rather--scenario where students choose what they think is the better choice

3rd grade:
Area Shapes game--good review interactive game for students to practice area
Perimeter Shapes game--online review game that practices perimeter
Quadrilateral Shapes game-- interactive game that has student practice with different types of quadrilaterals
Rectangle Interactive--this interactive activity helps kids connect area to the length of the sides of the rectangle
Paper Cut--3 Act Task that explores area
Numerically Equal--problem solving that asks students to look at area and perimeter
Quadrilaterals--problem solving that looks at different attributes of quadrilaterals

4th grade:
All the Digits--problem solving involving multiplication
Shape Times Shape--multiplication problem solving with an introduction to algebra
Table Patterns Gone Wild!--looking for patterns in multiplication tables
Multiplying two-digit numbers--Open Middle activity for finding a product
Massive Mosaic--3 Act Task which focuses on multiplication of two 2-digit numbers
Would you Rather--scenario where students have to choose and defend the better choice

5th grade:
Scooter Quest--online game to practice decimal place value
Rounding Decimals--Open Middle rounding decimals problem
Meteor Coordinates--This onlinegame gives students a chance to explore coordinate pairs.
Place Value Pirates--online game to practice decimal place value
Hungry Puppies--online game where students choose decimal values to combine to make the target
Matching--this online game has students match decimals, fractions, and percentages
Round the dice--an investigation about rounding decimals
Spiralling Decimals--a game of strategy and knowledge of decimal size

If you have other resources to share, please add them in the comments below!

Halloween and Logic

Construct viable arguments and critique the reasoning of others.

This mathematical practice standard is one that needs to be practiced often with our students.  However, some of them get so flustered by the math that they can't explain their reasoning to others let alone listen to other students' ideas.

Consider trying these logic puzzles with your students.  Logic is a great way for students to practice their thinking, and it is often easier for some of our kiddos who struggle with some of our grade level content.

These logic puzzles are October/Halloween themed and vary in difficulty. They are good practice at thinking skills but also in relational words.  I have also created a document for you that has the images for the puzzles.  Often, it helps the students to have something to move around on their desk.  You can just give them a strip of pictures that matches the puzzle you are doing, they can cut the images apart, and then move them as necessary to solve the problem.

If your students like these, consider an activity where groups try to make up their own.  It is more challenging than it looks.

Please share with a colleague.  Comment below if you find other ways to use them in your classroom.

A Parent Resource

I found this website recently, and have found some great resources on it.  It is intended to help parents talk math with their children, but I think it can give us some good ideas to tie math to the real world in our classrooms.

The site is called Table Talk Math.  This link will take you to the homepage, but the main place of inspiration for me is the Newsletters link.  In this link, Mr. Stevens shares everyday math examples and how we should talk to children about them.

Please consider sharing this link with your parents.  We need to continue to encourage parents that math is not about a set of problems on a worksheet or memorizing your facts.  It is real-world, and it is all around us all of the time.  I think this site will help them start to see that themselves!

I think the book by John Stevens looks like a good resource, too, so maybe I'll add it to my Christmas list.  It is only 11 weeks away, ya know? :)

One More,One Less

In a recent meeting with our building interventionists, they shared their concerns about students in upper grades who cannot count backwards--especially when they have to cross a ten (42, 41, 40, ?).  I have found a similar problem in a number of the Firsties that I work with.  These students can rote count, but they aren't always sure of the meaning of "before," "after," "one more," or "one less."

This lack of number sense is concerning, but I think we can find ways to strengthen our students' understanding through continued practice and modeling.  I have created this SMART Notebook resource as a way to help us meet this problem head on.  If this is a problem you know that some of your students face, you might be able to use this document in small group, or as a class warm-up every now and then.

Counting backward and understanding the relationship between consecutive numbers would fall into one of our Essential Skills.  Please share in the comments below if you have other ways to help build this understanding in our students.