Beading progress (almost done!)
We’ve finished up most of the beading, and now we are weaving in ends and gluing the hide to each side of our work.
We’ve started writing a little paragraph about the math that we see in the beadwork.
Happy long weekend! We’ll finish up the last of the work at lunch next week.
Building Exponent Models
Today in grade 10 we built exponent models out of toothpicks and plasticine.
We are working on understanding that anything squared can be physically represented as a square, and anything cubed can be physically represented as a cube.
We noticed that the coefficient of the x squared or x cubed tells us how many there are.
If there’s a base that is a bit complicated, like (3x) squared, it means that the side of the square is 3 toothpicks long. That means when we build it we can see that there are 9 little x squareds inside. This means (3x)^2=9x^2
This group made one that wasn’t asked for, the little squares. The base of the exponent in that case would be (1/2 x) and the exponent would be 2 because they are squares. Since they made 4 of them there’d be a coefficient of 4 in front of the expression. We also can see that the 4 put together are equivalent in area to one x squared.
Here’s a good example of (2x)^3, and below there’s an attempt in progress of (3x)^3, which is always a big challenge to build.
We can use this kind of math understanding to help us when we convert square or cube units. Here’s an example: One cubic yard is equal to 27 cubic feet. We can understand this by knowing that there are 3 ft in a yard, and 9 cubic feet on each of the 3 layers of the cube to make 27 cubic feet.
We will be using this knowledge when we do volume and surface area questions in the future.
Angle Day!
Today we did some work with angles. We drew triangles and extended sides to make exterior angles supplementary to the interior angles. We labelled these angles then cut out along the lines.
This left us with 4 pieces. We took the triangle and cut out the interior angles, and put them all together. We noticed that for all the triangles it made a straight line, 180 degrees.
We put the exterior angles together and noticed that they make 360 degrees, or a full circle.
We did the same with quadrilaterals, and noticed what was the same and different. The interior angles of the quadrilateral add up to 360 degrees, and the exterior angles do too!
We had a look at this video to see the exterior angles always add to 360 degrees.
Next we looked at how we can solve problems involving angles. This one involved algebra!
It was energizing to see everyone involved and learning before a long weekend.
3 Act Task
Today I was invited into a colleague’s grade 9 math class for a 3 act task that we led together. 3 act tasks start with act 1 to pique the interest. Students watch the video and write down what they notice and wonder.
Next comes Act 2, where more information is shared, and students use the information to solve a problem.
In this case we are figuring out how long it takes for the candle to burn out fully. Students use the data, in tables, and graphs and use logic to attempt to solve the problem.
This class has recently been working on scatter plots, so we encouraged a graphical representation to solve. Sometimes this can be done by loudly praising the graphical representation of one group, and others will latch onto that methodology. We worked on making sure axes were well scaled, and had labels, and then groups realized that they’d need to extend the trend a bit through extrapolation and a line of best fit. Some groups needed to extend beyond their graph!
One group didn’t want to scale their axis in a conventional way. We worked with them to see how their graph could still help them solve the problem.
In the end, when all groups had sorted through their responses, we consolidated their work, pointing out excellent communication, and including vocabulary about trends that they’d been using recently. At the end of class we watched the final act video which revealed the conclusion.
This task shows the use of a graph and extrapolation to solve, which made it a great fit for the recent topics.
I look forward to working with this class again soon!
Beading Progress
We worked hard at our beading projects again today. We are making solid progress!
Now that we know what we’re doing, it’s quite a calm meditative activity. We don’t have to remind ourselves as frequently to watch our energy. We need to make sure we are doing beading with good energy and intentions.
We’re making really interesting patterns too. Each one is unique and we’ll have lots of math to discuss when we get to finishing our projects.
Tomorrow most of us will be weaving in ends and gluing to prepare for attaching hide to make bracelets or keychains.
Beading Progress
Today we learned how to get started with our beading projects. We used our patterns to decide what beads we need. We put the first 11 beads on the needle and learned how to thread them to attach them to the warp threads on the loom.
Next we gave it a go! We ran into our fair share of frustrations: a loom came unthreaded, some knots happened where we didn’t want them, beads fell off the thread, needles came undone, but all in all we made good progress, and we kept calm when things were challenging.
It’s pretty neat to see what progress can be made in one day. We look forward to continuing the progress tomorrow. If all goes well we can be finishing them up before the PA day on Friday.
Great work grade 9s!
Multiplication Fluency
We’re working on multiplication strategies these days, and we got out the base 10 blocks to model some multiplication. We did 15×6 to start with.
Some students made 6 groups of 15, and then counted. They knew they had 6 groups of 10, and 6 groups of 5, so the total was 90. Others used doubling and halving with this question. They doubled the 15 to make 30, and they halved the 6 to make 3, then they multiplied 30×3 and got 90. They then used 9 rods of 10 to build the 90, or used 100 and a negative 10 rod to get back to 90. It was neat to see the different ways students approached the problem.
