# Christmas Maths Part 3: More open-ended tasks for Grades 3 – 6

In this final Christmas themed post, I am including a range of open-ended investigations that are suitable for upper primary and lower secondary students (from the book Engaging Maths: Everyday Investigations Years 3 to 6). You will notice that some of the investigations extend beyond the mathematics curriculum and integrate quite easily into other key learning areas. This is intentional. If we want to engage students in mathematics, then making it contextual often requires it to either be embedded within another subject area or at least have some connections to other areas. Another consideration is the General Capabilities of the Australian Curriculum: Mathematics. When we incorporate contextual mathematics and investigation-based tasks, we are more likely to include the General Capabilities and this is evidenced in the activities below.

Short activities:

1. If you have a Christmas tree in your house or school, how tall is it? Can you reach the top of the tree by reaching up? How much taller than you is the Christmas tree? What fraction of the height of the tree is your height?
2. Draw a picture of a Christmas tree. Use your drawing as a plan to show where you will place the decorations.
3. Tie a piece of tinsel to the very top of the Christmas Tree. Wind the tinsel around the tree until you reach the lowest branch. What is the length of the tinsel?
4. If the individual lights of a string of Christmas lights are 30 cm apart, how many lights would you need so decorate the perimeter of the classroom?
5. How would you work out how much wrapping paper needed to wrap 10 presents that were each the size of a shoe box? Record all of your working out. What mathematics did you use?

Investigations:

1. Plan a Christmas party for some of your friends. Show all the mathematics that you need to use for your planning.
2. Many families start to budget for Christmas presents several months before Christmas day. Design a budget for the Christmas presents that you would like to give to your family members, relatives and friends. Perhaps you might like to include your teachers.
3. Survey the other students in your class using the question, “Do you have a Christmas tree in your home?” “Is it a real tree or an artificial tree?” “Which type of tree do you prefer and why?” Present the data that you have collected and present a report to your class.

Extension Activities:

1. Investigate and research the tradition of decorating a tree for Christmas. Answer questions such as “When did the tradition start?”
2. Plan menus for the meals for family for Christmas Day and Boxing Day and include a budget.
3. Make a list of the things you would like for Christmas. Sort your items into needs and wants. How would your list compare to the list of a child in a different country? Investigate.

I hope you have enjoyed this series of posts that have included many rich activities to keep students engaged with mathematics until the very last day of the school year. If you do implement any of the tasks, I would love to hear from you and see your students’ work samples!

# Why saying “I’m not good at maths” is just not good enough!

How many times have you heard people say “I’m not good at maths”? Perhaps you’ve said it yourself. Often people make the statement with pride, almost implying it’s ‘cool’ to be bad at maths. Imagine if the same number of people claimed “I’m not good at reading”. I don’t think it would be deemed socially acceptable – in fact, most people would be embarrassed to make that claim. So why is it okay to by openly negative about mathematics? Why do so many in the media openly claim to dislike mathematics, and why is mathematics seen as a domain only accessible to an elite group of ‘smart’ people? Research has proven humans are born numerate, so what happens in those few years when children are in school to make them hate maths?

Firstly, we need to look at what happens in the home. Parents need to think carefully about how they talk to their children about mathematics. Regardless of how they experienced school mathematics and how they perceive mathematics, claims like “I was never good at maths when I was at school” are not helpful. Children notice. Molly, a  Year 6 participant in my PhD study, made this comment when asked about what her family think about mathematics: “My mum doesn’t really like me asking her because she thinks she doesn’t have a maths brain. She thinks that she’s got more of an English brain than anything else.” Not surprisingly, Molly was not the only child who made that kind of comment.

Parents’ negative attitudes or beliefs do have the potential to negatively influence children, particularly when not having a ‘maths brain’ can be used as an excuse for opting out of mathematics in the senior years of schooling. Evidence of this influence on children’s thinking can be seen in this quote, where Kristie, another participant, was describing her friends’ attitudes towards mathematics: “Maybe some just don’t enjoy it the way I do, they just think maybe it’s not their subject. They might enjoy English.”

So what can parents do to promote positive attitudes towards mathematics? Above all, they should never make negative comments about the subject. If you are a parent and you are having difficulty with helping your child, seek help. In the primary years, many schools are happy to provide parent workshops to help parents understand new teaching methods. Workshops could also be held to help parents ‘brush up’ on their own mathematics skills. If your child is in secondary school and the mathematics they are learning requires more than a quick revision, don’t panic. It’s okay to say “I don’t know” or “I don’t remember how to do that” – try and find a way to assist your child in finding an explanation, whether it is by seeking help online, encouraging them to seek help from their teacher, or, if required, finding an appropriate tutor who may be able to provide some remediation. It’s better to seek help early.

