NCETM_Mathematics_Department_Workshops_Fractions

Mathematics Department Workshops Topic: Operations with Fractions Overview Objectives related to this topic are: • add and subtract simple fractions and those with common denominators; multiply a fraction by an integer (Year 7) • add and subtract fractions by writing them with a common denominator; multiply and divide an integer by a fraction (Year 8) • use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse; cancel common factors before multiplying or dividing (Year 9) • understand and apply efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse (Year 10) Materials required • Resource sheets HT2.FRA.1 – HT2.FRA.9 • A4 paper • Glue • Large pens • Flip Chart paper • Data projector and internet access Suggested activities Activity 1: Getting Started Challenge your team to draw a diagram to explain the meaning of each of: • adding fractions; • subtracting fractions; • multiplying fractions. If required a possible prompt could be, ‘Can multiplying two fractions be described as finding the intersection of two sets?’ View http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html?from=grade_g_2.html Now challenge them to: • draw a diagram to represent division of a fraction by a whole number; • draw a diagram to represent division of a fraction by a fraction. Activity 2: Probing questions Provide each pair with the set of fraction cards HT2.FRA.1. Give each pair or group a set of cut-up cards. Using the resource sheet HT2.FRA.2, write examples of questions which can be answered using one or more of the cards. www.ncetm.org.uk A Department for Children, Schools and Families initiative to enhance professional development across mathematics teaching

Activity 3: Mistakes and Misconceptions Ask your team to consider the cards on resource sheet HT2.FRA.3. Stick the three headings, ‘Always True’, ‘Sometimes True’ and ‘Never True’ on a large piece of paper and then place the cards under the correct headings. When you all agree on where each card should be placed, glue down the cards with spaces below each of them and then write • an explanation of why each card is below its heading; • which misconception or common mistake is being addressed. When you are finished, write some other cards around learners’ misconceptions about the four operations with fractions. Activity 4: www.ncetm.org.uk Invite your team to investigate what the NCETM website has to offer when it comes to the four operations with fractions. In particular, you could direct them to: • ‘Focus on Fractions’ from Issue 17 of the Secondary Magazine • http://www.ncetm.org.uk/Default.aspx?page=13&module=res&mode=100&resid=11411 • http://www.ncetm.org.uk/Default.aspx?page=13&module=res&mode=100&resid=8856 • You may also want to download the Maths4life booklet from http://www.ncetm.org.uk/files/257666/fractions_booklet.pdf Use your department’s findings to write a Blog or Mathemapedia entry and submit it to the Portal. Activity 4: Making a Song and Dance Watch ‘Kylee’s Fraction Rap’ http://www.youtube.com/watch?v=obWJlb3mbFg. Mrs Morschetii wrote ‘After writing a poem to help my students remember how to add/subtract/multiply fractions, we created a rhythm in Garageband and made the poem into a rap.’ What do your team think are the benefits of doing such an activity? Are there any particular learners who would be helped by such an approach? If singing is not your department’s thing, how about the alternative approach of writing a short sketch which involves each of adding, subtracting, multiplying and dividing fractions? It can be quite a revealing activity with learners. www.ncetm.org.uk A Department for Children, Schools and Families initiative to enhance professional development across mathematics teaching

Activity 5: Evaluating Resources Evaluate the following resources for teaching the four operations with fractions: Resource Sheets HT2.FRA.4 (Fraction Dominoes) Resource Sheets HT2.FRA.5 (Fraction Dominoes) Slideshows HT2.FRA.6, HT2.FRA.7, HT2.FRA.8 and HT2.FRA.9 (Thanks to Tim Robbins) Weblink: http://illuminations.nctm.org/ActivityDetail.aspx?ID=45 Weblink: http://www.learnalberta.ca/content/mejhm/html/video_interactives/fractions/fractionsSmall.html As you look at each one ask questions such as: • Why would we use this with our learners? • What would be the benefits? • Would we have to change it, to use it with our learners? • How would we embed it in our scheme of work? • How could we differentiate it? Embedding in practice Hooks for Learning • Find out about how the ancient Egyptians used fractions at http://www.ics.uci.edu/~eppstein/numth/egypt/ Action points At the end of the session, spend time recording some actions. What do you need to do: • Next day? • Next week? • Next year? Further reading • http://scienceofwaldorf.blogspot.com/2007/03/learning-about-fractions.html • http://www.homeschoolmath.net/online/fractions.php www.ncetm.org.uk A Department for Children, Schools and Families initiative to enhance professional development across mathematics teaching