### Tag: Fractions

Age: 6
Presentations: Putting Fractiosn in order from 1 to tenth, Matching Fractions From Whole to a Tenth

Note: Here are my other posts on our Fraction presentations.

Traditionally, Montessori fractions start in first grade.  Now that Astroboy is officially in elementary, it is time to visit the subject.

I showed Astroboy a bit of it along side Thumper our first year homeschooling.  I spent a lot of time making materials and we zoomed through nomenclature,  The AMI style albums were a bit thin on follow up and the children weren’t too interested in making booklets.  Following the presentations, I tried having Thumper look for equivalence, she disliked the repetitive work.

Because of all this, we kind of gave up on fractions altogether our second year.  This year, with Thumper starting state testing, it is time to go back and cover all the subjects we were supposed to be teaching but never get around to.

In my Montessori albums, you start Fractions with nomenclature.  In Montessori primary, this is done with the skittles.  Astroboy did this once or twice.  He wasn’t too interested.  In elementary, you start with the fraction insets, which I did not bring to Taiwan.

After the confusion that was the fraction charts last semester, I sat down and re-did them this week since my fraction section of the album was due.  It helped that I’ve actually seen and illustrated the whole fraction section of the album.  It made organizing and understanding why the charts were there.

I do want to note that my trainer said it’s better if the kids are making these charts.  So I don’t know whether or not I’m going to be printing these out for Thumper.  A few weeks ago, she made a multiplication table when she needed them.  I kind of want the same thing to happen with the fraction charts.  It’s no use as a reference if she doesn’t need them.

I have 22 fraction charts.  It’s based on the album and also copies of my trainer’s fraction charts (which were not complete and also were missing charts or had extra charts).  I also used these three sites as reference:

It’s two more than the first two websites, because of chart 8 and chart 11.  Their charts do not have these “statements”.  One is imbedded in another chart.  But since my album says so, I made mine that way.  There’s also a mysterious chart 22, which isn’t listed in the album itself.  I’m guessing it probably should belong within a multiplication chart, but the trainer didn’t have space for it.  I also made a change from the original charts so it said like and unlike denominators.

1. Introduction to Quantity, Symbol, and Language
• Chart 1 – Fraction as circular units divided into pieces from 1 to 5.
• Chart 2 – Fraction as circular units divided into pieces from 6 to 10.
• Children may make square charts.
1. Equivalence
• Chart 3 – Equivalence for 1/2 fractions
• Chart 4 – Equivalence for 1/3 fractions
• Chart 5 – Equivalence for 1/4 and 1/5 fractions
• Chart 6 – Addition of fractions with like denominator, ending with whole number
• Chart 7 – Addition of fractions with like denominator, ending with fractions
• Chart 8 – Statement: How to add and subtract a fraction with like denominators
• Chart 9 – Addition of two numbers with unlike denominators
• Chart 10 – Addition of three numbers with unlike denominators
• Chart 11 – Statement: How to add and subtraction a fraction with unlike denominators
1. Subtraction
• Chart 12 – Subtraction with like denominators
• Chart 13 – Subtraction with unlike denominators
1. Multiplication
• Chart 14 – Fraction times whole number
• Chart 15 – Fraction times whole number plus rule
• Chart 16 – Fraction times whole number and fraction times fraction
• Chart 17 – Fraction times a fraction plus rule
1. Division
• Chart 18 – Fraction divided by whole number
• Chart 19 – Fraction divided by whole number plus rule
• Chart 20 – Group division
• Chart 21 – Fraction divided by fraction

Chart 22 – Extra chart on multiplication

According to Montessori curriculum, kids start in earnest with fractions in first grade.  Last semester, I tried to get Thumper to learn her fractions.  While it was obvious whenever we did it that she understands quickly and can advance to the next stage, she did not want to do it AT ALL.  Case in point, after introduction to fractions, we did nomenclature matching (Chinese to English to pictures to numbers), I had to kind of make her do it.  By that I mean putting it on her work plan and she dragged and dragged her feet till I pointed out to her it’s on her work plan.  Then it was fraction equivalence, I don’t even know when we started that work.   November? October?  She just finished that this week, mid January.  So that took 2+ months.

One thing I got out of homeschooling last semester is that maybe I need to really just accept the way my child learns and think of ways to appeal to her.  I know I know, such a Montessori concept.  But this means that I cannot just use the Montessori materials and presentations as I was taught.  Thumper is a creative one.  Show her how to do something, and more often than not she wants to play with it, see it used a different way.