We next looked at 26×15 to see if there were different approaches.
One group built a rectangle thar had dimensions of 26 and 15. We can see (top right) that this gives us a nice area model to work with. We can section the rectangle by friendly numbers and then calculate the small areas and add them up. Another group kept using the doubling and halving. They doubled the 15 to get 30, and halved the 26 to get 13 then did 13×30. Some did 13x3x10 to make it easier. Either way you get 390. One group made the 390 in a 3D shape and another made it in a flat rectangle, starting off with 400 and removing one by using a negative 10 rod.
I’m really glad my students are getting braver and are excited to share their strategies. Here’s one student’s area model. We needed a small correction, but it was a great way to show our work.
Next we used our multiplication strategies to work through a number string, doing one question at a time sequenced in an order to help us get to more complex problems by using work done in prior questions.
We’ll keep working on these strategies. It’s fun to see the learning happen!
Introduction to Loom Beading
Today we had the pleasure of learning from Jessi from the Indigenous Program Team at the board office, who brought some historical and cultural perspectives about loom beading, and some teachings to share with us before we embark on our project.
Over the next few days we will be planning and beading a bracelet/bookmark/keychain, and then reflecting on the math that is present in the work, and the other skills that we learn during the process.
Today we got our beading templates, and started to plan. Tomorrow and Wednesday we will be doing the beading, and then we will finish things off on Thursday, and let the glue dry over the long weekend.
It is always such an exciting time to see what our students can do creatively, and then analyse mathematically afterwards. More pictures will follow in the coming days.
Introduction to Algebra
Grade 10 applied students got their first test back today, and we started learning a new topic: algebra.
We got out the algebra tiles and remembered what we did in grade 9. We built polynomials, then added them.
We simplified using zero pairs, and worked on using vocabulary words to express what we made, and what the result is.
We’ll be solving equations next week using tiles. Hope that we’ve jogged enough memories to have a solid start on Monday. It’s so good that our grade 9 classes are using manipulatives so consistently now, so I know that my 10s will all have seen and used the tiles before. We’ve worked hard to build a solid grade 9 program which we are now spreading into grade 10. It takes work, but it is so worth it!
Correlations, and beans?
My grade 9s really wanted a “fun friday” today, so we did an activity involving everyone getting up, mixing mingling and taking off their shoes. It ended up with a nostalgic discussion that was all about beans. A memorable day for all!
The goal of the lesson was to make a scatter plot and talk about correlation, and to show how google sheets can be used to make a graph and see a trend-line and an r squared value, and then be used to make predictions.
We taped ikea rulers to the wall, then took turns being measured. We stepped on rulers and measured our foot length too. Then we made a graph to see if it’s true that you can guess someone’s height by looking at their shoe size.
In our class the trend is pretty weak. The r squared value is 0.53, but we can see that height correlates a bit to foot length. The larger the foot the taller the person, in general, but we wouldn’t be very confident in the height of someone if we just saw a foot print.
We talked a bit about how this graph really only represents grade 9s, and with a small class, and some absences, it is not even a really good sample of the whole grade 9 population. We noted that grade 9s are in the middle of growth spurts, and that this likely does not represent what a graph of adult height and foot length would be.
We discussed vocabulary about trends (postivie/negative, strong/weak, linear/non-linear) and we made lines of best fit by hand, and with technology on google sheets. The final step was to chat about making predictions using our trend-line, and how some predictions are interpolation (inside the data) and some are extrapolation (outside the data).
I then told the class a story about when we were back at kcvi and had deep windowsills. My classes used to take advantage and grow beans on the windowsills. We’d turn it into quite a project. We used the dry beans to explore counting, and then we germinated the beans in paper towel and water in a baggie for a few days. We looked at the fraction that germinated and the fraction that rotted.
we planted the beans in small paper cups and cared for them as they sprouted above the soil. The plants were measured daily, and data tracked in a table. We grew kidney beans and black eyed peas, and compared their growth over the first week or so that they sprouted above the soil.
Next step was to graph the bean data in scatter plots, we could compare growth rates of different types of beans and make predictions from the data about the height of the bean at the end of a month of growing.
The trick is that the beans start off with quite a linear trend for the first week, with a very different growth rate between kidney beans and black eyed peas. These plants do NOT maintain their linear growth though. They are bush beans which have a maximum height. Students predicted bean plants that would be about a meter tall after a month of growing, but they maxed out at maybe 30cm.
By then though we were attached to our little bean garden, and we kept watering them and caring for them and many times the bean plants would flower, and then after the flower dropped off a baby bean was there, growing and producing new bean seeds inside.
After me doing some show and tell (search for beans on this site and there are lots of progress pictures), my students were disappointed in our sleek windowsills and wanted to grow beans. I happen to still have a bag of dried beans in the closet, so many went home today with some black eyed peas in their pocket and dreams of making a bean garden of their own. We’ll see if any are successful.
It ended up being a pretty fun Friday after all!
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