One of the challenges with mathematics is that the concepts are hierarchical. That is, if children don’t  don’t develop a deep understanding of foundational topics such as place value, gaps in learning begin to occur. When mathematics becomes more complex, children who struggle with the foundations of mathematics cannot keep up with their peers and fall behind, often leading to negative attitudes, poor self-efficacy, and disengagement.

And now we turn to the classroom. What can teachers do to stop the “I’m not good at maths” comments from perpetuating a fear of mathematics? Firstly, talking to parents about this issue needs to be a priority. Next, think about how you can promote positive attitudes – I’ve written much about engagement and mathematics and there are lots of great teaching and learning ideas on this website and elsewhere. Another comment that we often hear is “when an I ever going to use this?”. It’s a fact that there is mathematics that some of us will never use once we leave school. But that doesn’t mean we shouldn’t learn it – if we don’t we may be minimising future opportunities. Professor Edward Frenkel (one of my mathematical heroes) claims that school mathematics is often not presented in a way that highlights the connections to our daily lives (check out his video on YouTube). We don’t always have to understand the complex mathematics that lies beneath Facebook, online shopping, traffic systems, etc., but we do need to be aware that mathematics plays a critical role in many aspects of our daily lives, regardless of what we do or where we are from.

Finally, I strongly believe we need to stop allowing those around us, in our lives and in the media, to make such negative statements about mathematics – if we don’t take a stand things will never change, and it’s definitely time for a positive change. Start your school week with this statement: “I love maths!” Feels good, doesn’t it?

# Free resources that every teacher, student and parent should know about!

There are two brilliant mathematics resources that I believe everyone should know about and use to improve mathematics in schools and in our community. One is designed for people of all ages, and the other is one of my favourite mathematics problem solving websites. Some of you would have seen and used these two websites. If you haven’t, I would encourage you to take a look – these resources are free and of high quality! Although quite different, these websites have educational resources that access a broad range of mathematics content, and more importantly, the processes of mathematics. That is, the Australian Curriculum: Mathematics proficiencies, or if you live in New South Wales, the Working Mathematically components of the current mathematics curriculum.

Last week I wrote about financial literacy and what it means in the context of mathematics and primary schools. Since then, I have spoken to several more teachers and children at schools in low socio-economic areas as part of my current research project on financial literacy and mathematics. A result of my conversations is that I am even more convinced of the importance of teaching consumer and financial literacy in the classroom and beyond, in the wider community.

Part of my research involves the participating teachers using the existing MoneySmart resources to introduce their students to consumer and financial literacy prior to developing their own context specific units of work. This requirement led to some professional development based on the MoneySmart resources (https://www.moneysmart.gov.au/), which have been funded by the Australian Securities and Investment Commission (ASIC). Prior to this professional development, almost all of the teachers I have spoken to did not fully understand that financial literacy is much more than being able to recognise currency and the adding and subtracting of dollars and cents. Some teachers also expressed a need to develop their own financial literacy to improve their own financial health.

After exploring the range of resources on the MoneySmart website I am convinced that this resource should be used in every school and community. The website provides educational resources for people of all ages and stages in life and could potentially change lives by promoting the development of healthy consumer and financial habits. It’s not enough that we are promoting financial literacy amongst children – the message needs to spread beyond the school gates, and I believe MoneySmart has the power to do this.

The second free resource that everyone needs to know about is the NRICH mathematics enrichment website (http://nrich.maths.org/teacher-primary), published by the University of Cambridge as part of the Millenium Mathematics Project. I have been using this site for many years now and it continues to improve and evolve. The standard of the mathematics problems on this site are excellent and an added benefit is that there are also many resources that provide professional development for teachers. Although the website is based on the British school curriculum, it aligns quite well with the Australian Curriculum.

The best thing about the NRICH website is that it is based on rich mathematical problem solving and investigation, which lies at the heart of our mathematics curriculum in Australia. The activities can be used in the classroom, for homework (if you have to set homework), and can be accessed by parents who are looking for some mathematics they can do with their children.

