Problem solving connects to the world outside the classroom

So there’s a thing called productive pedagogies and it forms part of the quality teaching framework. Each one is important, but my favourite is under significance - connectedness to the world! 

I still remember my high school days (although many years ago now), and sitting in maths wondering how I would ever use the stuff I was learning. I can honestly say that I have even used functions such as Cos, Tan and Sin in the real world. I would really have liked my teachers to show me the connectedness of what I was learning with contexts outside the classroom – maths would have been far more interesting!

So in this resource, Ask a Mathematician, problem solving has been put into a context in which learning could be applied in future careers. Not that all your students have career aspirations to be wildlife keepers at Wally’s Wildlife Park like Josie and Jack in the activity, but it does pose a real-life problem. Let’s hope when your students finish school and go to work that they don’t have a trickster boss like Wally!

And of course, it's a Project Nature-Ed resource, so there's nature mixed in with mainstream curriculum.

Some things about the critters in the problems that you will need to know:

• the sea stars referred to in this activity have five arms, and on the end of each arm is an eye (pretty cool!)
• snails have two eyes, one on each antennae, but not tail because they slide along on a big muscular foot
• sea snakes have no fins but do have a paddle-like tail to move along in water
• fish have two eyes, two fins and one tail (at least that one was easy)!

The Insect Files: THE BUTTERFLY EDITION aka Friends of 20 addition

With this ‘Friends of 20’ activity your students will be required to perform mental arithmetic to determine three numbers that add up to twenty.

Students are working with counting on strategies, even when working with three cards. They count on to add the first two numbers together and then count on again to twenty. Some students may be able to connect with their Friends of 10 knowledge to assist with their mental computation, for example:

3 and 8 .. means ... 8 and 2 makes 10 plus 1 ... then ...

11 and 9 counting on makes 20

The activity has six game options – three to play with a group, and three for students to play independently. Lots of scope for differentiation. You could use these activities as part of a week-long topic on addition where students are asked to compare, order and make collections to 20. Play a different game each day.

Get the activity on my Designed By Teachers store.

Ways to differentiate

• Use concrete materials such as counters and number lines to aid counting on and finding numbers that are Friends of 20.

Noticed the interesting facts on the bottom of each card about butterflies?
Keeping with the theme, why not make butterfly counters from bottle tops.
Recycling in action! This one was decorated with nail polish.

• Use a pack of number cards with numerals 1 to 20 rather than a deck of playing cards to expand the task to include addition with some two-digit numbers.

Card packs are usually available in book stores.

• Introduce the term “plus” by using an addition dice.

You could also use a write-on wipe-off whiteboard dice.

• Students can begin to record the number sentences of Friends of 20 by including mathematical symbols.

Use the operation cards at the back of the Friends of 20 resource.

That leaves just the butterflies …

Project Nature-Ed is about mixing nature with mainstream curriculum and generating conversations about topics beyond straight maths. I had a bunch of ideas on a previous blog for my Friends of 10 activity that showed some ways you can connect maths with the natural world outside of the classroom. Take a look.

In the meantime …

• Working on insects or lifecycles? A perfect time to do this maths activity.
• Studying the seasons, or just want to talk about changes in the weather, particularly if doing this topic close to winter? An ideal time for butterflies in maths. Comparing the daily and seasonal weather patterns of places is a content descriptor in the Australian Curriculum within Geography (ACHGK006). Keep reading for more information on this.

The Monarch (or Wandering) Butterfly.
Great pictures to use here.

One of the butterflies mentioned on the game cards is the Monarch Butterfly. They migrate up to 4,000 km each year, which may explain how they arrived in Australia in 1871. They don’t like the cold, so as winter approaches, Monarch Butterflies fly off to warmer places. A huge feat for a tiny butterfly! Great talking point for a class discussion. 

How to do this

Show where the Monarch’s live on map and ask your students to think about why they might not like the cold, and where they might go for warmer conditions, emphasising the need for the ecosystems that the Monarch’s depend on for their well-being and survival (Systems OI.2 from the Sustainability statements of the Australian Curriculum). 

This map isn't really detailed on the migration, but enough to show seasonal changes for Monarch Butterflies. I just used the information from the links below to plot the route - not very scientific, but adequate for Year 1/2. The red circles show the states in which the butterfly lives, the yellow lines plot their estimated migration routes and the "X" where they over-winter (south-east Queensland and northern New South Wales).

You can get some great info about Monarch Butterflies from the Australian Museum including where they live and their movements in winter.

