Lesson 4-6: Question

[Patricia Scheler]

I will use real/concrete items as we begin our unit on multiplication. Then, I will have students start working with base 10 blocks and manipulating them to demonstrate a stronger understanding of factors and products. Eventually, I hope that students will be able to just use numbers and steps to find answers. I love it when students are able to point out math connections when they see things. Examples: an egg carton with a dozen eggs, a dozen donuts in a box, our rows of desks in the classroom, the stars on the American flag.

[Dawn Oliver]

I will find a picture of something, like the donut box and donuts, to illustrate a factoring problem. I will use the methods to fade the concrete idea of the problem to an abstract, symbolic representation. I will try to ignite some curiosity instead of just teaching the regular way. I think I will use the American Flag or another flag.

• This reply was modified 4 months, 1 week ago by  Dawn Oliver.

[Jon]

Great Dawn! I’m curious about your idea with the flag?

[Maria Reynaga]

I will use the concrete model with a purpose. Manipulatives are a must, and I love my math stations. I will also be in the look out for the gaps that my students have.

[Stephanie Pritchett]

I am teaching 7th and 8th graders to solve equations and I have been showing them prompts from Bedtime from Math. Many of the prompts have triggered conversations about arrays. I think it would be helpful to backtrack and tie arrays to solving equations. The donut model would be great. Where can I find those pictures?

[Tarini Arte]

With our Geometry unit kicking off, I plan on using more concrete manipulatives like 3D shapes, filling them with liquid and demonstrating, and also perhaps showing more images like the layered donut box to invite students to make those concrete/visual connections before abstract formulas (and show how those are derived through the first two stages).

[Kerri Brodie]

I really like the idea of the concreteness fading model and I think that it really helps students with automaticity and flexible thinking. When I teach multiplication of polynomials, I typically do so with an area model but I will now try it with a more concrete model first like the donuts to be more “Prince” with my lesson. I think that anytime we have a model to refer back to in order to jog students memories it will help build the bridge between concrete and abstract.

[Katrina van Lierop]

I am already thinking about how I can use this model to work towards distributive property in algebra. As a grade 9 math teacher in Ontario I am struggling to make lessons with a low enough floor and still challenge students who have a good grasp of the underlying skills already. I feel like no matter what approach I take I am failing a group of students by either not challenging them enough or going over their heads and in both scenarios I lose their attention.

[Lizann “Lizzie” Herrera]

I remember listening to the “Be More Prince” podcast episode a while back! Yes, everyone should be more Prince <3

In my efforts to get more teachers to be more Prince, I will be pushing teachers to really see the value in concrete and visual representations. I feel that, even though teachers might have the concrete representation, some don’t trust that students will use manipulatives properly or they fear they’ll lose student’s focus on the lesson. My goal is to get teachers to trust the process and let students explore while using the manipulatives in the classroom.

[Kyle Pearce]

Good on you! Also we need to be confident in the actual model and strategy we are hoping students will leverage with the manipulatives which can be difficult to facilitate as well. Takes lots of time and effort on our part!

[David McKnight]

I Have a bunch of 3D figures in my room and we’re just getting into our geometry unit. I am excited about planning how to incorporate these as well as some miscellaneous 3D shapes that are sitting around my house.

[Stephen Levesque]

I have a perfect topic for this. I taught applications of systems of equations recently and did not give my students anything concrete when we started them. It did not go well. I am teaching that lesson to a different class now, and this session motivated me to create manipulatives so students can solve some of these problems in a more tangible way.

[Jonathan Lind]

Introducing radian measure next week in Geometry, and thinking this could be an opportunity to call back to some earlier understandings of pi. We can get out the string and see how many radii it takes to get around a circle. We can talk about why we use degrees, and why it doesn’t make great mathematical sense. That’s all I’m coming up with right now…

[Jon]

Great start here Jonathan! Great ideas always have great starts! Let us know how this flushes out.

[Debi Akin]

I am going to use more photos or items the kids and touch & feel to solve more problems.

[Zorica Lloyd]

For volume and SA we’ll use 3D shapes, cm cubes, and graduated cylinders and beakers to find volume before and let that lead into constructing formulas.

[Kyle Pearce]

Love it! Nice work here.