So what do these fabulous free resources have in common? Apart from the fact that they’re both free, they promote high quality mathematics education by using either contextual, real-life project based learning or rich tasks that can help children (and adults) learn mathematics in a much more engaging way than traditional text books and worksheets. They also promote the development of skills and understandings that can be applied beyond the mathematics classroom and have the potential to improve life opportunities – that’s got to be a good thing!

# Financial Literacy: What does it mean, and how can we teach it in schools and at home?

I am currently working on a research project funded by Financial Literacy Australia that is investigating the use of financial literacy education as a tool to promote primary students’ engagement with mathematics in low socio-economic areas. While working on the project, it has struck me that often we have a simplistic view of what financial literacy for young children means, and how influential it can be in their future lives.

There are many definitions of financial literacy, ranging from “basic money management: budgeting, saving, investing and insuring” (Hogarth, 2002) to definitions that incorporate a more critical perspective, such as that proposed by the Australian Association of Mathematics Teachers (AAMT): “enabling people to make informed decisions at the personal level…allowing citizens to properly analyse and make judgements about broader issues such as government policy, the influence of the media and activities of the finance industry” (AAMT, 2010, p.2). In the context of primary schools, financial literacy is much more complex than just teaching children to recognise currency, to add and subtract money amounts, or to be able to estimate the costs of items. It is about learning how to apply a range of mathematical skills and knowledge to consumer related situations in an informed, analytical and critical manner. These skills should be learned in the classroom, and just as importantly, at home.

So why teach mathematics through financial literacy? We know there is an ongoing problem around children disengaging from mathematics, and this often occurs from an early age. One of the biggest causes of students’ disengagement with mathematics is the fact that they fail to see the relevance of mathematics or its applications to real life situations. Added to this, there is concern relating to young people from low socio-economic areas in particular, as presented in a recent report by Thomson (2014):

• In Australia, 75 per cent of socioeconomically disadvantaged students hold a bank account compared with 89 per cent of advantaged students.
• “More students from disadvantaged backgrounds than students from an advantaged background responded that they were influenced by advertising in magazines, flyers and newspapers, and by the need to ‘fit in’ when making decisions about spending money” (p. viii).

Teaching mathematics via financial literacy makes sense. By using real-life contexts that involve financial literacy that is age appropriate and interesting to students, we can teach a range of mathematics and numeracy skills. Students are more likely to remember and understand because they have applied them to something they are interested in and something that is relevant to their present lives.

The following is some advice for teachers and parents in relation to promoting mathematics in the context of financial literacy education.

For teachers

In their Position Paper on Consumer and Financial Literacy in Schools (2012) the AAMT note that mathematics teachers need to address the cross-curricular learning in financial literacy though the mathematics curriculum and through “broader concepts and understandings” (p.3) of other key learning areas and in real life situations, with relevant contemporary resources. Such contemporary resources are available from the MoneySmart website (https://www.moneysmart.gov.au/teaching/teaching-resources/teaching-resources-for-primary-schools) at no cost. These resources are an excellent way to begin teaching financial literacy concepts with some units of work specifically designed around mathematics, however, if we want to ensure teaching and learning is truly contextual with the aim of engaging students with mathematics, these units can and should be adjusted to suit the specific needs of the students in your classroom.

Alongside the MoneySmart resources, consider using resources that are familiar to students’ everyday lives. These could include items that are in the news media, shopping catalogues, television commercials etc. Keep watch for interesting photographs or misleading advertisements such as the one above. They are great for instigating mathematical discussions. There is also a range of iPad apps that could be used alongside mathematics and financial literacy explorations, including budgeting apps and supermarket apps. If you like using picture books to introduce and teach concepts, the following website has an extensive list of books relating to financial literacy: http://www.moneyandstuff.info/books.htm

For Parents

Many young children don’t understand where money comes from and it’s important that they begin to develop some understanding of how our economy works, even from a young age (many children believe that money comes out of a hole in a wall). In my research there appears to be a pattern emerging where children whose parents talk to them about money develop an earlier understanding of its importance and are provided with more opportunities to deal with money and make decisions about money. If you have young children, it’s a great time to start their financial literacy and mathematics education. Take opportunities when you are out shopping to either include your child in discussions and decisions where appropriate, or explain financial decisions that are made on their behalf. Talk about the mathematics involved in financial decision-making and where possible, encourage children to make their own financial decisions with pocket money, banking, etc. If you feel you need to improve your own financial literacy first, MoneySmart have fantastic resources for adults too (https://www.moneysmart.gov.au/).