Migration Mysteries is helpful as it recounts the migration of the Monarch Butterfly. You could read this to the class and plot on a map of Australia displayed on an interactive whiteboard.

In eastern Australia, one annual migration takes Monarch Butterflies from breeding grounds in south-eastern Victoria up the east coast, passing through the southern highlands south-west of Sydney, where numbers of roosting trees occur, they mate and lay eggs on the way. They continue on, eventually reaching over-wintering trees in the Brisbane and south-east Queensland. 

Geography too …

One of the key inquiry questions in Geography within the Australian Curriculum is different features of places and suggests using maps to develop geographical knowledge. 

By creating the above labelled map students can:

• investigate the weather and seasons of places - the place being where the Monarch Butterflies lives and where they migrate to (ACHGK006). 
• develop their geographical, evaluating and representing skills by representing data and location information (ACHGS009)

For reading this blog, get your FREE bonus activity by clicking here. Addition problems have been included to reinforce the learning outcomes of the Friends of 20 activity so you could use the quiz as an assessment of the ability of your students to make Friends of 20.

Going on a froggie webquest

Ever run a webquest in your class?

I created a really short one as a bonus with a set of my free Buzz Brains cards. The webquest topic became relevant to the activity because I put frogs on the back of all the activity task cards. I’m all about mixing nature up with mainstream curriculum so why not include frogs in maths!

There are a number of ideas for including the webquest in your classroom in the activity description for the Buzz Brains cards, but here's another way to use it.

Unless students are explicitly taught how to search for information on the internet, they end up overloaded with FACTS, much of which needs to be filtered to get to what they really need. I’ve used simple webquests like this to teach about internet searching.

If a student plugged the three clues on the webquest into a search engine, they would find the answer, but to explicitly teach, I have demonstrated as a whole class about how to narrow down information.

First, let’s search for frogs (the first clue) .. about 150,000,000 hits. Far too many!

Next, let’s refine it a bit and only search for frogs in Australia (the second clue) … about 18,600,000. Still too many to sift through!

Let’s now include the third clue caerulea and … only about 58,400 results, but bingo … a quick scroll down will show that all hits are about Green Tree Frogs, the answer.

Happy webquesting.

Reflecting on thinking and processes

What? Another proforma asking students to reflect on their learning? Convenient … yes, but is there any real thinking involved? Depends what you do with it and the reasons for giving it!

If you hand out the surveys, get them back and don’t do anything with it, then what was the point, but if you use the information for something, then absolutely ... there is a purposeful use.

A survey is just one tool in a teaching toolbox, you can follow up what you find with one-on-one questioning with individual students, particularly if a student believes they understand content, but their work displays a conflicting outcome. A survey is just one of the tools in your toolbox, but can give you some useful results.

I first used this survey during a Science and Technology unit of work that I was delivering to a multi-stage (Year 3-6) class because I wanted them to be active participants in their learning and also evaluate if whether what I, as the teacher, was delivering was interesting to them. There was also gifted and talented students in this class as well a wide disparity between literacy skills due to the multi-stage scenario. It was a real juggling act within the group setting to extend some students and not lose others with content that was too in-depth and intricate for their level of understanding. Were they still with me? Was I boring them to tears? This is what I wanted them to tell me!

Get your free copy of my survey tool here!

As a straight statistical analysis of the data, I plugged it into a spreadsheet and out came my results visually!

Survey responses received from my students.

Although the survey was anonymous, often you can tell by the handwriting who owns it, and I pulled some of the kids aside for a one-on-one oral reflection. During this reflection, I wanted to get them to justify the thinking behind the choices they made so I asked them questions about their answers.

Asking open ended questions aids critical thinking.

If this reflection tool was a straight tick a box survey, I don’t think it would achieve much, but because it also contains an open ended question, students have the opportunity to tell a teacher about what they learnt.

For example, I used this survey during a unit on poetry for Year 5. After looking at a range of idioms, the task was to include an idiom in the poetry piece they were working on. What this returned survey told me was that this student:  

• enjoyed how the content was presented and their task (my teaching was good!) 
• believed they knew what an idiom was 
• was confused about how to include an idiom in their poetry task (if you know who the student is you can target this area, or if it was a common response, this provides you with a target for future lessons).

A returned student survey.

Responses on surveys aren’t everything as students could be replying based on what they think you want them to say, but as a tool in teaching students to learn to become critical thinkers, they are helpful.

