Today we have the pleasure of hearing from expert in real life math, Alice Aspinall of @EveryoneCanLearnMath. If you follow Alice on social media you will see her beautiful pictures of real life math and practical tips on how to use opportunities in our everyday life to incorporate math! I knew having a guest blog post from her would be super helpful as we start our year. This blog post if FULL of great ideas that you can use at the beginning of the year to get your students talking about real life math!
Introducing… Alice Aspinall of Everyone Can Learn Math
Alice Aspinall is a Portuguese-Canadian secondary mathematics educator in Ontario, Canada. She is a strong advocate of the growth mindset and is continually looking for ways to build young people’s confidence in math and to make math fun, challenging, and satisfying. Alice is also a champion for females in STEM by encouraging girls to pursue science and mathematics both in high school and in post-secondary education. Alice believes everyone can learn math and she is on a mission to prove it.
A Guest Post by Alice Aspinall: Starting Math Class with Real-Life Math
Starting the year with Real Life Math Examples
As the beginning of a new school year quickly approaches, we need to consider how we are going to build a positive math culture in our classrooms. I believe that every math class can be inviting and exciting for our students if we are intentional about creating joyful experiences. One of the key features of an engaging math class in the elementary grades is providing real-life math opportunities.
Math is visible all around us – if we are looking for it! When we are in a classroom with our students it might be more challenging to find those math moments, but we can bring the real-life math to the classroom using photos and math talks. I love a good math talk. I don’t necessarily structure my math talks in any specific way because I like to see where students go with their thinking and their questions.
Real Life Math Talk – Strategy #1
Years ago, my good friends Kyle and Jon over at Make Math Moments introduced me to one of my favourite ways to start a math talk from a photo. Present a photo to your class and simple pose the two questions:
What do you notice?
What do you wonder?
I tell students there are no obvious “noticings” and no wrong “wonderings.” This introduction to a math talk is non intimidating and allows for entry by all students, no matter their level. This also allows for some funny and non-math related answers – but this is all part of the fun! If students are not leading to the math you want to talk about, start guiding your questions toward the topics you want them to discuss. If you hold math talks often, students will start to catch on to the “math” part of the talk and will naturally look for the math.
Real Life Math Talk – Strategy #2
Another way to start a math talk is by posing a very open-ended question. For example, I first learned this technique from Christopher Danielson who poses a collection of items and asks:
How did you count them?
The photo for this questioning could have multiple different kinds of items, eliciting different answers from students depending on what they choose to count. Or the photo might have items arranged in a way that allows for subitizing in multiple ways, provoking a variety of methods to count the items.
I have chosen two photos to demonstrate how to use a real-life photo to start math talks in your classroom. For each photo, I am going to offer specific prompts I might use to get students talking about the math in the scenario. Consider using the notice/wonder questions before starting with the specific prompts to get students engaged and intrigued by the photo first. I like to give everyone a chance to participate if they want to and the notice/wonder questions are a good way to begin.
Real Life Math Example- Arrays
Possible topics: counting, repeated addition, skip counting, multiplication
Arrays are powerful in helping students learn to count items. They can cover many different topics and lead to subitizing. Arrays are found in many everyday scenarios and the arrangements make counting items faster than counting one-by-one.
Consider the following photo taken at a local playground:
For this math talk, my goal as the educator might vary depending on the topic/grade level of my class, but ultimately, I think we are looking for the total number of tires in the photo. It is how we get there that allows for differentiation.
Before getting to a final answer, estimating is always a good entry point. I would first ask my students to estimate the number of tires in the array. Take down their estimates to make everyone’s response feel valued.
Then, I would move on to discussing the number of rows and columns. Once this is established, I might continue with, “There are 4 rows and 5 columns. Which is the easier way for you to count the total: 4 groups of 5 or 5 groups of 4? Why?”
I might prod further to ask how they calculated the total number of tires, “Did you skip count? What number did you count by? Did you multiply? Is this a multiplication fact you know?”
If I had a younger class, my goal might simply be to have the students count the tires with correct one-to-one correspondence. If some students bring up skip counting, I would explore that further by asking the student to explain or by helping the whole class through it.
Estimation in Real World Math Talks
Possible topics: number sense, logic and reasoning, number ranges
Estimating is a necessary skill for students to develop. Good estimation skills can help in many real-life situations including purchasing enough items, putting out enough food at a party, gathering enough materials to build something, and many more. The objects and the quantities you ask your students to estimate will depend on their age level. You want to start with small quantities in the younger grades and work toward larger, more difficult quantities in older grades.
Consider the following photo taken at a local farm:
Questions that I might ask to get my students estimating include (but not limited to):
How many cows do you think there are?
How many ears?
How many legs?
At first, the estimating of how many ears and legs might seem like a straightforward calculation, but the estimating comes from the number of cows in the photo. It is impossible to count the exact number of cows that you can see, so we must estimate.
If I had an older class, I might take a strategy from Andrew Stadel and ask students to first develop an estimate that is “too low” and “too high.” This can be done as a whole class discussion or in small groups, but the key is to discuss why an estimate might be too high or too low. The purpose of this discussion is to create a reasonable range for the estimates.
Here is an example of how this thinking might go: I know there are at least 10 cows because I can count 10 definite cows in the photo. This number can be used to calculate “too low” estimates for the number of ears and legs in the photo. I know there are no more than 40 cows because I think I can count around 20 cows, and I don’t think there are twice as many as that in the photo.
If students are too conservative with their “too low” and “too high” numbers, challenge them to narrow the range a bit using some reasoning like the example above.
When students are ready to give their final estimates, write them down to acknowledge their responses. I think this goes a long way in a math classroom to show that every student’s thinking is valued. In this case, we don’t know the actual answer and that doesn’t matter. It is the thinking and reasoning in the math talk that is important here.
If I had a younger class, I might just stick to the four most prominent cows and use the photo to focus on counting and skip counting.
The Big Picture- Real Life Math in the Classroom
The important thing to remember when doing math talks is that they should be natural and not too forced. What I mean by this is that memorizing a script of questions will not necessarily produce the results we want as educators. With practice (by you and your students), the conversation will begin to flow, and the questioning will become more organic. What matters is that we are trying to present these everyday scenarios to our students so that they know that math is all around them and part of their lives beyond the classroom.
Arguably, the best part about math talks started from a real-life photo is that the outcome will always be different. Each photo and each class will produce a different conversation. This might make some of us uncomfortable, but beautiful things arise from discomfort. Imagine being able to pick a math concept out of a photo that one of your students provides. Unplanned and going with the flow, together with your students, talking about the math you see and trusting that strong thinking will result from it. To me, this is a powerful, productive, and positive math culture to have in any classroom.
A bit more about Alice…
Twitter: twitter.com/aliceaspinall, twitter.com/everyonecanmath
Alice Aspinall, B.Math(Hon), B.Ed, is a Portuguese-Canadian secondary mathematics educator in Ontario, Canada. Alice has written several children’s math books inspiring a love of mathematics through growth mindset, perseverance, and real-life math exploration. Her books have sold all over the globe and are highly rated and recommended by educators and parents. They are available at most online bookstores including Amazon: bit.ly/aliceaspinall
Math Discussion… Let’s Keep Talking…
Check out this blog post to Engage your Students in Math Discussions
Or this blog post👇🏽 about how I use problem of the day to engage students in math discussions.
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