The benefits of engaging children with mathematics through financial literacy are clear. By highlighting the relevance of mathematics to children’s current and future lives through real-life learning contexts relating to money we can better position young children for academic success and success in relation to their future economic lives.

View an interview about financial literacy on Weekend Sunrise on Sunday 26th April

References

Australian Association of Mathematics Teachers (2012) Position paper on Consumer and Financial Literacy in Schools. retrieved January 2015 from www.aamt.edu.au

Hogarth, J.M. (2002). Financial literacy and family and consumer sciences. Journal of Family and Consumer Sciences, 94, 15-28.

Thomson, Sue. (2014). Financing the future: Australian students’ results in the PISA 2012 Financial Literacy assessment. Victoria: Australian Council for Educational Research.

# Woolworths and Dominoes (Part 2): Even more mathematical opportunities for parents and teachers!

My last blog about the marketing promotion being run by Woolworths and Disney Pixar attracted so much interest that I thought I would look deeper into the mathematical potential of the whole campaign. Somehow, the incentive of receiving a domino for every \$20 spent seems to be very appealing to consumers, young and old. What is it about these little plastic objects that is so attractive? Perhaps the appealing aspect of the dominoes is the fact that children can actually play with these, as opposed to collections of character cards that are usually given away in such promotions.

So why are the dominoes appealing to teachers like me? My research on student engagement with mathematics has shown that when children have an interest in something, they are more likely to want to learn. They also like to use concrete materials to help them learn – things they can see, touch and manipulate (as opposed to the traditional maths worksheets and textbooks). In the case of Woolworths and dominoes, this is a perfect opportunity for parents and teachers alike to seize this amazing opportunity, take advantage of the hype and do some really good, interesting mathematics!

During the week, as I watched the statistics on my blog increase, I thought I would explore the Woolworths web site and dig around a little. I didn’t find too much of interest, although they have made an effort to publish some very basic educational ideas relating to the dominoes. What I did find, however, was that people are actually selling dominoes on eBay! You can buy whole sets (of characters), individual dominoes of specific characters (some up to \$3 each), or unopened dominoes. At this point my head started to hurt…..so many mathematical possibilities! Imagine children investigating the cost of dominoes (in shopping dollars), compared to the apparent worth of dominoes as advertised on eBay. All week I have had fantastic (well, I think they’re fantastic) ideas popping into my head, and these are a few that you might want to try out at home (if you are a parent), or at school, if you are a teacher. I will begin my list with simple tasks for younger children, and finish it with more complex tasks for older children:

• How many dominoes do you think you could hold in one hand? Try it and see if you were right or wrong. How close were you? What if you could use two hands? How many dominoes can you hold? Is this the same as an adult?
• How many dominoes have a one dot? Two dot? Three dot pattern?
• If I lay my dominoes flat, end to end (the short end), how long will my line be? How many dominoes will I need if I wanted to make a flat line that is as long as my foot? My leg? My arm? My body?
• Keep your character doubles, and use pairs of doubles to play a game of memory.
• Using the picture side of the dominoes (the characters are numbered), order the dominoes from 1 to 44.
• Are you missing any dominoes? What numbers are missing and how do you know?
• Using the picture side of the dominoes, imagine that the number of the character is equivalent to its worth. That is, character number 1 is worth \$1, character number 2 is worth \$2, etc. What would be the value of your collection? If you had every domino from number 1 to number 44, what is it worth?
• If I lined up my dominoes so they were standing (like in the photo), what would be the best distance apart (if they’re too close together, you might knock them down accidently).
• How many (standing) dominoes would you need to make a line of 1 metre? Imagine you needed to make a domino line for one kilometre – can you use the number of dominoes you have to work out how many dominoes you would need? How much would you have to spend at Woolworths to have enough dominoes?
• How long would it take to knock down a one metre line of standing up dominoes? Who can make the longest line?
• I received 18 dominoes with my shopping this week. How much did I spend?
• Do you think the Woolworths marketing campaign has been successful? Design a set of survey questions and conduct some research at your school. Analyse your data and prepare a report that you could send to the Chief Executive Officer of Woolworths.

Of course, there are many more ideas – perhaps there will be a Part 3 blog post over the Easter weekend. Oh, and by the way, Woolworths are giving away ‘double’ dominoes at the moment – this opens up another world of mathematical opportunity!