I wanted to share with you these new tools that I ordered for this year. I knew that we would be studying a lot of fractions, and we only had the linear models for a class set. Normally, when introducing fractions I start out with whole sheets of colored paper and have students cut them apart into halves, thirds, fourths, and so on. Then students can lay these pieces of paper on each other to find equivalent fractions. While this has value for students understanding that fractions are parts of a whole (piece of paper), students tend not to cut them out perfectly, so their equivalence investigation is a bit skewed. Because of this I move to manipulatives for the equivalence investigation, but again, I only had tools that were linear models…so here is what I ordered… Foamy fraction squares!
What is even better than the fact that they are brightly colored and quiet?
Students can easily see that one-half equals five-tenths, one-fifth equals two tenths, and one tenth equals ten hundredths.
I ordered a class set of these from EAI education here. I promise I make no money from telling you about these, but they make teaching fractions so much easier. Every teacher who has used them loves them!
To help 5th graders understand decimals last week, I built this number line using an old roll of fax machine paper. I measured off a little over two meters and then marked every two centimeters to put another number, so I would have room to write the numbers and for them to actually be seen. Students don’t usually have much of a problem ordering decimals to the hundredths place because they can visualize pennies and dimes, but past that students struggle. Also, thousandths are a bit daunting to teach…after all they don’t make “thousandths” manipulatives….at least that I am aware of. This coming week, students are going to build their own number line between two hundredths and we are going to connect all of the number lines and put them somewhere…I am not sure where because it will be VERY LONG because 100 numbers are written on it. Another something I did to the number line is I glued hundredths blocks down underneath the hundredths numbers, so students could see the concrete representation of these.
In case you aren’t familiar in decimal base ten block world:
a flat = 1 whole
a rod = 1 tenth
a unit= 1 hundredth
When explaining hundredths and thousandths to students I do the unthinkable. I take a blue foam base tenth block and a pair of scissors in front of the class and SNIP a hundredth goes flying a few feet away. This grabs students attention because #1, I just cut a holy math manipulative, and #2 something just went flying across the room for those students who may have just momentarily zoned out . No worries, I have had tubs and tubs of these math manipulatives (oh we are calling them “tools” now) that I could build a shrine to them with lit candles. In other words I have plenty that if I cut one it isn’t a big deal. THEN, I take the itty bitty hundredth that I just cut and SNIP another slice goes flying. I tell students that this slice is one thousandth. This visual really helps students to see how tenths, hundredths, and thousandths are related. A speck can even be cut off of the thousandth so that students can see what a ten thousandth looks like. After I have cut all of these pieces off, I put them underneath the document camera so students can see them up close.
Use pattern blocks to help students find equivalent fractions. Students simply take the blocks and trade them in for larger and larger blocks until they can not use any larger blocks to make the same shape. See below for some examples. The first row shows the blocks as fractions of 1 hexagon.
To make using hexagons for fractions more engaging, call them cookies since they are yellow and the size of a cookie. There is a TERC math investigation lesson called “Hexagon Cookies” which is in the Fair Shares book (for 3rd grade). Hexagon Cookies makes a great lesson to teach previous to simplifying fractions with the pattern blocks.
Keep it REAL! This fourth common core standard for mathematical practice could be summed up in that statement. Modeling with Mathematics doesn’t quite mean pull out the snap cubes, color tiles, and pattern blocks. The essence of this standard is to create problem solving experiences for students that they will encounter in real life. Some practical problem solving experiences could include:
- If I have to put 2/3 cups of flour in the recipe and I need to double the recipe, how many times do I need to fill a 1/3 measuring cup to put enough flour in the doubled recipe?
- Which cell phone data and calling package is the best buy?
- What time do I need to wake up for school to get dressed and be there fifteen minutes early?
- If I can only spend 25% of my income on renting a house, how much money do I need to make to rent a house that is $500 a month? $600? $900?
- How could you create a floor plan for a house with 1428 square feet?
- If a certain medicine is shown to be effective 33% of the time, should it be used to treat an illness?
Another math coach related to me today the story of how a student she taught had named fingers sections as something that comes in groups of threes. She took this concept and helped students use this to develop multiplication strategies to learn their threes multiplication tables. Fours multiplication tables can be learned as well if students include counting the top part of their palm. See the pictures below for more clarification.