5th Grade Math
August 30, 2023 Students learned about a contribution of Philosopher Rene Descartes to the the field of mathematics, namely, the Cartesian Plane or coordinate grid. The grid can make algebra visual and geometry symbolic. We discussed constant change that forms a line and how you can predict far into the future when you find a relationship that is always true for x and y. This activity prepares them for later work with functions, which in 5th grade math mostly deals with input/output rules and patterns. Student learned about substituting values for a variable. To end, we did a secret message find, with students having to follow directions on 4 large grids in the hallway, following directions given by ordered pairs. It was a little crazy!
Sept 6, 2023 Students looked at a place value chart they all have in their binders and noticed the notation in each place based on 10. For example, the unit or ones place is simply 1, the tens place is 1 x 10, and the hundreds place is 1 x 10 x 10. We learned how to write these using exponents and how places in our system were all 1 x a power of ten. We reviewed the identity property of multiplication as well. We introduced the chart of situations that use certain operations to solve. These foundational documents will b used all year. We then reviewed prime number. We studied Carl Gauss last year and today introduced his "Fundamental Theorem of Arithmetic" which says that every positive counting number except 1 is a product of a unique set of prime factors. We learned to make factor trees to show this and wrote equations to show what we did. We used exponents where possible.
Sept 13, 2023 Class times were all over the place this week, since students had their first big math test on our meeting day. We wrapped up work on factorization and then reviewed the big properties of multiplication (and addition). Namely, the Identity, Commutative, Associative, and Distributive Properties. We discussed how these allow us to "play" with numbers and solve problems in a way that is appealing to ourselves. Students are getting ready to take on volume in 5th grade math, so these properties will help them approach problems a little differently. We started to solve some problems, using this knowledge
Sept 20, 2023 This week we switched gears to something completely different (Thank you Monty Python). 5th graders worked on the box project, which incorporates a lot of different skills. Namely, measurement with a ruler, spatial understanding of how to mark measurement and draw a line (this was the most difficult thing) and prediction of volume by just looking at a box and using reasoning. We built nets, which are flattened out boxes. Each one or two students took the same sized paper, but had a different measurement for the height. They had to cut out the square corners and fold up the sides, building a box without a lid. Even after seeing the boxes, many students thought the one with the lowest side would have the largest volume. Their reasoning was that this one had the least amount of paper cut away (surface area come in 6th grade). Some thought the highest height would have the most volume until they saw the diminutive base. Some thought it was somewhere in between. We will continue next week graphing our results and seeing diminishing returns! Then we will investigate the effects of changing different dimensions in a different box project. This hands on work is very helpful in spatial knowledge and also finding out that without math, we can be easily fooled. There are business applications of this reality! I also hope that students knowledge of volume will become deep and wide (AND LONG)!
Sept 27, 2023 We created ordered pairs using the data in our box project where x was the height of the box and y the volume. Students graphed these after creating a coordinate grid and deciding on the best way to number and label it. The graph was in the shape of a mountain which visually showed the result of the greatest volume being in the box with height somewhere in the middle. When we started the project, most students thought it would be the box with the highest sides, but then found that to make those high sides, the base was shrinking. I hope students now understand that all three dimensions are important when looking for volume and that it can be hard to predict by just looking. The design made with the different boxes has become wall decoration in the hallway. More art from this special class!
October 2, 2023 This week has a lot of schedule changes because of field trips, but students are spending one last week diving into volume. Students explore a net and then make a completely closed box with a net they design. They learn in a hands on way what happens when you double one dimension, or two dimensions, or all three dimensions and see how the exponential growth occurs.
October 11, 2023 We go in depth into how we solve multi-operation problems and why we do it the way we do. We talk more about how writing an expression is writing the instructions for someone to end up with the result you want them to get. It has to be thorough, logical, and follow the order of operations. Students solve problems with exponents, the 4 operations, and 3 types of grouping symbols. This takes them past the 5th grade standard which does not include exponents and 2 grouping symbols.
October 18, 2023 Played a game of "rounds" and then dealt out playing cards which resulted in students writing the algorithm for long division on their own. Talked about the situations of division. Had time for a little practice. Division is a difficult thing for students to learn and too often it is process without meaning. My goal is to have them thinking about what makes sense rather than just memorizing steps.
October 27, 2023 Using the relationship among dividend, divisor, quotient, and remainder, students answered logic problems to find the unknowns in equations. (i.e., the remainder has to be less than the divisor, the divisor and quotient are factors of the dividend, etc.
October 30, 2023 Did a little test review then practiced multiplying outside the box. Problems from earlier this year. We are having a difficult time applying commutative and distributive property to solve things more easily, but are really stuck in learned procedures. My goal is to get students THINKING, instead of just doing a process.
November 7, 2023 Students worked on problems involving 2 or 3 patterns with different rules. They then compared them in different ways, using the vocabulary of "corresponding terms." I had seen on a report from a math assessment, that students were struggling with this concept. I wanted them to see how to solve these problems, but also see the value of putting in the work instead of just guessing.