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Category Archives: Fractions

Fractions!!!!! The Big Ideas!

Both classes have been working on fractions for the past few weeks (with some time off when some were swimming!).   The grade 5s have a test coming up on Monday, May 5th and the 4s will have on Wednesday, May 7th.   The grade 4s need to understand up to # 5 and the 5s need to understand all of the Big Ideas discussed below.

Fractions – Big Ideas

  1. A fraction has a numerator and a denominator.  The denominator tells how many equal parts the whole is divided into and the numerator tells how many parts there are.
  2. Fractions can mean different things and be modeled in different ways:  part of a set, part of a region, as a measure, division & as a ratio.

types of fractions 2types of fraction 1

3.  A fraction is not meaningful without knowing what the whole is (if you only see the numerals when comparing fractions you assume the whole is the same).

For example, in class one day I asked the students if they would rather have half of a chocolate bar or one fourth of a chocolate bar.  Most students said half but a few knew I was up to something.

The fourth came from this type of chocolate bar:

498_PC_Milk_Chocolate_Bar_-_(EN)_-_(500x500)

and the half from this:

kitkat

4.  If fractions have the same denominator, the one with the greater numerator is greater.  The denominator tells the total number of equal parts in the whole, and the numerator tells the number of parts accounted for.  Since both pies are cut into 8ths all the pieces are the same size.  Therefore 5 pieces or 5/8 is more than 3/8:

like denominators

4.  If fractions have the same numerator, the one with the greater denominator is less.  The denominator tells the total number of equal parts that the whole is divided into, and the numerator tells the number of parts accounted for.  The larger the denominator, the smaller the parts are:

unlike denominators

6.  There are proper fractions, improper fractions or mixed numbers.  The numerator is larger than the denominator in improper fractions.  The mixed number has a whole number and a fraction.  See below.

improper

..and the grade 5s discovered an algorithm to convert a mixed number to an improper fraction!  The whole number x the denominator + the numerator.   2 x 4 + 1 = 9

They also figured out how to go from improper fraction to mixed number.  Divide the numerator by the denominator (fractions are another way of expressing division after all!).  9 / 4 = 2 1/4

7.  Fraction can have different names, these are called equivalent fractions:

 

equivalent fractions

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Posted by on April 30, 2014 in Fractions, Math

 

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Decimals & Our Persuasive Pieces are Live on the Blogs

Please head over to the students’ individual blogs by clicking on Our Class Blogs to the right.  You will have to click on the link and then you will be there!  I know the students would love to have you chime in with your opinion on the topics they have chosen to write about.  Let them know if they have been persuasive and try to persuade them of your opinion.

Decmals

Here are some videos of students solving decimal riddles.  Following that will be an explantion of some of  the concepts we are studying. 

We have been learning about decimals for about a week now.    We have worked on the following decimal principles (from Marion Small, Big Ideas from Dr. Small):

  1. Using decimals extends the place value system to represent poarts of a whole. 

2.  The base ten place value system is built on symmetry around the ones place.

3.  Decimals can represent parts of a whole, as well as whole numbers or mixed numbers. 

4.  Decimals can be interpreted and read in more than one way.  For example, students should be comfortable reading 3.2 as  32 tenths AND 32 hundredths.  We try to avoid using the terms 3 point 2 or 3 decimal 2.    Decimals can be modeled with money, base ten blocks, ten-frames and more. 

ten frame

represent many ways

5.  Decimals can be renamed as other decimals or fractions. 

decimal fraction

More to come this week – estimating – VERY IMPORTANT!

 
 

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Revising & Editing Persuasive Writing + Fractions Test

In English we have been discussing revising & editing and how they are similar and diferrent. Editing is correcting errors in writing conventions such as:

  • spelling
  • punctuation
  • sentence structure
  • grammar
  • usage

usage

 

Revising is about making the content better using five of the six traits of good writing:

Six-Traits-of-Writing-poster

 

The students wrote a rough draft of a persuasive piece about a topic they cared about.  Some chose child labour, the water crisis, gaming in school, school uniforms…  They had to peer edit and revise with a partner.  Final drafts will be turning up on the students’ individual blogs soon. 