This week, I remembered that I saw a fractions game at a Montessori school I observed.  After asking around and looking at albums, I learned that it’s not in the albums.  It’s just an extension the teacher made up.  We played this game this week.  Thumper had much fun.  In fact, I had much fun.  This week, school in general felt great because most of our time spent together was happy times.

Fraction War

The game is simple.  Fractions cards from 1, 1/2, 2/2, 1/3, 2/3,….10/10 are shuffled.  Each player takes one card, takes the fraction circles to make up that number, and compare the fractions.  The person with the bigger fraction takes all the cards and the person with the most number of cards by the end wins.  The direct aim of the game is to see visually how a fraction is represented and become familiar with it.

Extensions: Take out the large fractions if you really want to illustrate the fraction equivalent concepts in a concrete way.  Ask children to name fractions in English. (more…)

Update: I figured out how to make the fraction charts 6 months later.  Here’s my post and pics of the final charts.

After about two weeks desponding over my incomprehension of using work plans, kids speeding through materials in 15 minutes, and a month of not really making new materials, I jumped back into fraction work.  Anything to keep my mind of my hated 3 hour work period (I semi-jest). Early November, Thumper was introduced to the fraction insets.  She got the concept of naming fractions in both Chinese and English in about 10 minutes.  I somehow convinced her to do a fractions match-up activity borrowed from What Did We Do All Day for about 10 minutes.  She dragged her feet.  Then the last 3 weeks we’ve been doing fraction equivalence; 1 page a week. I feel like I’m pulling teeth.  But I will leave my moping for another day. This week, I thought I would mix things up by introducing fraction addition.  But first I have to make those Fraction Charts.  According to my album, there are 21 charts.  They are not impressionistic as they’re more for reference, and therefore do not need to be big.  I cross referenced with What Did We Do Today and Montessori School At Home, and my own album.  I still don’t get what some of the charts should be.  My album says one thing, the charts online say another.  I’m going to wait till my class this Spring to ask the prof.

• Chart 1 & 2 –  Fraction circles
• Chart 3, 4, 5 – Equivalence for 1/2, 1/3, 1/4, 1/5
• Chart 6 – Addition with same denominator, ending with whole number
• Chart 7 – Addition with same denominator, ending with fractions
• Chart 8 – 12 – Not sure
• Chart 13 – Subtracting with different denominators
• Chart 14 – Multiplication with whole number
• Chart 15 – Multiplication with whole number, with rule
• Chart 16 – Multiplication of whole number with fraction and fraction with fraction
• Chart 17 – Multiplication of fraction with fraction, with rule
• Chart 18 – Division with whole number
• Chart 19 – Division with whole number, with rule
• Chart 20 – Group Division
• Chart 21 – Division of fraction with fraction

Last week and this week, both Astroboy (4) and Thumper (7) got their introduction to fractions.

In training, I was told that fractions come at the end of the series and that some kids don’t even get to it.  But reading my album I see that fractions can be introduced as young as 3 since it’s just a Sensorial experience.  For Thumper, we verbally introduced the idea pretty young with half, and half of half, etc.  I’m pretty sure she learned them in school too.

The Fractions curriculum is basically 6 parts: naming, equivalence, and the 4 operations. It appears that fractions are taught like other Montessori math, first manipulating concrete materials and then moving toward abstraction. The main materials are the fraction metal insets, and fraction insets in other shapes, plus lots of cut out fraction pieces, and reference charts. Fraction is something that is introduced in first grade.

I love seeing the difference in development and how that affects the way the children learn. For Thumper, I did the classic first presentation of all 10 fraction metal insets, naming them, and showing her how to name them in both Chinese and English.  In Chinese, you read the denominator first then numerator, 三分之一, for example for 1/3.  The nice thing about it is that you don’t have different names for the numbers like in English: halves, thirds, fourths, etc.  In Chinese the denominator is called 分母 and the numerator 分母.  分 means to divide, 母 is mother and 子 is child.  So super easy to remember.

As an older child, Thumper got the concept of fractions easily. We even started on equivalence. So I didn’t need to spend much time on the IDEA of fractions. But I could tell that she has trouble with the difference between the way we name fractions in English and Chinese. She keeps wanting to flip them when she says it in Chinese. I remember I did the same thing after years of naming fractions in English.  It’s making me wonder if I need to teach fractions in Chinese at all.

Astroboy really wanted the same presentation, so I did it for him.  But after the presentation, he couldn’t really name the fractions. So the next day I pulled out my fraction skittles instead.  These look like little people, color coded inside; compared with the insets which are just all red. It’s meant to be handled and “played” with.