The Insect Files: THE LADYBUG EDITION

Friends of 10 addition

With this Friends of 10 activity, you want to get your students using a range of mental strategies to build number relationships and understand that addition is the joining of two groups.

Get the activity here.

Quick recall of basic facts makes maths easier as it gets more complex. I've seen so many kids in the later years of primary school anguish over maths, not because they aren't good at it, but because their quick recall of number relationships isn't there.

A deck of playing cards and some whiteboard markers and you’re ready to go.

How to run this activity

Lots of options:

- at a maths rotation station
- as an independent activity
- use cards to guide whole group instruction.

Explicitly explain the task

Lots of ways to do this, but one way I have done this is during a whole class session by running a mini-lesson. Pick a random number from 1-9 and get that number of kids up the front of the classroom. Visually the students can see this, so they can then figure out the other number required to make ten.

Two groups of students helps make sense of grouping of numbers to make 10.

For fun, make your explanation a case study. For example, put it to your students like this:

Your parents said you can have 10 friends over for your birthday party. You have already given out 6 invitations to your friends. [Get six kids up]. How many more invitations can you give out? [Continue to get more kids up as your students count on, stopping at 10].

Write 6 and 4 on the whiteboard and say the numbers are “Friends of 10”. Then explain the activity using the cards. 

Students draw a card and then ask group members for its friend.

And now … the NATURE stuff!!!!

I have included different Ladybug facts on each of the five cards because I really want this activity to generate conversation about topics beyond straight maths (and not just keep the natural world in science)! Here are some ways you might be able to connect this activity with the natural world outside of the classroom.

If counters are needed to play this game, make ladybugs counters from bottle tops

Use a permanent marker for the spots and shading and stick on some googly eyes. Very cute!

Create a word wall or mind map. Use the facts as a literacy activity to build knowledge around a central theme, e.g. insects, gardening (ladybugs are beneficial insects), etc. You can even start to show ecological relationships.

sun → provides energy → plants can grow in your garden → attracts ladybirds → eat aphids which destroy your garden → food for you to eat 

Mind mapping helps students see connections.

After another way to use the activity?

Activity could be run as a whole class activity by displaying a resource card on an interactive whiteboard. Teacher chooses a number from a deck of cards and asks students to give the other number to make “Friends of 10”.

Use your imagination! Use this activity during whole class teaching.

Differentiation within the activity

• Provide concrete materials such as counters or number lines to help your students figure out the missing numbers. Some students may already be counting on from the biggest number and won’t need these, but others will.
• To extend students, get them to use small whiteboards and write out the groupings that make Friends of 10 in equation format.

Extend students by writing facts as equations.

Blog clipart - thanks to A Sketchy Guy, Happy Little Daydreams, Graphics from the Pond.

Children in nature and nature in the classroom

On top of Cathedral Rock.

I had the most fantastic outing with my family yesterday ... we climbed to the top of Cathedral Rock in Cathedral Rock National Park (New South Wales, Australia). 

What was so amazing about it was that, as teenagers, my kids still enjoyed getting outside! Their sense of wonder and awe about the natural world is still there! 

Climbing up through a crevice on the way to the top.

While walking we chatted about how the granite rocks got there, noticed that many of the plants had flower buds ready to pop open in spring and supported each other emotionally as the kids (and I) were pushed beyond our comfort zones as we scrambling to the top.

And the only time a device came out was on the way home to run a geocaching app to log a find!

Down we go holding onto the heavy chain.

This morning, I heard snippets from the interview between Sir David Attenborough and President Obama as they discussed the future of the planet and my ears pricked up when the conversation began discussing a kids sense of awe about the natural world.

This is how the conversation went ...

“Well, I've never met a child who’s not interested in natural history,” Attenborough said.

“Just the simplest thing – a five year-old turning over a stone and seeing a slug and saying ‘what a treasure’!

“Kids love it. Kids understand the natural world and they’re fascinated by it.

“So, the question is: how did anyone lose the interest in nature?

Not sure, but many have!

So how do we immerse kids in nature?

How do we keep them in awe of the outdoors? 

I don't have the answers, particularly considering, as Sir David said in his chat with President Obama that "over 50 per cent of the human population on the planet are urbanised which means that, to some degree, they are cut off from the natural world".

But I do think that classroom educators can keep nature in the minds of children by carefully selecting resources that include nature content in all curriculum areas, not just science or social study subjects.

I might be turning into a Pinterest junkie

My Pinterest board now has content. I'm going to like using this!