 

Fractions Test on Tuesday, April 9th.  There is a take home review package.  The students are also making All About Fractions books which review all the required concepts; see the last blog post for examples.  Here is the checklist they were given for their Fraction Books:

Fractions Checklist

 
 

Sharing Cookies, Comparing Fractions with like Denominators & Book Reports

For the past few days the students have been doing an activity called Sharing Cookies.  In this activity they show that they understand that fractions are equal pieces.  They choose a number of cookies to share amongst 3, for or 6 people.  The number of cookies cannot be a multiple of the number of people sharing (this is so the cookies have to be cut up into fractioinal pieces).  The fraction each person gets must be written as a mixed number and an improper fraction.  Here are some examples:

 

sharing cookies 1 shairng cookies3 sharing cookies2

 

 

Next we talked about how to compare fractions that have the same denominator.  We notices that if the denominator is the same, then all the pieces are the same size.  Therefore, we can look at the numerator to tell us the size of the fraction.  The larger the numerator, the larger the fraction is.  This ONLY works when the denominators are the same.

 

Tomorrow we will explore how to compare fractions when the denominators are different!

denominator

 

In English the students are finishing up their book reports. 

book report

 
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Posted by on March 26, 2013 in Fractions, Math

 

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Fractions & More Fractions!

We’re back from March Break and into the swing of things!   Today in math we continued with Fractions.

We’ve talked about how the numerator tells you how many pieces you have and the denominator tells you how many pieces there are. 

 

We’ve also looked at another way of modeling fractions, the area model.  Here are our fractions anchor charts:

 

fractions

fractions1

 

Our lesson today was to try to figure out different fractions of a set of balloons and brownies.  We started with the number 12.  First the students had to find one half of 12.  Most found this quite simple and were able to explain how they found the answer.  The answer was the same for both balloons and brownies.  It was when we got to one fifth of each that the problems began!  Hmmm. 

boo

 

Finally, someone asked a question that got us moving forward with our thinking:

 

Can we cut the balloons?

Hmmm?  Would they be useful if they were cut up?  Nope.  So that left us with remainders.   12 ballons, divided by 5 (for we were finding fifths) is two with a remainder of two.

 

balloons

 

The brownies were another story because we can cut them up.  The orange Cuisinaire Rods represent the whole brownie and the red rods represent one fifth of a brownie. 

brownies

We discovered that brownies CAN be divided up equally (balloons can’t) into fifths and everyone would get 2 and two fifths.  

 

The students are now working in pairs to solve a variety of fractions of 24 balloons and brownies.  They chose 24 because it is divisible by many of the denominators!

 

We also talked about the four categories of achievement in mathematics.  These come directly from the Mathematics 1-8 Ontario Curriculum:

 

levels of achievement2levels of achievement levels of achievementlevels of achievement1

 

All the levels are equally important and work is assessed for all of them. 

 

Watch out for the 6 + 1 traits of good writing coming later this week! 

 

 
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Posted by on March 19, 2013 in Fractions, Math

 

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Prefixes, Root Words & Etymology + Fractions! Awesome Day!

I apologize for not posting for a few weeks.  Things got busy and….you all know how that is.  We are back on track with blogging and I will try to post at least twice a week.

In English we have been looking at prefixes, root words and etymology.  Etymology is the study of words, their history, their origin and how the form and meaning  have changed over the years.    Wikipedia

We have been looking at prefixes such as:   un-  dis-  im-  in-  ir- & non- which all affect roots words in similar ways, changing the meaning to its opposite.  For example, irresponsible means not responsible, dislike means to not like, impossible means impossible.  We also looked at ex- meaning out of or from or upwards.  Words like expand means to spread out.  Some prefixes and roots can be quite complicated because they come from latin, old French or Old English  or other languages.  We can’t always rely on the trick of thinking “Can the root word stand alone?” like in nonsense; sense can stand alone and non- changes the meaning to its opposite.  See this example from the online etymology dicitonary for expand:

 

dictionary expand top

 

Dictionary Latin

 

dictionary expand

Fractions!

I love fractions.  Really.  I know they are a challenge but once kids get it – WOW!  It is critically important that students understand the value of fractions, can compare fractions, understand equivalency, etc. 

Friday we talked about the set model or concept of fractions.  We had a discussion about the fractions of girls and boys in our class.  The class, or set, is 26 people so 26 is the whole or 1.  The girls are part of the set, 20 out of 26 to be exact and the boys are another part of the set, 6 out of 26.  Here is our chart to represent the set model based on the students in the class:

fractions set model

Today we made our Fraction Kits which are based on the linear model of fractions.  The black strip is 1 or the whole, and the other colours are different parts, or fractions, of the whole:

fractions linear model

After we made the kits, which helps students understand equivalency, we played a game called Cover Up.  Here are the rules:

Cover Up Rules

This game helps students to compare the value of fractions and to understand equivalency.  Tomorrow we play uncover!  Here are some students playing cover up:

 
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Posted by on March 4, 2013 in Fractions, Math, Word Work

 

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