Fractions Eight Different Ways

Learning Intention: Students will understand that there are many different ways to express the concept of ‘part of a whole’.

Success criteria: Each student will produce a poster that demonstrates eight different ways to express a certain fraction, chosen by the distribution of individual fraction cards. We will use these cards and our ‘Fraction Walls’ to demonstrate adding, subtracting, multiplying and dividing fractions.

Each student will recieve a card with a fraction and create a poster that shows this fraction eight different ways (as above for one half). When you have finished, place your poster on the number line in the room.

Equivalent fractions with a Fraction Wall

Screen Shot 2014-03-03 at 2.49.00 PM

Image Source

This week we will continue making our fraction wall and learning how to calculate equivalent fractions. Using your fraction wall, find equivalent fractions for the following: 1/2 (one half); 1/3 (one third); 1/4 (one quarter) 2/3 (two thirds) and 3/4 (three quarters). What are some other equivalent fractions that are “off the scale” – using fifteenths, sixteenths, twentieths or hundredths?

To add or subtract fractions we need to make sure they have the same denominator (bottom number). We can convert fractions so that they have the same denominator by multiplying both the numerator and the denominator by the same number. This interactive from NLVM helps to compare fractions and create fractions with the same denominator.

Here are some links to sites for learning more about fractions:

Year 7 Favourites

favouritesImage Source

Learning Intention: Students will understand how to collect data using a tally and create a frequency table and bar graph using the data. They will understand how to convert fractions to decimals and percentages. They will create a pie chart using this data by converting 100% to 360 degrees.

Success Criteria: Each student will produce a poster that includes a frequency table (including fractions, decimals and percentages), bar graph and pie chart of their chosen data, collected from the Year 7 Maths Survey.

  1. First collect your data in tally form.
  2. Add each category and find the total.
  3. Represent each category as a fraction.
  4. Convert to a decimal (2/25 = 16/100)
  5. Convert to a percentage 16/100 = 16%
  6. Create a bar graph using this data
  7. Remember to add SALT to your graph – Scale, Axes, Labels, Title
  8. Turn your bar chart into a pie chart (multiply percentage by 3.6 because 100% = 360 degrees)
  9. Make sure you have a key to interpret your data.
  10. Add a beautiful title and colour to present your poster.
  11. Go to Create-A-Graph and use your data to check that your graphs are correct.
  12. Print out the computer generated graphs to add to your poster.

Fractions interactives from NLVM

Fractions as we know them today weren’t used in Europe until the 17th century. However, Egyptians have been using fractions since at least 1800BC, although they never wrote fractions with a numerator greater than one. These are called unit fractions. Fractions with a numerator greater than one were expressed as the sum of unit fractions. Find out more at the History of fractions and Egyptian fractions.

The National Library of Virtual Manipulatives has a range of interactive applets that you can access to learn about fractions:

Try at least three of these interactives and write a comment below about what you have learned.

Equivalent fractions

Learning intention: Students will be able to identify and name equivalent fractions (halves, thirds, quarters, fifths and sixths) and describe how they are calculated.

Success criteria: Students will successfully identify equivalent fractions on their fraction walls and name equivalent fractions on a number line.

Maths Playground – Visual fractions (the visuals are good, but the program doesn’t always allow the right answer?)

Maths is Fun – Equivalent fractions

Maths Games – Matching equivalent fractions

Fractions Eight Different Ways

Learning Intention: Students will understand that there are many different ways to express the concept of ‘part of a whole’.

Success criteria: Each student will produce a poster that demonstrates eight different ways to express a certain fraction, chosen by the distribution of individual fraction cards. We will use these cards and our ‘Fraction Walls’ to demonstrate adding, subtracting, multiplying and dividing fractions.

Each student will recieve a card with a fraction and create a poster that shows this fraction eight different ways (as above for one half). When you have finished, place your poster on the number line in the room.

The next task is to go to Mathletics and do the required tasks.

When you have finished, you  can go to the following sites:

BBC Skillswise – Fractions and Percentages

BBC Bitesize – Fractions, Decimals and Percentages

Interactive Maths Games and Activities

Five Fraction activities and two Percentages activities at the National Library of Virtual Manipulatives

**Important – Please leave a comment below about what you have learnt about fractions, decimals and percentages over the past three weeks this term.

 

Fractions Apps on the iPad

Learning Intention: This lesson we will be using three different apps on the iPads to learn about the value of fractions, decimals and percentages.

Success Criteria: Students will understand the value of common fractions (1/2, 3/4, 1/3, 2/3 etc) and be able to order a list of common fractions, decimals and percentages.

1. Motion Math HD – Bounce the fraction ball at the corresponding point on the number line by moving the iPad (10 minutes).

2. Fraction Factory – Move the factory cog to the correct point on the number line (10 minutes).

3. Number Line – Order the fractions, decimals and percentages from smallest to largest (10 minutes).

Please leave a comment below about which app you liked best, why you liked it and what you learnt.

Last week of term 3!

This week is our last week of school before September holidays and we also have Parent-Student-Teacher interviews on Wednesday afternoon and evening. I expect each of you to come along and discuss your progress in Maths with your parents as well as show them some of the great work you have been doing this semester. We will talk about your goals for Term 4 and beyond and how Maths is relevant to your future.
Well done to all of you who completed the Probability test last week – I was very pleased with the results.
Monday (period 3): Mathsmate and discuss the answers for the Proability test.
Tuesday (period 3): Skill builders for areas of improvement from Mathsmate
Wednesday (period 1): Converting fractions to decimals and percentages.
Thursday (period 1): Rates and Ratios.
Friday (period 3): Mathletics

Areas of Difficulty:
Some of you have been having problems with the following Mathsmate Questions:
Number 18 Expressing numbers as a product of it’s prime factors – Try this interactive at the NLVM “Factor Trees”.
Number 13 Operations with negative integers – “Color Chips – Subtraction”

Why do we need to learn about fractions?

drill_bit_sizes

Still on the subject of fractions, why in the decimal, digital age do students still need to learn about fractions? Fractions are an important concept and very useful for discussions about measurement, probability and data. Although Australia and the U.K. , and almost all other countries in the world, have adopted the metric system, the United States still uses imperial measurements. One example is with drill bits, where there are conversion charts available to convert imperial sizes (increments of 1/64 of an inch) to millimetres.

Prior to learning operations with fractions, students should be able to order fractions, convert between mixed numbers and improper fractions and convert between decimals and fractions. BBC KS3 Bitesize has revision activities and a test about Fractions. If students can find ten fractions between 1/3 and 2/3 , they have a good understanding of the concept of fractions.

This article, “Teaching Fractions with Understanding: Part-whole concept” is based on research by Grace Lopez-Charles – “Assessment of Children’s Understanding of Rational Numbers” – PhD Thesis. It describes several different perspectives that students have and some ways of teaching fractions more effectively.