[Terry Hill]

I am being more prince this week by using the shoveling the driveway task to help my students learn how to multiply fractions. We are starting with the concrete from the videos or problems, then the students are modeling the problem through drawing it out, and then finally we move to actually using numerical fractions to determine the answer. It has really been great so far, and it has really helped with student engagement.

[Laura Compean]

I’m getting ready to have a summer school month with my own children and their cousins. They are all in middle school (Grade 6-8). My goal is to give them a month of concrete manipulatives and conceptual understanding of multiplication and ratios. I really liked the Prince example that you can’t just go straight to the symbols for students to understand. That hit home!

[Kyle Pearce]

Fantastic goal for you and your kiddos! Have you checked out the problem based units for ideas ? I use the contexts all the time with my own kids.

[Jared Sliger]

I can only access the Act 1 video for the Doughnut Delight problem. Is there another video that uses the giant box?

[Jared Sliger]

I like the concept of fading…when they finally tire of all the extra steps and can make the connection to math facts…this would be a good day. I teach low 8th grade students who, I am sure leave my room befuddled every day because of all the crazy symbols and language used in there. Hopefully next year I can make things more concrete for them.

[Renee Holmquist]

I work a lot on solving word problems with my students and I will start doing equation writing from those problems with the donut example and having them draw out concrete examples. I need to have them model the word problem with a visual, work with it using a finite number, and then go to the variable version. I also liked how you wrote out what each variable was before writing an equation, that is something I do but need to re-emphasize in my teaching.

[Jacqueline Joseph]

I love this idea of teaching a concrete version of a task to drive a need for substitution or rather a use for an algebraic representation. Usually I start with an abstract procedure for how to evaluate an expression for different values using order of operations. There is no curiosity in that. I am looking forward to replacing this with concrete representations like this donut task.

[Kyle Pearce]

Awesome to hear. Context goes such a long way by helping all learners enter tasks and stay grounded throughout the solving of the task.

[Karl Hirschmann]

in the upcoming school year, I will utilize problems that incorporate real objects like donuts or energy drinks. [Aside: has anyone else noticed that their students engage more completely if the problem is about food?] Then I will move toward visual representations such as the use of manipulatives or sketches. I will introduce my students to abstract representation only after they have looked at a problem concretely and visually. The concreteness fading model makes a lot of sense to me if only because many of my students have an issue with abstraction. Unfortunately, traditional ways of teaching math assume that all students are ready to think abstractly. My goal in the upcoming school year is to make the math real and the concreteness fading model will help me do that.

[Deanna Semyon]

I was pretty excited to see Prince as I am from Midwest, just as Prince! I also am excited about manipulatives and using them all the way through Algebra. I had to watch the last video a few times to make sure I was processing the information. I was soooooo happy to see that the manipulatives are natural in quadratic equations. I will be teaching pull out math classes in our high school and 8th grade Lesson 1 starts with exponents. I truly do not know that my students will know how to explain or compute exponents versus multiplication. I have have algebra kids who are not able to identify the raised exponent and know what to do when they see it.

I do not have a plan yet, but I know I want to start with manipulatives before I even get to lesson 1. Do you have any suggestions for lessons?

[Kyle Pearce]

How comfortable are students in using manipulatives or visual models for multiplication ?

[Deanna Semyon]

I feel like my high school students would feel like I was treating them as very young children if I pulled out base 10 blocks or any type of counters. I feel like maybe teaching them how to sketch a module would be a better fit.

[Christine Pomatto]

I don’t think I’ve ever seen base ten blocks used in a multiplication model like this, even though I’m quite familiar with area models and frequently use them with my 7th graders when they get stuck on the standard algorithm (because they’ve just been asked to memorize it with little understanding). When I do my intervention lessons, I will use base-ten blocks to represent multiplication and let students move toward an area model, eventually developing their own algorithms.

I usually introduce integer operations with two-color counting chips, but sometimes I push students away from them too quickly. I love seeing students (on their own) decide to draw a picture and then come up with their own rules (opposite signs –> subtract, etc.). I will facilitate opportunities for them to do this with most concepts.

[Jon]

@christine-pomatto I also used to push to fast to eliminate the need. Now I don’t even bring up the idea of eliminating them. Students choose to move to abstract models when ready.