Ratios help us understand and solve the relationships between values in real life situations.
Throughout the year, we have tapped into ratios occasionally, but we haven't enquired into them in depth as yet. (Tuning in: What ratio connections are there with the human body? and Creating Perimeter Ratio Maps of Our Countries )
To make the best use of our classroom learning time and to cater to the varying levels of understandings the children harbour with ratios, we flipped our classroom. For home learning this week, the children were given a Google doc with YouTubes that help explain the concepts of ratios from easier key understandings to more advanced understandings.
The children selected two YouTubes to watch at a level they felt comfortable in understanding, made notes of the key understandings presented and then applied their knowledge by creating a word problem question for their peers to solve in class.
Some of the benefits of flipping our classroom like this include:
° Each child's level of understanding is catered to.
° An opportunity to develop a sense of ownership and responsibility towards their own learning.
° They can process the new concepts at their own pace rather than perhaps being 'rushed' in the classroom setting.
° It helps each child to develop foundation or key conceptual understandings before we begin applying them.
° We are not needing to begin a unit all starting at the same lower conceptual understandings to then slowly build up over time in our classroom. With this strategy, children are exploring the concepts of ratios at varying levels according to where they are at.
° It forms an interesting pre and formative assessment: Which children are selecting the easier understandings, the mid or the more advanced? This helps me to gain a sense of where each child feels they are at and so I can group and structure enquiries accordingly later in the unit.
° It helps the children to tune into what we will be learning about.
The Google doc: Enquiry into Ratios (feel free to copy and use!)
What the Google doc looked like:
Central Idea:
Ratios help us understand and solve the relationships between values in real life situations.
Choose two videos below to help you learn about ratios.
Record the key understandings on your paper.
Create two word problems using what you have learnt from the videos. You will give these word problems to a classmate to solve on Friday.
Key Understandings

More Advanced Understandings
 
(This video starts off a bit slowly, but eventually explains key understandings with a good visual example)
 
When the children returned with their enquiries, we gathered in groups and discussed what we had discovered about ratios.
We then wrote the word problems we had created based upon our enquiries, placed them in levelled columns and complexity and then we chose questions to try to solve:
Having children create their own word problems helps them to transfer their understandings and apply it. Additionally, having them create a word problem helps them to understand real life situations where we might use ratios which then helps them to appreciate why we are learning about them.
The word problems they create also serve as a interesting informal formative assessment and they really love challenging each other and seeing how their peers tackle their questions. Peer teaching takes the front seat as they help their peers that need it.
Loads of great ticks and student ownership taking place.
Below are some samples of their notetaking, wonderings they have and their word problems:
We gathered the wonderings and will use these to guide our unit and enquiry into ratios. This makes the learning student owned using authentic wonderings rather than the unit being teacher driven.
We have some really interesting questions to explore such as:
° Can we have decimal ratios?
° Can we have ratios with more than two numbers? Eg, 2:5:4
° What is the difference between fractions and ratios?
° How often do people really use ratios in their daily lives?
° Can we multiply, subtract or add two different ratios?
° Can we use the same ratio strategies with all types of numbers and problems?
° To find the correct ratio, do the first numbers in the ratio get converted to the simplest form all the time?
° Can we use negative numbers with ratios?
° Can we have ratios using fractions, decimals or percentages or do they have to be whole numbers?
° Can we find equivalent ratios for lengths (cm, km etc)?
° Since ratios are easier to understand, why do we need fractions?
° Can there be more complex ratio problems?
Looking at these wonderings, there is such a broad range of really great questions. I'll ask the children next week what they feel we should do with them. Whole class enquiries? Partners? Groups? Individual etc
All of this amazing learning and development of key understandings happened from flipping our classroom and now we are in a much better position to leap ahead with our enquiries into ratios.
This is what a I love about enquirybased maths  the children own their learning rather than the teacher!
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