Meet the Parents
Today in grade 11 we are learning about parent functions
We made tables of values to help us draw each function. We noticed that f(x)=1/x has a gap in the domain since it is not defined when x=0. We needed to check what happens close to 0, on both sides, to see the behaviour near the asymptote.
we are continuing to work on domain and range, and we are identifying key points and features thar will help us when we explore transformations of the parent functions in the coming days.
Knot Tying Experiment
After we got our bean data recorded in mfm2p we started a new experiment. We had 2 different lengths and thicknesses of ropes. We measured the lengths, and then tied a knot, then repeated that process as long as we could.
Each time we tied a knot, the rope shrunk. We kept track of the data in a table of values, and then we made graphs of our data.
We could make some interesting observations and conclusions. Thicker ropes had lines that were steeper. Each knot used up a lot of rope, so it shrunk a lot. Thin ropes had a less steep slope. Each knot used less rope so the length shrunk less each time. When graphed we could see that the lines crossed. This is the point where the ropes would be the same length with the same number of knots tied.
Further extensions from this task could be modelling the data with equations, and then calculating intersections with an algebraic method.
I’m helping each week to incorporate a modelling/data collection task so that we can work on these skills over the term. It has been great fun so far.
Bean Update
Today I was back working with my colleague’s grade 10 applied class. We are in the middle of an experiment with beans.
We had some beans start growing over the long weekend. We measured them, and watered them, and we will keep measuring them each day and adding to our tables of values.
We will graph the growth after we have some more data. We can compare how the black eyed peas and kidney beans grow.
Multiplication Diagnostic
I had the opportunity to work with some grade 9s to see what strategies they use for multiplying. Some students built models or drew pictures, and some are using additive strategies and others are using partial products and using doubling or other strategies.
here are some examples of student work, to see how differently they approach some questions.
we will be doing some fluency tasks this term and hopefully can help students explore some different efficient strategies
Introduction to Algebra Tiles
Grade 9s have been learning about algebra tiles, and how to model algebraic expressions with concrete tools.
We started by doing some art. We then simplified our art by removing the zero pairs, and then we wrote our final expressions in algebra. We have learned some vocabulary, and can classify polynomials by the number of terms. We can add polynomials, and are working on subtracting them too using zero pairs to help us.
Painted Cube
Today I was invited to lead the painted cube problem in a colleague’s grade 10 math class. We are working on modelling and representing, creating equations, tables and graphs.
The problem: imagine a 3x3x3 cube that is dipped in paint, then dried. The cube is then disassembled, and we need to determine how many little cubes had 3 sides painted, 2 sides painted, 1 side painted or no paint at all.
As we worked through the task groups were prompted to try a 4x4x4 or 5x5x5 or nxnxn cube.
Groups had different ways to represent the number of painted sides. Many did drawings, and made tables.
Groups realized quickly that using a 3D model was really helpful. We used linking cubes to build different sized cubes. Some used colours as a legend for the number of sides painted, which was a neat idea.
It was excellent to see groups connecting the physical representation of the cube, and the algebraic representation. We saw that there was a quadratic equation which was connected to squares on the face of the cube, and a cubic equation that was connected to the interior cube.
Students made tables of values and saw that one relation had first differences that were the same, one had second differences that were the same, and one had third differences that were the same.
Students made graphs and saw trends. They explored all kinds of relationships, finding some patterns that have piqued my interest.
It was a lovely way to end our week. Good job grade 10s.
Introduction to Pseudocode
Today we had a busy day. We worked on multiplication skills, and had our first quiz, and then we started to learn about pseudocode.
We watched this video and debriefed about how it shows specific instructions and how important it is to be clear with our communication. We also talked about feeling the emotions and frustration sometimes in math, and how we can manage those feelings.
We then had a challenge! Groups had 2 puzzles to put together.
Each puzzle was made of lines of code that we had to out in the right order. The students told me that they had learned some Python last year, so this was an easy task for most. We saw that we need to initialize variables first, then input values, then do calculations. We saw that there is special syntax, * is multiply / is divide and ^ is exponent. We will build on our skills bit by bit over the term. We are not learning a coding language but we are working on the logic and writing it in pseudocode.
Word Problems
In Grade 11 we’ve been working on word problems and applying our skills with quadratics.
We work in random groupings each day, so we are getting to know each other and to work well with each other. It’s not always easy to know how to solve problems. We are building our confidence in starting problems, and making a plan to get to the answer.
It was interesting to see how various groups decided to place the bridge on the graph. Some placed the y axis at one of the foundations, others placed the y axis as the axis of symmetry of the parabola. Some decided to use vertex form, and some decided to use factored form. No matter what, we all got to the same “a” value which was a neat observation to bring forward in consolidation. There can be many correct models, and many paths to get to them.
This problem was fun. We worked on this one until the end of class, and left it as a cliff hanger, and started it again the next day.
There was a lot of perseverance while working on this one. Reading and re-reading and making sense of how to use all the words was an interesting challenge. We wanted to maximize the area of the rectangle, so we need an equation for the area of the rectangle, and then we need to make sure that it is in terms of one variable, and THEN we need to find the vertex (maximum). Some groups missed that we are maximizing the rectangle. Some groups needed prompting about substitution, some needed help visualizing where the parabola is, because it’s not evident in the drawing that there is a parabola.
Today we started the class by finishing the problem. Some students had come in at lunch to try it again. We are developing more than just skills with finding the vertex, we are getting better at modelling a situation, creating equations, substituting when needed, and then finding the vertex.
It’s an impressive sight to see all 34 students engaged and working hard. It’s been a fun 2 weeks so far!
Plotting Points
Grade 9s have been working on introductory skills, and today we looked at plotting points and determining composite perimeter and area.
Groups were given a list of points to plot. Each set made a composite shape made up of rectangles.
They worked well together and remembered how to plot positive and negative values, and then cut up the region to calculate the area. They know the perimeter is the outside edges.
Our next task was to plot points from a table of values
We each chose different side lengths for squares and calculated the perimeter and area and kept the values in the table. We made graphs of the tables and saw that the perimeter data is linear and the area data is non linear.
Beans Update
I’m working with a grade 10 applied math class this semester introducing data collection and modelling tasks. Today we looked at the beans that we attempted to germinate over the past week. We opened up the sandwich baggies and unwrapped the paper towel and noticed thar some beans sprouted, and some rotted, becoming slimy and moldy. There were some different fungus too!
We noted the fraction of the beans that germinated and we will compare that to our predictions we made before planting.
We put the beans in little pots of soil and labelled each one with a popsicle stick. Each bean has a name so we can track the growth of each bean over time. We watered the little pots and have them in a clear bin by the window.
Our data tables are ready for when the beans start to grow. We will be watching every day for signs of sprouts, and adding water as needed.
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